SIDIS CLASNOTE 2013 - Revision history

Foretony at 20:10, 3 June 2014

2014-06-03T20:10:14Z

← Older revision		Revision as of 20:10, 3 June 2014
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	http://www.jlab.org/Hall-B/secure/eg1/EG2000/nevzat/Analysis_Note_Thesis/Analysis_Note/LongDpaper_20130105/AnalysisNote/		http://www.jlab.org/Hall-B/secure/eg1/EG2000/nevzat/Analysis_Note_Thesis/Analysis_Note/LongDpaper_20130105/AnalysisNote/

	%=Abstract=		=Abstract=
	Semi-inclusive deep inelastic scattering (SIDIS) experiments may be used to identify the flavor of the quark that participates in the scattering process. Semi-inclusive scattering is defined as an electron scattering experiment in which the scattered electron and one hadron are detected in the final state. Experiments at Jefferson Lab have used longitudinally polarized electrons to probe longitudinally polarized hydrogen <math> \left ( {15 \atop\; }NH_{3} \right )</math> and deuterium <math> \left ( {15 \atop\; }ND_{3} \right )</math> targets and investigate the quark’s contribution to nucleon properties. This work reports on a measurement of SIDIS pion asymmetries using the CEBAF Large Acceptance Spectrometer (CLAS) at Thomas Jefferson National Accelerator Facility. The incident electron’s energy was 4.2 GeV and covered a kinematic region where the struck quark carries at least 30% of the nucleons total momentum (<math>x_B \le 0.3</math>). The electrons scatter mostly from valence quarks in this kinematic region allowing measurements which are less sensitive to the ocean of quark-antiquark pairs that are also inside a nucleon.		Semi-inclusive deep inelastic scattering (SIDIS) experiments may be used to identify the flavor of the quark that participates in the scattering process. Semi-inclusive scattering is defined as an electron scattering experiment in which the scattered electron and one hadron are detected in the final state. Experiments at Jefferson Lab have used longitudinally polarized electrons to probe longitudinally polarized hydrogen <math> \left ( {15 \atop\; }NH_{3} \right )</math> and deuterium <math> \left ( {15 \atop\; }ND_{3} \right )</math> targets and investigate the quark’s contribution to nucleon properties. This work reports on a measurement of SIDIS pion asymmetries using the CEBAF Large Acceptance Spectrometer (CLAS) at Thomas Jefferson National Accelerator Facility. The incident electron’s energy was 4.2 GeV and covered a kinematic region where the struck quark carries at least 30% of the nucleons total momentum (<math>x_B \le 0.3</math>). The electrons scatter mostly from valence quarks in this kinematic region allowing measurements which are less sensitive to the ocean of quark-antiquark pairs that are also inside a nucleon.

Foretony at 20:10, 3 June 2014

2014-06-03T20:10:03Z

← Older revision		Revision as of 20:10, 3 June 2014
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	sample TeX file for CLAS note		sample TeX file for CLAS note

	http://www.jlab.org/Hall-B/secure/eg1/EG2000/nevzat/Analysis_Note_Thesis/Analysis_Note/LongDpaper_20130105/AnalysisNote/		http://www.jlab.org/Hall-B/secure/eg1/EG2000/nevzat/Analysis_Note_Thesis/Analysis_Note/LongDpaper_20130105/AnalysisNote/

	=Abstract=		%=Abstract=
	Semi-inclusive deep inelastic scattering (SIDIS) experiments may be used to identify the flavor of the quark that participates in the scattering process. Semi-inclusive scattering is defined as an electron scattering experiment in which the scattered electron and one hadron are detected in the final state. Experiments at Jefferson Lab have used longitudinally polarized electrons to probe longitudinally polarized hydrogen <math> \left ( {15 \atop\; }NH_{3} \right )</math> and deuterium <math> \left ( {15 \atop\; }ND_{3} \right )</math> targets and investigate the quark’s contribution to nucleon properties. This work reports on a measurement of SIDIS pion asymmetries using the CEBAF Large Acceptance Spectrometer (CLAS) at Thomas Jefferson National Accelerator Facility. The incident electron’s energy was 4.2 GeV and covered a kinematic region where the struck quark carries at least 30% of the nucleons total momentum (<math>x_B \le 0.3</math>). The electrons scatter mostly from valence quarks in this kinematic region allowing measurements which are less sensitive to the ocean of quark-antiquark pairs that are also inside a nucleon.		Semi-inclusive deep inelastic scattering (SIDIS) experiments may be used to identify the flavor of the quark that participates in the scattering process. Semi-inclusive scattering is defined as an electron scattering experiment in which the scattered electron and one hadron are detected in the final state. Experiments at Jefferson Lab have used longitudinally polarized electrons to probe longitudinally polarized hydrogen <math> \left ( {15 \atop\; }NH_{3} \right )</math> and deuterium <math> \left ( {15 \atop\; }ND_{3} \right )</math> targets and investigate the quark’s contribution to nucleon properties. This work reports on a measurement of SIDIS pion asymmetries using the CEBAF Large Acceptance Spectrometer (CLAS) at Thomas Jefferson National Accelerator Facility. The incident electron’s energy was 4.2 GeV and covered a kinematic region where the struck quark carries at least 30% of the nucleons total momentum (<math>x_B \le 0.3</math>). The electrons scatter mostly from valence quarks in this kinematic region allowing measurements which are less sensitive to the ocean of quark-antiquark pairs that are also inside a nucleon.

