DeltaDoverD Progress

9/5/08

SIDIS Analysis

a.) Cross-Section comparison

i.) Calculate absolute cross section for [math]\displaystyle{ \cos(\theta_{pi}) }[/math] = 0.5, 1 < Q^2 < 4 GeV^2 , W = 1.45 +/- 0.2 GeV

[math]\displaystyle{ {\sigma} = \frac{1}{ L_{int}}dN = \frac{35}{3.3 \times 10^{34}} \times cm^2 = 10.61 \times10^{-34} \times 10^{24} \times [barn] = 1.061 \times 10^{-3} [\mu barn] }[/math]

Luminosity Calculation

ii.) Plot [math]\displaystyle{ \phi_{diff}^{CM} }[/math]-vs-[math]\displaystyle{ cos{\theta}_{\pi}^{LAB} }[/math] when [math]\displaystyle{ cos{\theta}_{e}^{CM} }[/math] = -0.3 also plot [math]\displaystyle{ \phi_{diff}^{CM} }[/math]-vs- [math]\displaystyle{ cos{\theta}_{e}^{LAB} }[/math]

As one can see from histograms of the pion_theta_angle_vs_phi_angle_in_CM_Frame and the electron_theta_angle_vs_phi_angle_in_CM_Frame, the pion and electron acceptance in the region of [math]\displaystyle{ \phi_{diff}^{CM}=180 }[/math] is nearly zero(significantly low).

electron sector	pion_theta_angle_vs_phi_angle_in_CM_Frame_after_cuts(EC_inner>0.06, EC_tot/p>0.2, nphe>2.5, [math]\displaystyle{ 0.9<M_x<1.1 }[/math], [math]\displaystyle{ 1.1<W<1.5 }[/math] )	electron_theta_angle_vs_phi_angle_in_CM_Frame_after_cuts(EC_inner>0.06, EC_tot/p>0.2, nphe>2.5, [math]\displaystyle{ 0.9<M_x<1.1 }[/math], [math]\displaystyle{ 1.1<W<1.5 }[/math] )
1
2
3
4
5
6

[math]\displaystyle{ Q^2 }[/math]_vs_[math]\displaystyle{ \phi_{diff}^{CM} }[/math] plot shows that the [math]\displaystyle{ Q^2 }[/math] cut should not make much difference on [math]\displaystyle{ \phi_{diff}^{CM} }[/math] plot. The cut around [math]\displaystyle{ 1 GeV^2 < Q^2< 2 GeV^2 }[/math] should reduce the number of pions around 0 and 360 of phi angle.

9/19/08

SIDIS Analysis

a.) Cross-Section comparison

i.) Calculate absolute cross section for [math]\displaystyle{ \cos(\theta_{pi}) }[/math] = 0.5, 1 < Q^2 < 4 GeV^2 , W = 1.45 +/- 0.2 GeV

[math]\displaystyle{ \frac{d \sigma}{d \Omega^*_{\pi}} = \frac{1.061 \times 10^{-3} [\mu barn]}{0.88} = 0.0012 \ne 2.4 }[/math]?

Documentation

The five-fold differential cross section for single pion production is equal to the following:

[math]\displaystyle{ \frac{\partial^5 \sigma}{\partial E_f \partial \Omega_e \partial {\Omega_{\pi}}^*} = \frac{1}{2 \pi} \Sigma \frac{1}{L_{int} A_{cc} \epsilon_{CC} \Delta W \Delta Q^2 \Delta cos {\theta_{\pi}}^* {\phi_{\pi}}^*} \frac{d(W, Q^2)}{d(E_f, cos \theta_e)} }[/math]

The Jacobian term can be given as:

[math]\displaystyle{ \frac{d(W, Q^2)}{d(E_f, cos \theta_e)} = \frac{2 M_p E_i E_f}{W} }[/math]

[math]\displaystyle{ \frac{\partial^5 \sigma}{\partial E_f \partial \Omega_e \partial {\Omega_{\pi}}^*} = \Gamma_{v}\times \frac{d^2 \sigma}{d {\Omega_{\pi}}^*} }[/math]

where [math]\displaystyle{ \Gamma_{v} }[/math] is the virtual photon flux and can be written as

