Difference between revisions of "DeltaDoverD Progress"

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<math>{I_{Asymmetry}}^{NH3,B<0} = 0.00015724 \pm 0.000156</math><br>
 
<math>{I_{Asymmetry}}^{NH3,B<0} = 0.00015724 \pm 0.000156</math><br>
 
<math>{I_{Asymmetry}}^{NH3,B>0} = 0.00013867 \pm 0.000112</math><br>
 
<math>{I_{Asymmetry}}^{NH3,B>0} = 0.00013867 \pm 0.000112</math><br>
 +
 +
Add some text describing the difference in the charge asymmetry plots.
 +
I dont understand what makes the plot below so different from the ones above.
 +
 +
[[File:ChargeAsymmetryNH3Bp_2.png|400px]]
 +
[[File:ChargeAsymmetryNH3Bp_2.pdf|400px]]
  
 
==Calculating <math>\frac{\Delta d_v}{d_v}</math>and <math>\partial \frac{\Delta d_v}{d_v}</math>==
 
==Calculating <math>\frac{\Delta d_v}{d_v}</math>and <math>\partial \frac{\Delta d_v}{d_v}</math>==
Line 1,374: Line 1,380:
  
 
I copied the following from the JLab cache disk to isulinux1
 
I copied the following from the JLab cache disk to isulinux1
 +
==outbending==
 +
scp /cache/mss/clas/eg1b/production/pass1/v4/4p2out/misc/dst/dst2828* isulinux1:/local/scratch/tforest/4.2negND3
 +
 +
scp /cache/mss/clas/eg1b/production/pass1/v4/4p2out/misc/dst/dst283* isulinux1:/local/scratch/tforest/4.2negND3
 +
 +
scp /cache/mss/clas/eg1b/production/pass1/v4/4p2out/misc/dst/dst2829* isulinux1:/local/scratch/tforest/4.2negND3
 +
 +
scp /cache/mss/clas/eg1b/production/pass1/v4/4p2out/misc/dst/dst284* isulinux1:/local/scratch/tforest/4.2negNH3
 +
 +
==in bending==
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scp /w/cache/mss/home/nguler/dst/dst282* isulinux1:/local/scratch/tforest/4.2PosNH3
 +
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scp /w/cache/mss/home/nguler/dst/dst281* isulinux1:/local/scratch/tforest/4.2PosND3
 +
 +
=10/7/11 sftp file copying=
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 +
Another way to copy files from JLab is to copy them from the /cache disk to the /u/scratch disk and then sftp them from JLab.
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 +
sftp username@ftp.jlab.org
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cd /u/scratch/tforest
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mget *
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=12/16/11=
 +
 +
==Charge Asymmetry==
 +
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[[File:ChargeAsymmetry14_23.gif|400px]]
 +
 +
 +
 +
==<math>\frac{\Delta d_v}{d_v}</math>==
 +
<math>F(d) = \frac{\Delta d_v}{d_v} = \frac{Y}{Z}= \frac{\Delta \sigma_p^{\pi^+ \pm \pi^-} - 4\Delta \sigma_{2H}^{\pi^+ \pm \pi^-}}{\sigma_p^{\pi^+ \pm \pi^-} - 4\sigma_{2H}^{\pi^+ \pm \pi^-}} (x,Q^2) = </math> <br>
 +
 +
:<math> = \frac{([({\sigma_p}^{\pi^+})_{1/2}-({\sigma_p}^{\pi^+})_{3/2}] - [({\sigma_p}^{\pi^-})_{1/2}-({\sigma_p}^{\pi^-})_{3/2}]) - 4 \times ([({\sigma_{2H}}^{\pi^+})_{1/2}-({\sigma_{2H}}^{\pi^+})_{3/2}] - [({\sigma_{2H}}^{\pi^-})_{1/2}-({\sigma_{2H}}^{\pi^-})_{3/2}])}{([({\sigma_p}^{\pi^+})_{1/2}+({\sigma_p}^{\pi^+})_{3/2}] - [({\sigma_p}^{\pi^-})_{1/2}+({\sigma_p}^{\pi^-})_{3/2}]) - 4 \times ([({\sigma_{2H}}^{\pi^+})_{1/2} + ({\sigma_{2H}}^{\pi^+})_{3/2}] - [({\sigma_{2H}}^{\pi^-})_{1/2} + ({\sigma_{2H}}^{\pi^-})_{3/2}])} </math> <br>
 +
 +
 +
 +
=01/30/12=
 +
 +
==Charge Asymmetry==
 +
 +
 +
In double spin asymmetry measurements it is important to eliminate any source of false asymmetry, like charge asymmetry. The helicity of the electron beam was flipped with a rate of 1 HZ and its original state was chosen at the injector in a pseudo-random way. The next state of the electron helicity, so called complement state, is always with opposite helicity. The diagram on Fig. 3.1 represents the helicity state.
 +
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
[[File:Helicity_state.png|400px|thumb|'''Figure 3.1. The Helicity State''']]
 +
|}<br>
 +
 +
A one bit signal from the beam injector gives the helicity information, whereas a sync bit with a 2 HZ frequency is generated at the same time and is equal to the helicity flip time. However, the electron beam helicity sequence can be interrupted by the Data Acquisition System(DAQ), like leaving unpaired helicity states and dead time problems. In order to eliminate the asymmetry caused by the DAQ, the Faraday cup was installed to measure the charge simultaneously with the helicity state flip. The stored data files include accumulated charge value for each helicity state. The measured charge asymmetry is shown bellow for 4.2 GeV data that has been collected for ND3 target while torus magnetic field was negative.
 +
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lifetime only takes data when daq is ready.
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{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
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[[File:ChargeAsymmetry.png|350px]]
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|}
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{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
'''Figure 3.2. Run Number vs Charge Asymmetry (ND3 target, B<0)'''
 +
|}
 +
 +
The charge asymmetry measured for each run number, thats is used for this analysis is shown on Fig. 3.3.
 +
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{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
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[[File:ChargeAsymvsRunNumber1234.png|400px|thumb|'''Black and red data points represent uncorrected measured charge asymmetry using Faraday cup. The green line shows the sign of half wave plane, while the purple one the sign of target polarization.''']][[File:ChargeAsymvsRunNumber1234grouped.png|400px|thumb|'''Run groups vs measured charge asymmetry. The runs that have the same half wave plane, target polarization sign, target type and torus current were combined into one data point.''']]
 +
|}<br>
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{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
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'''Figure 3.2. Run Number vs Charge Asymmetry for All Runs'''
 +
|}
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Charge Asym no sign correction
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The uncertainty should be the same for the (1-4) and (2-3) distributions in the same run group.  Use 12 groups of files (slugs) to create a histogram of the asymemtry and fit it with a gaussian.
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 +
Inclusive asymmetry as a function of X_B for all <math>Q^2</math> is shown on Fig. 3.4.  The electron paddle numbers 10 and 5 were chosen respectively for B<0 and B>0, because they contained the most electron events in a first pass semi-inclusive pion analysis of the data set.
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inclusive includes sign correction
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For inclusive do run number vs inclusive Asymmetry
 +
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{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
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[[File:InclusiveAsymmetry01_30_12y.png|350px]]
 +
|}
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{| border="0" style="background:transparent;"  align="center"
 +
|-
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|
 +
'''Figure 3.4. X_{bjorken} vs Inclusive Asymmetry(All data)'''
 +
|}
 +
 +
=02/06/12=
 +
 +
 +
==Charge Asymmetry==
 +
 +
 +
In double spin asymmetry measurements it is important to eliminate any source of false asymmetry, like charge asymmetry. The helicity of the electron beam was flipped with a rate of 1 HZ and its original state was chosen at the injector in a pseudo-random way. The next state of the electron helicity, so called complement state, is always with opposite helicity. The diagram on Fig. 3.1 represents the helicity state.
 +
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
[[File:Helicity_state.png|400px|thumb|'''Figure 3.1. The Helicity State''']]
 +
|}<br>
 +
 +
A one bit signal from the beam injector gives the helicity information, whereas a sync bit with a 2 HZ frequency is generated at the same time and is equal to the helicity flip time. However, the electron beam helicity sequence can be interrupted by the Data Acquisition System(DAQ), like dead time problems. In order to eliminate the asymmetry caused by the DAQ, the Faraday cup was installed to measure the charge simultaneously with the helicity state flip. The stored data files include accumulated charge value for each helicity state. The measured charge asymmetry is shown bellow for 4.2 GeV data that has been collected for ND3 target while torus magnetic field was negative.
 +
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
[[File:ChargeAsymmetry.png|350px]]
 +
|}
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
'''Figure 3.2. Run Number vs Charge Asymmetry (ND3 target, B<0)'''
 +
|}
 +
 +
The charge asymmetry measured for each run number, thats is used for this analysis is shown on Fig. 3.3.
 +
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
[[File:ChargeAsymvsRunNumber1234_1.png|400px|thumb|'''Black and red data points represent uncorrected measured charge asymmetry using Faraday cup. The green line shows the sign of half wave plane, while the purple one the sign of target polarization.''']][[File:ChargeAsymvsRunNumber1234grouped_1.png|400px|thumb|'''Run groups vs measured charge asymmetry. The runs that have the same half wave plane, target polarization sign, target type and torus current were combined into one data point.''']]
 +
|}<br>
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
'''Figure 3.2. Run Number vs Charge Asymmetry for All Runs'''
 +
|}
 +
 +
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Inclusive asymmetry as a function of X_B for all <math>Q^2</math> is shown on Fig. 3.4.  The electron paddle numbers 10 and 5 were chosen respectively for B<0 and B>0, because they contained the most electron events in a first pass semi-inclusive pion analysis of the data set.
 +
 +
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
[[File:InclusiveAsymmetry01_30_12y.png|350px]]
 +
|}
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
'''Figure 3.4. X_{bjorken} vs Inclusive Asymmetry(All data)'''
 +
|}
 +
 +
 +
The Figures 3.5 and 3.6  show inclusive asymmetry for each run number and for run groups used for these analysis
 +
 +
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
[[File:RunNumber_vs_InclusiveAsymmetry.png|350px]]
 +
|}
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
'''Figure 3.5. Run Number vs Inclusive Asymmetry'''
 +
|}
 +
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
[[File:RunNumber_vs_InclusiveAsymmetrygroups.png|350px]]
 +
|}
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
'''Figure 3.5. Run groups vs Inclusive Asymmetry'''
 +
|}
 +
 +
 +
=03/06/12=
 +
 +
 +
==NES Asymmetry==
 +
 +
 +
 +
The double spin asymmetry measurements performed in this thesis are performed by comparing scattering events that occur when the incident probe spin and nuclear target spin are parallel to scattering events that occur when the spins are anti-parallel. The helicity of the electron beam was flipped at a rate of 1 HZ.  The helicity is prepared at the source such that helicity pairs are produced pseudo randomly.  If the first electron bunch is pseudo randomly chosen to be positive (negative) then it is labeled as the original helicity state and denoted in software by a 2 (1).  The next helicity state is prepared to be a complement to the first state and labeled in the software as either a 4, if the original helicity state was a 1 (negative), or 3 if the original helicity state was a 2 (positive).  The helicity process is then repeated.  Figure NES.1 illustrates the signals used to label helicity state.  The clock pulse (SYNC) is used to indicate that a change in the pockel cell used to define the helicity state may have occurred.  The helicity bit indicates the helicity state that was set.  The original/complement pulse identifies if the state is an original or complement helicity state.  All three bits are recorded in the raw data file for each event and then converted to the labels 1,2,3,4 during DST file production once the particles have been reconstructed.
 +
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
[[File:Helicity_state.png|400px|thumb|'''Figure NES.1. The Helicity State: A one bit signal from the beam injector gives the helicity information, whereas a sync bit with a 2 HZ frequency is generated at the same time and is equal to the helicity flip time.''']]
 +
|}<br>
 +
 +
 +
Two scalers were used to record several ancillary detectors, such as a Faraday cup and several PMTs mounted on the beam line,  according to their helicity label.  One of the scalers was gated by the DAQ live time in order to record beam conditions when the DAQ was able to take data and not busy recording data.  The second scaler remained ungated.  Both scalers recorded the SYNC and Helicity signals from the injector along with the counts observed from ancillary detectors during the SYNC interval.  The Faraday cup signal recorded by the gated  helicity scaler is used to normalize the events reconstructed during the same helicity interval.  The beam charge asymmetry measured by the gated helicity scaler is shown in Figure NES. 2. as a function of run number.  For each run number the gaussian fit was used to extract the mean values of the asymmetry and corresponding error(Figure NES. 3).
 +
 +
:::::::::<math>A_{BeamCharge} = \frac{ \Sigma FC^{hel1,hel2}-\Sigma FC^{hel4,hel3}}{\Sigma FC^{hel1,hel2}+\Sigma FC^{hel4,hel3}}</math>
 +
 +
 +
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{| border="0" style="background:transparent;"  align="center"
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|-
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|
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[[File:RunNumber_vs_BeamChargeAsymmetryPulsePair07_03_2012.png|400px]]
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|}
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{| border="0" style="background:transparent;"  align="center"
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|-
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|
 +
'''Figure NES. 2. Run Number vs the beam charge Asymmetry'''
 +
|}
 +
 +
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{| border="0" style="background:transparent;"  align="center"
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|-
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|
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[[File:FC_ChargeAsymmetry_282101RunNumber_14_23HelPairs_03_12_12.png|400px]]
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|}
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{| border="0" style="background:transparent;"  align="center"
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|-
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|
 +
'''Figure NES. 3. Beam charge asymmetry for run #28101 using the gated faraday cup counts for two helicity pairs(1-4 and 2-3 helicity pairs).<math>A_{1-4}=(11.5 \pm 4.4) \times 10^{-5}</math> and <math>A_{2-3}=(-2.3 \pm  4.4) \times 10^{-5}</math>'''
 +
|}
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[[File:RunNumber_vs_BeamChargeAsymmetryPulsePair14_19_03_2012.png|400px]][[File:RunNumber_vs_BeamChargeAsymmetryPulsePair23_19_03_2012.png|400px]]
 +
 +
{| border="1"  |cellpadding="20" cellspacing="0
 +
|-
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|Run Group || Half wave plane(HWP) || <math>A_{1-4}</math> || <math>A_{2-3}</math>
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|-
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| 28100 - 28105 || +1 || <math>(5.88 \pm 34.40) \times 10^{-4}</math>  || <math>(4.03 \pm 34.36) \times 10^{-4}</math>
 +
|-
 +
| 28106 - 28115 || -1 ||<math> (7.53 \pm 22.30) \times 10^{-4}</math> ||<math> (8.28 \pm 22.30) \times 10^{-4}</math>
 +
|-
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| 28145 - 28240 || +1 || <math>(31.70 \pm 7.99) \times 10^{-4}</math> || <math>(30.40 \pm 7.99) \times 10^{-4}</math>
 +
|-
 +
| 28242 - 28284 || -1 ||<math> (49.6 \pm 10.8) \times 10^{-4}</math> ||<math> (47.9 \pm 10.8) \times 10^{-4}</math>
 +
|-
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| 28286 - 28324 || +1 ||<math> (36.3 \pm 11.6) \times 10^{-4}</math> ||<math> (37.0 \pm 11.5) \times 10^{-4}</math>
 +
|-
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| 28325 - 28447 || -1 ||<math> (21.1 \pm 13.4) \times 10^{-4}</math> || <math>(22.2 \pm 13.4) \times 10^{-4}</math>
 +
|-
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| 28449 - 28479 || +1 ||<math> (-11.6 \pm 16.5) \times 10^{-4}</math> || <math>(-21.6 \pm 16.5) \times 10^{-4}</math>
 +
|}
 +
 +
 +
A measurement of the electron cross section helicity difference needs to account for the possible helicity dependence of the incident electron flux ( Charge Asymmetry).  Fig. NES. 4 shows the reconstructed electron asymmetry before it is normalized by the gated Faraday Cup as a function of the run number for the 4.2 GeV data set.  The reconstructed electron asymmetry can be defined following way:
 +
 +
:::::<math>A_{NES}^{+-} = \frac{NES^{+} - NES^{-}}{NES^{+} + NES^{-}}  \equiv (2-3)</math> or <math>A_{NES}^{-+} = \frac{NES^{-} - NES^{+}}{NES^{-} + NES^{+}} \equiv (1-4)</math>
 +
 +
where <math>NES^+</math>(<math>NES^-</math>) represents number of reconstructed electrons in the final state for the positive(negative) beam helicity.
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
[[File:NES_Asymmetry_Before_FCNormalization.png|400px|thumb|'''Run Number vs NES Asymmetry before FC normalization. The red points represent NES asymmetry for the helicity 2-3 pair and the black points - the helicity pair 1-4. The green line shows the sing of the half wave plane and purple line - the sign of the target polarization. ''']]
 +
|}<br>
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
'''Figure NES.4. Run Number vs NES Asymmetry for All Runs before FC normalization'''
 +
|}
 +
 +
 +
Sysstematic effects on the asymmetry measurement may be investigated  by separating the data into two groups based on which helicity state is set first.  The first group(black data points) represents the electron asymmetry observed when the first (original) helicity state is negative and its complement state is positive(helicity state #1 - state #4). The second group(red data points) represents the asymmetry observed, when the first state is positive and the complement state is negative(helicity state #2 - #3). Both groups were divided into two subgroups based the target type used. The diamond points on the histogram represent the data for the NH3 target and the squares for the ND3 target.  On the same histograms are presented the signs of the half wave plane(HWP) and the target polarization(TPol).  The relative spin orientation can be changed by either inserting a half wave (HWP) or by populating a different target polarization state with a different RF frequency.  One would expect the asymmetry to change sign if either the HWP is inserted or the target polarization is rotated 180 degrees.  As one can see, the electron asymmetry sign ( sign(hel1-hel4) && sign(hel3-hel2) ) is opposite of the sign of (HWP<math>\times</math>Target_Polarization). The NES asymmetry has been calculated the following way before accounting for the Faraday cup:
 +
 +
:::::::::<math>A_{NES} = \frac{NES^{hel1,hel2} - NES^{hel4,hel3}}{NES^{hel1,hel2} + NES^{hel4,hel3}}</math>
 +
 +
The NES asymmetry after the gated faraday cup normalization is defined as:
 +
 +
:::::::::<math>A_{NES}^{FCnormalized} = \frac{\frac{NES^{hel1,hel2}}{FC^{hel1,hel2}} - \frac{NES^{hel4,hel3}}{FC^{hel4,hel3}}}{\frac{NES^{hel1,hel2}}{FC^{hel1,hel2}} + \frac{NES^{hel4,hel3}}{FC^{hel4,hel3}}}</math>
 +
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
[[File:NES_Asymmetry_After_FCNormalization.png|400px|thumb|''' Run Number vs NES Asymmetry after applying FC normalization. The red points represent NES asymmetry for the helicity 2-3 pair and the black points - the helicity pair 1-4. The green line shows the sing of the half wave plane and purple line - the sign of the target polarization.  ''']]
 +
|}<br>
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
'''Figure NES.5. Run Number vs NES Asymmetry for All Runs after FC normalization'''
 +
|}
 +
 +
On the Fig. NES. 6 data runs are combined for the same target type, target polarization, beam torus and half wave plane.
 +
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
[[File:NES_Asymmetry_BeforeandAfter_FCNormalizationgrouped.png|400px]]
 +
|}
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
'''Figure NES. 6. Run groups vs NES Asymmetry before and after FC Normalization'''
 +
|}
 +
 +
=03/12/12=
 +
 +
 +
==SIDIS Asymmetry==
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 +
SIDIS asymmetries:
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 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
<math>A_{NH3}^{\pi^+}=\frac{N_{NH3,\pi^+}^{hel1,hel2} - N_{NH3, \pi^+}^{hel4,hel3}}{N_{NH3,\pi^+}^{hel1,hel2} + N_{NH3, \pi^+}^{hel4,hel3}}</math>
 +
|}
 +
 +
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
<math>A_{ND3}^{\pi^-}=\frac{N_{ND3,\pi^-}^{hel1,hel2} - N_{ND3, \pi^-}^{hel4,hel3}}{N_{ND3,\pi^-}^{hel1,hel2} + N_{ND3, \pi^-}^{hel4,hel3}}</math>
 +
|}
 +
 +
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
[[File:SIDIS_Asymmetry_Before_FCNormalization03_12_12.png|400px]]
 +
|}
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
'''Figure NES. 6. Run Number vs Semi inclusive asymmetry before FC Normalization.'''
 +
|}
 +
 +
 +
 +
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
[[File:SIDIS_Asymmetry_After_FCNormalization03_12_12.png|400px]]
 +
|}
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
'''Figure NES. 6. Run Number vs Semi inclusive asymmetry after FC Normalization.'''
 +
|}
 +
 +
 +
 +
{| border="1"  |cellpadding="20" cellspacing="0
 +
|-
 +
| Target type, Beam Torus sign (B) || <math>A_{hel1-hel4}</math> || <math>A_{hel2-hel3}</math>  || <math>A_{hel13-hel42}</math>
 +
|-
 +
| NH3, B>0, <math>\pi^+</math> || <math>(-139.84 \pm 81.52) \times 10^{-4}</math>
 +
|| <math>(143.15 \pm 81.78) \times 10^{-4}</math> ||<math> (-136.2 \pm 57.74) \times 10^{-4}</math>
 +
|-
 +
| NH3, B<0, <math>\pi^+</math> ||<math> (-223.76 \pm 117.10) \times 10^{-4}</math>
 +
|| <math>(247.65 \pm 116.59) \times 10^{-4}</math> || <math>(-237.69 \pm 82.65) \times 10^{-4}</math>
 +
|-
 +
| ND3, B>0, <math>\pi^-</math> || <math>(-6.37 \pm 188.73) \times 10^{-4}</math>
 +
|| <math>(-98.11 \pm 188.03) \times 10^{-4}</math> ||<math> (-9.21 \pm 127.22) \times 10^{-4}</math>
 +
|-
 +
| ND3, B<0, <math>\pi^-</math> || <math>(-63.73 \pm 105.14) \times 10^{-4}</math>
 +
|| <math>(-30.34 \pm 6085.54) \times 10^{-4}</math> ||<math> (-12.37 \pm 71.10) \times 10^{-4}</math>
 +
|-
 +
| NH3, B>0, <math>\pi^-</math> || <math>(-155.45 \pm 128.21) \times 10^{-4}</math>
 +
|| <math>(-72.55 \pm 128.92) \times 10^{-4}</math> ||<math>(-35.11 \pm 90.91) \times 10^{-4}</math>
 +
|-
 +
| NH3, B<0, <math>\pi^-</math> ||<math>(9.60 \pm 119.31) \times 10^{-4}</math>|| <math>(72.94 \pm 119.36) \times 10^{-4}
 +
</math> || <math>(-32.39 \pm 84.38) \times 10^{-4}</math>
 +
|-
 +
| ND3, B>0, <math>\pi^+</math> || <math>(-76.59 \pm 126.60) \times 10^{-4}</math>
 +
|| <math>(110.28 \pm 126.13) \times 10^{-4}</math> ||<math> (-92.25 \pm 85.38) \times 10^{-4} </math>
 +
|-
 +
| ND3, B<0, <math>\pi^+</math> || <math>(-29.22 \pm 107.53) \times 10^{-4}</math>
 +
|| <math>(123.98 \pm 106.86) \times 10^{-4}</math> ||<math> (-92.25 \pm 85.38) \times 10^{-4}</math>
 +
|}
 +
 +
 +
{| border="1"  |cellpadding="20" cellspacing="0
 +
|-
 +
|Run Group || Target type, Beam Torus sign (B) || A_{1-4} || A_{2-3}
 +
|-
 +
| 28214 - || NH3, B>0 || <math>-0.02704757 \pm 0.01711263</math> || 0.02399480 \pm 0.01700174
 +
|-
 +
| 28231 - || NH3, B>0 || <math>0.00069178
 +
\pm 0.01545227</math> || -0.01372286
 +
\pm 0.01559729
 +
|-
 +
| 28252 - || NH3, B>0 || <math>-0.01229841
 +
\pm 0.01693271</math> || -0.00048034 \pm 0.01685103
 +
|-
 +
| 28266 - || NH3, B>0 || <math>0.01589835 \pm 0.01590701</math> || -0.02002048 \pm 0.01610756
 +
|-
 +
| 28413 - || NH3, B<0 || 0.02205009 \pm 0.01799869 || -0.02291024 \pm 0.01795956
 +
|-
 +
| 28469 - || NH3, B<0 || 0.02270121 \pm 0.01543980 || -0.02662038 \pm 0.01532731
 +
|-
 +
| 28102 - || ND3, B>0 || 0.04443768 \pm 0.06093347 || 0.01055158 \pm 0.06066387
 +
|-
 +
| 28109 - || ND3, B>0 || 0.01068017 \pm  0.03953670 || -0.00764924 \pm 0.03970762
 +
|-
 +
| 28150 - || ND3, B>0 || -0.01238850 \pm 0.03640693 || 0.02901657 \pm 0.03642766
 +
|-
 +
| 28182 - || ND3, B>0 || -0.02497960 \pm 0.02660287 || 0.00797540 \pm 0.02634698
 +
|-
 +
| 28295 - || ND3, B<0 || -0.01323095 \pm 0.01636848 || -0.01008145 \pm 0.01636433
 +
|-
 +
| 28315 - || ND3, B<0 || -0.01026453 \pm 0.01768742 || 0.00621953 \pm 0.01758502
 +
|-
 +
| 28393 - || ND3, B<0 || 0.01615151 \pm 0.01853525 || -0.00719786 \pm 0.01834110
 +
|}
 +
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
[[File:SIDIS_Asymmetry_After_FCNormalizationRunsGrouped03_13_12.png|400px]]
 +
|}
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|
 +
'''Figure NES. 6. Run groups vs Semi inclusive asymmetry after FC Normalization.'''
 +
|}
 +
 +
===X and Z count distribution===
 +
 +
 +
{| border="1"  |cellpadding="20" cellspacing="0
 +
|-
 +
| SIDI Asymmetry  || <math>X_B=0.3</math> || <math>X_B=0.4</math>
 +
|-
 +
|<math> A_{NH3}^{\pi^+,hel13-hel24}</math>||<math>(-150.08 \pm 65.96) \times 10^{-4}</math> || <math>(-217.20 \pm 69.06) \times 10^{-4}</math>
 +
|-
 +
|<math> A_{ND3}^{\pi^-,hel13-hel24}</math>||<math>(-39.04 \pm 81.44) \times 10^{-4}</math> || <math>(-91.90 \pm 96.14) \times 10^{-4}</math>
 +
|-
 +
|<math> A_{NH3}^{\pi^-,hel13-hel24}</math>||<math>(-100.81 \pm 83.49) \times 10^{-4}</math> || <math>(23.98 \pm 94.92) \times 10^{-4}</math>
 +
|-
 +
|<math> A_{ND3}^{\pi^+,hel13-hel24}</math>||<math>(-53.17 \pm 74.89) \times 10^{-4}</math> || <math>(-85.17 \pm 82.97) \times 10^{-4}</math>
 +
|}
 +
 +
 +
====<math> A_{NH3}^{\pi^+,hel13-hel24}</math>====
 +
 +
{| border="1"  |cellpadding="20" cellspacing="0
 +
|-
 +
| <math>z</math> || <math>X_B=0.3</math> || <math>X_B=0.4</math>
 +
|-
 +
| 0.3 ||<math>(-142.39 \pm 106.42) \times 10^{-4}</math> ||<math>( -131.49 \pm 116.96) \times 10^{-4}</math>
 +
|-
 +
| 0.5 || <math>(-101.14 \pm 128.36) \times 10^{-4}</math>||<math>(-207.76 \pm 129.37) \times 10^{-4}</math>
 +
|-
 +
| 0.7 ||<math>(-140.32 \pm 158.98) \times 10^{-4}</math>||<math>(-238.34 \pm 156.79) \times 10^{-4}</math>
 +
|-
 +
| 0.9 ||<math>(-355.44 \pm 200.23) \times 10^{-4}</math> ||<math>(-438.76 \pm 189.03) \times 10^{-4}</math>
 +
|}
 +
 +
 +
{| border="1"  |cellpadding="20" cellspacing="0
 +
|-
 +
| <math>z</math> || <math>X_B=0.3</math> || <math>X_B=0.4</math>
 +
|-
 +
| 0.45 ||<math>(-125.62 \pm 81.92) \times 10^{-4}</math> ||<math>( -165.81 \pm 86.76) \times 10^{-4}</math>
 +
|-
 +
| 0.7 ||<math>(-140.32 \pm 158.98) \times 10^{-4}</math>||<math>(-238.34 \pm 156.79) \times 10^{-4}</math>
 +
|-
 +
| 0.9 ||<math>(-355.44 \pm 200.23) \times 10^{-4}</math> ||<math>(-438.76 \pm 189.03) \times 10^{-4}</math>
 +
|}
 +
 +
====<math> A_{ND3}^{\pi^-,hel13-hel24}</math>====
 +
 +
{| border="1"  |cellpadding="20" cellspacing="0
 +
|-
 +
| <math>z</math> || <math>X_B=0.3</math> || <math>X_B=0.4</math>
 +
|-
 +
| 0.3 ||<math>(9.18 \pm 120.73) \times 10^{-4}</math> ||<math>( -46.32 \pm 147.45) \times 10^{-4}</math>
 +
|-
 +
| 0.5 || <math>(-66.91 \pm 161.28) \times 10^{-4}</math>||<math>(-78.88 \pm 182.05) \times 10^{-4}</math>
 +
|-
 +
| 0.7 ||<math>(-96.54 \pm 232.06) \times 10^{-4}</math>||<math>(-236.67 \pm 257.03) \times 10^{-4}</math>
 +
|-
 +
| 0.9 ||<math>(-147.74 \pm 297.50) \times 10^{-4}</math> ||<math>(-78.69 \pm 320.29) \times 10^{-4}</math>
 +
|}
 +
 +
 +
<math>\Delta R_{np}^{\pi^+ + \pi^-} = \frac{\Delta \sigma_p^{\pi^+ + \pi^-} - \Delta \sigma_{n}^{\pi^+ + \pi^-}}{\sigma_p^{\pi^+ + \pi^-} - \sigma_{n}^{\pi^+ + \pi^-}}=</math>
 +
 +
<math>=\frac{\Delta \sigma_p^{\pi^+ + \pi^-}}{\sigma_p^{\pi^+ + \pi^-} - \sigma_{n}^{\pi^+ + \pi^-}} - \frac{\Delta \sigma_{n}^{\pi^+ + \pi^-}}{\sigma_p^{\pi^+ + \pi^-} - \sigma_{n}^{\pi^+ + \pi^-}}=</math>
 +
 +
<math> = \frac{(\sigma_p^{\pi^+,hel13} - \sigma_p^{\pi^+,hel24}) + (\sigma_p^{\pi^-,hel13} - \sigma_p^{\pi^-,hel24})}{\sigma_p^{\pi^+ + \pi^-} - \sigma_{n}^{\pi^+ + \pi^-}}  - \frac{(\sigma_n^{\pi^+,hel13} - \sigma_n^{\pi^+,hel24}) + (\sigma_n^{\pi^-,hel13} - \sigma_n^{\pi^-,hel24})}{\sigma_p^{\pi^+ + \pi^-} - \sigma_{n}^{\pi^+ + \pi^-}} = </math>
 +
 +
 +
 +
<math>=\frac{(\Delta u +\Delta \bar{u}) - (\Delta d + \Delta \bar{d})}{(u+\bar{u}) - (d+\bar{d})}(x,Q^2)=</math>
 +
 +
 +
 +
<math>= \frac{g_1^p - g_1^n}{F_1^p - F_1^n}(x,Q^2)</math>
 +
 +
 +
"If each observable (<math>x_i</math>)  is accompanied by an estimate of the uncertainty in that observable (<math>\sigma_i</math>) then the weighted mean is defined as
 +
 +
:<math>\bar{x} = \frac{ \sum_{i=1}^{i=n} \frac{x_i}{\sigma_i^2}}{\sum_{i=1}^{i=n} \frac{1}{\sigma_i^2}}</math>"
 +
 +
"The variance of the distribution is defined as
 +
 +
:<math>\frac{1}{\sigma^2} = \sum_{i=1}^{i=n} \frac{1}{\sigma_i^2}</math> = weighted variance"
 +
[[TF_ErrorAna_PropOfErr]]
 +
 +
{| border="1" style="text-align: center;" align="center"
 +
|-
 +
| <math>z</math> || <math>X_B=0.3</math> || <math>X_B=0.4</math>
 +
|-
 +
| 0.3 ||<math>(1453.94
 +
\pm 236.39) \times 10^{-4}</math> ||<math>(-104.24  \pm 277.69) \times 10^{-4}</math>
 +
|-
 +
| 0.5 ||<math>(550.18 \pm 298.65) \times 10^{-4}</math>||<math>(149.78 \pm 320.13) \times 10^{-4}</math>
 +
|-
 +
| 0.7 ||<math>(-650.12
 +
\pm 407.30) \times 10^{-4}</math> ||<math>(79.69  \pm 430.29) \times 10^{-4}</math>
 +
|-
 +
| 0.9 ||<math>(2285.22 \pm 525.13) \times 10^{-4}</math>||<math>(5.59 \pm 545.08) \times 10^{-4}</math>
 +
|}
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|'''Table 4.5.''' Experimental Results of The Fragmentation Function <math>\Delta R_{np}^{\pi^+ + \pi^-} </math> vs <math>z</math> and <math>X_B</math> for four values of <math>z</math>.
 +
|}<br><br>
 +
 +
{| border="1" style="text-align: center;" align="center"
 +
|-
 +
| <math>z</math> || <math>X_B=0.3</math> || <math>X_B=0.4</math>
 +
|-
 +
| 0.45 ||<math>(582.79
 +
\pm 186.97) \times 10^{-4}</math> ||<math>( 55.32 \pm 214.92) \times 10^{-4}</math>
 +
|-
 +
| 0.85 ||<math>(504.20 \pm 321.74) \times 10^{-4}</math>||<math>(57.35 \pm 337.48) \times 10^{-4}</math>
 +
|}
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|'''Table 4.6.''' Experimental Results of The Fragmentation Function <math>\Delta R_{np}^{\pi^+ + \pi^-} </math>  vs <math>z</math> and <math>X_B</math>(Combined <math>z</math>).
 +
|}<br>
 +
 +
 +
{| border="1" style="text-align: center;" align="center"
 +
|-
 +
| <math>Q^{2}</math> || <math>W^{2}</math> || <math>X_{b}</math> || <math>\Delta R_{deuteron,p}^{\pi^+ + \pi^-} </math> || <math>\Delta R_{np}^{\pi^+ + \pi^-} </math>
 +
|-
 +
| 0.8 || 2.4 || 0.344712 || 0.089457 || 1.215956
 +
|-
 +
| 0.8 || 2.56 || 0.322805 || 0.087636 || 1.144319
 +
|-
 +
| 0.8 || 2.72 || 0.302941 || 0.087324 || 1.142601
 +
|-
 +
| 0.8 || 2.89 || 0.284872 || 0.080418 || 1.081259
 +
|-
 +
| 0.8 || 3.06 || 0.268386 || 0.046144 || 0.971948
 +
|-
 +
| 0.8 || 3.24 || 0.253303 || -0.001413 || 0.904000
 +
|-
 +
| 0.8 || 3.42 || 0.239465 || -0.039615 || 0.888457
 +
|-
 +
| 0.85 || 2.4 || 0.358532 || 0.095124 || 1.179011
 +
|-
 +
| 0.85 || 2.56 || 0.336197 || 0.092376 || 1.118478
 +
|-
 +
| 0.85 || 2.72 || 0.315894 || 0.091414 || 1.126200
 +
|-
 +
| 0.85 || 2.89 || 0.297382 || 0.083684 || 1.073062
 +
|-
 +
| 0.85 || 3.06 || 0.280456 || 0.047397 || 0.965145
 +
|-
 +
| 0.85 || 3.24 || 0.264940 || 0.000751 || 0.897095
 +
|-
 +
| 0.85 || 3.42 || 0.250680 || -0.037185 || 0.879470
 +
|-
 +
| 0.9 || 2.4 || 0.371781 || 0.101758 || 1.124929
 +
|-
 +
| 0.9 || 2.56 || 0.349070 || 0.097293 || 1.077209
 +
|-
 +
| 0.9 || 2.72 || 0.328374 || 0.095640 || 1.097502
 +
|-
 +
| 0.9 || 2.89 || 0.309461 || 0.087175 || 1.064119
 +
|-
 +
| 0.9 || 3.06 || 0.292134 || 0.050127 || 0.968564
 +
|-
 +
| 0.9 || 3.24 || 0.276219 || 0.003136 || 0.902680
 +
|-
 +
| 0.9 || 3.42 || 0.261569 || -0.034673 || 0.882556
 +
|-
 +
| 0.95 || 2.4 || 0.384494 || 0.107726 || 1.079087
 +
|-
 +
| 0.95 || 2.56 || 0.361453 || 0.102269 || 1.040995
 +
|-
 +
| 0.95 || 2.72 || 0.340407 || 0.099848 || 1.072015
 +
|-
 +
| 0.95 || 2.89 || 0.321133 || 0.090544 || 1.055804
 +
|-
 +
| 0.95 || 3.06 || 0.303439 || 0.052833 || 0.971023
 +
|-
 +
| 0.95 || 3.24 || 0.287158 || 0.005393 || 0.907107
 +
|-
 +
| 0.95 || 3.42 || 0.272146 || -0.032200 || 0.884625
 +
|-
 +
| 1 || 2.4 || 0.396703 || 0.113466 || 1.036707
 +
|-
 +
| 1 || 2.56 || 0.373374 || 0.106727 || 1.007923
 +
|-
 +
| 1 || 2.72 || 0.352016 || 0.103726 || 1.047463
 +
|-
 +
| 1 || 2.89 || 0.332416 || 0.093605 || 1.045933
 +
|-
 +
| 1 || 3.06 || 0.314388 || 0.055305 || 0.970792
 +
|-
 +
| 1 || 3.24 || 0.297772 || 0.007453 || 0.909048
 +
|-
 +
| 1 || 3.42 || 0.282424 || -0.029966 || 0.884723
 +
|-
 +
| 1.05 || 2.4 || 0.408437 || 0.118939 || 0.992592
 +
|-
 +
| 1.05 || 2.56 || 0.384858 || 0.111105 || 0.971331
 +
|-
 +
| 1.05 || 2.72 || 0.363224 || 0.107103 || 1.019267
 +
|-
 +
| 1.05 || 2.89 || 0.343330 || 0.095852 || 1.029986
 +
|-
 +
| 1.05 || 3.06 || 0.324999 || 0.057266 || 0.964081
 +
|-
 +
| 1.05 || 3.24 || 0.308073 || 0.009820 || 0.906637
 +
|-
 +
| 1.05 || 3.42 || 0.292416 || -0.027198 || 0.883994
 +
|-
 +
| 1.1 || 2.4 || 0.419723 || 0.125251 || 0.947155
 +
|-
 +
| 1.1 || 2.56 || 0.395929 || 0.115416 || 0.938049
 +
|-
 +
| 1.1 || 2.72 || 0.374051 || 0.110297 || 0.993433
 +
|-
 +
| 1.1 || 2.89 || 0.353894 || 0.098076 || 1.014245
 +
|-
 +
| 1.1 || 3.06 || 0.335286 || 0.059359 || 0.956429
 +
|-
 +
| 1.1 || 3.24 || 0.318077 || 0.012982 || 0.905373
 +
|-
 +
| 1.1 || 3.42 || 0.302133 || -0.024350 || 0.882958
 +
|-
 +
| 1.15 || 2.4 || 0.430586 || 0.130979 || 0.910430
 +
|-
 +
| 1.15 || 2.56 || 0.406608 || 0.119423 || 0.907506
 +
|-
 +
| 1.15 || 2.72 || 0.384515 || 0.113163 || 0.969323
 +
|-
 +
| 1.15 || 2.89 || 0.364122 || 0.100019 || 0.998793
 +
|-
 +
| 1.15 || 3.06 || 0.345265 || 0.061046 || 0.948539
 +
|-
 +
| 1.15 || 3.24 || 0.327796 || 0.015164 || 0.901680
 +
|-
 +
| 1.15 || 3.42 || 0.311587 || -0.021709 || 0.880861
 +
|-
 +
| 1.2 || 2.4 || 0.441050 || 0.136174 || 0.877989
 +
|-
 +
| 1.2 || 2.56 || 0.416916 || 0.123376 || 0.879867
 +
|-
 +
| 1.2 || 2.72 || 0.394636 || 0.116022 || 0.947092
 +
|-
 +
| 1.2 || 2.89 || 0.374032 || 0.101867 || 0.984262
 +
|-
 +
| 1.2 || 3.06 || 0.354948 || 0.062766 || 0.940538
 +
|-
 +
| 1.2 || 3.24 || 0.337242 || 0.017174 || 0.897860
 +
|-
 +
| 1.2 || 3.42 || 0.320789 || -0.019216 || 0.878344
 +
|-
 +
| 1.25 || 2.4 || 0.451137 || 0.141522 || 0.851328
 +
|-
 +
| 1.25 || 2.56 || 0.426872 || 0.127836 || 0.854448
 +
|-
 +
| 1.25 || 2.72 || 0.404429 || 0.119066 || 0.924399
 +
|-
 +
| 1.25 || 2.89 || 0.383638 || 0.104151 || 0.966286
 +
|-
 +
| 1.25 || 3.06 || 0.364349 || 0.064626 || 0.929040
 +
|-
 +
| 1.25 || 3.24 || 0.346426 || 0.019518 || 0.890588
 +
|-
 +
| 1.25 || 3.42 || 0.329748 || -0.016436 || 0.873707
 +
|-
 +
| 1.3 || 2.4 || 0.460866 || 0.146979 || 0.827067
 +
|-
 +
| 1.3 || 2.56 || 0.436494 || 0.131843 || 0.832123
 +
|-
 +
| 1.3 || 2.72 || 0.413910 || 0.122206 || 0.903273
 +
|-
 +
| 1.3 || 2.89 || 0.392954 || 0.106218 || 0.949548
 +
|-
 +
| 1.3 || 3.06 || 0.373480 || 0.066537 || 0.917721
 +
|-
 +
| 1.3 || 3.24 || 0.355358 || 0.021675 || 0.883594
 +
|-
 +
| 1.3 || 3.42 || 0.338473 || -0.013711 || 0.868901
 +
|-
 +
| 1.35 || 2.4 || 0.470256 || 0.151920 || 0.806259
 +
|-
 +
| 1.35 || 2.56 || 0.445798 || 0.135925 || 0.812231
 +
|-
 +
| 1.35 || 2.72 || 0.423094 || 0.125351 || 0.884403
 +
|-
 +
| 1.35 || 2.89 || 0.401992 || 0.108521 || 0.933955
 +
|-
 +
| 1.35 || 3.06 || 0.382352 || 0.068511 || 0.907321
 +
|-
 +
| 1.35 || 3.24 || 0.364050 || 0.023938 || 0.877039
 +
|-
 +
| 1.35 || 3.42 || 0.346974 || -0.011047 || 0.864389
 +
|}<br>
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|'''Table 4.7.''' <math> \frac{g_1^p - g_1^n}{F_1^p - F_1^n}(x,Q^2)</math>.
 +
|}<br>
 +
 +
 +
{| border="1" style="text-align: center;" align="center"
 +
|-
 +
| <math>n_{C,MT,\pi^{+} \pi^{-}}</math> || <math>x_{B}=0.3</math> || <math>x_{B}=0.4</math>
 +
|-
 +
| <math>n_{C,\pi^{+}}</math>, <math>z=0.45</math> || 0.006584 || 0.004943
 +
|-
 +
| <math>n_{C,\pi^{-}}</math>, <math>z=0.45</math> || 0.006382 || 0.004355
 +
|-
 +
| <math>n_{MT,\pi^{+}}</math>, <math>z=0.45</math> || 0.005769 || 0.004544
 +
|-
 +
| <math>n_{MT,\pi^{-}}</math>, <math>z=0.45</math> || 0.005856 || 0.004021
 +
|-
 +
| <math>n_{C,\pi^{+}}</math>, <math>z=0.85</math> || 0.002893 || 0.002574
 +
|-
 +
| <math>n_{C,\pi^{-}}</math>, <math>z=0.85</math> || 0.001664 || 0.001361
 +
|-
 +
| <math>n_{MT,\pi^{+}}</math>, <math>z=0.85</math> || 0.002673 || 0.002399
 +
|-
 +
| <math>n_{MT,\pi^{-}}</math>, <math>z=0.85</math> || 0.001565 || 0.001307
 +
|}<br>
 +
 +
{| border="1" style="text-align: center;" align="center"
 +
|-
 +
| <math>n_{NH3,ND,\pi^{+} \pi^{-}}</math> || <math>x_{B}=0.3</math> || <math>x_{B}=0.4</math>
 +
|-
 +
| <math>n_{NH3,\pi^{+}}</math>, <math>z=0.45</math> || 0.00611464
 +
|| 0.00545206
 +
|-
 +
| <math>n_{NH3,\pi^{-}}</math>, <math>z=0.45</math> || 0.00428864
 +
|| 0.00330646
 +
|-
 +
| <math>n_{ND3,\pi^{+}}</math>, <math>z=0.45</math> || 0.00552027
 +
|| 0.00392858
 +
|-
 +
| <math>n_{ND3,\pi^{-}}</math>, <math>z=0.45</math> || 0.00552027
 +
|| 0.00392858
 +
|-
 +
| <math>n_{NH3,\pi^{+}}</math>, <math>z=0.85</math> || 0.00265003
 +
|| 0.00282080
 +
|-
 +
| <math>n_{NH3,\pi^{-}}</math>, <math>z=0.85</math> || 0.00097612
 +
|| 0.00090184
 +
|-
 +
| <math>n_{ND3,\pi^{+}}</math>, <math>z=0.85</math> || 0.00264221
 +
|| 0.00243020
 +
|-
 +
| <math>n_{ND3,\pi^{-}}</math>, <math>z=0.85</math> ||0.00154130
 +
|| 0.00128547
 +
|}<br>
 +
 +
{| border="1" style="text-align: center;" align="center"
 +
|-
 +
|<math>x_{B}=0.3</math> || <math>x_{B}=0.4</math>
 +
|-
 +
| <math>0.969 \pm 0.095</math> || <math>0.947 \pm 0.08</math>
 +
|}<br>
 +
{| border="0" style="background:transparent;"  align="center"
 +
|-
 +
|'''Table 4.7.''' Average <math> \Delta R_{np}^{\pi^+ + \pi^-} = \frac{g_1^p - g_1^n}{F_1^p - F_1^n}(x,Q^2)</math>.
 +
|}<br>
 +
  
