Difference between revisions of "Analysis"

From New IAC Wiki
Jump to navigation Jump to search
Line 598: Line 598:
  
 
<math>\vec {P_{tot}}^{\prime} = (p_{ex}^{\prime} + p_{px}^{\prime} + p_{\pi^-x}^{\prime})\hat{x} + (p_{ey}^{\prime} + p_{py}^{\prime} + p_{\pi^-y}^{\prime})\hat{y} + (p_{ez}^{\prime} + p_{pz}^{\prime} + p_{\pi^-z}^{\prime})\hat{z} = - 0.0741 \hat{x} + 0.1899 \hat{y} + 0.13 \hat{z} </math><br>
 
<math>\vec {P_{tot}}^{\prime} = (p_{ex}^{\prime} + p_{px}^{\prime} + p_{\pi^-x}^{\prime})\hat{x} + (p_{ey}^{\prime} + p_{py}^{\prime} + p_{\pi^-y}^{\prime})\hat{y} + (p_{ez}^{\prime} + p_{pz}^{\prime} + p_{\pi^-z}^{\prime})\hat{z} = - 0.0741 \hat{x} + 0.1899 \hat{y} + 0.13 \hat{z} </math><br>
 +
 +
[[Image:missing_mass_calculation.ods]]
  
  

Revision as of 22:02, 25 November 2007

EG1 run database
run summary
polarization info

Particle Identification

Cherenkov

Cherenkov Theory

The number of photons produced per unit path length of a particle with charge ze and per unit energy interval of the photons is[1]

[math]\frac{d^2 N}{dEdx}=\frac{\alpha z^2}{\hbar c}sin ^2 \theta_c=\frac{\alpha z^2}{\hbar c}[1-\frac{1}{\beta^2 n^2 (E)}][/math]


[math]\frac{d^2 N}{d\lambda dx} = \frac{2 \pi \alpha z^2}{\lambda^2}[1-\frac{1}{\beta^2 n^2 (\lambda)}][/math]

where [math]\theta_c[/math] is the angle of Cerenkov radiation relative to the particle's direction, [math]\beta c[/math] - the particle's velocity and n - index of refraction of the medium.

[math]cos \theta_c=\frac{1}{n \beta}[/math]

[math]\beta=\frac{v}{c}=\frac{pc}{\sqrt{(pc)^2 + (mc^2)^2}}[/math]

after deriving the Taylor expansion of our function and considering only the first two terms, we get
[math]\frac{d^2 N}{dEdx}=\frac{\alpha z^2}{\hbar c}sin ^2 \theta_c=\frac{\alpha z^2}{\hbar c}[\beta^2 n^2 (E) - 1][/math]

The gas used in the CLAS Cerenkov counter is perfluorobutane [math]C_4 F_{10}[/math] with index of refraction equal to 1.00153.


Electrons

Insert number of Photo-electrons calculation and sentence saying that themean should be about 10PEs.

Used file dst27095_05.B00 energy=5.7GeV and torus=2250(B>0). Target NH3

E momentum vs numb of photoelectrons 27095 theory.gif

Pions([math]\pi^-[/math])

The threshold energy for pions is ~2.5 GeV and for electrons 9 MeV.

Example for [math]\pi^-[/math]

[math]m_{\pi^-}=139.57[\frac{MeV}{c^2}][/math], momentum [math]p=mv=3 [\frac{GeV}{c}][/math] and n=1.00153

where [math]\frac{\alpha}{\hbar c}=370[ eV^{-1} cm^{-1}] [/math]

[math]\frac{d^2 N}{dEdx}=370 \times 1 \times [(\frac{3 GeV}{\sqrt{(3 GeV)^2 + (0.13957 GeV)^2}})^2 \times 1.00153^2 - 1][\frac{1}{eV \times cm}]=0.3315 [eV^{-1} cm^{-1}] [/math]

The Hall B cherenkov detector is [math]\sim \; 0.7[/math] m thick radiator. We assume the PMTs used to collect light have a constant quantum efficiency of 8% for photons with wavelength between 300 and 600 nm.

[math]\frac{dN}{dx} = \frac{2 \pi \alpha z^2}{\lambda^2}[1-\frac{1}{\beta^2 n^2 (\lambda)}]=[/math]
[math]= 2 \pi \alpha z^2 [1-\frac{1}{\beta^2 n^2 (\lambda)}]\int_{300nm}^{600nm} \frac{1}{\lambda^2} d\lambda \times (0.08)=[/math]
[math]= 2 \pi \alpha z^2 [1-\frac{1}{\beta^2 n^2 (\lambda)}] (\frac {1}{\lambda})|_{600nm}^{300nm} \times (0.08) [/math]=
[math]= 2\times 3.14 \times \frac{1}{137} \times 1^2 \times [1-\frac{1}{0.998919^2 \times 1.00153^2}] \times \frac{1}{600} \times 0.08 [nm^{-1}] = [/math]
[math]= 5.465 \times 10^{-9} [nm^{-1}][/math]

For the number of photons we have the following(for pions)

[math] N = 5.465 \times 10^{-9} \times 0.7 m [\frac{10^9}{m}] = 3.8255 [/math]

Used file dst27095_05.B00 energy=5.7GeV and torus=2250(B>0). Target NH3

Pi momentum vs numb of photons 27095 theory.gif

CLAS Cherenkov signal

Electrons

The cherenkov signal measured in CLAS for particles identified as electrons by the tracking algorithm is shown below. There are two distributions present. One distribution is centered around 1.5 PEs and the second distribution is at 7 PEs when two gaussians are fit to the spectrum. As we will show below, the first peak is due to the misidentification of a negative pion as an electron.