[math]\displaystyle{ \Gamma_{v} = \frac{\alpha}{2 \pi^2 Q^2} \frac{(W^2 - {M_p}^2)E_f}{2M_p E_e} \frac{1}{1-\epsilon} }[/math]

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

The reason of having low cross section might be binning

In paper they use the following number of bins:

Variable	Num. Bin	Range	Bin Size
W	27	1.15 - 1.7 GeV	20 MeV
[math]\displaystyle{ Q^2 }[/math]	7	1.1 - 5.0 [math]\displaystyle{ GeV^2 }[/math]	variable
[math]\displaystyle{ cos {\theta_{\pi}}^* }[/math]	10	-1.0 - 1.0	0.2
[math]\displaystyle{ {\phi_{\pi}}^* }[/math]	24	-180. - 180	15

Number of bins in my case were 360.

Number of bins equal is ~24

When i applied [math]\displaystyle{ 1.6<Q^2<1.84 }[/math] cut, the number of entries were reduced to 152.

In paper they use liquid-hydrogen unpolarized target(we have NH3 and ND3 polarized). The polarized electron beam current is 8 nA(in our case it is about 6 nA). and luminosity is different too. It also depends on statistics.

ii.) What is smallest angular coverage of EC (8 degrees?) Determine phi region where there is no acceptance ( where should we stop plotting data)?

iii.) Asymmetry Calculation

a.) Beam Asymmetry Plot

In order to plot Beam Asymmetry we need to plot for the first time the histogram of the invariant_mass_vs_cross_section. Then determine the structure function fitting the cross section and calculating the beam asymmetry function which is given as :

[math]\displaystyle{ A_{TL^'} = \sqrt{2\epsilon (1 - \epsilon)} \sigma_{LT^'} \times sin{\phi_{\pi}}^* }[/math]

for given cos(theta) of the pion in cm, Q^2 and W invariant mass.

Choose kinematics ( a single theta and phi point )to max our stats and comparison to paper Histogram the following

1. Number of e-pi coincidence events, number of FC counts
2. Number of e-pi coincidence events/FC counts
3. Number of e-pi coincidence events/FC count/Pt

for groups of runs with h_e,P_t = ++, +-, -+, --

table with 4 columns of h_e, P_t and 3 rows of the above histograms

9/26/08

SIDIS Analysis

1.) make semi-inclusive spectrum:

a.) h>0 Pt>0 b.) h > 0 pt<0 c.)h<0 pt>0 d.)h<0 pt<0

2.) ad up opposite target polarization histograms

3.) subtract h> 0 and h<0

helflag = 1 =>

helflag = 2 =>

helflag = 3 =>

helflag = 4 =>

Phi_angle_CM vs Asymmetry

Compared data(there is no table for asymmetry values like cross section):

11/21/08

0.) insert run summarry table, Pb, Pt, PB*Pt, Btorus

1.) make semi-inclusive spectrum:

a.) h>0 Pt>0

b.) h > 0 pt<0

c.)h<0 pt>0

d.)h<0 pt<0

2.) helicity difference plots for Pt>0 and Pt<0

3.) Asym plots for Pt>0 and Pt< 0

4.) unpolarized target asymmetry

Rebin asymmetry hisograms and combine the two into a total asymmetry histogram

Run Summary Table

The table below should have run ranges with 
[math]\displaystyle{ P_b*P_t \pm \Delta (P_b *P_t) }[/math] according 
to the elastic asymmetry measurements stored at
http://www.jlab.org/Hall-B/secure/eg1/EG2000/eg1b_analysis_progress.htm.