−
scp /cache/mss/clas/eg1b/production/pass1/v4/4p2out/misc/dst/dst2828* isulinux1:/scratch/tforest/
+
{| border="1" style="text-align: center;" align="center"
 +
|-
 +
| <math>z</math> || <math>X_B=0.3</math> || <math>X_B=0.4</math>
 +
|-
 +
| 0.45 ||<math>-0.297 \pm 0.071</math> ||<math> -0.379 \pm 0.071</math>
 +
|-
 +
| 0.7 ||<math>-0.120 \pm 0.072</math>||<math>-0.122 \pm 0.072</math>
 +
|}<br>
  
−
scp /cache/mss/clas/eg1b/production/pass1/v4/4p2out/misc/dst/dst2823* isulinux1:/scratch/tforest/
 
  
−
scp /cache/mss/clas/eg1b/production/pass1/v4/4p2out/misc/dst/dst2829* isulinux1:/scratch/tforest/4.2negNH3
+
[http://wiki.iac.isu.edu/index.php/User_talk:Didbtama Go Back]

Latest revision as of 05:07, 8 December 2012

TD_Ddoverd_2008

TD_Ddoverd_2009

TD_Ddoverd_2010

The goal

Fragmentation Function test

A complete test of independent fragmentation can be performed with polarized proton and neutron targets. The ratio of the difference of polarized to unpolarized cross sections for proton and neutron targets [math]\Delta R_{np}^{\pi^+ + \pi^-}[/math] can be written in terms of the structure functions:

[math]\Delta R_{np}^{\pi^+ + \pi^-} = \frac{\Delta \sigma_p^{\pi^+ + \pi^-} - \Delta \sigma_{n}^{\pi^+ + \pi^-}}{\sigma_p^{\pi^+ + \pi^-} - \sigma_{n}^{\pi^+ + \pi^-}}= \frac{g_1^p - g_1^n}{F_1^p - F_1^n}(x,Q^2)[/math]

Delta d over d

[math]\frac{\Delta d_v}{d_v}(x,Q^2) = \frac{\Delta \sigma_p^{\pi^+ \pm \pi^-} - 4\Delta \sigma_{2H}^{\pi^+ \pm \pi^-}}{\sigma_p^{\pi^+ \pm \pi^-} - 4\sigma_{2H}^{\pi^+ \pm \pi^-}} (x,Q^2)[/math]

1/24/2011

1.) Find energy range with substantial ND3, pi- events when B <0.