Number of photoelectrons


Theory
E number of photoelectrons 27095 1.gif E number of photoelectrons 27095 3.gif E number of photoelectrons 27095 4 30.gif
E number of photoelectrons 27095 flag 10 1.gif E number of photoelectrons 27095 flag 10 3.gif E number of photoelectrons 27095 flag 10 4 30.gif



e_Momentum_vs_Number_of_Photoelectrons


Experiment B>0 without cuts flag>10 5<nphe<15 5<nphe<15 and flag>10
E momentum vs numb of photoelectrons 27095 exp without cuts 1.gif

E momentum vs numb of photoelectrons 27095 exp without cuts 2.gif E momentum vs numb of photoelectrons 27095 exp without cuts 3.gif

E momentum vs numb of photoelectrons 27095 exp with cuts flag 10 1.gif

E momentum vs numb of photoelectrons 27095 exp with cuts flag 10 2.gif E momentum vs numb of photoelectrons 27095 exp with cuts flag 10 3.gif

E momentum vs numb of photoelectrons 27095 exp with cuts ? nphe ?.gif 200px

Pions([math]\pi^-[/math])

[math]\pi^-[/math]_Momentum_vs_Number_of_Photons


Experiment B>0 without cuts e_flag>10 0<e_nphe<5 0<nphe<5 and e_flag>10
Pi momentum vs numb of photoelectrons 27095 exp without cuts 1 1.gif

Pi momentum vs numb of photoelectrons 27095 exp without cuts 2 1.gif Pi momentum vs numb of photoelectrons 27095 exp without cuts 3 1.gif

Pi momentum vs numb of photoelectrons 27095 exp with cuts flag 10 1 1.gif

Pi momentum vs numb of photoelectrons 27095 exp with cuts flag 10 2 1.gif Pi momentum vs numb of photoelectrons 27095 exp with cuts flag 10 3 1.gif

Pi momentum vs numb of photoelectrons 27095 exp with cuts ? nphe ?.gif 200px

Calorimeter

Electron-pion contamination

Osipenko's CLAS Note 2004-20 File:CLAS Note-2004-020.pdf

Electron

Cuts

Calorimeter based cuts

The distributions below represent two types of cuts applied to improve the electron particle identification (PID) using a 4 GeV electron beam incident on an NH3 target. The electron calorimeter is segmented into an inner[math]EC_{inner}[/math] and an outer[math]EC_{outer}[/math] region. The total energy absorbed by the calorimeter system is recorded in the variable [math]EC_{tot}[/math]. The momentum ([math]P[/math]) is calculated using the reconstructed track and the known torus magnetic field. The distributions of [math]EC_{tot}[/math] and [math]EC_{inner}[/math] are shown below where both have been divided by the electron momentum and no cuts have been applied.


[math]EC_{tot}\gt 0.2*p[/math]

Without any cuts we have 181018 entries. After using the following cut [math]EC_{tot}\gt 0.2*p[/math] we are getting 127719 entries, which is about 70.55% of 181018.

Etotal P using tot cut.gif Einner P using tot cut.gif

[math]EC_{inner}\gt 0.08*p[/math]

After the cut on the energy deposited into inner part of electron calorimeter, number of entries decreases by 22%.

Etotal P using inner cut.gif Einner P using inner cut.gif

Both cuts [math] EC_{tot}\gt 0.2*p [/math] and [math] EC_{inner}\gt 0.08*p [/math]

In case of using the cuts of the total deposited energy and the energy deposited into inner calorimeter number of entries decreases ~36%

Etotal P using both cuts.gif Einner P using both cuts.gif

summary table

The "# of triggers" columns represents the number of events which generated a signal above threshold in the calorimeter and the scintillator. The expected # of events column represents the number of reconstructed events with tracks that also make it through the cuts defined in the table.

The semi-inclusive analysis will focus on the 4 GeV and 6 GeV data which have both inbending and outbending torus settings. Specifically runs 28074 - 28579 ( 4 GeV) and Runs 27356 - 27499 and 26874 - 27198 (6 GeV)


Beam Energy Torus Current Begin Run End Run file used cuts # trig([math]10^6[/math]) expected # evts([math]10^6[/math]) p<3,[math]EC_{tot}\gt 0.2*p [/math],[math] EC_{inner}\gt 0.08*p[/math](%) p>3,[math]EC_{tot}\gt 0.24*p [/math],[math] EC_{inner}\gt 0.06*p[/math](%)
[math]EC_{tot}\gt 0.2*p[/math] [math]EC_{inner}\gt 0.08*p[/math] [math]EC_{tot}\gt 0.2*p [/math] and [math] EC_{inner}\gt 0.08*p[/math]
1606 1500 25488 25559 dst25504_02.B00 64% 49.5% 78% 60 3.2
1606 1946 25560 25605 44
1606 1500 25669 25732 dst25669_02.B00 64% 49% 78% 226 10
1606 1500 25742 26221 dst25754_02.B00 21% 11% 24% 3154 13.3
1606 -1500 26222 26359 dst26224_02.B00 4.6% 3% 6.6% 703 13.1
1724 -1500 27644 27798 dst27649_02.B00 4.8% 2.2% 5.9% 211 20
1724 1500 28512 28526 159
1724 -1500 28527 28532 93
2288 1500 27205 27351 dst27225_02.B00 20.2% 13% 25.6% 1647 16.1
2562 -1500 27799 27924 dst27809_02.B00 5.7% 4.6% 8.6% 1441 13.1
2562 -1500 27942 27995 dst27942_02.B00 6.1% 4.4% 8.9% 841 32.3
2562 1500 28001 28069 dst28002_02.B00 27.8% 13% 29.6% 1013 30.7
2792 -1500 27936 27941 dst27937_02.B00 6.7% 5% 9.9% 69 20.6
3210 -2250 28549 28570 436
4239 2250 28074 28277 dst28075_02.B00 35.3% 23.9% 40.5% 2278 19.6
4239 -2250 28280 28479 dst28281_02.B00 9.1% 9.4% 13.6% 2620 15.2
4239 2250 28482 28494 7
4239 -2250 28500 28505 107
4239 2250 28506 28510 dst28509_02.B00 29.5% 22% 36% 75 18.1
5627 2250 27356 27364 dst27358_02.B00 33.2% 27.8% 41.3% 56 19.4 44.6 40.1
5627 -2250 27366 27380 dst27368_02.B00 12.6% 14.8% 19.5% 130 13.6 25.3 8.8
5627 2250 27386 27499 dst27388_02.B00 33.4% 27.8% 41.4% 1210 20.2 44.8 40.1
5627 965 27502 27617 493
5735 -2250 26874 27068 dst26904_02.B00 13% 15% 20% 1709 19.9 25.6 9.1
5735 2250 27069 27198 dst27070_02.B00 33.3% 28.8% 42.2% 1509 15 46 40.2
5764 -2250 26468 26722 dst26489_02.B00 12.2% 14.4% 19.1% 1189 10 24.6 9.3
5764 0 26723 26775 268
5764 -2250 26776 26851 dst26779_02.B00 13.5% 15.5% 20.5% 662 15.9 26.4 9.2

Cut on the number of photoelectrons

In this case is used a cut on the number of photoelectrons, which is [math]nphe\gt 2.5[/math]. The plots below show the effect of the number of photoelectrons cuts on the Cerenkov distribution. We see that after using cut the number of entries decreases ~40.7%