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

5.73 in
pos = 0.45743 +/- 0.04269
neg = -0.38816 +/- 0.04556

5.73 out
pos = 0.46604 +/- 0.03496
neg = -0.50684 +/- 0.03578

Start Run Number	Beam Polarization(Pb)	Target Polarization(Pt) from dstdump file	Pb*Pt	Beam Torus	Beam Energy (MeV)
26998	0	-0.69	0.46604	-2250	5736
26996	-0.71	-0.69	0.46604	-2250	5736
26995	-0.71	-0.69	0.46604	-2250	5736
26994	-0.71	-0.73	0.46604	-2250	5736
26993	-0.71	-0.72	0.46604	-2250	5736
26992	-0.71	-0.73	0.46604	-2250	5736
26991	-0.71	-0.75	0.46604	-2250	5736
26990	-0.71	-0.76	0.46604	-2250	5736
26989	0.71	-0.67	-0.38816	2250	5736
26988	0.71	-0.68	-0.38816	2250	5736
26987	0.71	-0.67	-0.38816	2250	5736
26986	0.71	-0.68	-0.38816	2250	5736
26985	0.71	-0.68	-0.38816	2250	5736
26984	0.71	-0.68	-0.38816	2250	5736
26983	0.71	-0.68	-0.38816	2250	5736
26981	0.71	-0.68	-0.38816	2250	5736
26980	0.71	-0.7	-0.38816	2250	5736
26979	0.71	-0.71	-0.38816	2250	5736
26966	0.71	0.74	0.45743	2250	5736
26965	0.71	0.74	0.45743	2250	5736
26964	0.71	0.74	0.45743	2250	5736
26963	0.71	0.74	0.45743	2250	5736
26962	0.71	0.74	0.45743	2250	5736
26961	0.71	0.75	0.45743	2250	5736
26960	0.71	0.76	0.45743	2250	5736
26959	0.71	0.69	0.45743	2250	5736
26958	0.71	0.69	0.45743	2250	5736
26957	0.71	0.69	0.45743	2250	5736
26956	0.71	0.69	0.45743	2250	5736
26955	0.71	0.69	0.45743	2250	5736
26954	0.71	0.69	0.45743	2250	5736
26953	0.71	0.69	0.45743	2250	5736
26952	0.71	0.7	0.45743	2250	5736
26951	0.71	0.7	0.45743	2250	5736
26948	0.71	0.7	0.45743	2250	5736
26947	0.71	0.7	0.45743	2250	5736
26946	0.71	0.7	0.45743	2250	5736
26945	0.71	0.7	0.45743	2250	5736
26943	0.7	0.7	0.45743	2250	5736
26942	0.7	0.7	0.45743	2250	5736
26941	0.7	0.7	0.45743	2250	5736
26940	0.7	0.7	0.45743	2250	5736
26939	0.7	0.7	0.45743	2250	5736
26938	0.7	0.7	0.45743	2250	5736
26937	0.7	0.7	0.45743	2250	5736
26934	0.7	0.7	0.45743	2250	5736
26933	0.7	0.71	0.45743	2250	5736
26932	0.7	0.71	0.45743	2250	5736
26931	0.7	0.71	0.45743	2250	5736
26930	0.7	0.71	0.45743	2250	5736
26929	0.7	0.71	0.45743	2250	5736
26928	0.7	0.72	0.45743	2250	5736
26927	0.7	0.72	0.45743	2250	5736
26926	0.7	0.73	0.45743	2250	5736
26925	0.7	0.73	0.45743	2250	5736
27074	0.71	-0.81	-0.38816	2250	5736
27075	0.71	-0.77	-0.38816	2250	5736
27076	0.71	-0.74	-0.38816	2250	5736
27077	0.71	-0.74	-0.38816	2250	5736
27078	071	-0.75	-0.38816	2250	5736
27079	0.71	-0.72	-0.38816	2250	5736
27100	0.71	0.76	0.45743	2250	5736
27101	0.71	0.76	0.45743	2250	5736
27102	0.71	0.73	0.45743	2250	5736