Ratio plot for Q^2 and X_{BJ}

once you find the Q^2 and X_BJ range holding a reasonable amount of data.



2.) Inclusive electron scattering ratio of

Inclusiveelectrons -vs- Q-squared Inclusive Missing Mass (W) for 1.0 Q^2 <1.2
[[|300px|thumb|The ratio of inclusive electrons detected in scintillator paddle #7 when Btorus >0 (B_p)to inclusive electrons detected by paddle 11 when B<0(B_n) NH3 Target]] [[|300px|thumb|The inclusive missing mass W for each torus setting. Dashed line is B>0 and solid line is B<0]]
[[|300px|thumb|The ratio of inclusive electrons detected in scintillator paddle #7 when Btorus >0 (B_p)to inclusive electrons detected by paddle 11 when B<0(B_n)]]ND3 Target [[|300px|thumb|The inclusive missing mass W for each torus setting. Dashed line is B>0 and solid line is B<0]]
[[|300px|thumb|The ratio of inclusive electrons detected in scintillator paddle #7 when Btorus >0 (B_p)to inclusive electrons detected by paddle 11 when B<0(B_n)]] Both Targets 300px|thumb|The inclusive missing mass W for each torus setting. Dashed line is B>0 and solid line is B<0

3.) Semi Inclusive pion production ratios -vs- Q^2, Only electron cuts

/cache/mss/clas/eg1b/production/pass1/v4/4p2out/misc/dst/dst2828*



ND3 4.2-

28287 28288 28289 28290 28291 28292 28293 28294 28295 28296 28298 28299 28300 28301 28302 28306 28307 28309 28311 28312 28313 28314 28315 28316 28317 28319 28320 28321 28322 28323 28335 28336 28337 28338 28339 28340 28341 28351 28352 28367 28368 28369 28370 28371 28372 28373 28374 28375 28376 28377 28378 28379 28380 28381 28385 28386 28389 28390 28391 28392 28393 28394 28396 28397 28398 28399 28400 28401

ND3 4.2+

28074 28075 28076 28077 28078 28079 28081 28082 28083 28086 28087 28088 28089 28093 28094 28095 28096 28097 28098 28099 28100 28101 28102 28106 28107 28108 28109 28110 28111 28112 28113 28115 28145 28146 28147 28148 28149 28152 28154 28158 28166 28167 28168 28171 28172 28180 28181 28182 28185 28186 28187 28188 28189 28190


NH3 4.2-

28407 28408 28409 28410 28411 28412 28413 28414 28415 28416 28417 28422 28423 28424 28425 28426 28427 28428 28429 28432 28433 28438 28439 28443 28445 28446 28447 28448 28449 28450 28456 28457 28458 28460 28461 28462 28463 28464 28467 28469 28471 28472 28473 28476 28478 28479


NH3 4.2+

28205 28207 28208 28209 28210 28211 28212 28214 28215 28216 28217 28222 28223 28224 28225 28226 28227 28230 28231 28232 28233 28234 28235 28236 28240 28242 28244 28245 28246 28247 28249 28250 28252 28253 28254 28255 28256 28260 28261 28262 28263 28264 28265 28266 28272 28274 28275 28276 28277

File locations:

http://www.jlab.org/Hall-B/secure/eg1/EG2000/nevzat/UPGRADE_DST/

/cache/mss/clas/eg1b/production/pass1/v4/4p2out/misc/dst/dst2828*

/cache/mss/home/nguler/dst

Rates before and after requiring pions

all the cuts are applied, except NPHE>2.5 cut.

NPHE ND3 4 2- nopions.gifNPHE ND3 4 2- withpions.gif

4.2 GeV, ND3 target, 98 files, B<0[math]\frac{\mbox{SemiInclusive Events}}{\mbox{Inclusive Events}}= 14.5% [/math]

NPHE ND3 4 2+ nopions.gifNPHE ND3 4 2+ withpions.gif

4.2 GeV, ND3 target, 32 files, B>0[math]\frac{\mbox{SemiInclusive Events}}{\mbox{Inclusive Events}}= 4.4 %[/math]

The ratio for ND3 4.2 GeV data

Electron paddle selection

Inclusive

ElectronPaddleNumber4 2GeVND3negativewithoutpions.gif ElectronPaddleNumber4 2GeVND3positivewithoutpions.gif
Electron Paddle Number(Inclusive, B<0, 4.2 GeV Beam, ND3 Target) Electron Paddle Number(Inclusive, B>0, 4.2 GeV Beam, ND3 Target)

Semi-Inclusive

ElectronPaddleNumber4 2GeVND3negativewithpions.gif ElectronPaddleNumber4 2GeVND3positivewithpions.gif
Electron Paddle Number(Semi-Inclusive, B<0, 4.2 GeV Beam, ND3 Target) Electron Paddle Number(Semi-Inclusive, B>0, 4.2 GeV Beam, ND3 Target)


B>0, ND3 Electron paddle number=5

B<0, ND3 Electron paddle number=10

The Ratio

X_B [math]\frac{ND3,Epaddle=5,B\gt 0}{ND3,Epaddle=10,B\lt 0}[/math] without pions [math]\frac{ND3,Epaddle=5,B\gt 0}{ND3,Epaddle=10,B\lt 0}[/math] with pions
0.3 [math]1.01 \pm 0.02[/math] [math] 1.2 \pm 0.1[/math]
0.35 [math]1.06 \pm 0.01[/math] [math]1.1 \pm 0.06[/math]
0.4 [math]1.1 \pm 0.01[/math] [math]1.03 \pm 0.08[/math]
0.45 [math]1.1 \pm 0.01[/math] [math]1.1 \pm 0.09[/math]
0.5 [math]0.9 \pm 0.02[/math] [math]0.6 \pm 0.2[/math]
0.55 [math]0.23 \pm 0.06[/math] [math]0.13 \pm 0.5[/math]


The ratio for NH3 4.2 GeV data

Electron paddle selection

Inclusive

ElectronPaddleNumber4 2GeVNH3negativewithoutpions.gif ElectronPaddleNumber4 2GeVNH3positivewithoutpions.gif
Electron Paddle Number(Inclusive, B<0, NH3 target, 4.2 GeV Beam) Electron Paddle Number(Inclusive, B>0, NH3 target, 4.2 GeV Beam)

Semi-Inclusive

ElectronPaddleNumber4 2GeVNH3negativewithpions.gif positive
Electron Paddle Number(Semi-Inclusive, B<0, NH3 target, 4.2 GeV Beam) Electron Paddle Number(Semi-Inclusive, B>0, NH3 target, 4.2 GeV Beam)


B>0, NH3 Electron paddle number=5

B<0, NH3 Electron paddle number=10

The Ratio

X_B [math]\frac{NH3,Epaddle=5,B\gt 0}{NH3,Epaddle=10,B\lt 0}[/math] without pions [math]\frac{NH3,Epaddle=5,B\gt 0}{NH3,Epaddle=10,B\lt 0}[/math] with pions
0.3 [math]1.02 \pm 0.01[/math] [math] 1.2 \pm 0.03[/math]
0.35 [math]1.08 \pm 0.008[/math] [math]1.01 \pm 0.02[/math]
0.4 [math]1.09 \pm 0.009[/math] [math]1.04 \pm 0.02[/math]
0.45 [math]1.19 \pm 0.01[/math] [math]1.1 \pm 0.03[/math]
0.5 [math]0.9 \pm 0.01[/math] [math]0.8 \pm 0.03[/math]
0.55 [math]0.2 \pm 0.03[/math] [math]0.18 \pm 0.09[/math]

1/31/11

Electron paddle number for B>0 is 5 and for B<0 - 10. The cut was applied on [math]X_B[/math] : [math]0.3\lt X_B\lt 0.6[/math]

Inclusive

1.) Overlap electron kinematic ([math]\theta[/math], W, Momentum) for B>0 and B<0 and ND3 and NH3.

(NH3,B>0), (NH3,B<0), (ND3,B>0) && (ND3,B<0)

EmomInclusiveoverlay4-2GeV.gif EthetaInclusiveoverlay4-2GeV.gif WInclusiveoverlay4-2GeV.gif
Electron Momentum((NH3,B>0), (NH3,B<0), (ND3,B>0) && (ND3,B<0)) Electron [math]\theta[/math] Angle((NH3,B>0), (NH3,B<0), (ND3,B>0) && (ND3,B<0)); can create angle cut on electron to be sure flipping B-field contains same electrons W mass((NH3,B>0), (NH3,B<0), (ND3,B>0) && (ND3,B<0))

2.) Now plot ratio (B< 0/B>0) electron kinematic ([math]\theta[/math], W, Momentum) for ND3 and NH3. ( I expect 2 curves in one plot)

[math]\frac{ND3 B\lt 0}{ND3 B\gt 0}[/math], [math]\frac{NH3 B\lt 0}{NH3 B\gt 0}[/math]

Emomratioinclusive4-2GeV.jpg Ethetaratioinclusive4-2GeV.jpg Wratioinclusive4-2GeV.jpg
Electron Momentum([math]\frac{ND3 B\lt 0}{ND3 B\gt 0}[/math], [math]\frac{NH3 B\lt 0}{NH3 B\gt 0}[/math]) Electron [math]\theta[/math] Angle([math]\frac{ND3 B\lt 0}{ND3 B\gt 0}[/math], [math]\frac{NH3 B\lt 0}{NH3 B\gt 0}[/math]) W mass([math]\frac{ND3 B\lt 0}{ND3 B\gt 0}[/math], [math]\frac{NH3 B\lt 0}{NH3 B\gt 0}[/math])

2.) Target ratio (B< 0/B>0) Difference electron kinematic ([math]\theta[/math], W, Momentum) (Ration for ND3 target - Ratio for NH3 target). ( I expect 1 curves in one plot)

[math]\frac{ND3 B\lt 0}{ND3 B\gt 0} - \frac{NH3 B\lt 0}{NH3 B\gt 0}[/math]

Emomratiodiffinclusive4-2GeV.jpg Ethetaratiodiffinclusive4-2GeV.jpg Wratiodiffinclusive4-2GeV.jpg
Electron Momentum ([math]\frac{ND3 B\lt 0}{ND3 B\gt 0} - \frac{NH3 B\lt 0}{NH3 B\gt 0}[/math]) [math]\theta[/math] Theta Angle([math]\frac{ND3 B\lt 0}{ND3 B\gt 0} - \frac{NH3 B\lt 0}{NH3 B\gt 0}[/math]) W mass([math]\frac{ND3 B\lt 0}{ND3 B\gt 0} - \frac{NH3 B\lt 0}{NH3 B\gt 0}[/math])

Semi-Inclusive

(NH3,B>0), (NH3,B<0), (ND3,B>0) && (ND3,B<0)

EmomSemiInclusiveoverlay4-2GeV.gif EthetaSemiInclusiveoverlay4-2GeV.gif WSemiInclusiveoverlay4-2GeV.gif
Electron Momentum((NH3,B>0), (NH3,B<0), (ND3,B>0) && (ND3,B<0)) Electron [math]\theta[/math] Angle((NH3,B>0), (NH3,B<0), (ND3,B>0) && (ND3,B<0)) W mass((NH3,B>0), (NH3,B<0), (ND3,B>0) && (ND3,B<0))

2

2/7/11

1.) Now look a specific electron kinematic which appear to have unity ratio. P=2.5 GeV, \theta =18 degrees

W NH3,B<0 NH3,B>0 ND3,B<0 ND3,B>0 NH3,B>0 - NH3,B<0 NH3,B>0 - NH3,B<0
1.72 [math]1.2 X 10^{-5} \pm 0.05[/math] [math]2.9 × 10^{-5} \pm 0.04[/math] [math]11.8 x 10^{-5} \pm 0.05[/math] [math]2.1125 × 10^{-5} \pm 0.075[/math] 1.7 -9.7
1.74 [math] 3.9× 10^{-5} \pm 0.03[/math] [math] 9.0 × 10^{-5} \pm 0.02[/math] 3[math]8.5x 10^{-5} \pm 0.03[/math] [math]7.25 × 10^{-5} \pm 0.05[/math] 5.1 -3.2
1.76 [math]5.0× 10^{-5} \pm 0.024[/math] [math]10 x 10_{-5} \pm 0.02[/math] [math]51.8x 10^{-5} \pm 0.025[/math] [math]8.2 × 10^{-5} \pm 0.047[/math] 5.0 -43.6
1.78 [math]4.2 × 10^{-5} \pm 0.03[/math] [math] 8.4 × 10^{-5} \pm 0.02[/math] [math]40.4x 10^{-5} \pm 0.03[/math] [math]7.3 × 10^{-5} \pm 0.05[/math] 4.2 -33.1
1.8 [math] 5.8 × 10^{-6} \pm 0.07[/math] [math] 1.4 × 10^{-5} \pm 0.05[/math] [math]6.2 × 10-5 \pm 0.07[/math] [math]1.05 × 10^{-5} \pm 0.1[/math] 0.8 -5.2

2.) Semi-Inclusive using above electrons

Semiinclusivepionpaddlenumber.gif Semiinclusivepionmomentum.gif
Paddle Number Pion Momentum

3.) Semi-Inclusive using above electrons and choosing a single paddle from 2.)