Nphe before cut file 27070.gif Nphe1 after cut file 27070.gif


Used cuts [math]EC_{tot}\gt 0.24p[/math] and [math]EC_{inner}\gt 0.06p[/math]


Nphe before electron cuts file 27070.gif Nphe1 after electron cuts file 27070.gif


Used file dst28181_03(energy 4.2GeV). In this case was applied cuts on the polar angle([math]15\lt \theta\lt 20[/math]) and momentum([math]2.2\lt P\lt 2.6[/math]). Number of entries decreased by 96%(?????????????/)


Nphe before cuts file 28181.gif Nphe1 after cuts file 28181.gif

Tamuna: follow this link to see the OSIPENKO cuts described in part 5 add graphs of their effect below

Plot of [math]EC_{tot}/p[/math] vs [math]EC_{inner}/p[/math]

In this case is used file dst27070(Energy 5.735 GeV and Torus 2250) and are applied the following EC cuts: For ECtotal - [math]EC_{tot}\gt 0.2p[/math], for EC inner - [math]EC_{inner}\gt 0.08p[/math].

P<3

After using above cuts the number of entries decreases ~46%

E total vs e inner1 before cuts file dst27070.gif E total vs e inner1 after cuts file dst27070.gif

0.5<P<1

The number of entries decreased by ~51.8%

E total vs e inner1 before cuts P1 file dst27070.gif E total vs e inner1 after cuts P1 file dst27070.gif

1<P<1.5

The number of entries decreased approximately by 47.8%

E total vs e inner1 before cuts P1.5 file dst27070.gif E total vs e inner1 after cuts P1.5 file dst27070.gif

1.5<P<2

In this case the number of entries decreased by 46.1%

E total vs e inner1 before cuts P2 file dst27070.gif E total vs e inner1 after cuts P2 file dst27070.gif

2<P<2.5

In this case the number of entries decreased by 38%

E total vs e inner1 before cuts P2.5 file dst27070.gif E total vs e inner1 after cuts P2.5 file dst27070.gif

P>3

Used file dst27070(Energy 5.735 GeV and Torus 2250) and are applied the following EC cuts: For ECtotal - [math]EC_{tot}\gt 0.24p[/math], for EC inner - [math]EC_{inner}\gt 0.06p[/math].

The number of entries decreased by~40.2%

E total vs e inner1 before cuts P3 file dst27070.gif E total vs e inner1 after cuts P3 file dst27070.gif

Plot of EC_tot/P vs nphe for Electrons

Used file dst27070(Energy 5.735 GeV and Torus 2250)

p<3 GeV

The graphs below represents all electron candidates having a momentum smaller than 3 GeV. Negatively charged pions are the most likely particle to be misidentified as an electrons by the tracking software. A negatively charged pion having a momentum of 3 GeV would generate less than ?? photons in the cerenkov counter. As a result the electron candidates which [math]n_{pe} \lt 1.xx [/math] are thought to be misidentified pions. The images which follow represent the effects of several cuts made for the purpose of removing misidentified particles.

E total vs nphe momentum cut file dst27070.gif

Insert writeup on Cherenkov light for [math]e^-[/math] and [math]\pi^-[/math] 



Add experiment number of PEs for pions after Theory
chi_sqr for pions

Chi sqr 27095 pions.gif

[math]\pi[/math]_Momentum_vs_Number_of_Photons for pions([math]\pi[/math])

Used file:27095_05.B00(energy=5.735GeV and torus=2250), everything is done for [math]\pi^-[/math]

Theory
Pi momentum vs numb of photons 27095 pions minus theory 1.gif Pi momentum vs numb of photons 27095 pions minus theory 2.gif
Experiment B>0 without cuts e_flag>10 5<e_nphe<15 5<e_nphe<15 and e_flag>10
Pi momentum vs numb of photoelectrons 27095 exp without cuts 1.gif

Pi momentum vs numb of photoelectrons 27095 exp without cuts 2.gif Pi momentum vs numb of photoelectrons 27095 exp without cuts 3.gif

Pi momentum numb of photoelectrons 27095 exp with cuts e flag 10 1.gif

Pi momentum vs numb of photoelectrons 27095 exp with cuts e flag 10 2.gif Pi momentum vs numb of photoelectrons 27095 exp with cuts e flag 10 3.gif

Pi momentum vs numb of photoelectrons 27095 exp with cuts 5 e nphe 15 1.gif

Pi momentum vs numb of photoelectrons 27095 exp with cuts 5 e nphe 15 2.gif Pi momentum vs numb of photoelectrons 27095 exp with cuts 5 e nphe 15 3.gif

Pi momentum vs numb of photoelectrons 27095 exp with cuts e flag 10 5 e nphe 15 1.gif

Pi momentum vs numb of photoelectrons 27095 exp with cuts e flag 10 5 e nphe 15 2.gif

ELECTRONS
e_momentum_vs_number_of_photoelectrons_theory


Numb of photoelectrons 27095 theory without cuts.gif 

Add number of detected photons
Number of Photoelectrons
Experiment B>0 without cuts flag>10
Numb of photoelectrons 27095 exp without cuts 1 1.gif

Numb of photoelectrons 27095 exp without cuts 2 1.gif

Numb of photoelectrons 27095 exp with cuts flag 10 1 1.gif

Numb of photoelectrons 27095 exp with cuts flag 10 2 1.gif


e_Momentum_vs_Number_of_Photoelectrons
Now put a cut on the number of cherenkov photons from electrons ( 5 < Npe < 15) and plot the number of pion cherenkov photons.


Experiment B>0 without cuts flag>10 5<nphe<15 5<nphe<15 and flag>10
Numb of photoelectrons vs momentum 27095 exp without cuts 1 1.gif

Numb of photoelectrons vs momentum 27095 exp without cuts 2 1.gif

Numb of photoelectrons vs momentum 27095 exp with cuts flag 10 1 1.gif

Numb of photoelectrons vs momentum 27095 exp with cuts flag 10 2 1.gif

Numb of photoelectrons vs momentum 27095 exp with cuts 5 nphe 15.gif Numb of photoelectrons vs momentum 27095 exp with cuts 5 nphe 15 flag 10.gif
p<3 GeV and [math]EC_{inner}\gt 0.08p[/math]

E total P vs nphe momentum Ec inner cuts file dst27070.gif

p<3 GeV, [math]EC_{inner}\gt 0.08p[/math] and [math]EC_{tot}\gt 0.2p[/math]