27105	0.61	0.73	0.45743	2250	5736
27106	0.61	0.73	0.45743	2250	5736
27107	0.61	-0.71	-0.38816	2250	5736
27108	0.61	-0.7	-0.38816	2250	5736
27109	0.61	-0.7	-0.38816	2250	5736
27111	0.61	-0.71	-0.38816	2250	5736
27112	0.61	-0.69	-0.38816	2250	5736
27114	0.61	0		2250	5736
27116	-0.58	0.2	-0.38816	2250	5736
27124	-0.7	0.24	-0.38816	2250	5736
27125	-0.7	0.25	-0.38816	2250	5736
27126	-0.7	0.26	-0.38816	2250	5736
27127	-0.7	0.26	-0.38816	2250	5736
27128	-0.7	0.26	-0.38816	2250	5736
27129	-0.7	0.26	-0.38816	2250	5736
27131	-0.7	0.26	-0.38816	2250	5736
27132	-0.7	0.26	-0.38816	2250	5736
27133	-0.7	0.26	-0.38816	2250	5736
27134	-0.7	0.26	-0.38816	2250	5736
27135	-0.7	0.26	-0.38816	2250	5736
27136	-0.7	0.26	-0.38816	2250	5736
27137	-0.7	0.25	-0.38816	2250	5736
27138	-0.7	0.25	-0.38816	2250	5736
27139	-0.7	0.25	-0.38816	2250	5736
27141	-0.7	0.25	-0.38816	2250	5736
27142	-0.7	0.25	-0.38816	2250	5736
27143	-0.7	0.25	-0.38816	2250	5736
27145	-0.7	0.24	-0.38816	2250	5736
27146	-0.7	0.24	-0.38816	2250	5736
27148	-0.7	0.24	-0.38816	2250	5736
27149	-0.7	-0.09	0.45743	2250	5736
27150	-0.7	-0.12	0.45743	2250	5736
27152	-0.64	-0.18	0.45743	2250	5736
27153	-0.64	-0.19	0.45743	2250	5736
27154	-0.64	-0.19	0.45743	2250	5736
27155	-0.64	-0.19	0.45743	2250	5736
27156	-0.64	-0.19	0.45743	2250	5736
27157	-0.64	-0.19	0.45743	2250	5736
27160	-0.64	-0.18	0.45743	2250	5736
27161	-0.64	-0.18	0.45743	2250	5736
27162	-0.64	-0.19	0.45743	2250	5736
27163	-0.64	-0.19	0.45743	2250	5736
27165	-0.64	-0.19	0.45743	2250	5736
27166	-0.64	0.18	-0.38816	2250	5736
27167	-0.64	0.22	-0.38816	2250	5736
27168	-0.64	0.23	-0.38816	2250	5736
27169	-0.64	0.23	-0.38816	2250	5736
27170	-0.64	0.23	-0.38816	2250	5736
27171	-0.64	0.23	-0.38816	2250	5736
27172	-0.64	-0.35	0.45743	2250	5736
27175	-0.7	-0.78	0.45743	2250	5736
27176	-0.7	-0.72	0.45743	2250	5736
27177	-0.7	-0.7	0.45743	2250	5736
27178	-0.7	-0.69	0.45743	2250	5736
27179	-0.7	-0.67	0.45743	2250	5736
27180	-0.7	-0.67	0.45743	2250	5736
27181	-0.7	-0.66	0.45743	2250	5736
27182	-0.7	-0.72	0.45743	2250	5736
27183	-0.7	-0.68	0.45743	2250	5736
27184	-0.7	-0.63	0.45743	2250	5736
27186	-0.7	0.72	-0.38816	2250	5736
27187	-0.7	0.71	-0.38816	2250	5736
27188	-0.7	0.71	-0.38816	2250	5736
27189	-0.7	0.7	-0.38816	2250	5736
27190	-0.7	0.69	-0.38816	2250	5736
27191	-0.7	0.69	-0.38816	2250	5736
27192	-0.7	0.68	-0.38816	2250	5736
27193	-0.7	0.69	-0.38816	2250	5736
27194	-0.7	0.7	-0.38816	2250	5736
27195	-0.7	0.69	-0.38816	2250	5736
27113	0.61	0.68	0.45743	2250	5736