Pi+/Pi- hitting paddle # Pi+/Pi- hitting paddle #


2/14/11

1.) Get all files

2.) Do semi-inclusive paddle number for pions again

3.) Paddle Number ratio (with more files in order to double check, the same cuts on electrons)

2/23/11

1.) Plot pi^-/pi^+ -vs paddle #

2.) Paddle 7 has ratio 0f 0.9. Plot W, Q^2 and M_{\pi}

W

ND3BpW.gifNH3BnW.gif

Q^2

ND3BpQ.gifNH3BnQ.gif

3.) Paddle 25 has ratio 0f 0.3. Plot W, Q^2, M (our goal is to determine if the detector has same efficiency for detector same reaction when the Torus filed is flipped)


W

ND3BnW.gifNH3BpW.gif

Q^2

ND3BnQ.gifNH3BpQ.gif


3/04/11

Pionpaddlenumberratio.jpg


Table. 1 Pion Paddle Number ratio

  • 1.) ND3Bn/NH3Bp
Pion Paddle Number Number of Events ND3Bn Number of Events NH3Bp Ratio(ND3Bn/NH3Bp) [math]\pm[/math] error
3.89 81 69 0.4 [math]\pm[/math] 0.000896
4.89 84 87 0.33 [math]\pm[/math] 0.000595
5.89 84 76 0.38 [math]\pm[/math]0.000757
6.89 75 98 0.26 [math]\pm[/math]0.000488
7.89 91 123 0.25 [math]\pm[/math] 0.000348
8.89 115 141 0.28 [math]\pm[/math] 0.000283
9.89 207 254 0.28 [math]\pm[/math] 0.000117
10.89 212 300 0.24 [math]\pm[/math]0.000092
11.89 284 413 0.24 [math]\pm[/math]0.000057
12.89 322 501 0.22 [math]\pm[/math] 0.000043
13.89 359 521 0.24 [math]\pm[/math] 0.000040
14.89 365 565 0.22 [math]\pm[/math] 0.000036
15.89 415 523 0.27 [math]\pm[/math]0.000040
16.89 444 526 0.29 [math]\pm[/math] 0.000039
17.89 405 555 0.25 [math]\pm[/math] 0.000036
18.89 414 528 0.27 [math]\pm[/math] 0.000039
19.89 387 502 0.27 [math]\pm[/math] 0.000042
20.89 408 505 0.28 [math]\pm[/math] 0.000042
21.89 352 457 0.27 [math]\pm[/math] 0.000048
22.89 298 358 0.29 [math]\pm[/math] 0.000070
23.89 522 547 0.33 [math]\pm[/math] 0.000038
24.89 530 608 0.3 [math]\pm[/math] 0.000032
25.89 571 590 0.33 [math]\pm[/math] 0.000034
26.89 523 564 0.32 [math]\pm[/math] 0.000036
27.89 422 440 0.33 [math]\pm[/math] 0.000052
28.89 368 342 0.37 [math]\pm[/math] 0.000079
29.89 101 108 0.32 [math]\pm[/math] 0.000427


  • 2.) ND3Bp/NH3Bn
Pion Paddle Number Number of Events ND3Bp Number of Events NH3Bn Ratio(ND3Bp/NH3Bn) [math]\pm[/math] error
0.91 45 89 1.29 [math]\pm[/math]0.004556
1.91 86 127 1.73[math]\pm[/math] 0.002488
2.91 82 133 1.58[math]\pm[/math] 0.002361
3.91 91 330 0.71 [math]\pm[/math]0.000822
4.91 94 348 0.69 [math]\pm[/math]0.000766
5.91 125 360 0.89 [math]\pm[/math]0.000649
6.91 120 399 0.77 [math]\pm[/math]0.000594
7.91 148 443 0.86 [math]\pm[/math]0.000484
8.91 128 387 0.85 [math]\pm[/math]0.000595
9.91 121 510 0.61 [math]\pm[/math]0.000459
10.91 104 417 0.64 [math]\pm[/math]0.000607
11.91 145 449 0.83 [math]\pm[/math]0.000481
12.91 108 469 0.59 [math]\pm[/math]0.000528
13.91 113 449 0.64 [math]\pm[/math]0.000541
14.91 104 401 0.66 [math]\pm[/math]0.000631
15.91 98 427 0.59 [math]\pm[/math]0.000609
16.91 100 335 0.76 [math]\pm[/math]0.000774
17.91 70 316 0.57 [math]\pm[/math]0.000973
18.91 65 269 0.62 [math]\pm[/math]0.001189
19.91 56 270 0.53 [math]\pm[/math]0.001273
20.91 37 200 0.47 [math]\pm[/math]0.002111
21.91 27 149 0.46 [math]\pm[/math]0.003316
22.91 28 99 0.72[math]\pm[/math] 0.004942
23.91 32 112 0.73 [math]\pm[/math]0.004087
24.91 42 103 1.04[math]\pm[/math] 0.003963
25.91 25 70 0.91 [math]\pm[/math]0.007479
26.91 24 66 0.93 [math]\pm[/math]0.008105
27.91 27 39 1.77 [math]\pm[/math]0.014578
28.91 24 48 1.28 [math]\pm[/math]0.011546



W

ND3BpW4.gifNH3BnW4.gif

Q^2

ND3BpQ4.gifNH3BnQ4.gif


W

ND3BnW4.gifNH3BpW4.gif

Q^2

ND3BnQ4.gifNH3BpQ4.gif

3/21/11

1.) Efficiency Ratios.

  • 0.a.) Table . [math]\frac{N(\pi^+,ND_3,B\lt 0)}{N(\pi^-,ND_3,B\gt 0)}[/math]
Pion Paddle Number [math]\frac{N(\pi^+,ND_3,B\lt 0)}{N(\pi^-,ND_3,B\gt 0)}[/math] error
1 0.52 0.00188670
2 0.56 0.00075818
3 0.55 0.00080325
4 1.31 0.00152123
5 1.44 0.00158249
6 1.18 0.00084919
7 1.26 0.00096229
8 1.19 0.00066468
9 1.12 0.00077990
10 1.5 0.00113494
11 1.45 0.00137556
12 1.22 0.00070398
13 1.65 0.00147872
14 1.47 0.00122783
15 1.63 0.00154233
16 1.57 0.00162007
17 1.38 0.00138704
18 1.68 0.00288459
19 1.68 0.00321234
20 1.65 0.00394896
21 2.23 0.00993885
22 2.42 0.01726570
23 1.29 0.00877380
24 1.17 0.00650948
25 0.74 0.00280451
26 1 0.00808644
27 1.25 0.01073753
28 0.84 0.00615573
29 1.11 0.00957284



  • 0.b.) Table . [math]\frac{N(\pi^+,NH_3,B\lt 0)}{N(\pi^-,NH_3,B\gt 0)}[/math]
Pion Paddle Number [math]\frac{N(\pi^+,NH_3,B\lt 0)}{N(\pi^-,NH_3,B\gt 0)}[/math] error
1 0.61 0.00136217
2 0.58 0.00072875
3 0.56 0.00063600
4 1.16 0.00084147
5 1.09 0.00067329
6 1.22 0.00084552
7 1.26 0.00077718
8 1.3 0.00071299
9 1.35 0.00095814
10 1.91 0.00150046
11 1.6 0.00131397
12 1.32 0.00072210
13 1.71 0.00129895
14 1.46 0.00093334
15 1.93 0.00219770
16 1.76 0.00160711
17 1.29 0.00106561
18 1.63 0.00205808
19 1.49 0.00210549
20 1.87 0.00366838
21 2.01 0.00692445
22 1.73 0.00746426
23 1.51 0.00978854
24 1.5 0.00801872
25 1.01 0.00349049
26 0.86 0.00424348
27 1.04 0.00729985
28 0.69 0.00620402
29 1.12 0.01390308


PionpaddlenumberratioTargettypeisthesame.jpg 

Perhaps we see if the MAID model can tell us what this ratio should be

Media:NH3positivepionMAID.pdfMedia:ND3negativepionMAID.pdf


  • 1.) Table 1. [math]\frac{N(\pi^+,ND_3,B\lt 0)}{N(\pi^-,NH_3,B\gt 0)}[/math]
Pion Paddle Number [math]N(\pi^+,ND_3,B\lt 0)[/math] [math]N(\pi^-,NH_3,B\gt 0)[/math] [math]\frac{N(\pi^+,ND_3,B\lt 0)}{N(\pi^-,NH_3,B\gt 0)}[/math] error
1 77 65 0.4075770 0.0009842584
2 159 97 0.5639721 0.0006539302
3 149 105 0.4882354 0.0005272353
4 393 126 1.0731347 0.0007711509
5 444 141 1.0834182 0.0006573745
6 484 130 1.2809561 0.0008725428
7 496 140 1.2189500 0.0007440855
8 578 151 1.3169920 0.0007160697
9 471 127 1.2759964 0.0009002428
10 599 118 1.7465341 0.0013677534
11 497 115 1.4869309 0.0012131589
12 582 151 1.3261062 0.0007208959
13 588 121 1.6719536 0.0012616248
14 546 136 1.3812936 0.0008776225
15 558 92 2.0867894 0.0023701069
16 505 107 1.6238274 0.0014740763
17 454 115 1.3582830 0.0011103103
18 388 86 1.5522638 0.0019569046
19 359 80 1.5439624 0.0021696589
20 304 64 1.6342777 0.0032068058
21 272 44 2.1269069 0.0073027548
22 215 38 1.9466466 0.0083331144
23 119 29 1.4118261 0.0091055132
24 123 33 1.2823997 0.0068297700
25 102 45 0.7798659 0.0026920919
26 82 36 0.7836887 0.0037785779
27 99 28 1.2164924 0.0083029104
28 75 25 1.0321754 0.0084089279
29 88 19 1.5935340 0.0193377338
30 43 10 1.4794514 0.0470776577
31 30 5 2.0643508 0.1850680665
32 59 17 1.1940853 0.0172383351
33 83 24 1.1898689 0.0102416449
34 85 26 1.1248065 0.0086048876
35 93 24 1.3332266 0.0114363482
36 79 23 1.1817660 0.0108450951
37 34 9 1.2997764 0.0485842596
38 32 20 0.5504936 0.0068650227
39 38 4 3.2685555 0.4088076301
40 12 4 1.0321754 0.1313894981
41 30 10 1.0321754 0.0332392060
42 5 3 0.5734308 0.1216930868



  • 2.) Table 2. [math]\frac{N(\pi^+,ND_3,B\gt 0)}{N(\pi^-,NH_3,B\lt 0)}[/math]
paddleNumber [math]N(\pi^+,ND_3,B\gt 0)[/math] [math]N(\pi^-,NH_3,B\lt 0)[/math] [math]\frac{N(\pi^+,ND_3,B\gt 0)}{N(\pi^-,NH_3,B\lt 0)}[/math] error
1 59 5 30.21 2.70258040
2 79 14 14.45 0.27652327
3 73 8 23.36 1.03300637
4 65 59 2.82 0.00822726
5 55 49 2.87 0.01094524
6 80 52 3.94 0.01185748
7 65 49 3.4 0.01183225
8 113 75 3.86 0.00675056
9 117 72 4.16 0.00756073
10 200 115 4.45 0.00393821
11 226 166 3.49 0.00192550
12 328 178 4.72 0.00213914
13 391 259 3.86 0.00105330
14 360 287 3.21 0.00081064
15 389 278 3.58 0.00090286
16 426 274 3.98 0.00098738
17 437 284 3.94 0.00092912
18 444 241 4.72 0.00135761
19 419 291 3.69 0.00085791
20 397 329 3.09 0.00064841
21 407 286 3.64 0.00087414
22 346 260 3.41 0.00096976
23 274 235 2.98 0.00105807
24 430 361 3.05 0.00056086
25 478 388 3.15 0.00051121
26 471 390 3.09 0.00050259
27 420 385 2.79 0.00049185
28 342 326 2.69 0.00062326
29 266 280 2.43 0.00076396
30 78 103 1.94 0.00337017
31 33 29 2.91 0.02416684
32 34 30 2.9 0.02293226
33 32 32 2.56 0.01999906
34 28 30 2.39 0.02171314
35 17 22 1.98 0.03411592
36 21 14 3.84 0.08345855
37 7 9 1.99 0.13036518
38 27 20 3.46 0.04582149
39 24 33 1.86 0.01863261
40 31 35 2.27 0.01710150
41 76 71 2.74 0.00617114
42 16 31 1.32 0.02201769
43 18 22 2.09 0.03411970
44 23 18 3.27 0.05209530


  • 3.) Table 3. [math]\frac{N(\pi^-,ND_3,B\gt 0)}{N(\pi^+,NH_3,B\lt 0)}[/math]
Pion Paddle Number [math] N(\pi^-,ND_3,B\gt 0)[/math] [math]N(\pi^+,NH_3,B\lt 0)[/math] [math]\frac{N(\pi^-,ND_3,B\gt 0)}{N(\pi^+,NH_3,B\lt 0)}[/math] [math]\pm[/math] error
0.91 45 89 1.29 [math]\pm[/math]0.004556
1.91 86 127 1.73[math]\pm[/math] 0.002488
2.91 82 133 1.58[math]\pm[/math] 0.002361
3.91 91 330 0.71 [math]\pm[/math]0.000822
4.91 94 348 0.69 [math]\pm[/math]0.000766
5.91 125 360 0.89 [math]\pm[/math]0.000649
6.91 120 399 0.77 [math]\pm[/math]0.000594
7.91 148 443 0.86 [math]\pm[/math]0.000484
8.91 128 387 0.85 [math]\pm[/math]0.000595
9.91 121 510 0.61 [math]\pm[/math]0.000459
10.91 104 417 0.64 [math]\pm[/math]0.000607
11.91 145 449 0.83 [math]\pm[/math]0.000481
12.91 108 469 0.59 [math]\pm[/math]0.000528
13.91 113 449 0.64 [math]\pm[/math]0.000541
14.91 104 401 0.66 [math]\pm[/math]0.000631
15.91 98 427 0.59 [math]\pm[/math]0.000609
16.91 100 335 0.76 [math]\pm[/math]0.000774
17.91 70 316 0.57 [math]\pm[/math]0.000973
18.91 65 269 0.62 [math]\pm[/math]0.001189
19.91 56 270 0.53 [math]\pm[/math]0.001273
20.91 37 200 0.47 [math]\pm[/math]0.002111
21.91 27 149 0.46 [math]\pm[/math]0.003316
22.91 28 99 0.72[math]\pm[/math] 0.004942
23.91 32 112 0.73 [math]\pm[/math]0.004087
24.91 42 103 1.04[math]\pm[/math] 0.003963
25.91 25 70 0.91 [math]\pm[/math]0.007479
26.91 24 66 0.93 [math]\pm[/math]0.008105
27.91 27 39 1.77 [math]\pm[/math]0.014578
28.91 24 48 1.28 [math]\pm[/math]0.011546


  • 4.) Table 4. [math]\frac{N(\pi^-,ND_3,B\lt 0)}{N(\pi^+,NH_3,B\gt 0)}[/math]


Pion Paddle Number [math]N(\pi^-,ND_3,B\lt 0)[/math] [math]N(\pi^+,NH_3,B\gt 0)[/math] [math]\frac{N(\pi^-,ND_3,B\lt 0)}{N(\pi^+,NH_3,B\gt 0)}[/math][math]\pm[/math] error
3.89 81 69 0.4 [math]\pm[/math] 0.000896
4.89 84 87 0.33 [math]\pm[/math] 0.000595
5.89 84 76 0.38 [math]\pm[/math]0.000757
6.89 75 98 0.26 [math]\pm[/math]0.000488
7.89 91 123 0.25 [math]\pm[/math] 0.000348
8.89 115 141 0.28 [math]\pm[/math] 0.000283
9.89 207 254 0.28 [math]\pm[/math] 0.000117
10.89 212 300 0.24 [math]\pm[/math]0.000092
11.89 284 413 0.24 [math]\pm[/math]0.000057
12.89 322 501 0.22 [math]\pm[/math] 0.000043
13.89 359 521 0.24 [math]\pm[/math] 0.000040
14.89 365 565 0.22 [math]\pm[/math] 0.000036
15.89 415 523 0.27 [math]\pm[/math]0.000040
16.89 444 526 0.29 [math]\pm[/math] 0.000039
17.89 405 555 0.25 [math]\pm[/math] 0.000036
18.89 414 528 0.27 [math]\pm[/math] 0.000039
19.89 387 502 0.27 [math]\pm[/math] 0.000042
20.89 408 505 0.28 [math]\pm[/math] 0.000042
21.89 352 457 0.27 [math]\pm[/math] 0.000048
22.89 298 358 0.29 [math]\pm[/math] 0.000070
23.89 522 547 0.33 [math]\pm[/math] 0.000038
24.89 530 608 0.3 [math]\pm[/math] 0.000032
25.89 571 590 0.33 [math]\pm[/math] 0.000034
26.89 523 564 0.32 [math]\pm[/math] 0.000036
27.89 422 440 0.33 [math]\pm[/math] 0.000052
28.89 368 342 0.37 [math]\pm[/math] 0.000079
29.89 101 108 0.32 [math]\pm[/math] 0.000427


Pionpaddlenumberratio1.jpg


Corrected one just has values of 1.