E total P vs nphe momentum EC inner EC total cuts file dst27070.gif

p<3 GeV, [math]EC_{inner}\gt 0.08p[/math], [math]EC_{tot}\gt 0.2p[/math] and nphe>2.5

E total P vs nphe momentum EC inner EC total nphe cuts file dst27070.gif

Plot of EC_total vs EC_inner

In this case file dst28181_03.B00 was used(Energy 4.2 GeV and Torus +2250). The following cuts were applied:[math]EC_{inner}\gt 0.005[/math], [math]EC_{tot}\gt 0.2*p[/math], ec_chi_sqr<0.1 and nphe>3.
http://www.jlab.org/Hall-B/secure/eg1/EG2000/sharon/ec_cut_4p2gev/Final_ec_cuts/Electron_cuts.html Etotal vs Einner file dst28181 03 before cuts.gif Etotal vs Einner file dst28181 03 after cuts.gif

Raster and vertex correction

A raster calibration and a cut on the vertex distribution was made in order to select electrons from the polarized target, also the ones scattered from other materials in the beam path. A plot of the uncorrected vertex distribution is presented below for dst27070_02.B00 file(energy=5.7GeV Torus=2250)

Vertex before corrections dst27070 file.gif

Pion

Summary Table

Tamuna:  
The pion id code is at:

http://www.jlab.org/Hall-B/secure/eg1/EG2000/josh/pion.cc
Beam Energy Torus Current Begin Run End Run file used # trig([math]10^6[/math]) expected # evts([math]10^6[/math]) p>3,[math]EC_{tot}\lt 0.2*p [/math],[math] EC_{inner}\lt 0.08*p[/math](%) p<3,[math]EC_{tot}\lt 0.24*p [/math],[math] EC_{inner}\lt 0.06*p[/math](%)
1606 1500 25488 25559 dst25504_02.B00 60 3.2
1606 1500 25669 25732 dst25669_02.B00 226 10
1606 1500 25742 26221 dst25754_02.B00 3154 13.3
1606 -1500 26222 26359 dst26224_02.B00 703 13.1
1724 -1500 27644 27798 dst27649_02.B00 211 20
2288 1500 27205 27351 dst27225_02.B00 1647 16.1
2562 -1500 27799 27924 dst27809_02.B00 1441 13.1
2562 -1500 27942 27995 dst27942_02.B00 841 32.3
2562 1500 28001 28069 dst28002_02.B00 1013 30.7
2792 -1500 27936 27941 dst27937_02.B00 69 20.6
4239 2250 28074 28277 dst28075_02.B00 2278 19.6
4239 -2250 28280 28479 dst28281_02.B00 2620 15.2
4239 2250 28506 28510 dst28509_02.B00 75 18.1
5627 2250 27356 27364 dst27358_02.B00 56 19.4 36.1 31.5
5627 -2250 27366 27380 dst27368_02.B00 130 13.6 25 43.8
5627 2250 27386 27499 dst27388_02.B00 1210 20.2 39.8 32.4
5735 -2250 26874 27068 dst26904_02.B00 1709 19.9 22.5 46.4
5735 2250 27069 27198 dst27070_02.B00 1509 15 34.6 32.9
5764 -2250 26468 26722 dst26489_02.B00 1189 10 25.2 44.3
5764 -2250 26776 26851 dst26779_02.B00 662 15.9 21.3 44

Table for Pions

I used the pion id code(both subroutines):

http://www.jlab.org/Hall-B/secure/eg1/EG2000/josh/pion.cc

Beam Energy Torus Current Begin Run End Run file used events remaining after cuts # trig([math]10^6[/math]) expected # evts([math]10^6[/math])
first(%) second(%)
1606 1500 25488 25559 dst25504_02.B00 96.8 99 60 3.2
1606 1500 25669 25732 dst25669_02.B00 98.1 98.9 226 10
1606 1500 25742 26221 dst25754_02.B00 13.4 22.8 3154 13.3
1606 -1500 26222 26359 dst26224_02.B00 11.3 15.3 703 13.1
1724 -1500 27644 27798 dst27649_02.B00 15.3 18.7 211 20
2288 1500 27205 27351 dst27225_02.B00 16.4 18.9 1647 16.1
2562 -1500 27799 27924 dst27809_02.B00 11.1 14.2 1441 13.1
2562 -1500 27942 27995 dst27942_02.B00 11.1 14.2 841 32.3
2562 1500 28001 28069 dst28002_02.B00 22.4 23.1 1013 30.7
2792 -1500 27936 27941 dst27937_02.B00 12.3 15.4 69 20.6
4239 2250 28074 28277 dst28075_02.B00 16.7 14.3 2278 19.6
4239 -2250 28280 28479 dst28281_02.B00 10.4 12.6 2620 15.2
4239 2250 28506 28510 dst28509_02.B00 % % 75 18.1
5627 2250 27356 27364 dst27358_02.B00 40.5 40.8 56 19.4
5627 -2250 27366 27380 dst27368_02.B00 9.7 12.7 130 13.6
5627 2250 27386 27499 dst27388_02.B00 14.1 15.5 1210 20.2
5735 -2250 26874 27068 dst26904_02.B00 12.1 14.5 1709 19.9
5735 2250 27069 27198 dst27070_02.B00 19.5 22.9 1509 15
5764 -2250 26468 26722 dst26489_02.B00 9.6 13.3 1189 10
5764 -2250 26776 26851 dst26779_02.B00 10.3 13.9 662 15.9

Plot of EC_tot/P vs nphe for Pions

E total vs nphe pions file dst27070.gif E total vs nphe electrons file dst27070.gif

Quality Checks

Run Summary Table

The table below uses a characteristic DST file to try and estimate the sample size for a semi-inclusive analysis of pion electroproduction. The column marked "cuts" below indicates the number of events kept when the standard EC based electron identification cuts, described above, are used: [math]EC_{tot}\gt 0.2*p [/math] and
[math] EC_{inner}\gt 0.08*p[/math]. The next step will be to compare unpolarized pion production rates in order to evaluate the CLAS detectors efficiencies for measuring charged pions with different torus polarities. The question is whether you get the same rates for negatively charged pions in one torus polarity to positively charged pions using the opposite torus polarity. 