Phi_Angle_CM_Frame for Positive and Negative Target Polarization

Helcode #	Negative Target Polarization	Positive Target Polarization
1 h>0
2 h<0
3
4

Helicity Difference Plots for Pt>0 and Pt<0

Helicity Difference	Negative Target Polarization	Positive Target Polarization
h1-h4
h3-h2

5-01-2009

Target and Beam Polarization are positive

Helcode #	Negative Beam Torus	Positive Beam Torus
1 h>0
2 h<0
3
4

Target Polarization Positive and Beam Polarization Negative

Helcode #	Negative Beam Torus	Positive Beam Torus
1 h>0	No Data
2 h<0	No Data
3	No Data
4	No Data

Inclusive Histograms For Invariant Mass

Invariant Mass Histograms for Each Sector

All helicities

Helcode=1

3/20/09

1.) plot Wdiff

2.) plot PE using Osipenko/Josh cuts

06/6/09

Invariant Mass

Difference of Invariant Mass for two differnet cuts:

Run Number	EC Cuts+ requiring pion	OSI Cuts	EC Cuts
26991

On x-axis of FC difference between the "+" heliciy FC  and the "-" helicity FC.

Run Number	W difference	FC difference	End of Run sum [math]\displaystyle{ \equiv \frac {\sum_i(FC(i)^+) - \sum(FC(i)^-)}{\sum (FC(i)^+) + \sum(FC(i)^-)}) }[/math]
26991		File:FC difference RunNumber26991 OSICuts.gif	0.00354260538 [math]\displaystyle{ \pm }[/math] 0.00000044134
26994			0.00367 [math]\displaystyle{ \pm }[/math] 0.000000474
26993			0.002559223 [math]\displaystyle{ \pm }[/math] 0.000000502
26992			0.003781 [math]\displaystyle{ \pm }[/math] 0.00000047529
26990			0.00331986321 [math]\displaystyle{ \pm }[/math] 0.00000057926
26989			0.00303841557 [math]\displaystyle{ \pm }[/math] 0.00000064228
26988			0.00380169243 [math]\displaystyle{ \pm }[/math] 0.00000048178
26987			0.00280163240 [math]\displaystyle{ \pm }[/math] 0.00000091842
26986			0.00352882616 [math]\displaystyle{ \pm }[/math] 0.00000048897
26979
26965			0.00454140439 [math]\displaystyle{ \pm }[/math] 0.00000094242
26964			0.00509434283 [math]\displaystyle{ \pm }[/math] 0.00000097001
26963			0.00405285155 [math]\displaystyle{ \pm }[/math] 0.00000099233
26961			0.00507456102 [math]\displaystyle{ \pm }[/math] 0.00000113268
26959			0.00523761694 [math]\displaystyle{ \pm }[/math] 0.00000088674
26958			0.00444205478 [math]\displaystyle{ \pm }[/math] 2031209
26956			0.00504401620 [math]\displaystyle{ \pm }[/math] 0.00000080302
26955			0.00559913829 [math]\displaystyle{ \pm }[/math] 0.00000081312
26954			0.00494690728 [math]\displaystyle{ \pm }[/math] 0.00000083304
26953			0.00562598448 [math]\displaystyle{ \pm }[/math] 0.00000093125
26952			0.00485295834 [math]\displaystyle{ \pm }[/math] 0.00000066879
26951			0.00545485906 [math]\displaystyle{ \pm }[/math] 0.00000097177
26947			0.00465697160 [math]\displaystyle{ \pm }[/math] 0.00000052377
26945			-0.00556456389 [math]\displaystyle{ \pm }[/math] 0.00000077272
26943			-0.00656109472 [math]\displaystyle{ \pm }[/math] 0.00000094910
26942			-0.00669169106 [math]\displaystyle{ \pm }[/math] 0.00000093245
26941			-0.00676460417 [math]\displaystyle{ \pm }[/math] 0.00000048435
26940			-0.00643597022 [math]\displaystyle{ \pm }[/math] 0.00000078091
26939			-0.00650047456 [math]\displaystyle{ \pm }[/math] 0.00000078964
26938			-0.00632630313 [math]\displaystyle{ \pm }[/math] 0.00000079735
26937			-0.00533169794 [math]\displaystyle{ \pm }[/math] 0.00000080405
26934			-0.00601497156 [math]\displaystyle{ \pm }[/math] 0.00000080950
26933			-0.00586540500 [math]\displaystyle{ \pm }[/math] 0.00000080085
26932			-0.00587687192 [math]\displaystyle{ \pm }[/math] 0.00000076534
26931			-0.00630232566 [math]\displaystyle{ \pm }[/math] 0.00000089411
26930			-0.00684205010 [math]\displaystyle{ \pm }[/math] 0.00000095069
26929			-0.00521666944 [math]\displaystyle{ \pm }[/math] 0.00000096755
26928			-0.00682185316 [math]\displaystyle{ \pm }[/math] 0.00000094444
26927			-0.00599647483 [math]\displaystyle{ \pm }[/math] 0.00000094626
26926			-0.00649932378 [math]\displaystyle{ \pm }[/math] 0.00000067845
26925			-0.00575464099 [math]\displaystyle{ \pm }[/math] 0.00000093666
27079			-0.01025869470 [math]\displaystyle{ \pm }[/math] 0.00000215745
27078			-0.01128036266 [math]\displaystyle{ \pm }[/math] 0.00000182450
27075			-0.01037443017 [math]\displaystyle{ \pm }[/math] 0.00000178719
27109			-0.00876887465 [math]\displaystyle{ \pm }[/math] 0.00000232599
27107			0.01044530752 [math]\displaystyle{ \pm }[/math] 0.00000191625
27116			0.00173242954 [math]\displaystyle{ \pm }[/math] 0.00000380546
27112			-0.01142682761 [math]\displaystyle{ \pm }[/math] 0.00000251199
27111			-0.00872760886 [math]\displaystyle{ \pm }[/math] 0.00000179327
27128			0.00193441756 [math]\displaystyle{ \pm }[/math] 0.00000189649
27127			0.00215712098 [math]\displaystyle{ \pm }[/math] 0.00000191150
27124			0.00309070808 [math]\displaystyle{ \pm }[/math] 0.00000199918
27139			-0.00288862444 [math]\displaystyle{ \pm }[/math] 0.00000288144
27138			-0.00061608634 [math]\displaystyle{ \pm }[/math] 0.00000229669
27137			-0.00275066778 [math]\displaystyle{ \pm }[/math] 0.00000184982
27136			-0.00239423237 [math]\displaystyle{ \pm }[/math] 0.00000185134
27134			-0.00355581434 [math]\displaystyle{ \pm }[/math] 0.00000168285
27133			-0.00252193724 [math]\displaystyle{ \pm }[/math] 0.00000190408
27132			0.00096332202 [math]\displaystyle{ \pm }[/math] 0.00000197909
27143			-0.00210486278 [math]\displaystyle{ \pm }[/math] 0.00000322339
27141			-0.00301990556 [math]\displaystyle{ \pm }[/math] 0.00000253085
27160			0.00171264744
27161			0.00224287304
27162			0.00118844445
27166			0.00077237006
27167			0.00216041281
27168			0.00083650625
27170			0.00151247511
27175			-0.01217485668
27176			-0.01049635167
27177			-0.01147445288
27179			-0.01025340153
27180			-0.00868272418
27181			-0.00973324188
27182			-0.00983862460
27183			-0.01901615252
27186			0.01079090635
27187			0.01155519076
27188			0.01086898605