Didbtama: /* Semi-Inclusive Asymmetries */

2013-06-20T22:07:14Z

Semi-Inclusive Asymmetries

← Older revision		Revision as of 22:07, 20 June 2013
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	The asymmetries from semi-inclusive pion electroproduction using proton or deuteron targets can be written in terms of the difference of the yield when the electron spin is parallel and antiparallel to the spin of the nucleon. There are four combinations of semi-inclusive asymmetries: <math>A_{NH_{3}}^{\pi^{+}}</math>, <math>A_{NH_{3}}^{\pi^{-}}</math>, <math>A_{ND_{3}}^{\pi^{+}}</math> and <math>A_{ ND_{3}}^{\pi^{-}}</math>		The asymmetries from semi-inclusive pion electroproduction using proton or deuteron targets can be written in terms of the difference of the yield when the electron spin is parallel and antiparallel to the spin of the nucleon. There are four combinations of semi-inclusive asymmetries: <math>A_{NH_{3}}^{\pi^{+}}</math>, <math>A_{NH_{3}}^{\pi^{-}}</math>, <math>A_{ND_{3}}^{\pi^{+}}</math> and <math>A_{ ND_{3}}^{\pi^{-}}</math>

	<math>A_{NH_{3}}^{\pi^{+}} \equiv \frac{\Sigma N_{NH_{3},\pi^{+}}^{\uparrow \uparrow} - \Sigma N_{NH_{3}, \pi^{+}}^{\uparrow \downarrow}}{\Sigma N_{NH_{3},\pi^{+}}^{\uparrow \uparrow} + \Sigma N_{NH_{3}, \pi^{+}}^{\uparrow \downarrow}}</math>		{\| border="0" style="background:transparent;" align="center"
			\|-
			\|<math>A_{NH_{3}}^{\pi^{+}} \equiv \frac{\Sigma N_{NH_{3},\pi^{+}}^{\uparrow \uparrow} - \Sigma N_{NH_{3}, \pi^{+}}^{\uparrow \downarrow}}{\Sigma N_{NH_{3},\pi^{+}}^{\uparrow \uparrow} + \Sigma N_{NH_{3}, \pi^{+}}^{\uparrow \downarrow}}</math>
			\|}

	<math>A_{NH_{3}}^{\pi^{-}} \equiv \frac{\Sigma N_{NH_{3},\pi^{-}}^{\uparrow \uparrow} - \Sigma N_{NH_{3}, \pi^{-}}^{\uparrow \downarrow}}{\Sigma N_{NH_{3},\pi^{-}}^{\uparrow \uparrow} + \Sigma N_{NH_{3}, \pi^{-}}^{\uparrow \downarrow}}</math>		{\| border="0" style="background:transparent;" align="center"
			\|-
			\|<math>A_{NH_{3}}^{\pi^{-}} \equiv \frac{\Sigma N_{NH_{3},\pi^{-}}^{\uparrow \uparrow} - \Sigma N_{NH_{3}, \pi^{-}}^{\uparrow \downarrow}}{\Sigma N_{NH_{3},\pi^{-}}^{\uparrow \uparrow} + \Sigma N_{NH_{3}, \pi^{-}}^{\uparrow \downarrow}}</math>
			\|}

	<math>A_{ND_{3}}^{\pi^{+}} \equiv \frac{\Sigma N_{ND_{3},\pi^{+}}^{\uparrow \uparrow} - \Sigma N_{ND_{3}, \pi^{+}}^{\uparrow \downarrow}}{\Sigma N_{ND_{3},\pi^{+}}^{\uparrow \uparrow} + \Sigma N_{ND_{3}, \pi^{+}}^{\uparrow \downarrow}}</math>		{\| border="0" style="background:transparent;" align="center"
			\|-
			\|<math>A_{ND_{3}}^{\pi^{+}} \equiv \frac{\Sigma N_{ND_{3},\pi^{+}}^{\uparrow \uparrow} - \Sigma N_{ND_{3}, \pi^{+}}^{\uparrow \downarrow}}{\Sigma N_{ND_{3},\pi^{+}}^{\uparrow \uparrow} + \Sigma N_{ND_{3}, \pi^{+}}^{\uparrow \downarrow}}</math>
			\|}

	<math>A_{ND_{3}}^{\pi^{-}} \equiv \frac{\Sigma N_{ND_{3},\pi^{-}}^{\uparrow \uparrow} - \Sigma N_{ND_{3}, \pi^{-}}^{\uparrow \downarrow}}{\Sigma N_{ND_{3},\pi^{-}}^{\uparrow \uparrow} + \Sigma N_{ND_{3}, \pi^{-}}^{\uparrow \downarrow}},</math>		{\| border="0" style="background:transparent;" align="center"
			\|-
			\|<math>A_{ND_{3}}^{\pi^{-}} \equiv \frac{\Sigma N_{ND_{3},\pi^{-}}^{\uparrow \uparrow} - \Sigma N_{ND_{3}, \pi^{-}}^{\uparrow \downarrow}}{\Sigma N_{ND_{3},\pi^{-}}^{\uparrow \uparrow} + \Sigma N_{ND_{3}, \pi^{-}}^{\uparrow \downarrow}},</math>
			\|}

	where <math>N_{NH_{3},\pi^{+},\pi^{-}}^{\uparrow \downarrow}</math>(<math>N_{NH_{3},\pi^{+},\pi^{-}}^{\uparrow \uparrow}</math>) and <math>N_{ND_{3},\pi^{+},\pi^{-}}^{\uparrow \downarrow}</math>(<math>N_{ND_{3},\pi^{+},\pi^{-}}^{\uparrow \uparrow}</math>) represent the number of <math>\pi^{+}</math> and <math>\pi^{-}</math> hadrons detected in the final state with the scattered electron when the spin of the initial electron beam was antiparallel (parallel) to the spin of the proton and neutron respectively.		where <math>N_{NH_{3},\pi^{+},\pi^{-}}^{\uparrow \downarrow}</math>(<math>N_{NH_{3},\pi^{+},\pi^{-}}^{\uparrow \uparrow}</math>) and <math>N_{ND_{3},\pi^{+},\pi^{-}}^{\uparrow \downarrow}</math>(<math>N_{ND_{3},\pi^{+},\pi^{-}}^{\uparrow \uparrow}</math>) represent the number of <math>\pi^{+}</math> and <math>\pi^{-}</math> hadrons detected in the final state with the scattered electron when the spin of the initial electron beam was antiparallel (parallel) to the spin of the proton and neutron respectively.
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	The ratio of the combined semi-inclusive deep inelastic asymmetries (Araw) from Table 1.3, for two different torus settings have been corrected for the electron reconstruction efficiency. The Figure 1.20 represents the raw asymmetry ratios before and after electron reconstruction efficiency corrections. The ratios have been calculated for each target and charged pion type. The SIDIS asymmetries before and after the correction are statistically the same. The result indicates that the electron reconstruction efficiency does not change the asymmetries.		The ratio of the combined semi-inclusive deep inelastic asymmetries (Araw) from Table 1.3, for two different torus settings have been corrected for the electron reconstruction efficiency. The Figure 1.20 represents the raw asymmetry ratios before and after electron reconstruction efficiency corrections. The ratios have been calculated for each target and charged pion type. The SIDIS asymmetries before and after the correction are statistically the same. The result indicates that the electron reconstruction efficiency does not change the asymmetries.