 Tamar: We need  a convention for choosing only one of the pions in events with 
multiple pions.  I believe I chose the pion with the highest momentum before.
Beam Energy Torus Current Target Begin Run End Run file used # trig([math]10^6[/math]) events remaining after [math]e^-[/math] cuts(%) expected # evts([math]10^6[/math]) events remaining after [math]e^-[/math] and [math]\pi^+[/math] cuts(%) expected # evts([math]10^6[/math]) events remaining after [math]e^-[/math] and [math]\pi^-[/math] cuts(%) expected # evts([math]10^6[/math])
4239 2250 NH3 28205 28277 /cache/mss/home/nguler/dst/dst28205_05.B00 1108.72 60.8 674.1 8.3 92.02 3.24 35.92
ND3 28074 28190 /cache/mss/home/nguler/dst/dst28187_05.B00 1117.87 59.6 666.25 7.99 89.32 3.3 36.9
-2250 NH3 28407 28479 /cache/mss/home/nguler/dst/dst28409_05.B00 1013.57 24.2 245.28 0.12 1.22 0 0
ND3 28278 28403 /cache/mss/home/nguler/dst/dst28400_05.B00 1556.04 23.9 371.89 0.02 0.31 0.05 0.51
5735 2250 NH3 27074 27195 /cache/mss/home/nguler/dst/dst27095_05.B00 1442.25 57.7 832.18 9.3 134.13 3.8 59.13
ND3 27116 27170 /cache/mss/home/nguler/dst/dst27141_05.B00 624.55 59.1 369.10 9.53 59.52 3.9 24.36
-2250 NH3 26911 27015 /cache/mss/home/nguler/dst/dst26988.B00 900.93 80.7 727.05 7.14 64.33 9.9 89.19
ND3 27022 27068 /cache/mss/home/nguler/dst/dst27055_05.B00 711.53 80 569.22 6.97 49.59 10.1 71.86

Rates

Unpolarized Pion electroproduction

Rates from other experiments in our Kinematic range

[math]\vec{e}p \rightarrow n \pi^+[/math] from CLAS

Center of Mass Frame Transformation

We have proton and electron. In the Lab frame electron is moving along the x-axis with momentum ;[math]\vec{p_e}[/math] and proton is at rest. The 4-vectors are:

Lab Frame
[math]P_e=[/math]([math]E_e[/math],[math]p_e[/math],0,0) and for proton :[math]P_p=[/math]([math]m_p[/math],0,0,0)
CM Frame
:[math]{P_e}^{\prime}=[/math]([math]{E_e}^{\prime}[/math],[math]{p_e}^{\prime}[/math],[math]0[/math],[math]0[/math]) and for proton :[math]{P_p}^{\prime}=[/math]([math]{E_p}^{\prime}[/math],[math]{p_p}^{\prime}[/math],[math]0[/math],[math]0[/math])
Find [math] \beta_{CM} [/math] such that [math]P_{tot}^{CM}=0 =p_e^{\prime} + {p_p}^{\prime}[/math]
[math]\left ( \begin{matrix} {E_e}^{\prime} \\ p_e^{\prime} \\ 0 \\ 0 \end{matrix} \right )= \left [ \begin{matrix} \gamma & -\gamma \beta & 0 & 0 \\ -\gamma \beta & \gamma &0 &0 \\ 0 &0 &1 &0 \\ 0 &0 &0 & 1 \end{matrix} \right ] \left ( \begin{matrix} E_e \\ p_e \\ 0 \\ 0 \end{matrix} \right )[/math]


[math]\left ( \begin{matrix} {E_p}^{\prime} \\ p_p^{\prime} \\ 0 \\ 0 \end{matrix} \right )= \left [ \begin{matrix} \gamma & -\gamma \beta & 0 & 0 \\ -\gamma \beta & \gamma &0 &0 \\ 0 &0 &1 &0 \\ 0 &0 &0 &1\end{matrix} \right ] \left ( \begin{matrix} m_p \\ 0 \\ 0 \\ 0 \end{matrix} \right )[/math]

Using the last two equations we will get the following for x component:

[math]{p_e}^{\prime}=-\gamma_{cm}(\beta_{cm} E_e-p_e)[/math]
[math]p_p^{\prime} = - \gamma_{cm} \beta_{cm} m_p[/math]
[math] \gamma_{cm}(p_e - \beta_{cm} E_e)= \gamma_{cm} \beta_{cm} m_p [/math]
[math]\beta_{cm} = \frac {p_e}{m_p + E_e}[/math]
Example
[math]p_e = 4.239 Gev \sim E_e[/math] : electron mass is neglibible
[math]m_p = 0.938 GeV[/math] : Mass of a proton
[math]\beta_{cm} = \frac{4.239}{5.177} = 0.819 \lt 1[/math]
;Insert an example event with missing mass close to the proton mass ~ 1 GeV ( 0.8 < W < 1.2).

Event number 3143292 1.jpg Event number 3143292 2.jpg Event number 3143292 3.jpg

[math]p_e = 5.736 Gev \sim E_e[/math] : electron mass is neglibible
[math]m_p = 0.938 GeV[/math] : Mass of a proton
[math]\beta_{cm} = \frac{5.736}{6.674} = 0.859 \lt 1[/math]
[math]\gamma_{cm} = \frac{1}{\sqrt{1 - \beta_{cm}^2}} = \frac{1}{\sqrt{1 - 0.859^2}} = 1.9532[/math]
[math]\left ( \begin{matrix} {E_e}^{\prime} \\ p_{ex}^{\prime} \\ p_{ey}^{\prime} \\ p_{ez}^{\prime} \end{matrix} \right )= \left [ \begin{matrix} \gamma_{cm} & 0 & 0 & -\gamma_{cm} \beta_{cm} \\ 0 & 1 &0 &0 \\ 0 &0 &1 &0 \\ -\gamma_{cm} \beta_{cm} &0 &0 &\gamma_{cm}\end{matrix} \right ] \left ( \begin{matrix} E_e=4.4915 \\ -0.549 \\ 0.974 \\ 4.3501 \end{matrix} \right )[/math]
[math]\left ( \begin{matrix} {E_p}^{\prime} \\ p_{px}^{\prime} \\ p_{py}^{\prime} \\ p_{pz}^{\prime} \end{matrix} \right )= \left [ \begin{matrix} \gamma_{cm} & 0 & 0 & -\gamma_{cm} \beta_{cm} \\ 0 & 1 &0 &0 \\ 0 &0 &1 &0 \\ -\gamma_{cm} \beta_{cm} &0 &0 & \gamma_{cm} \end{matrix} \right ] \left ( \begin{matrix} E_p = 1.4563 \\ 0.3697 \\ -0.3447 \\ 0.9924 \end{matrix} \right )[/math]
[math]\left ( \begin{matrix} {E_{\pi^-}}^{\prime} \\ p_{\pi^- x}^{\prime} \\ p_{{\pi^-} y}^{\prime} \\ p_{{\pi^-} z}^{\prime} \end{matrix} \right )= \left [ \begin{matrix} \gamma_{cm} & 0 & 0 & -\gamma_{cm} \beta_{cm} \\ 0 & 1 &0 &0 \\ 0 &0 &1 &0 \\ -\gamma_{cm} \beta_{cm} &0 &0 & \gamma_{cm} \end{matrix} \right ] \left ( \begin{matrix} E_{\pi^-} = 0.5757 \\ 0.1052 \\ -0.4394 \\ 0.3282 \end{matrix} \right )[/math]