NPHE

To find out pion contamination in the electron sample i used Osipenko geometrical cuts. The number of photoelectrons before and after osipenko cuts are shown below:

No cuts	OSI Cuts
The number of photoelectrons without cuts	The number of photoelectrons with OSI cuts

For different fits:

The number of photoelectrons after OSICuts with two Gaussian fits

The number of photoelectrons after OSICuts with Landau+Gaussian fits

Pion Contamination

No cuts	OSI Cuts (Gauss(0)+Landau(3)+Gauss(6))	OSI Cuts (Gauss(0)+Gauss(3))	OSICuts + NPHE>2.5 (Gauss)
The number of photoelectrons without cuts	The number of photoelectrons with OSI cuts(gauss+landau+gauss)	The number of photoelectrons with OSI cuts two gaussian fits	The number of photoelectrons with OSI+NPHE cuts

OSICuts (Gauss(0)+Landau(3)+Gauss(6))

Assuming that the two gaussians represent number of photoelectrons and landau number of photons produced by high energy pions, the ratio of number of pions over the sum of electrons and pion in the electron candidate sample can be calculated in the following way:

OSIcut

[math]\displaystyle{ Pion Contamination = }[/math]
[math]\displaystyle{ = \frac {Integral(landau(3))}{Integral(gauss(0) + landau(3) + gauss(6))} = }[/math]
[math]\displaystyle{ = \frac{1.643 \times 10^9}{ 7.682 \times 10^9 + 1.643 \times 10^9 + 7.732 \times 10^9} = }[/math]
[math]\displaystyle{ = 9.6324 % }[/math]

OSICut+NPHE>2.5

[math]\displaystyle{ Pion Contamination = }[/math]
[math]\displaystyle{ = \frac {Integral(landau(3))}{Integral(gauss(0) + landau(3) + gauss(6))} = }[/math]
[math]\displaystyle{ = \frac{5.905 \times 10^8}{ 6.656 \times 10^9 + 5.905 \times 10^8 + 7.395 \times 10^9} = }[/math]
[math]\displaystyle{ = 4.03305% }[/math]

OSICuts (Gauss(0)+Gauss(3))

In case of only two gaussians, the number of photoelectrons produced by pions is described by Gauss(0) and the number of photoelectrons created by electrons is Gauss(3). Pion contamination is calculated below for both cases, without and with NPHE>2.5 cut.