	Target type, Beam Torus~~& $~~A_{~~\mbox{\rm~~ hel1-hel4}} \times 10^{-4}~~$ & $~~A_{~~\mbox{\rm~~ hel2-hel3}} \times 10^{-4}~~$ & $~~A^{~~\mbox{\rm~~ raw}} \times 10^{-4}~~$ \\ \hline~~		{\| border="1" style="text-align: center;" align="center"
	~~NH$_~~{3}$, B>0, $\pi^{+}~~$ & $~~-139.84 \pm 81.52~~$ & $~~143.15 \pm 81.78~~$ & $~~136.2 \pm 57.74 ~~\\ \hline~~		\|-
	~~NH$_~~{3}$, B<0, $\pi^{+}~~$ & $~~-223.76 \pm 117.10~~$ & $~~247.65 \pm 116.59~~$ & $~~237.69 \pm 82.65~~$ \\ \hline~~		\| Target type, Beam Torus \|\| <math>A_{hel1-hel4} \times 10^{-4}</math> \|\| <math>A_{hel2-hel3} \times 10^{-4}</math> \|\| <math>A^{raw} \times 10^{-4}</math>
	~~ND$_~~{3}$, B>0, $\pi^{-}~~$ & $~~-6.37 \pm 188.73~~$ & $~~-98.11 \pm 188.03~~$ & $~~ 9.21 \pm 127.22~~$ \\ \hline~~		\|-
	~~ND$_~~{3}$, B<0, $\pi^{-}~~$ & $~~-63.73 \pm 105.14~~$ & $~~-30.34 \pm 6085.54~~$ & $~~12.37 \pm 71.10~~$ \\ \hline~~		\| <math>NH_{3}</math>, B>0, <math>\pi^{+}</math> \|\| <math>-139.84 \pm 81.52</math> \|\| <math>143.15 \pm 81.78</math> \|\| <math>136.2 \pm 57.74 </math>
	~~NH$_~~{3}$, B>0, $\pi^{-}~~$ & $~~-155.45 \pm 128.21~~$ & $~~-72.55 \pm 128.92~~$ & $~~ 35.11 \pm 90.91~~$ \\ \hline~~		\|-
	~~NH$_~~{3}$, B<0, $\pi^{-}~~$ & $~~9.60 \pm 119.31~~$ & $~~72.94 \pm 119.36~~$ & $~~32.39 \pm 84.38~~$ \\ \hline~~		\| <math>NH_{3}</math>, B<0, <math>\pi^{+}</math> \|\| <math>-223.76 \pm 117.10</math> \|\| <math>247.65 \pm 116.59</math> \|\| <math>237.69 \pm 82.65</math>
	~~ND$_~~{3}$, B>0, $\pi^{+}~~$ & $~~-76.59 \pm 126.60~~$ & $~~110.28 \pm 126.13~~$ & $~~92.25 \pm 85.38~~$ \\ \hline~~		\|-
	~~ND$_~~{3}$, B<0, $\pi^{+}$ & $-29.22 \pm 107.53$ & $123.98 \pm 106.86$ & $92.25 \pm 85.38$		\| <math>ND_{3}</math>, B>0, <math>\pi^{-}</math> \|\| <math>-6.37 \pm 188.73</math> \|\| <math>-98.11 \pm 188.03</math> \|\| <math> 9.21 \pm 127.22</math>
			\|-
			\| <math>ND_{3}</math>, B<0, <math>\pi^{-}</math> \|\| <math>-63.73 \pm 105.14</math> \|\| <math>-30.34 \pm 6085.54</math> \|\| <math>12.37 \pm 71.10</math>
			\|-
			\| <math>NH_{3}</math>, B>0, <math>\pi^{-}</math> \|\| <math>-155.45 \pm 128.21</math> \|\| <math>-72.55 \pm 128.92</math> \|\| <math> 35.11 \pm 90.91</math>
			\|-
			\| <math>NH_{3}</math>, B<0, <math>\pi^{-}</math> \|\| <math>9.60 \pm 119.31</math> \|\| <math>72.94 \pm 119.36</math> \|\| <math>32.39 \pm 84.38</math>
			\|-
			\| <math>ND_{3}</math>, B>0, <math>\pi^{+}</math> \|\| <math>-76.59 \pm 126.60</math> \|\| <math>110.28 \pm 126.13</math> \|\| <math>92.25 \pm 85.38</math>
			\|-
			\| ND_{3}$, B<0, $\pi^{+}$ & $-29.22 \pm 107.53$ & $123.98 \pm 106.86$ & $92.25 \pm 85.38$
			\|}

	'''Table 1.3''': SIDIS Asymmetry for Each Type Target material and Beam Torus.		'''Table 1.3''': SIDIS Asymmetry for Each Type Target material and Beam Torus.

Didbtama: /* Semi-Inclusive Asymmetries */

2013-06-20T21:28:50Z

Semi-Inclusive Asymmetries

← Older revision		Revision as of 21:28, 20 June 2013
Line 483:		Line 483:
	The asymmetries from semi-inclusive pion electroproduction using proton or deuteron targets can be written in terms of the difference of the yield when the electron spin is parallel and antiparallel to the spin of the nucleon. There are four combinations of semi-inclusive asymmetries: <math>A_{NH_{3}}^{\pi^{+}}</math>, <math>A_{NH_{3}}^{\pi^{-}}</math>, <math>A_{ND_{3}}^{\pi^{+}}</math> and <math>A_{ ND_{3}}^{\pi^{-}}</math>		The asymmetries from semi-inclusive pion electroproduction using proton or deuteron targets can be written in terms of the difference of the yield when the electron spin is parallel and antiparallel to the spin of the nucleon. There are four combinations of semi-inclusive asymmetries: <math>A_{NH_{3}}^{\pi^{+}}</math>, <math>A_{NH_{3}}^{\pi^{-}}</math>, <math>A_{ND_{3}}^{\pi^{+}}</math> and <math>A_{ ND_{3}}^{\pi^{-}}</math>