Electron
[math]\left ( \begin{matrix} {E_e}^{\prime} \\ p_{ex}^{\prime} \\ p_{ey}^{\prime} \\ p_{ez}^{\prime} \end{matrix} \right )= \left ( \begin{matrix} 4.4915 \gamma_{cm} - 4.3501 \gamma_{cm} \beta_{cm} \\ -0.549 \\ 0.974 \\ -4.4915 \gamma_{cm} \beta_{cm} + 4.3501 \gamma_{cm} \end{matrix} \right ) = \left ( \begin{matrix} 1.4742 \\ -0.549 \\ 0.974 \\ 0.96078 \end{matrix} \right )[/math]
Proton
[math]\left ( \begin{matrix} {E_p}^{\prime} \\ p_{px}^{\prime} \\ p_{py}^{\prime} \\ p_{pz}^{\prime} \end{matrix} \right )= \left ( \begin{matrix} 1.4563\gamma_{cm} - 0.9924 \gamma_{cm} \beta_{cm} \\ 0.3697 \\ -0.3447 \\-1.4563 \gamma_{cm} \beta_{cm} + 0.9924\gamma_{cm} \end{matrix} \right ) = \left ( \begin{matrix} 1.17939 \\ 0.3697 \\ -0.3447 \\ -0.505023 \end{matrix} \right )[/math]
[math]\pi^-[/math]
[math]\left ( \begin{matrix} {E_{\pi^-}}^{\prime} \\ p_{\pi^- x}^{\prime} \\ p_{{\pi^-} y}^{\prime} \\ p_{{\pi^-} z}^{\prime} \end{matrix} \right )= \left ( \begin{matrix} 0.5757\gamma_{cm} - 0.3282 \gamma_{cm} \beta_{cm} \\ 0.1052 \\ -0.4394 \\ -0.5757 \gamma_{cm} \beta_{cm} + 0.3282\gamma_{cm} \end{matrix} \right ) = \left ( \begin{matrix} 0.5738 \\ 0.1052 \\ -0.4394 \\ -0.324868 \end{matrix} \right )[/math]

[math]\vec {P_{tot}}^{\prime} = (p_{ex}^{\prime} + p_{px}^{\prime} + p_{\pi^-x}^{\prime})\hat{x} + (p_{ey}^{\prime} + p_{py}^{\prime} + p_{\pi^-y}^{\prime})\hat{y} + (p_{ez}^{\prime} + p_{pz}^{\prime} + p_{\pi^-z}^{\prime})\hat{z} = - 0.0741 \hat{x} + 0.1899 \hat{y} + 0.13 \hat{z} [/math]

File:Missing mass calculation.ods 


Found Event     3939492 with 3 Particles
Start Time=60.46
Raster= 3762    2417
TRIGBITS=16392
        Electron Momentum(x,y,z):-0.0183:-0.2849:0.414
DrForest p_id[1]=2
        Momentum(x,y,z):0.3127:0.6473:0.7845
DrForest p_id[2]=5
        Momentum(x,y,z):-0.4141:-0.3148:0.5887


[math]\left ( \begin{matrix} {E_e}^{\prime} \\ p_{ex}^{\prime} \\ p_{ey}^{\prime} \\ p_{ez}^{\prime} \end{matrix} \right )= \left [ \begin{matrix} \gamma_{cm} & 0 & 0 & -\gamma_{cm} \beta_{cm} \\ 0 & 1 &0 &0 \\ 0 &0 &1 &0 \\ -\gamma_{cm} \beta_{cm} &0 &0 &\gamma_{cm}\end{matrix} \right ] \left ( \begin{matrix} E_e=0.5029 \\ -0.0183 \\ -0.2849 \\ 0.414 \end{matrix} \right )[/math]
[math]\left ( \begin{matrix} {E_p}^{\prime} \\ p_{px}^{\prime} \\ p_{py}^{\prime} \\ p_{pz}^{\prime} \end{matrix} \right )= \left [ \begin{matrix} \gamma_{cm} & 0 & 0 & -\gamma_{cm} \beta_{cm} \\ 0 & 1 &0 &0 \\ 0 &0 &1 &0 \\ -\gamma_{cm} \beta_{cm} &0 &0 & \gamma_{cm} \end{matrix} \right ] \left ( \begin{matrix} E_p = 1.4185 \\ 0.3127 \\ 0.6473 \\ 0.7845 \end{matrix} \right )[/math]
[math]\left ( \begin{matrix} {E_{\pi^-}}^{\prime} \\ p_{\pi^- x}^{\prime} \\ p_{{\pi^-} y}^{\prime} \\ p_{{\pi^-} z}^{\prime} \end{matrix} \right )= \left [ \begin{matrix} \gamma_{cm} & 0 & 0 & -\gamma_{cm} \beta_{cm} \\ 0 & 1 &0 &0 \\ 0 &0 &1 &0 \\ -\gamma_{cm} \beta_{cm} &0 &0 & \gamma_{cm} \end{matrix} \right ] \left ( \begin{matrix} E_{\pi^-} = 0.7979 \\ -0.4141 \\ -0.3148 \\ 0.5887 \end{matrix} \right )[/math]
[math]\beta_{cm} = \frac{4.239}{5.177} = 0.819[/math]
[math]\gamma_{cm} = \frac{1}{\sqrt{1 - \beta_{cm}^2}} = \frac{1}{\sqrt{1 - 0.819^2}} = 1.743[/math]