2.) Kinematic plots for all 8 conditions


W mass vs Counts eightcases.gif

4/4/11

1.) Document the electron efficiency -vs- paddle ( for each target separately) and pion efficiency -vs- paddle in thesis

Inclusive detected electrons -vs- Q-squared
The ratio of inclusive electrons detected in scintillator paddle #7 when Btorus >0 (B_p)to inclusive electrons detected by paddle 11 when B<0(B_n)

PionpaddlenumberratioTargettypeisthesame.jpg 

*Inclusive

Media:ND3andNH3electronpaddlenumberinclusive.pdf
Media:NH3Q2inclusive.pdfMedia:ND3Q2inclusive.pdf

  • Semi Inclusive

Media:ND3electronpaddlenumbersemi_inclusive.pdfMedia:NH3electronpaddlenumbersemi_inclusive.pdf


2.) Compare to MAI2007 for paddles with unity pion efficiency ratios

Total Cross Section:

[math]\sigma = \sigma_{T} + \epsilon \sigma_{L} + \sqrt{2\epsilon(1 + \epsilon)}\sigma_{LT} cos{\phi_{\pi}}^{CM} + \epsilon \sigma{TT} cos2{\phi_{\pi}}^{CM} + h \sqrt{2\epsilon (1-\epsilon)}\sigma_{LT^{\prime}}sin{\phi_{\pi}}^{CM} [/math]


where

[math]{\phi_{\pi}}^{CM}[/math] is pion azimuthal angle in CM frame, [math]\epsilon[/math] - virtual photon polarization.

[math]\epsilon = (1 + 2(1 + \frac{\nu^2}{Q^2})tan^2\frac{\theta_e}{2})^{-1}[/math]

where [math]\nu=E_i - E_f[/math], (the difference between the initial and final energy of the electron).

[math]Q^2 = 4 E_i E_f sin^2\frac{\theta_e}{2}[/math] - Four momentum transferred square.

[math]\theta_e[/math] - electron scattering angle.

h - electron helicity.



[math]\left ( \begin{matrix} p_{\pi x}^{LAB{\prime}} \\ p_{\pi y}^{LAB{\prime}} \\p_{\pi z}^{LAB{\prime}} \end{matrix} \right )= \left [ \begin{matrix} cos {\theta}_x & 0 & -sin {\theta_x} \\ 0 & 1 &0 \\ sin {\theta_x} &0 & cos {\theta_x} \end{matrix} \right ] \left [ \begin{matrix} cos {\phi_{\gamma}} & sin {\phi_{\gamma}} & 0 \\ -sin {\phi_{\gamma}} & cos {\phi_{\gamma}} &0 \\ 0 &0 & 1 \end{matrix} \right ] \left ( \begin{matrix} p_{\pi x}^{LAB} \\p_{\pi y}^{LAB} \\ p_{\pi z}^{LAB} \end{matrix} \right ) = [/math]

[math]= \left ( \begin{matrix} cos {\theta}_x (cos {\phi_{\gamma}} p_{\pi x}^{LAB} + sin {\phi_{\gamma}} p_{\pi y}^{LAB}) - sin {\theta}_x p_{\pi z}^{LAB} \\ -sin {\phi_{\gamma}} p_{\pi x}^{LAB} + cos {\phi_{\gamma}} p_{\pi y}^{LAB} \\ sin {\theta}_x (cos {\phi_{\gamma}} p_{\pi x}^{LAB} + sin {\phi_{\gamma}} p_{\pi y}^{LAB}) + cos {\theta}_x p_{\pi z}^{LAB} \end{matrix} \right ) [/math]


[math]{\phi}_{\pi}^{LAB{\prime}} = tan^{-1}(\frac{{p_{\pi y}}^{LAB{\prime}}}{{p_{\pi x}}^{LAB{\prime}}}) = tan^{-1}(\frac{-sin{\phi_{\gamma}} \times p_{\pi x}^{LAB} + cos{\phi_{\gamma}} \times p_{\pi y}^{LAB}}{cos {\theta}_x (cos {\phi_{\gamma}} p_{\pi x}^{LAB} + sin {\phi_{\gamma}} p_{\pi y}^{LAB}) - sin {\theta}_x p_{\pi z}^{LAB}})[/math]

[math]{\phi}_{\pi}^{CM} = tan^{-1}(\frac{{p_{\pi y}}^{CM}}{{p_{\pi x}}^{CM}}) = tan^{-1}(\frac{-sin{\phi_{\gamma}} \times p_{\pi x}^{CM} + cos{\phi_{\gamma}} \times p_{\pi y}^{CM}}{cos {\theta}_x (cos {\phi_{\gamma}} p_{\pi x}^{CM} + sin {\phi_{\gamma}} p_{\pi y}^{CM}) - sin {\theta}_x p_{\pi z}^{CM}})[/math]


[math]p_{\pi x}^{CM} = p_{\pi x}^{LAB}[/math]

[math]p_{\pi y}^{CM} = p_{\pi y}^{LAB}[/math]

[math]p_{\pi z}^{CM} = -E_{\pi} \gamma_{CM} \beta_{CM} + p_{\pi z}^{LAB} \gamma_{CM}[/math]


where


[math]\phi_{\gamma} = tan^{-1}(\frac{p_{e y}^{\prime}}{p_{e x}^{\prime}})[/math]


[math]\theta_x = cos^{-1}(\frac{p_{e z}^{\prime} - p_{e z}}{\sqrt{{p_{e x}^{\prime}}^2 + {p_{e y}^{\prime}}^2 + ({p_{e z}^{\prime} - p_{e z}})^2}})[/math]


[math]\beta_{cm} = \frac {p_e}{m_p + E_e}[/math]
[math]\gamma_{cm} = \frac{1}{\sqrt{1 - \beta_{cm}^2}}[/math]

Media:NH3positivepionMAID.pdfMedia:ND3negativepionMAID.pdf

5/11/11

1.) Document the electron efficiency -vs- paddle ( for each target separately) and pion efficiency -vs- paddle in thesis 

Zoom in on the Q^2 range from 0.9 to 1.3 fine binning.

2.) Media:X_BEpaddlenumber5and10.pdf

3.)

MAID vs Exp nd3bnnh3bpratio.png 

MAID is the dominant error?  The data agree with MAID statistically.

Yes it is.


5/23/11

1.) Detector is not working. Two GEM foils are packed for shipping. The current measured across the GEM Foils at ~120 Volts is 1-5 nAmp.

Paddenumbvsratio.jpg

Black red maid.png

Green blue.png

Green blue maidnorm.pngGreen blue maidnorm errormaid.png

Media:theorynd3bn_nh3bp_ratio.pdf

5/25/11

In this case, corrections from the inclusive data are applied.

Black red inclusive.png Green blue inclusive.png


Black red maid inclusiveerror.png Green blue inclusiveerror.png

6/27/11

1.) Analyze data for asymmetries.

a.) Charge asymmetry -vs- run number plot

b.) Rate sums and difference plots i.) Insert histogram names here and their definitions


2.)Histograms for error calculation


3.) Dilution factor histogram names and definition


07/23/11

Make it easier to see the differences.  Subtract experiment from Maid2007 and put 
the before and after corrections results on the same graph.    
Use different error bars for the error from the correction factor 
and the statistical uncertainties (1/sqrt(N).

Exclusive cases

NegativepionND3beforecorrection.png NegativepionND3aftercorrection.png

PositivepionND3beforecorrection.png PositivepionND3aftercorrection.png


07/28/11

  • 1.) Pion Paddle number vs ratio for MAID2007-Experiment :

Maid2007minusexperiment.png

You need to make the above graph in black and white then it will be ready for your thesis. 
This means you need to change the error bars so you can identify them when they
are in black and white.
I would conclude from the above that the correction does not impact inclusive single pion production while it does make the semi-inclusive data less dependent on Torus polarity.

Maid2007minusexperiment 1.png
Maid2007minusexperiment 2.png 

You should add the systematic error as a separate uncertainty to the graph.  
Usually you can remove the riser from the larger uncertainty and include the riser (the horizontal bar) on the smaller uncertainty..


  • 2.) Charge Asymmetry:
You have a choice for the charge asymmetry, either do a linear fit to run number 
or average over all runs.  I prefer averaging over all runs and displaying it as a 
histogram for the data set to measure false asymmetries from the beam alone


ND3Bn

ChargeAsymmetryND3Bn.png

08/01/11

Charge Asymmetry

  • 1). ND3Bp

ChargeAsymmetryND3Bp.png

  • 2). NH3Bn

ChargeAsymmetryNH3Bn.png

  • 3). NH3Bp

ChargeAsymmetryNH3Bp.png


Average charge(beam) Asymmetry:

[math]{I_{Asymmetry}}^{ND3,B\lt 0} = 0.00014484 \pm 0.000125[/math]
[math]{I_{Asymmetry}}^{ND3,B\gt 0} = 0.00030047 \pm 0.0003[/math]
[math]{I_{Asymmetry}}^{NH3,B\lt 0} = 0.00015724 \pm 0.000156[/math]
[math]{I_{Asymmetry}}^{NH3,B\gt 0} = 0.00013867 \pm 0.000112[/math]

Add some text describing the difference in the charge asymmetry plots.
I dont understand what makes the plot below so different from the ones above.

ChargeAsymmetryNH3Bp 2.png File:ChargeAsymmetryNH3Bp 2.pdf

Calculating [math]\frac{\Delta d_v}{d_v}[/math]and [math]\partial \frac{\Delta d_v}{d_v}[/math]

This calculation will contain many terms.  It may be best to break it up into several parts.

[math]F(d) = \frac{\Delta d_v}{d_v} = \frac{Y}{Z}= \frac{\Delta \sigma_p^{\pi^+ \pm \pi^-} - 4\Delta \sigma_{2H}^{\pi^+ \pm \pi^-}}{\sigma_p^{\pi^+ \pm \pi^-} - 4\sigma_{2H}^{\pi^+ \pm \pi^-}} (x,Q^2) = [/math]

[math] = \frac{([({\sigma_p}^{\pi^+})_{1/2}-({\sigma_p}^{\pi^+})_{3/2}] - [({\sigma_p}^{\pi^-})_{1/2}-({\sigma_p}^{\pi^-})_{3/2}]) - 4 \times ([({\sigma_{2H}}^{\pi^+})_{1/2}-({\sigma_{2H}}^{\pi^+})_{3/2}] - [({\sigma_{2H}}^{\pi^-})_{1/2}-({\sigma_{2H}}^{\pi^-})_{3/2}])}{([({\sigma_p}^{\pi^+})_{1/2}+({\sigma_p}^{\pi^+})_{3/2}] - [({\sigma_p}^{\pi^-})_{1/2}+({\sigma_p}^{\pi^-})_{3/2}]) - 4 \times ([({\sigma_{2H}}^{\pi^+})_{1/2} + ({\sigma_{2H}}^{\pi^+})_{3/2}] - [({\sigma_{2H}}^{\pi^-})_{1/2} + ({\sigma_{2H}}^{\pi^-})_{3/2}])} = [/math]
[math]= \frac{[(N_1 - N_2) - (N_3 - N_4)] - 4 \times [(N_5 - N_6) - (N_7 - N_8)]}{[(N_1 + N_2) - (N_3 + N_4)] - 4 \times [(N_5 + N_6) - (N_7 + N_8)]}[/math]


[math]\partial F(d)= \{ \frac{\partial}{\partial N_1} \times \partial N_1 + \frac{\partial}{\partial N_2} \times \partial N_2 + \frac{\partial}{\partial N_3} \times \partial N_3 + \frac{\partial}{\partial N_4} \times \partial N_4 + \frac{\partial}{\partial N_5} \times \partial N_5 + \frac{\partial}{\partial N_6} \times \partial N_6 + \frac{\partial}{\partial N_7} \times \partial N_7 + \frac{\partial}{\partial N_8} \times \partial N_8 \}^2 F [/math]

[math]= \frac{1}{Z^4} \{ Y ( - \partial N_1 - \partial N_2 + \partial N_3 + \partial N_4 + 4\partial N_5 + 4\partial N_6 - 4\partial N_7 - 4\partial N_8) + [/math]
[math]+ Z (\partial N_1 - \partial N_2 - \partial N_3 + \partial N_4 - 4\partial N_5 + 4\partial N_6 + 4\partial N_7 - 4\partial N_8) \}^2[/math]

9/30/11 DST copies from JLab

I copied the following from the JLab cache disk to isulinux1

outbending

scp /cache/mss/clas/eg1b/production/pass1/v4/4p2out/misc/dst/dst2828* isulinux1:/local/scratch/tforest/4.2negND3

scp /cache/mss/clas/eg1b/production/pass1/v4/4p2out/misc/dst/dst283* isulinux1:/local/scratch/tforest/4.2negND3

scp /cache/mss/clas/eg1b/production/pass1/v4/4p2out/misc/dst/dst2829* isulinux1:/local/scratch/tforest/4.2negND3

scp /cache/mss/clas/eg1b/production/pass1/v4/4p2out/misc/dst/dst284* isulinux1:/local/scratch/tforest/4.2negNH3

in bending

scp /w/cache/mss/home/nguler/dst/dst282* isulinux1:/local/scratch/tforest/4.2PosNH3

scp /w/cache/mss/home/nguler/dst/dst281* isulinux1:/local/scratch/tforest/4.2PosND3

10/7/11 sftp file copying

Another way to copy files from JLab is to copy them from the /cache disk to the /u/scratch disk and then sftp them from JLab. 

sftp username@ftp.jlab.org
cd /u/scratch/tforest
mget *

12/16/11

Charge Asymmetry

ChargeAsymmetry14 23.gif


[math]\frac{\Delta d_v}{d_v}[/math]

[math]F(d) = \frac{\Delta d_v}{d_v} = \frac{Y}{Z}= \frac{\Delta \sigma_p^{\pi^+ \pm \pi^-} - 4\Delta \sigma_{2H}^{\pi^+ \pm \pi^-}}{\sigma_p^{\pi^+ \pm \pi^-} - 4\sigma_{2H}^{\pi^+ \pm \pi^-}} (x,Q^2) = [/math]

[math] = \frac{([({\sigma_p}^{\pi^+})_{1/2}-({\sigma_p}^{\pi^+})_{3/2}] - [({\sigma_p}^{\pi^-})_{1/2}-({\sigma_p}^{\pi^-})_{3/2}]) - 4 \times ([({\sigma_{2H}}^{\pi^+})_{1/2}-({\sigma_{2H}}^{\pi^+})_{3/2}] - [({\sigma_{2H}}^{\pi^-})_{1/2}-({\sigma_{2H}}^{\pi^-})_{3/2}])}{([({\sigma_p}^{\pi^+})_{1/2}+({\sigma_p}^{\pi^+})_{3/2}] - [({\sigma_p}^{\pi^-})_{1/2}+({\sigma_p}^{\pi^-})_{3/2}]) - 4 \times ([({\sigma_{2H}}^{\pi^+})_{1/2} + ({\sigma_{2H}}^{\pi^+})_{3/2}] - [({\sigma_{2H}}^{\pi^-})_{1/2} + ({\sigma_{2H}}^{\pi^-})_{3/2}])} [/math]


01/30/12

Charge Asymmetry

In double spin asymmetry measurements it is important to eliminate any source of false asymmetry, like charge asymmetry. The helicity of the electron beam was flipped with a rate of 1 HZ and its original state was chosen at the injector in a pseudo-random way. The next state of the electron helicity, so called complement state, is always with opposite helicity. The diagram on Fig. 3.1 represents the helicity state.