	A_{~~\mbox{\rm NH}_~~{3}}^{\pi^{+}} \equiv \frac{\Sigma N_{~~\mbox{\rm NH}_~~{3},\pi^{+}}^{\uparrow \uparrow} - \Sigma N_{~~\mbox{\rm NH}_~~{3}, \pi^{+}}^{\uparrow \downarrow}}{\Sigma N_{~~\mbox{\rm NH}_~~{3},\pi^{+}}^{\uparrow \uparrow} + \Sigma N_{~~\mbox{\rm NH}_~~{3}, \pi^{+}}^{\uparrow \downarrow}}		<math>A_{NH_{3}}^{\pi^{+}} \equiv \frac{\Sigma N_{NH_{3},\pi^{+}}^{\uparrow \uparrow} - \Sigma N_{NH_{3}, \pi^{+}}^{\uparrow \downarrow}}{\Sigma N_{NH_{3},\pi^{+}}^{\uparrow \uparrow} + \Sigma N_{NH_{3}, \pi^{+}}^{\uparrow \downarrow}}</math>

			<math>A_{NH_{3}}^{\pi^{-}} \equiv \frac{\Sigma N_{NH_{3},\pi^{-}}^{\uparrow \uparrow} - \Sigma N_{NH_{3}, \pi^{-}}^{\uparrow \downarrow}}{\Sigma N_{NH_{3},\pi^{-}}^{\uparrow \uparrow} + \Sigma N_{NH_{3}, \pi^{-}}^{\uparrow \downarrow}}</math>

	A_{~~\mbox{\rm NH}_~~{3}}^{\pi^{-}} \equiv \frac{\Sigma N_{~~\mbox{\rm NH}_~~{3},\pi^{-}}^{\uparrow \uparrow} - \Sigma N_{~~\mbox{\rm NH}_~~{3}, \pi^{-}}^{\uparrow \downarrow}}{\Sigma N_{~~\mbox{\rm NH}_~~{3},\pi^{-}}^{\uparrow \uparrow} + \Sigma N_{~~\mbox{\rm NH}_~~{3}, \pi^{-}}^{\uparrow \downarrow}}		<math>A_{ND_{3}}^{\pi^{+}} \equiv \frac{\Sigma N_{ND_{3},\pi^{+}}^{\uparrow \uparrow} - \Sigma N_{ND_{3}, \pi^{+}}^{\uparrow \downarrow}}{\Sigma N_{ND_{3},\pi^{+}}^{\uparrow \uparrow} + \Sigma N_{ND_{3}, \pi^{+}}^{\uparrow \downarrow}}</math>

			<math>A_{ND_{3}}^{\pi^{-}} \equiv \frac{\Sigma N_{ND_{3},\pi^{-}}^{\uparrow \uparrow} - \Sigma N_{ND_{3}, \pi^{-}}^{\uparrow \downarrow}}{\Sigma N_{ND_{3},\pi^{-}}^{\uparrow \uparrow} + \Sigma N_{ND_{3}, \pi^{-}}^{\uparrow \downarrow}},</math>

	A_{~~\mbox{\rm ND}_~~{3}}^{\pi^{+}} \~~equiv~~ \~~frac{\Sigma~~ N_{~~\mbox~~{\~~rm ND}_~~{3},\pi^{+}}^{\uparrow \uparrow} ~~- \Sigma~~ N_{~~\mbox~~{\~~rm ND}_~~{3}, \pi^{+}}^{\uparrow \downarrow}~~}{\Sigma~~ N_{~~\mbox~~{\~~rm ND}_~~{3},\pi^{+}}^{\uparrow \uparrow} ~~+ \Sigma N_{\mbox{\rm ND}_{3},~~ \pi^{+}}^{~~\uparrow \downarrow}~~}		where <math>N_{NH_{3},\pi^{+},\pi^{-}}^{\uparrow \downarrow}</math>(<math>N_{NH_{3},\pi^{+},\pi^{-}}^{\uparrow \uparrow}</math>) and <math>N_{ND_{3},\pi^{+},\pi^{-}}^{\uparrow \downarrow}</math>(<math>N_{ND_{3},\pi^{+},\pi^{-}}^{\uparrow \uparrow}</math>) represent the number of <math>\pi^{+}</math> and <math>\pi^{-}</math> hadrons detected in the final state with the scattered electron when the spin of the initial electron beam was antiparallel (parallel) to the spin of the proton and neutron respectively.

			The kinematic coverage for the events used in the measured asymmetries are shown on Figure~\ref{fig:InvariantMassvsQ2} and Figure~\ref{fig:MissingMassM_X}. The semi-inclusive asymmetries are listed in Table~\ref{tab:RunvsSIDISAsym}. The first group <math>A_{hel1-hel4}</math> represents the asymmetry measured when the first original electron spin (hel1) is antiparallel to the target nucleon spin and its complement state (hel4) is parallel, whereas the second group <math>A_{hel2-hel3}</math> represents measuring the SIDIS asymmetry when the first helicity state is parallel (hel2) and its complement state (hel3) is antiparallel to the spin of the nucleon. For the final measurement, the two groups are combined into one <math>A_{hel42-hel13}</math> set, in order to increase statistics. Instead of looking at original and complement electron helicity states, they have been combined into the positive (hel42) and negative (hel13) helicity states, which are parallel and antiparallel to the spin of the target nucleon respectively.