Electron
[math]\left ( \begin{matrix} {E_e}^{\prime} \\ p_{ex}^{\prime} \\ p_{ey}^{\prime} \\ p_{ez}^{\prime} \end{matrix} \right )= \left ( \begin{matrix} 0.5029 \gamma_{cm} - 0.414 \gamma_{cm} \beta_{cm} \\ -0.0183 \\ -0.2849 \\ -0.5029 \gamma_{cm} \beta_{cm} + 0.414 \gamma_{cm} \end{matrix} \right ) = \left ( \begin{matrix} 0.2855 \\ -0.0183 \\ -0.2849 \\ 0.0037 \end{matrix} \right )[/math]
Proton
[math]\left ( \begin{matrix} {E_p}^{\prime} \\ p_{px}^{\prime} \\ p_{py}^{\prime} \\ p_{pz}^{\prime} \end{matrix} \right )= \left ( \begin{matrix} 1.4185\gamma_{cm} - 0.7845 \gamma_{cm} \beta_{cm} \\ 0.3127 \\ 0.6473 \\-1.4185 \gamma_{cm} \beta_{cm} + 0.7845\gamma_{cm} \end{matrix} \right ) = \left ( \begin{matrix} 1.3525 \\ 0.3127 \\ 0.6473 \\ -0.6575 \end{matrix} \right )[/math]
[math]\pi^-[/math]
[math]\left ( \begin{matrix} {E_{\pi^-}}^{\prime} \\ p_{\pi^- x}^{\prime} \\ p_{{\pi^-} y}^{\prime} \\ p_{{\pi^-} z}^{\prime} \end{matrix} \right )= \left ( \begin{matrix} 0.7979\gamma_{cm} - 0.5887 \gamma_{cm} \beta_{cm} \\ -0.4141 \\ -0.3148 \\ -0.7979 \gamma_{cm} \beta_{cm} + 0.5887\gamma_{cm} \end{matrix} \right ) = \left ( \begin{matrix} 0.5504 \\ -0.4141 \\ -0.3148 \\ -0.1129 \end{matrix} \right )[/math]

[math]\vec {P_{tot}}^{\prime} = (p_{ex}^{\prime} + p_{px}^{\prime} + p_{\pi^-x}^{\prime})\hat{x} + (p_{ey}^{\prime} + p_{py}^{\prime} + p_{\pi^-y}^{\prime})\hat{y} + (p_{ez}^{\prime} + p_{pz}^{\prime} + p_{\pi^-z}^{\prime})\hat{z} = -0.1197 \hat{x} + 0.0476 \hat{y} - 0.7667 \hat{z} [/math]

Missing Mass
Table
file 27141(energy=5.7GeV, B>0, ND3) event number missing mass(W)
3114490 1.24007
3114802 0.983069
3116718 0.868544
3116940 1.14841
3118561 0.949136
3118771 0.877746
3120003 1.00759
3120133 1.18326
3120266 1.24695
3121495 0.977593
3122514 0.902853
3122695 1.25198
3122705 1.22147
3122989 1.05754
3123206 0.81068
3124104 0.948446
3124352 1.12121
3124590 1.21016
3124638 1.14262
3124941 0.990202
3125075 1.08905
3125102 1.19703


Conservation of the 4-momentum gives us following

[math](P_e)^\mu + (P_p)^\mu = ({P_e}^{\prime})^\mu + ({P_X}^{\prime})^\mu + ({P_{\pi^-}}^{\prime})^\mu[/math]
[math](P_e)_\mu + (P_p)_\mu = ({P_e}^{\prime})_\mu + ({P_X}^{\prime})_\mu + ({P_{\pi^-}}^{\prime})_\mu[/math]


Solving it for the final proton state

[math]W^2 = ({P_X}^{\prime})_\mu({P_X}^{\prime})^\mu = [(P_e)_\mu + (P_p)_\mu - ({P_e}^{\prime})_\mu - ({P_{\pi^-}}^{\prime})_\mu][(P_e)^\mu + (P_p)^\mu - ({P_e}^{\prime})^\mu - ({P_{\pi^-}}^{\prime})^\mu][/math]


In our case 4-vectors for particles are

[math](P_e)_\mu = ( 4.2, 0, 0, 4.2 GeV)[/math]
[math](P_p)_\mu = (m_p, 0, 0, 0)[/math]
[math]({P_e}^{\prime})_\mu = (0.5029, -0.0183, -0.2849, 0.414 )[/math]
[math]({P_p}^{\prime})_\mu = (1.4185, 0.3127, 0.6473, 0.7845)[/math]
[math]({P_{\pi^-}}^{\prime})_\mu = (0.7979, -0.4141, -0.3148, 0.5887)[/math]

Plug and chug

[math]W^2 = [(4.2,0,0,4.2) + ( m_p, 0, 0, 0 ) - ( 0.5029, -0.0183, -0.2849, 0.414 ) - (0.7979, -0.4141, -0.3148, 0.5887)[/math]] [[math]\left (\begin{matrix} 4.2 \\ 0 \\ 0 \\ 4.2 \end{matrix} \right )[/math] + [math]\left (\begin{matrix} m_p \\ 0 \\ 0 \\ 0 \end{matrix} \right) [/math] - [math]\left (\begin{matrix} 0.5029 \\ -0.0183 \\ -0.2849 \\ 0.414 \end{matrix} \right) [/math] - [math]\left ( \begin{matrix} 0.7979 \\ -0.4141 \\ -0.3148 \\ 0.5887 \end{matrix} \right) ] = 3.9 GeV^2[/math]


[math]W = 1.97 GeV[/math]


From [math]\vec{e}p \rightarrow n \pi^+[/math] from CLAS
[math]{M_x}^2 = ((k_i + p_i) - (k_f + q_{\pi^-}))[/math]

where [math]k_i[/math] and [math]k_f[/math] - are the 4-momentum of the incident and final electron, [math]p_i[/math] - the 4-momentum of the target(proton), [math]q_{\pi^-}[/math] - the 4-vector of the [math]\pi^-[/math].

Write equation for[math] \phi_{\pi}^{CM}[/math] in terms of Lab frame Momentum and energy.

Graph [math]\phi_{\pi}^{CM}[/math] for Pions hitting paddle #7. The y-axis should be pion counting rate in units of pions per nanCoulomb.