OSICut

[math]\displaystyle{ Pion Contamination = }[/math]
[math]\displaystyle{ = \frac {Integral(gauss(0))}{Integral(gauss(0) + gauss(3))} = }[/math]
[math]\displaystyle{ = \frac{2.151 \times 10^8}{ 2.151 \times 10^8 + 1.594 \times 10^{10} } }[/math]
[math]\displaystyle{ = 1.3 % }[/math]

With NPHE>2.5 Cut

[math]\displaystyle{ Pion Contamination = 0 }[/math]

Number of Events after NPHE>2.5 Cut

[math]\displaystyle{ Number of Events after NPHE>2.5 Cut }[/math] =
[math]\displaystyle{ = \frac{2.978 \times 10^8}{3.496 \times 10^8} = }[/math]
[math]\displaystyle{ = 85.18 % }[/math]

Counts in FCup

[math]\displaystyle{ Ratio of Counts 24/13 = \frac{2.131 \times 10^6}{2.116 \times 10^6} = 1.007 }[/math]

6/12/09

1.) Improve Chi^2 in NPe fits.

2.) Calculate uncertainty in pion contamination measurement by changing mean and widths according to fit error.

3.) Pulse pair FC asymmetry, and End of Run accumulated FC asym.

pulse pair [math]\displaystyle{ \equiv \sum_i(\frac{FC(i)^+ - FC(i)^-}{FC(i)^+ + FC(i)^-}) }[/math]

End of Run sum [math]\displaystyle{ \equiv \frac {\sum_i(FC(i)^+) - \sum(FC(i)^-)}{\sum (FC(i)^+) + \sum(FC(i)^-)}) }[/math]

4.) Determine semi-inclusive statistic as function of X

Uncertainty in Pion Contamination

Maximum

[math]\displaystyle{ Pion Contamination = }[/math]
[math]\displaystyle{ = \frac {Integral(landau(3))}{Integral(gauss(0) + landau(3) + gauss(6))} = }[/math]
[math]\displaystyle{ = \frac{1.645 \times 10^9}{ 7.695 \times 10^9 + 1.645 \times 10^9 + 7.745 \times 10^9} = }[/math]
[math]\displaystyle{ = 9.6283 % }[/math]

[math]\displaystyle{ Pion Contamination = }[/math]
[math]\displaystyle{ = \frac {Integral(landau(3))}{Integral(gauss(0) + landau(3) + gauss(6))} = }[/math]
[math]\displaystyle{ = \frac{5.914 \times 10^8}{ 6.666 \times 10^9 + 5.914 \times 10^8 + 7.427 \times 10^9} = }[/math]
[math]\displaystyle{ = 4.02740 % }[/math]

Minimum

[math]\displaystyle{ Pion Contamination = }[/math]
[math]\displaystyle{ = \frac {Integral(landau(3))}{Integral(gauss(0) + landau(3) + gauss(6))} = }[/math]
[math]\displaystyle{ = \frac{1.642 \times 10^9}{ 7.67 \times 10^9 + 1.642 \times 10^9 + 7.719 \times 10^9} = }[/math]
[math]\displaystyle{ = 9.64124 % }[/math]

[math]\displaystyle{ Pion Contamination = }[/math]
[math]\displaystyle{ = \frac {Integral(landau(3))}{Integral(gauss(0) + landau(3) + gauss(6))} = }[/math]
[math]\displaystyle{ = \frac{5.895 \times 10^8}{ 6.645 \times 10^9 + 5.895 \times 10^8 + 7.401 \times 10^9} = }[/math]
[math]\displaystyle{ = 4.02788 % }[/math]

Delta_D_over_D