	A_{\mbox{\rm ND}_{3}}^{\pi^{-}} \equiv \frac{\Sigma N_{\mbox{\rm ND}_{3},\pi^{-}}^{\uparrow \uparrow} - \Sigma N_{\mbox{\rm ND}_{3}, \pi^{-}}^{\uparrow \downarrow}}{\Sigma N_{\mbox{\rm ND}_{3},\pi^{-}}^{\uparrow \uparrow} + \Sigma N_{\mbox{\rm ND}_{3}, \pi^{-}}^{\uparrow \downarrow}},

	where <math>N_{NH_{3},\pi^{+},\pi^{-}}^{\uparrow \downarrow}</math>(<math>N_{NH_{3},\pi^{+},\pi^{-}}^{\uparrow \uparrow}</math>) and <math>N_{ND_{3},\pi^{+},\pi^{-}}^{\uparrow \downarrow}</math>(<math>N_{ND_{3},\pi^{+},\pi^{-}}^{\uparrow \uparrow}</math>) represent the number of <math>\pi^{+}</math> and <math>\pi^{-}</math> hadrons detected in the final state with the scattered electron when the spin of the initial electron beam was antiparallel (parallel) to the spin of the proton and neutron respectively.

	\hspace{0.5in}The kinematic coverage for the events used in the measured asymmetries are shown on Figure~\ref{fig:InvariantMassvsQ2} and Figure~\ref{fig:MissingMassM_X}. The semi-inclusive asymmetries are listed in Table~\ref{tab:RunvsSIDISAsym}. The first group $A_{\mbox{\rm hel1-hel4}}$ represents the asymmetry measured when the first original electron spin (hel1) is antiparallel to the target nucleon spin and its complement state (hel4) is parallel, whereas the second group $A_{\mbox{\rm hel2-hel3}}$ represents measuring the SIDIS asymmetry when the first helicity state is parallel (hel2) and its complement state (hel3) is antiparallel to the spin of the nucleon. For the final measurement, the two groups are combined into one $A_{\mbox{\rm hel42-hel13}}$ set, in order to increase statistics. Instead of looking at original and complement electron helicity states, they have been combined into the positive (hel42) and negative (hel13) helicity states, which are parallel and antiparallel to the spin of the target nucleon respectively.

	'''Fig. 1.18''': Invariant Mass versus <math>Q^2</math>.		'''Fig. 1.18''': Invariant Mass versus <math>Q^2</math>.
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	The ratio of the combined semi-inclusive deep inelastic asymmetries (Araw) from Table 1.3, for two different torus settings have been corrected for the electron reconstruction efficiency. The Figure 1.20 represents the raw asymmetry ratios before and after electron reconstruction efficiency corrections. The ratios have been calculated for each target and charged pion type. The SIDIS asymmetries before and after the correction are statistically the same. The result indicates that the electron reconstruction efficiency does not change the asymmetries.		The ratio of the combined semi-inclusive deep inelastic asymmetries (Araw) from Table 1.3, for two different torus settings have been corrected for the electron reconstruction efficiency. The Figure 1.20 represents the raw asymmetry ratios before and after electron reconstruction efficiency corrections. The ratios have been calculated for each target and charged pion type. The SIDIS asymmetries before and after the correction are statistically the same. The result indicates that the electron reconstruction efficiency does not change the asymmetries.

			Target type, Beam Torus& $A_{\mbox{\rm hel1-hel4}} \times 10^{-4}$ & $A_{\mbox{\rm hel2-hel3}} \times 10^{-4}$ & $A^{\mbox{\rm raw}} \times 10^{-4}$ \\ \hline
			NH$_{3}$, B>0, $\pi^{+}$ & $-139.84 \pm 81.52$ & $143.15 \pm 81.78$ & $136.2 \pm 57.74 \\ \hline
			NH$_{3}$, B<0, $\pi^{+}$ & $-223.76 \pm 117.10$ & $247.65 \pm 116.59$ & $237.69 \pm 82.65$ \\ \hline
			ND$_{3}$, B>0, $\pi^{-}$ & $-6.37 \pm 188.73$ & $-98.11 \pm 188.03$ & $ 9.21 \pm 127.22$ \\ \hline
			ND$_{3}$, B<0, $\pi^{-}$ & $-63.73 \pm 105.14$ & $-30.34 \pm 6085.54$ & $12.37 \pm 71.10$ \\ \hline
			NH$_{3}$, B>0, $\pi^{-}$ & $-155.45 \pm 128.21$ & $-72.55 \pm 128.92$ & $ 35.11 \pm 90.91$ \\ \hline
			NH$_{3}$, B<0, $\pi^{-}$ & $9.60 \pm 119.31$ & $72.94 \pm 119.36$ & $32.39 \pm 84.38$ \\ \hline
			ND$_{3}$, B>0, $\pi^{+}$ & $-76.59 \pm 126.60$ & $110.28 \pm 126.13$ & $92.25 \pm 85.38$ \\ \hline
			ND$_{3}$, B<0, $\pi^{+}$ & $-29.22 \pm 107.53$ & $123.98 \pm 106.86$ & $92.25 \pm 85.38$

	~~Araw × 10−4~~		'''Table 1.3''': SIDIS Asymmetry for Each Type Target material and Beam Torus.
	~~Ahel1-hel4 × 10−4~~
	~~Ahel2-hel3 × 10−4~~
	~~Target type, Beam Torus~~
	~~NH3, B>0, π+~~
	~~NH3, B<0, π+~~
	~~ND3, B>0, π−~~
	~~ND3, B<0, π−~~
	~~NH3, B>0, π−~~
	~~NH3, B<0, π−~~
	~~ND3, B>0, π+~~
	~~ND3, B<0, π+~~
	~~−139.84 ± 81.52 −223.76 ± 117.10 −6.37 ± 188.73 −63.73 ± 105.14 −155.45 ± 128.21 9.60 ± 119.31 −76.59 ± 126.60 −29.22 ± 107.53~~
	~~143.15 ± 81.78 247.65 ± 116.59 −98.11 ± 188.03 −30.34 ± 6085.54 −72.55 ± 128.92 72.94 ± 119.36 110.28 ± 126.13 123.98 ± 106.86~~
	~~136.2 ± 57.74 237.69 ± 82.65 9.21 ± 127.22 12.37 ± 71.10 35.11 ± 90.91 32.39 ± 84.38 92.25 ± 85.38 92.25 ± 85.38~~
	~~Table~~ 1.3: SIDIS Asymmetry for Each Type Target material and Beam Torus.