Pion Rates -vs- Paddle for opposite sign Torus fields

using all events in which the first particle (the one which caused the trigger) is defined as an electrons and passes the

above electron cuts.

sc_paddle vs X_bjorken 5.7 GeV Beam Energy
no cuts cuts no cuts cuts
Electrons B > 0 B<0
Electrons sc paddle vs X dst 27095 without cuts.gif Electrons sc paddle vs X dst 27095 with cuts.gif Electrons sc paddle vs X dst 26988 without cuts.gif Electrons sc paddle vs X dst 26988 with cuts.gif
[math]\pi^-[/math] B > 0 B<0
Pions^- sc paddle vs X dst 27095 without cuts.gif Pions^- sc paddle vs X dst 27095 with cuts.gif Pions^- sc paddle vs X dst 26988 without cuts.gif Pions^- sc paddle vs X dst 26988 with cuts.gif
[math]\pi^+[/math] B > 0 B<0
Pions^plus sc paddle vs X dst 27095 without cuts.gif Pions^plus sc paddle vs X dst 27095 with cuts.gif Pions^plus sc paddle vs X dst 26988 without cuts.gif Pions^plus sc paddle vs X dst 26988 with cuts.gif
sc_paddle vs X_bjorken with cuts 5.7 GeV Beam Energy(number of events=2)
[math]\pi^-[/math] [math]\pi^-[/math]
B>0 B<0
Pions^- sc paddle vs X dst 27095 with cuts num events 2.gif Pions^- sc paddle vs X dst 26988 with cuts num events 2.gif
[math]\pi^+[/math] [math]\pi^+[/math]
B>0 B<0
Pions^plus sc paddle vs X dst 27095 with cuts num events 2.gif Pions^plus sc paddle vs X dst 26988 with cuts num events 2.gif
sc_paddle vs Momentum 5.7 GeV Beam Energy
There is a curvature problem.  When B > 0 then I expect the high momentum electrons to hit the lower
paddle numbers   (inbending).   I can see this when I look at the B>0 plot for electrons with cuts.  
When B < 0 then the electrons  are bending outwards which makes me expect the the higher momentum
electrons will high the higher numbered paddles.  I do not see this for B>0 with electron cuts.
no cuts cuts no cuts cuts
Electons B > 0 B<0
Electrons sc paddle vs momentum dst 27095 without cuts.gif Electrons sc paddle vs momentum dst 27095 with cuts.gif Electrons sc paddle vs momentum dst 26988 without cuts.gif Electrons sc paddle vs momentum dst 26988 with cuts.gif
[math]\pi^-[/math] B > 0 B<0
Pions^- sc paddle vs momentum dst 27095 without cuts.gif Pions^- sc paddle vs momentum dst 27095 with cuts.gif
 Pions^- sc paddle vs momentum dst 26988 without cuts.gif Pions^- sc paddle vs momentum dst 26988 with cuts.gif
[math]\pi^+[/math] B > 0 B<0
Pions^plus sc paddle vs momentum dst 27095 without cuts.gif Pions^plus sc paddle vs momentum dst 27095 with cuts.gif
 Pions^plus sc paddle vs momentum dst 26988 without cuts.gif Pions^plus sc paddle vs momentum dst 26988 with cuts.gif
sc_paddle vs Momentum with cuts 5.7 GeV Beam Energy(number of events=2)
[math]\pi^-[/math] [math]\pi^-[/math]
B>0 B<0
Pions^- sc paddle vs momentum dst 27095 with cuts num events 2.gif Pions^- sc paddle vs momentum dst 26988 with cuts num events 2.gif
[math]\pi^+[/math] [math]\pi^+[/math]
B>0 B<0
Pions^plus sc paddle vs momentum dst 27095 with cuts num events 2.gif Pions^plus sc paddle vs momentum dst 26988 with cuts num events 2.gif


Used file dst26988_05.B00(Energy=5.7GeV and Torus=-2250)

F cup dst26988 05.gif F cup int dst26988 05.gif Number of pions dst26988 05.gif

Electrons X -vs - paddle number when pion hits paddle 6
Now ask which paddle the electrons hit as a function of X bjorken when we require
 that the pion hits paddle #6.
Paddle 7 Rates and statistics

The number of events per trigger is measured for the respective DST file above and then the Total number events in the data set is estimated from that.

[math]X_{bj}[/math] [math]\pi^-[/math](B>0) [math]\pi^+[/math](B<0)
Total Number Events [math](10^{3})[/math] Number events per [math]10^6[/math] triggers Total Number Events [math](10^{3})[/math] Number events per [math]10^6[/math] trigger
0.1 5.1 71 24.6 547
0.2 6.9 96 13.7 305
0.3 3.7 51 6.2 137
0.4 3.3 45 2.7 60
0.5 0.9 13 0.99 22
Paddle 17 Rates and statistics
[math]X_{bj}[/math] [math]\pi^-[/math](B<0) [math]\pi^+[/math](B>0)
Total Number Events [math](10^{3})[/math] Number events per [math]10^{6}[/math] trigger Total Number Events [math](10^{3})[/math] Number events per [math]10^{6}[/math] trigger
0.1 6.2 137 4.6 64
0.2 3.5 79 4.9 67
0.3 1.7 39 2.6 36
0.4 0.3 7 2.1 29
0.5 0.1 2 0.6 8
Paddle 5 and 8 Rates and statistics for electrons
[math]X_{bj}[/math] [math]e^-[/math] sc_paddle=5 (B>0) [math]e^-[/math] sc_paddle=8 (B<0)
Total Number Events [math](10^{3})[/math] Number events per [math]10^{6}[/math] trigger [math](10^{3})[/math] Total Number Events [math](10^{3})[/math] Number events per [math]10^{6}[/math] trigger [math](10^{4})[/math]
0.1 384.9 5.314 1665.2 3.706
0.2 382.5 5.282 977.8 2.176
0.3 264.9 3.657 567.1 1.262
0.4 159.5 2.202 328.6 0.7313
0.5 99 1.367 218.2 0.4856
Histograms for 5.7 GeV Beam Energy
Electron energy/momentum Electron Theta ([math]\theta[/math]) Electron Qsqrd Electron X_bjorken
B>0 and sc_paddle=5
Electrons energy momentum dst 27095 with cuts.gif Electrons theta dst 27095 with cuts.gif Electrons Qsqrd dst 27095 with cuts.gif Electrons X bjorken dst 27095 with cuts.gif
B<0 and sc_paddle=8
Electrons energy momentum dst 26988 with cuts.gif Electrons theta dst 26988 with cuts.gif Electrons Qsqrd dst 26988 with cuts.gif Electrons X bjorken dst 26988 with cuts.gif
Normalized X_bjorken for electrons
B>0 and sc_paddle=5 B<0 and sc_paddle=8
X bjorken electrons with cuts sc paddle 5 dst27095.gif X bjorken electrons with cuts sc paddle 8 dst26988.gif
Pion Momentum
Pion Scattering Angle
Pion scint paddle number

Make plots using your new analysis code of [math]\phi[/math]

Asymmetries

Systematic Errors

Media:SebastianSysErrIncl.pdf Sebastian's Writeup

Retrieved from "https://wiki.iac.isu.edu/index.php?title=Analysis&oldid=20098"