Figure 3.1. The Helicity State


A one bit signal from the beam injector gives the helicity information, whereas a sync bit with a 2 HZ frequency is generated at the same time and is equal to the helicity flip time. However, the electron beam helicity sequence can be interrupted by the Data Acquisition System(DAQ), like leaving unpaired helicity states and dead time problems. In order to eliminate the asymmetry caused by the DAQ, the Faraday cup was installed to measure the charge simultaneously with the helicity state flip. The stored data files include accumulated charge value for each helicity state. The measured charge asymmetry is shown bellow for 4.2 GeV data that has been collected for ND3 target while torus magnetic field was negative.

lifetime only takes data when daq is ready.

ChargeAsymmetry.png

Figure 3.2. Run Number vs Charge Asymmetry (ND3 target, B<0)

The charge asymmetry measured for each run number, thats is used for this analysis is shown on Fig. 3.3.

Black and red data points represent uncorrected measured charge asymmetry using Faraday cup. The green line shows the sign of half wave plane, while the purple one the sign of target polarization.
Run groups vs measured charge asymmetry. The runs that have the same half wave plane, target polarization sign, target type and torus current were combined into one data point.


Figure 3.2. Run Number vs Charge Asymmetry for All Runs 

Charge Asym no sign correction

The uncertainty should be the same for the (1-4) and (2-3) distributions in the same run group.  Use 12 groups of files (slugs) to create a histogram of the asymemtry and fit it with a gaussian.

Inclusive asymmetry as a function of X_B for all [math]Q^2[/math] is shown on Fig. 3.4. The electron paddle numbers 10 and 5 were chosen respectively for B<0 and B>0, because they contained the most electron events in a first pass semi-inclusive pion analysis of the data set. 

inclusive includes sign correction



For inclusive do run number vs inclusive Asymmetry

InclusiveAsymmetry01 30 12y.png

Figure 3.4. X_{bjorken} vs Inclusive Asymmetry(All data)

02/06/12

Charge Asymmetry

In double spin asymmetry measurements it is important to eliminate any source of false asymmetry, like charge asymmetry. The helicity of the electron beam was flipped with a rate of 1 HZ and its original state was chosen at the injector in a pseudo-random way. The next state of the electron helicity, so called complement state, is always with opposite helicity. The diagram on Fig. 3.1 represents the helicity state.

Figure 3.1. The Helicity State


A one bit signal from the beam injector gives the helicity information, whereas a sync bit with a 2 HZ frequency is generated at the same time and is equal to the helicity flip time. However, the electron beam helicity sequence can be interrupted by the Data Acquisition System(DAQ), like dead time problems. In order to eliminate the asymmetry caused by the DAQ, the Faraday cup was installed to measure the charge simultaneously with the helicity state flip. The stored data files include accumulated charge value for each helicity state. The measured charge asymmetry is shown bellow for 4.2 GeV data that has been collected for ND3 target while torus magnetic field was negative.

ChargeAsymmetry.png

Figure 3.2. Run Number vs Charge Asymmetry (ND3 target, B<0)

The charge asymmetry measured for each run number, thats is used for this analysis is shown on Fig. 3.3.

Black and red data points represent uncorrected measured charge asymmetry using Faraday cup. The green line shows the sign of half wave plane, while the purple one the sign of target polarization.
Run groups vs measured charge asymmetry. The runs that have the same half wave plane, target polarization sign, target type and torus current were combined into one data point.


Figure 3.2. Run Number vs Charge Asymmetry for All Runs


Inclusive asymmetry as a function of X_B for all [math]Q^2[/math] is shown on Fig. 3.4. The electron paddle numbers 10 and 5 were chosen respectively for B<0 and B>0, because they contained the most electron events in a first pass semi-inclusive pion analysis of the data set.


InclusiveAsymmetry01 30 12y.png

Figure 3.4. X_{bjorken} vs Inclusive Asymmetry(All data)


The Figures 3.5 and 3.6 show inclusive asymmetry for each run number and for run groups used for these analysis


RunNumber vs InclusiveAsymmetry.png

Figure 3.5. Run Number vs Inclusive Asymmetry

RunNumber vs InclusiveAsymmetrygroups.png

Figure 3.5. Run groups vs Inclusive Asymmetry


03/06/12

NES Asymmetry

The double spin asymmetry measurements performed in this thesis are performed by comparing scattering events that occur when the incident probe spin and nuclear target spin are parallel to scattering events that occur when the spins are anti-parallel. The helicity of the electron beam was flipped at a rate of 1 HZ. The helicity is prepared at the source such that helicity pairs are produced pseudo randomly. If the first electron bunch is pseudo randomly chosen to be positive (negative) then it is labeled as the original helicity state and denoted in software by a 2 (1). The next helicity state is prepared to be a complement to the first state and labeled in the software as either a 4, if the original helicity state was a 1 (negative), or 3 if the original helicity state was a 2 (positive). The helicity process is then repeated. Figure NES.1 illustrates the signals used to label helicity state. The clock pulse (SYNC) is used to indicate that a change in the pockel cell used to define the helicity state may have occurred. The helicity bit indicates the helicity state that was set. The original/complement pulse identifies if the state is an original or complement helicity state. All three bits are recorded in the raw data file for each event and then converted to the labels 1,2,3,4 during DST file production once the particles have been reconstructed.

Figure NES.1. The Helicity State: A one bit signal from the beam injector gives the helicity information, whereas a sync bit with a 2 HZ frequency is generated at the same time and is equal to the helicity flip time.



Two scalers were used to record several ancillary detectors, such as a Faraday cup and several PMTs mounted on the beam line, according to their helicity label. One of the scalers was gated by the DAQ live time in order to record beam conditions when the DAQ was able to take data and not busy recording data. The second scaler remained ungated. Both scalers recorded the SYNC and Helicity signals from the injector along with the counts observed from ancillary detectors during the SYNC interval. The Faraday cup signal recorded by the gated helicity scaler is used to normalize the events reconstructed during the same helicity interval. The beam charge asymmetry measured by the gated helicity scaler is shown in Figure NES. 2. as a function of run number. For each run number the gaussian fit was used to extract the mean values of the asymmetry and corresponding error(Figure NES. 3).

[math]A_{BeamCharge} = \frac{ \Sigma FC^{hel1,hel2}-\Sigma FC^{hel4,hel3}}{\Sigma FC^{hel1,hel2}+\Sigma FC^{hel4,hel3}}[/math]


RunNumber vs BeamChargeAsymmetryPulsePair07 03 2012.png

Figure NES. 2. Run Number vs the beam charge Asymmetry


FC ChargeAsymmetry 282101RunNumber 14 23HelPairs 03 12 12.png

Figure NES. 3. Beam charge asymmetry for run #28101 using the gated faraday cup counts for two helicity pairs(1-4 and 2-3 helicity pairs).[math]A_{1-4}=(11.5 \pm 4.4) \times 10^{-5}[/math] and [math]A_{2-3}=(-2.3 \pm 4.4) \times 10^{-5}[/math]


RunNumber vs BeamChargeAsymmetryPulsePair14 19 03 2012.pngRunNumber vs BeamChargeAsymmetryPulsePair23 19 03 2012.png

Run Group Half wave plane(HWP) [math]A_{1-4}[/math] [math]A_{2-3}[/math]
28100 - 28105 +1 [math](5.88 \pm 34.40) \times 10^{-4}[/math] [math](4.03 \pm 34.36) \times 10^{-4}[/math]
28106 - 28115 -1 [math] (7.53 \pm 22.30) \times 10^{-4}[/math] [math] (8.28 \pm 22.30) \times 10^{-4}[/math]
28145 - 28240 +1 [math](31.70 \pm 7.99) \times 10^{-4}[/math] [math](30.40 \pm 7.99) \times 10^{-4}[/math]
28242 - 28284 -1 [math] (49.6 \pm 10.8) \times 10^{-4}[/math] [math] (47.9 \pm 10.8) \times 10^{-4}[/math]
28286 - 28324 +1 [math] (36.3 \pm 11.6) \times 10^{-4}[/math] [math] (37.0 \pm 11.5) \times 10^{-4}[/math]
28325 - 28447 -1 [math] (21.1 \pm 13.4) \times 10^{-4}[/math] [math](22.2 \pm 13.4) \times 10^{-4}[/math]
28449 - 28479 +1 [math] (-11.6 \pm 16.5) \times 10^{-4}[/math] [math](-21.6 \pm 16.5) \times 10^{-4}[/math]


A measurement of the electron cross section helicity difference needs to account for the possible helicity dependence of the incident electron flux ( Charge Asymmetry). Fig. NES. 4 shows the reconstructed electron asymmetry before it is normalized by the gated Faraday Cup as a function of the run number for the 4.2 GeV data set. The reconstructed electron asymmetry can be defined following way:

[math]A_{NES}^{+-} = \frac{NES^{+} - NES^{-}}{NES^{+} + NES^{-}} \equiv (2-3)[/math] or [math]A_{NES}^{-+} = \frac{NES^{-} - NES^{+}}{NES^{-} + NES^{+}} \equiv (1-4)[/math]

where [math]NES^+[/math]([math]NES^-[/math]) represents number of reconstructed electrons in the final state for the positive(negative) beam helicity.

Run Number vs NES Asymmetry before FC normalization. The red points represent NES asymmetry for the helicity 2-3 pair and the black points - the helicity pair 1-4. The green line shows the sing of the half wave plane and purple line - the sign of the target polarization.


Figure NES.4. Run Number vs NES Asymmetry for All Runs before FC normalization


Sysstematic effects on the asymmetry measurement may be investigated by separating the data into two groups based on which helicity state is set first. The first group(black data points) represents the electron asymmetry observed when the first (original) helicity state is negative and its complement state is positive(helicity state #1 - state #4). The second group(red data points) represents the asymmetry observed, when the first state is positive and the complement state is negative(helicity state #2 - #3). Both groups were divided into two subgroups based the target type used. The diamond points on the histogram represent the data for the NH3 target and the squares for the ND3 target. On the same histograms are presented the signs of the half wave plane(HWP) and the target polarization(TPol). The relative spin orientation can be changed by either inserting a half wave (HWP) or by populating a different target polarization state with a different RF frequency. One would expect the asymmetry to change sign if either the HWP is inserted or the target polarization is rotated 180 degrees. As one can see, the electron asymmetry sign ( sign(hel1-hel4) && sign(hel3-hel2) ) is opposite of the sign of (HWP[math]\times[/math]Target_Polarization). The NES asymmetry has been calculated the following way before accounting for the Faraday cup:

[math]A_{NES} = \frac{NES^{hel1,hel2} - NES^{hel4,hel3}}{NES^{hel1,hel2} + NES^{hel4,hel3}}[/math]

The NES asymmetry after the gated faraday cup normalization is defined as:

[math]A_{NES}^{FCnormalized} = \frac{\frac{NES^{hel1,hel2}}{FC^{hel1,hel2}} - \frac{NES^{hel4,hel3}}{FC^{hel4,hel3}}}{\frac{NES^{hel1,hel2}}{FC^{hel1,hel2}} + \frac{NES^{hel4,hel3}}{FC^{hel4,hel3}}}[/math]
Run Number vs NES Asymmetry after applying FC normalization. The red points represent NES asymmetry for the helicity 2-3 pair and the black points - the helicity pair 1-4. The green line shows the sing of the half wave plane and purple line - the sign of the target polarization.


Figure NES.5. Run Number vs NES Asymmetry for All Runs after FC normalization

On the Fig. NES. 6 data runs are combined for the same target type, target polarization, beam torus and half wave plane.

NES Asymmetry BeforeandAfter FCNormalizationgrouped.png

Figure NES. 6. Run groups vs NES Asymmetry before and after FC Normalization

03/12/12

SIDIS Asymmetry

SIDIS asymmetries:

[math]A_{NH3}^{\pi^+}=\frac{N_{NH3,\pi^+}^{hel1,hel2} - N_{NH3, \pi^+}^{hel4,hel3}}{N_{NH3,\pi^+}^{hel1,hel2} + N_{NH3, \pi^+}^{hel4,hel3}}[/math]


[math]A_{ND3}^{\pi^-}=\frac{N_{ND3,\pi^-}^{hel1,hel2} - N_{ND3, \pi^-}^{hel4,hel3}}{N_{ND3,\pi^-}^{hel1,hel2} + N_{ND3, \pi^-}^{hel4,hel3}}[/math]


SIDIS Asymmetry Before FCNormalization03 12 12.png

Figure NES. 6. Run Number vs Semi inclusive asymmetry before FC Normalization.



SIDIS Asymmetry After FCNormalization03 12 12.png

Figure NES. 6. Run Number vs Semi inclusive asymmetry after FC Normalization.


Target type, Beam Torus sign (B) [math]A_{hel1-hel4}[/math] [math]A_{hel2-hel3}[/math] [math]A_{hel13-hel42}[/math]
NH3, B>0, [math]\pi^+[/math] [math](-139.84 \pm 81.52) \times 10^{-4}[/math] [math](143.15 \pm 81.78) \times 10^{-4}[/math] [math] (-136.2 \pm 57.74) \times 10^{-4}[/math]
NH3, B<0, [math]\pi^+[/math] [math] (-223.76 \pm 117.10) \times 10^{-4}[/math] [math](247.65 \pm 116.59) \times 10^{-4}[/math] [math](-237.69 \pm 82.65) \times 10^{-4}[/math]
ND3, B>0, [math]\pi^-[/math] [math](-6.37 \pm 188.73) \times 10^{-4}[/math] [math](-98.11 \pm 188.03) \times 10^{-4}[/math] [math] (-9.21 \pm 127.22) \times 10^{-4}[/math]
ND3, B<0, [math]\pi^-[/math] [math](-63.73 \pm 105.14) \times 10^{-4}[/math] [math](-30.34 \pm 6085.54) \times 10^{-4}[/math] [math] (-12.37 \pm 71.10) \times 10^{-4}[/math]
NH3, B>0, [math]\pi^-[/math] [math](-155.45 \pm 128.21) \times 10^{-4}[/math] [math](-72.55 \pm 128.92) \times 10^{-4}[/math] [math](-35.11 \pm 90.91) \times 10^{-4}[/math]
NH3, B<0, [math]\pi^-[/math] [math](9.60 \pm 119.31) \times 10^{-4}[/math] [math](72.94 \pm 119.36) \times 10^{-4} [/math] [math](-32.39 \pm 84.38) \times 10^{-4}[/math]
ND3, B>0, [math]\pi^+[/math] [math](-76.59 \pm 126.60) \times 10^{-4}[/math] [math](110.28 \pm 126.13) \times 10^{-4}[/math] [math] (-92.25 \pm 85.38) \times 10^{-4} [/math]
ND3, B<0, [math]\pi^+[/math] [math](-29.22 \pm 107.53) \times 10^{-4}[/math] [math](123.98 \pm 106.86) \times 10^{-4}[/math] [math] (-92.25 \pm 85.38) \times 10^{-4}[/math]


Run Group Target type, Beam Torus sign (B) A_{1-4} A_{2-3}
28214 - NH3, B>0 [math]-0.02704757 \pm 0.01711263[/math] 0.02399480 \pm 0.01700174
28231 - NH3, B>0 [math]0.00069178 \pm 0.01545227[/math] -0.01372286 
\pm	0.01559729
28252 - NH3, B>0 [math]-0.01229841 \pm 0.01693271[/math] -0.00048034 \pm 0.01685103
28266 - NH3, B>0 [math]0.01589835 \pm 0.01590701[/math] -0.02002048 \pm 0.01610756
28413 - NH3, B<0 0.02205009 \pm 0.01799869 -0.02291024 \pm 0.01795956
28469 - NH3, B<0 0.02270121 \pm 0.01543980 -0.02662038 \pm 0.01532731
28102 - ND3, B>0 0.04443768 \pm 0.06093347 0.01055158 \pm 0.06066387
28109 - ND3, B>0 0.01068017 \pm 0.03953670 -0.00764924 \pm 0.03970762
28150 - ND3, B>0 -0.01238850 \pm 0.03640693 0.02901657 \pm 0.03642766
28182 - ND3, B>0 -0.02497960 \pm 0.02660287 0.00797540 \pm 0.02634698
28295 - ND3, B<0 -0.01323095 \pm 0.01636848 -0.01008145 \pm 0.01636433
28315 - ND3, B<0 -0.01026453 \pm 0.01768742 0.00621953 \pm 0.01758502
28393 - ND3, B<0 0.01615151 \pm 0.01853525 -0.00719786 \pm 0.01834110

SIDIS Asymmetry After FCNormalizationRunsGrouped03 13 12.png

Figure NES. 6. Run groups vs Semi inclusive asymmetry after FC Normalization.