	The data have been combined for each target type and asymmetries measured for two xB values (Table 1.4). The SIDIS asymmetries were calcu- lated for the following kinematic range: electron scattering angle 17.5<θe<18.5, electron momentum 2.55 GeV< Pe<2.75 GeV, invariant mass 1.6 GeV<W<1.8 GeV and momentum transfer squared 0.9 ~~GeV2~~<Q2<1.3 ~~GeV2~~.		The data have been combined for each target type and asymmetries measured for two <math>x_B</math> values (Table 1.4). The SIDIS asymmetries were calcu- lated for the following kinematic range: electron scattering angle 17.5<<math>\theta_e</math><18.5, electron momentum 2.55 GeV< <math>P_e</math><2.75 GeV, invariant mass 1.6 GeV<W<1.8 GeV and momentum transfer squared 0.9 <math>GeV^2</math><<math>Q^2</math><1.3 <math>GeV^2</math>.

	Fig. 1.20: The ratio of the SIDIS asymmetries for two torus field settings Araw(B>0) versus target and the charged pion type. The black squares represent the data before electron reconstruction efficiency and the red data - after		Fig. 1.20: The ratio of the SIDIS asymmetries for two torus field settings Araw(B>0) versus target and the charged pion type. The black squares represent the data before electron reconstruction efficiency and the red data - after

Didbtama: /* Semi-Inclusive Asymmetries */

2013-06-20T19:30:53Z

Semi-Inclusive Asymmetries

← Older revision		Revision as of 19:30, 20 June 2013
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	==Semi-Inclusive Asymmetries==		==Semi-Inclusive Asymmetries==

	The asymmetries from semi-inclusive pion electro-production using proton or deuteron targets can be written in terms of the difference of the yield when the electron spin is parallel and anti-parallel to the spin of the ~~nucleon. There are four combinations of~~ semi-inclusive asymmetries: <math>A_{~~NH_3}^{\pi^+}</math>, <math>A_{NH_3}^{\pi^~~-}</math>, ~~<math>A_{ND_3}^{\pi^+}</math>, <math>A_{ND_3}^{\pi^-}</math>~~		%The ratio of the combined semi-inclusive deep inelastic asymmetries (<math>A_{hel13-hel42}</math>) from the Table. 4.3 , for two different torus settings have been corrected for the electron reconstruction efficiency. The Fig. 4.7 represents asymmetry ratios before and after electron reconstruction efficiency. The ratios have been calculated for each target and charged pion type. SIDIS asymmetries are statistically the same. The results suggest electron reconstruction efficiency do not make significant change on the asymmetries.

			The asymmetries from semi-inclusive pion electroproduction using proton or deuteron targets can be written in terms of the difference of the yield when the electron spin is parallel and antiparallel to the spin of the nucleon. There are four combinations of semi-inclusive asymmetries: <math>A_{NH_{3}}^{\pi^{+}}</math>, <math>A_{NH_{3}}^{\pi^{-}}</math>, <math>A_{ND_{3}}^{\pi^{+}}</math> and <math>A_{ ND_{3}}^{\pi^{-}}</math>
	~~where N↑↓~~
	~~NH3,π~~+,~~π− NH3,π+,π− ND3,π+,π− ND3,π+~~,π−
	~~represent the number of~~<math> \pi^+</math> and <math>\pi^-</math> ~~hadrons detected in the final state with the scattered electron when the spin of the initial electron was antiparallel(parallel) to the spin of the proton and neutron respectively.~~

	~~The kinematic coverage for the events used in the measured asymmetries are shown in Figure 1.18 and Figure 1.19. The semi-inclusive asymmetries are listed in Table 1.~~3~~. The first group <math>A_~~{~~hel1-hel4~~}~~</math> represents the asymmetry measured when the first original electron spin (hel1) is antiparallel to the target nucleon spin and its complement state (hel4) is parallel~~, ~~whereas the~~		A_{\mbox{\rm NH}_{3}}^{\pi^{+}} \equiv \frac{\Sigma N_{\mbox{\rm NH}_{3},\pi^{+}}^{\uparrow \uparrow} - \Sigma N_{\mbox{\rm NH}_{3}, \pi^{+}}^{\uparrow \downarrow}}{\Sigma N_{\mbox{\rm NH}_{3},\pi^{+}}^{\uparrow \uparrow} + \Sigma N_{\mbox{\rm NH}_{3}, \pi^{+}}^{\uparrow \downarrow}}
	~~second group Ahel2~~-~~hel3 represents measuring the SIDIS asymmetry when the first helicity state is parallel (hel2) and its complement state is antiparallel to the spin of the nucleon. For the final measurement~~, ~~the two groups are combined into one Ahel42-hel13 set. Instead of looking at original and complement electron helicity states~~, ~~they have been combined into the positive (hel42) and nega- tive (he13) helicity states~~, ~~which are parallel and antiparallel to the spin of the target nucleon respectively.~~

	Fig. 1.18: Invariant Mass versus Q2.
			A_{\mbox{\rm NH}_{3}}^{\pi^{-}} \equiv \frac{\Sigma N_{\mbox{\rm NH}_{3},\pi^{-}}^{\uparrow \uparrow} - \Sigma N_{\mbox{\rm NH}_{3}, \pi^{-}}^{\uparrow \downarrow}}{\Sigma N_{\mbox{\rm NH}_{3},\pi^{-}}^{\uparrow \uparrow} + \Sigma N_{\mbox{\rm NH}_{3}, \pi^{-}}^{\uparrow \downarrow}}


			A_{\mbox{\rm ND}_{3}}^{\pi^{+}} \equiv \frac{\Sigma N_{\mbox{\rm ND}_{3},\pi^{+}}^{\uparrow \uparrow} - \Sigma N_{\mbox{\rm ND}_{3}, \pi^{+}}^{\uparrow \downarrow}}{\Sigma N_{\mbox{\rm ND}_{3},\pi^{+}}^{\uparrow \uparrow} + \Sigma N_{\mbox{\rm ND}_{3}, \pi^{+}}^{\uparrow \downarrow}}


			A_{\mbox{\rm ND}_{3}}^{\pi^{-}} \equiv \frac{\Sigma N_{\mbox{\rm ND}_{3},\pi^{-}}^{\uparrow \uparrow} - \Sigma N_{\mbox{\rm ND}_{3}, \pi^{-}}^{\uparrow \downarrow}}{\Sigma N_{\mbox{\rm ND}_{3},\pi^{-}}^{\uparrow \uparrow} + \Sigma N_{\mbox{\rm ND}_{3}, \pi^{-}}^{\uparrow \downarrow}},

			where <math>N_{NH_{3},\pi^{+},\pi^{-}}^{\uparrow \downarrow}</math>(<math>N_{NH_{3},\pi^{+},\pi^{-}}^{\uparrow \uparrow}</math>) and <math>N_{ND_{3},\pi^{+},\pi^{-}}^{\uparrow \downarrow}</math>(<math>N_{ND_{3},\pi^{+},\pi^{-}}^{\uparrow \uparrow}</math>) represent the number of <math>\pi^{+}</math> and <math>\pi^{-}</math> hadrons detected in the final state with the scattered electron when the spin of the initial electron beam was antiparallel (parallel) to the spin of the proton and neutron respectively.

			\hspace{0.5in}The kinematic coverage for the events used in the measured asymmetries are shown on Figure~\ref{fig:InvariantMassvsQ2} and Figure~\ref{fig:MissingMassM_X}. The semi-inclusive asymmetries are listed in Table~\ref{tab:RunvsSIDISAsym}. The first group $A_{\mbox{\rm hel1-hel4}}$ represents the asymmetry measured when the first original electron spin (hel1) is antiparallel to the target nucleon spin and its complement state (hel4) is parallel, whereas the second group $A_{\mbox{\rm hel2-hel3}}$ represents measuring the SIDIS asymmetry when the first helicity state is parallel (hel2) and its complement state (hel3) is antiparallel to the spin of the nucleon. For the final measurement, the two groups are combined into one $A_{\mbox{\rm hel42-hel13}}$ set, in order to increase statistics. Instead of looking at original and complement electron helicity states, they have been combined into the positive (hel42) and negative (hel13) helicity states, which are parallel and antiparallel to the spin of the target nucleon respectively.

			'''Fig. 1.18''': Invariant Mass versus <math>Q^2</math>.


			'''Fig. 1.19''': Missing Mass. The line represents a cute used to remove events with <math>M_X</math> < 1.6 GeV from the semi-inclusive analysis.

	The ratio of the combined semi-inclusive deep inelastic asymmetries (Araw) from Table 1.3, for two different torus settings have been corrected for the electron reconstruction efficiency. The Figure 1.20 represents the raw asymmetry ratios before and after electron reconstruction efficiency corrections. The ratios have been calculated for each target and charged pion type. The SIDIS asymmetries before and after the correction are statistically the same. The result indicates that the electron reconstruction efficiency does not change the asymmetries.		The ratio of the combined semi-inclusive deep inelastic asymmetries (Araw) from Table 1.3, for two different torus settings have been corrected for the electron reconstruction efficiency. The Figure 1.20 represents the raw asymmetry ratios before and after electron reconstruction efficiency corrections. The ratios have been calculated for each target and charged pion type. The SIDIS asymmetries before and after the correction are statistically the same. The result indicates that the electron reconstruction efficiency does not change the asymmetries.

	~~Fig. 1.19: Missing Mass. The line represents a cute used to remove events with M_X < 1.6 GeV from the semi-inclusive analysis.~~

	Araw × 10−4		Araw × 10−4

Didbtama: /* Electron Asymmetry */

2013-06-20T18:46:12Z

Electron Asymmetry

← Older revision		Revision as of 18:46, 20 June 2013
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	{\| border="0" style="background:transparent;" align="center"		{\| border="0" style="background:transparent;" align="center"
	\|-		\|-
	\|<math>A_{NES}^{-+} = \frac{\Sigma NES^{-} - \Sigma NES^{+}}{\Sigma NES^{-} + \Sigma NES^{+}}= \frac{\Sigma NES^{~~\mbox{\rm~~ hel1}} - \Sigma NES^{~~\mbox{\rm~~ hel4}}}{\Sigma NES^{~~\mbox{\rm~~ hel1}} + \Sigma NES^{~~\mbox{\rm~~ hel4}}} \equiv (1-4),</math>		\|<math>A_{NES}^{-+} = \frac{\Sigma NES^{-} - \Sigma NES^{+}}{\Sigma NES^{-} + \Sigma NES^{+}}= \frac{\Sigma NES^{hel1} - \Sigma NES^{hel4}}{\Sigma NES^{hel1} + \Sigma NES^{hel4}} \equiv (1-4),</math>
	\|}		\|}

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	The un-normalized reconstructed electron asymmetry has been calculated as:		The un-normalized reconstructed electron asymmetry has been calculated as:

	~~NEShel1,hel2 − NEShel4,hel3 ANES~~ = ~~NEShel1,hel2 + NEShel4,hel3,~~		{\| border="0" style="background:transparent;" align="center"
	~~and the Faraday cup normalized asymmetry as~~:		\|-
			\|<math>A_{NES}^{-+} = \frac{\Sigma NES^{hel1} - \Sigma NES^{hel4}}{\Sigma NES^{hel1} + NES^{hel4}},</math>
	A_{NES}^{-+} = \frac{\Sigma NES^{hel1} - \Sigma NES^{hel4}}{\Sigma NES^{hel1} + NES^{hel4}},		\|}

			{\| border="0" style="background:transparent;" align="center"
			\|-
			\|<math>A_{NES}^{+-} = \frac{\Sigma NES^{hel2} - \Sigma NES^{hel3}}{\Sigma NES^{hel2} + NES^{hel3}},</math>
			\|}

	~~A_{NES}^{+-} = \frac{\Sigma NES^{hel2} - \Sigma NES^{hel3}}{\Sigma NES^{hel2} + NES^{hel3}},~~		and the Faraday cup normalized asymmetry as:

			{\| border="0" style="background:transparent;" align="center"
	~~and the Faraday cup normalized as~~		\|-
			\|<math>A_{NES}^{+-} = \frac{\frac{\Sigma NES^{hel2}}{\Sigma FC^{hel2}} - \frac{\Sigma NES^{hel3}}{\Sigma FC^{hel3}}}{\frac{\Sigma NES^{hel2}}{\Sigma FC^{hel2}} + \frac{\Sigma NES^{hel3}}{\Sigma FC^{hel3}}}.</math>
	A_{NES}^{+-} = \frac{\frac{\Sigma NES^{hel2}}{\Sigma FC^{hel2}} - \frac{\Sigma NES^{hel3}}{\Sigma FC^{hel3}}}{\frac{\Sigma NES^{hel2}}{\Sigma FC^{hel2}} + \frac{\Sigma NES^{hel3}}{\Sigma FC^{hel3}}}.		\|}