X and Z count distribution

SIDI Asymmetry [math]X_B=0.3[/math] [math]X_B=0.4[/math]
[math] A_{NH3}^{\pi^+,hel13-hel24}[/math] [math](-150.08 \pm 65.96) \times 10^{-4}[/math] [math](-217.20 \pm 69.06) \times 10^{-4}[/math]
[math] A_{ND3}^{\pi^-,hel13-hel24}[/math] [math](-39.04 \pm 81.44) \times 10^{-4}[/math] [math](-91.90 \pm 96.14) \times 10^{-4}[/math]
[math] A_{NH3}^{\pi^-,hel13-hel24}[/math] [math](-100.81 \pm 83.49) \times 10^{-4}[/math] [math](23.98 \pm 94.92) \times 10^{-4}[/math]
[math] A_{ND3}^{\pi^+,hel13-hel24}[/math] [math](-53.17 \pm 74.89) \times 10^{-4}[/math] [math](-85.17 \pm 82.97) \times 10^{-4}[/math]


[math] A_{NH3}^{\pi^+,hel13-hel24}[/math]

[math]z[/math] [math]X_B=0.3[/math] [math]X_B=0.4[/math]
0.3 [math](-142.39 \pm 106.42) \times 10^{-4}[/math] [math]( -131.49 \pm 116.96) \times 10^{-4}[/math]
0.5 [math](-101.14 \pm 128.36) \times 10^{-4}[/math] [math](-207.76 \pm 129.37) \times 10^{-4}[/math]
0.7 [math](-140.32 \pm 158.98) \times 10^{-4}[/math] [math](-238.34 \pm 156.79) \times 10^{-4}[/math]
0.9 [math](-355.44 \pm 200.23) \times 10^{-4}[/math] [math](-438.76 \pm 189.03) \times 10^{-4}[/math]


[math]z[/math] [math]X_B=0.3[/math] [math]X_B=0.4[/math]
0.45 [math](-125.62 \pm 81.92) \times 10^{-4}[/math] [math]( -165.81 \pm 86.76) \times 10^{-4}[/math]
0.7 [math](-140.32 \pm 158.98) \times 10^{-4}[/math] [math](-238.34 \pm 156.79) \times 10^{-4}[/math]
0.9 [math](-355.44 \pm 200.23) \times 10^{-4}[/math] [math](-438.76 \pm 189.03) \times 10^{-4}[/math]

[math] A_{ND3}^{\pi^-,hel13-hel24}[/math]

[math]z[/math] [math]X_B=0.3[/math] [math]X_B=0.4[/math]
0.3 [math](9.18 \pm 120.73) \times 10^{-4}[/math] [math]( -46.32 \pm 147.45) \times 10^{-4}[/math]
0.5 [math](-66.91 \pm 161.28) \times 10^{-4}[/math] [math](-78.88 \pm 182.05) \times 10^{-4}[/math]
0.7 [math](-96.54 \pm 232.06) \times 10^{-4}[/math] [math](-236.67 \pm 257.03) \times 10^{-4}[/math]
0.9 [math](-147.74 \pm 297.50) \times 10^{-4}[/math] [math](-78.69 \pm 320.29) \times 10^{-4}[/math]


[math]\Delta R_{np}^{\pi^+ + \pi^-} = \frac{\Delta \sigma_p^{\pi^+ + \pi^-} - \Delta \sigma_{n}^{\pi^+ + \pi^-}}{\sigma_p^{\pi^+ + \pi^-} - \sigma_{n}^{\pi^+ + \pi^-}}=[/math]

[math]=\frac{\Delta \sigma_p^{\pi^+ + \pi^-}}{\sigma_p^{\pi^+ + \pi^-} - \sigma_{n}^{\pi^+ + \pi^-}} - \frac{\Delta \sigma_{n}^{\pi^+ + \pi^-}}{\sigma_p^{\pi^+ + \pi^-} - \sigma_{n}^{\pi^+ + \pi^-}}=[/math]

[math] = \frac{(\sigma_p^{\pi^+,hel13} - \sigma_p^{\pi^+,hel24}) + (\sigma_p^{\pi^-,hel13} - \sigma_p^{\pi^-,hel24})}{\sigma_p^{\pi^+ + \pi^-} - \sigma_{n}^{\pi^+ + \pi^-}} - \frac{(\sigma_n^{\pi^+,hel13} - \sigma_n^{\pi^+,hel24}) + (\sigma_n^{\pi^-,hel13} - \sigma_n^{\pi^-,hel24})}{\sigma_p^{\pi^+ + \pi^-} - \sigma_{n}^{\pi^+ + \pi^-}} = [/math]


[math]=\frac{(\Delta u +\Delta \bar{u}) - (\Delta d + \Delta \bar{d})}{(u+\bar{u}) - (d+\bar{d})}(x,Q^2)=[/math]


[math]= \frac{g_1^p - g_1^n}{F_1^p - F_1^n}(x,Q^2)[/math]


"If each observable ([math]x_i[/math]) is accompanied by an estimate of the uncertainty in that observable ([math]\sigma_i[/math]) then the weighted mean is defined as

[math]\bar{x} = \frac{ \sum_{i=1}^{i=n} \frac{x_i}{\sigma_i^2}}{\sum_{i=1}^{i=n} \frac{1}{\sigma_i^2}}[/math]"

"The variance of the distribution is defined as

[math]\frac{1}{\sigma^2} = \sum_{i=1}^{i=n} \frac{1}{\sigma_i^2}[/math] = weighted variance"

TF_ErrorAna_PropOfErr

[math]z[/math] [math]X_B=0.3[/math] [math]X_B=0.4[/math]
0.3 [math](1453.94 \pm 236.39) \times 10^{-4}[/math] [math](-104.24 \pm 277.69) \times 10^{-4}[/math]
0.5 [math](550.18 \pm 298.65) \times 10^{-4}[/math] [math](149.78 \pm 320.13) \times 10^{-4}[/math]
0.7 [math](-650.12 \pm 407.30) \times 10^{-4}[/math] [math](79.69 \pm 430.29) \times 10^{-4}[/math]
0.9 [math](2285.22 \pm 525.13) \times 10^{-4}[/math] [math](5.59 \pm 545.08) \times 10^{-4}[/math]
Table 4.5. Experimental Results of The Fragmentation Function [math]\Delta R_{np}^{\pi^+ + \pi^-} [/math] vs [math]z[/math] and [math]X_B[/math] for four values of [math]z[/math].



[math]z[/math] [math]X_B=0.3[/math] [math]X_B=0.4[/math]
0.45 [math](582.79 \pm 186.97) \times 10^{-4}[/math] [math]( 55.32 \pm 214.92) \times 10^{-4}[/math]
0.85 [math](504.20 \pm 321.74) \times 10^{-4}[/math] [math](57.35 \pm 337.48) \times 10^{-4}[/math]
Table 4.6. Experimental Results of The Fragmentation Function [math]\Delta R_{np}^{\pi^+ + \pi^-} [/math] vs [math]z[/math] and [math]X_B[/math](Combined [math]z[/math]).



[math]Q^{2}[/math] [math]W^{2}[/math] [math]X_{b}[/math] [math]\Delta R_{deuteron,p}^{\pi^+ + \pi^-} [/math] [math]\Delta R_{np}^{\pi^+ + \pi^-} [/math]
0.8 2.4 0.344712 0.089457 1.215956
0.8 2.56 0.322805 0.087636 1.144319
0.8 2.72 0.302941 0.087324 1.142601
0.8 2.89 0.284872 0.080418 1.081259
0.8 3.06 0.268386 0.046144 0.971948
0.8 3.24 0.253303 -0.001413 0.904000
0.8 3.42 0.239465 -0.039615 0.888457
0.85 2.4 0.358532 0.095124 1.179011
0.85 2.56 0.336197 0.092376 1.118478
0.85 2.72 0.315894 0.091414 1.126200
0.85 2.89 0.297382 0.083684 1.073062
0.85 3.06 0.280456 0.047397 0.965145
0.85 3.24 0.264940 0.000751 0.897095
0.85 3.42 0.250680 -0.037185 0.879470
0.9 2.4 0.371781 0.101758 1.124929
0.9 2.56 0.349070 0.097293 1.077209
0.9 2.72 0.328374 0.095640 1.097502
0.9 2.89 0.309461 0.087175 1.064119
0.9 3.06 0.292134 0.050127 0.968564
0.9 3.24 0.276219 0.003136 0.902680
0.9 3.42 0.261569 -0.034673 0.882556
0.95 2.4 0.384494 0.107726 1.079087
0.95 2.56 0.361453 0.102269 1.040995
0.95 2.72 0.340407 0.099848 1.072015
0.95 2.89 0.321133 0.090544 1.055804
0.95 3.06 0.303439 0.052833 0.971023
0.95 3.24 0.287158 0.005393 0.907107
0.95 3.42 0.272146 -0.032200 0.884625
1 2.4 0.396703 0.113466 1.036707
1 2.56 0.373374 0.106727 1.007923
1 2.72 0.352016 0.103726 1.047463
1 2.89 0.332416 0.093605 1.045933
1 3.06 0.314388 0.055305 0.970792
1 3.24 0.297772 0.007453 0.909048
1 3.42 0.282424 -0.029966 0.884723
1.05 2.4 0.408437 0.118939 0.992592
1.05 2.56 0.384858 0.111105 0.971331
1.05 2.72 0.363224 0.107103 1.019267
1.05 2.89 0.343330 0.095852 1.029986
1.05 3.06 0.324999 0.057266 0.964081
1.05 3.24 0.308073 0.009820 0.906637
1.05 3.42 0.292416 -0.027198 0.883994
1.1 2.4 0.419723 0.125251 0.947155
1.1 2.56 0.395929 0.115416 0.938049
1.1 2.72 0.374051 0.110297 0.993433
1.1 2.89 0.353894 0.098076 1.014245
1.1 3.06 0.335286 0.059359 0.956429
1.1 3.24 0.318077 0.012982 0.905373
1.1 3.42 0.302133 -0.024350 0.882958
1.15 2.4 0.430586 0.130979 0.910430
1.15 2.56 0.406608 0.119423 0.907506
1.15 2.72 0.384515 0.113163 0.969323
1.15 2.89 0.364122 0.100019 0.998793
1.15 3.06 0.345265 0.061046 0.948539
1.15 3.24 0.327796 0.015164 0.901680
1.15 3.42 0.311587 -0.021709 0.880861
1.2 2.4 0.441050 0.136174 0.877989
1.2 2.56 0.416916 0.123376 0.879867
1.2 2.72 0.394636 0.116022 0.947092
1.2 2.89 0.374032 0.101867 0.984262
1.2 3.06 0.354948 0.062766 0.940538
1.2 3.24 0.337242 0.017174 0.897860
1.2 3.42 0.320789 -0.019216 0.878344
1.25 2.4 0.451137 0.141522 0.851328
1.25 2.56 0.426872 0.127836 0.854448
1.25 2.72 0.404429 0.119066 0.924399
1.25 2.89 0.383638 0.104151 0.966286
1.25 3.06 0.364349 0.064626 0.929040
1.25 3.24 0.346426 0.019518 0.890588
1.25 3.42 0.329748 -0.016436 0.873707
1.3 2.4 0.460866 0.146979 0.827067
1.3 2.56 0.436494 0.131843 0.832123
1.3 2.72 0.413910 0.122206 0.903273
1.3 2.89 0.392954 0.106218 0.949548
1.3 3.06 0.373480 0.066537 0.917721
1.3 3.24 0.355358 0.021675 0.883594
1.3 3.42 0.338473 -0.013711 0.868901
1.35 2.4 0.470256 0.151920 0.806259
1.35 2.56 0.445798 0.135925 0.812231
1.35 2.72 0.423094 0.125351 0.884403
1.35 2.89 0.401992 0.108521 0.933955
1.35 3.06 0.382352 0.068511 0.907321
1.35 3.24 0.364050 0.023938 0.877039
1.35 3.42 0.346974 -0.011047 0.864389


Table 4.7. [math] \frac{g_1^p - g_1^n}{F_1^p - F_1^n}(x,Q^2)[/math].



[math]n_{C,MT,\pi^{+} \pi^{-}}[/math] [math]x_{B}=0.3[/math] [math]x_{B}=0.4[/math]
[math]n_{C,\pi^{+}}[/math], [math]z=0.45[/math] 0.006584 0.004943
[math]n_{C,\pi^{-}}[/math], [math]z=0.45[/math] 0.006382 0.004355
[math]n_{MT,\pi^{+}}[/math], [math]z=0.45[/math] 0.005769 0.004544
[math]n_{MT,\pi^{-}}[/math], [math]z=0.45[/math] 0.005856 0.004021
[math]n_{C,\pi^{+}}[/math], [math]z=0.85[/math] 0.002893 0.002574
[math]n_{C,\pi^{-}}[/math], [math]z=0.85[/math] 0.001664 0.001361
[math]n_{MT,\pi^{+}}[/math], [math]z=0.85[/math] 0.002673 0.002399
[math]n_{MT,\pi^{-}}[/math], [math]z=0.85[/math] 0.001565 0.001307


[math]n_{NH3,ND,\pi^{+} \pi^{-}}[/math] [math]x_{B}=0.3[/math] [math]x_{B}=0.4[/math]
[math]n_{NH3,\pi^{+}}[/math], [math]z=0.45[/math] 0.00611464 0.00545206
[math]n_{NH3,\pi^{-}}[/math], [math]z=0.45[/math] 0.00428864 0.00330646
[math]n_{ND3,\pi^{+}}[/math], [math]z=0.45[/math] 0.00552027 0.00392858
[math]n_{ND3,\pi^{-}}[/math], [math]z=0.45[/math] 0.00552027 0.00392858
[math]n_{NH3,\pi^{+}}[/math], [math]z=0.85[/math] 0.00265003 0.00282080
[math]n_{NH3,\pi^{-}}[/math], [math]z=0.85[/math] 0.00097612 0.00090184
[math]n_{ND3,\pi^{+}}[/math], [math]z=0.85[/math] 0.00264221 0.00243020
[math]n_{ND3,\pi^{-}}[/math], [math]z=0.85[/math] 0.00154130 0.00128547


[math]x_{B}=0.3[/math] [math]x_{B}=0.4[/math]
[math]0.969 \pm 0.095[/math] [math]0.947 \pm 0.08[/math]


Table 4.7. Average [math] \Delta R_{np}^{\pi^+ + \pi^-} = \frac{g_1^p - g_1^n}{F_1^p - F_1^n}(x,Q^2)[/math].



[math]z[/math] [math]X_B=0.3[/math] [math]X_B=0.4[/math]
0.45 [math]-0.297 \pm 0.071[/math] [math] -0.379 \pm 0.071[/math]
0.7 [math]-0.120 \pm 0.072[/math] [math]-0.122 \pm 0.072[/math]



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