	(1.23)		(1.23)

Didbtama: /* Beam Charge Asymmetry */

2013-06-20T18:27:10Z

Beam Charge Asymmetry

← Older revision		Revision as of 18:27, 20 June 2013
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	\|}		\|}

	(1.20)		(1.20)

	where <math>FC^{hel1,hel2}</math> (<math>FC^{hel4,hel3}</math>) represents the Faraday cup counts observed for the original helicity 1 and 2 states (the complement helicity 3 and 4 states).		where <math>FC^{hel1,hel2}</math> (<math>FC^{hel4,hel3}</math>) represents the Faraday cup counts observed for the original helicity 1 and 2 states (the complement helicity 3 and 4 states).

Didbtama: /* Electron Asymmetry */

2013-06-20T18:25:15Z

Electron Asymmetry

@@ Line 406: / Line 406: @@
 ==Electron Asymmetry==
-Systematic 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
+A measurement of the electron cross section helicity difference needs to account for a possible helicity dependence of the incident electron flux (charge asymmetry). Figure~\ref{fig:RunvsEAsym} shows the reconstructed electron rate 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:
-Fig. 1.15: Run Number versus Electron Asymmetry before FC normalization. The black and red points represent reconstructed electron asymmetry for the helicity 1-4 pair for ND3 and NH3 target respectively. The blue and green points represent the helicity pair 2-3 for ND3 and NH3 respectively. The green line shows the sign of the half wave plane (HWP) and the purple line is the sign of the target polarization (TPol).
+or
-(a) NH3, Tpol>0 and HWP>0.
+where <math>NES^{+}</math> (<math>NES^{-}</math>) represents number of electron scattered for the positive (negative) beam helicity state.
-Fig. 1.16: W versus (NEShel42 − NEShel13). The electron asymmetry (sign(hel42-hel13)) changes sign when the target polarization direction is reversed.
+{| border="0" style="background:transparent;"  align="center"
 The un-normalized reconstructed electron asymmetry has been calculated as:
 NEShel1,hel2 − NEShel4,hel3 ANES = NEShel1,hel2 + NEShel4,hel3,
-and the Faraday cup normalized asymmetry as
+and the Faraday cup normalized asymmetry as:
-NEShel1,hel2 − NEShel4,hel3
-AFCnormalized = F C hel1,hel2 F C hel4,hel3 . NES NEShel1,hel2 + NEShel4,hel3
+A_{NES}^{-+} = \frac{\Sigma NES^{hel1} - \Sigma NES^{hel4}}{\Sigma NES^{hel1} + NES^{hel4}},
-F C hel1,hel2 F C hel4,hel3
 (1.23)
 (1.24)
-Fig. 1.17: Run number versus electron asymmetry after applying FC normaliza- tion. The black and red points represent the reconstructed electron asymmetry for the helicity 1-4 pair for ND3 and NH3 target respectively. The blue and green points are the helicity pair 2-3 for ND3 and NH3 respectively. The green line shows the sign of the half wave plane (HWP) and the purple line is the sign of the target polarization (TPol).
+{| border="0" style="background:transparent;"  align="center"
 ==Semi-Inclusive Asymmetries==

Didbtama: /* Beam Charge Asymmetry */

2013-06-20T17:57:00Z

Beam Charge Asymmetry

← Older revision		Revision as of 17:57, 20 June 2013
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	==Beam Charge Asymmetry==		==Beam Charge Asymmetry==
	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.		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.
	Fig. 1.13: 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~~.
			{\| border="0" style="background:transparent;" align="center"
			\|-
			\|
			[[File:Helicity_state.png\|400px]]
			\|}<br>

			'''Fig. 1.13''': The Helicity State: A one bit signal from the beam injector gives the helicity information. A sync bit with a 2 Hz frequency is generated to indicate the start of a helicity state.

	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 selection process is then repeated.		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 selection process is then repeated.

	Figure 1.13 illustrates the signals used to label the helicity states. The 21		Figure 1.13 illustrates the signals used to label the helicity states. 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 identifies 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.
	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 identifies 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.

	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 ob- served 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.		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 ob- served 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 is defined in Eq. 1.21 and measured using the gated helicity scaler. For each run number, a gaussian fit was used to fit the beam charge asymmetry distributions as in Figure 1.14. The beam charge asymmetry is defined as		The beam charge asymmetry is defined in Eq. 1.21 and measured using the gated helicity scaler. For each run number, a gaussian fit was used to fit the beam charge asymmetry distributions as in Figure 1.14. The beam charge asymmetry is defined as
	~~ΣF C hel1,hel2 − ΣF C hel4,hel3~~
	~~ABeam Charge = ΣF C hel1,hel2 + ΣF C hel4,hel3 , (1.20)~~
	~~where FChel1,hel2 (FChel4,hel3) represents the Faraday cup counts observed for the original helicity 1 and 2 states (the complement helicity 3 and 4 states).~~

	Fig. 1.14: Beam charge asymmetry for run #28101 using the gated Faraday cup counts for two helicity pairs (1-4 and 2-3 helicity pairs). ~~A1−4~~ = (11.5 ± 4.4) ~~× 10−5~~ and ~~A2−3~~ = (−2.3 ± 4.4) ~~× 10−5~~.		{\| border="0" style="background:transparent;" align="center"
			\|-
			\|<math>A_{14} = \frac{ \Sigma FC_{i}^{hel1}-\Sigma FC_{i}^{hel4}}{\Sigma FC_{i}^{hel1}+\Sigma FC_{i}^{hel4}},</math>
			\|}

			{\| border="0" style="background:transparent;" align="center"
			\|-
			\|<math>A_{23} = \frac{ \Sigma FC_{i}^{hel2}-\Sigma FC_{i}^{hel3}}{\Sigma FC_{i}^{hel2}+\Sigma FC_{i}^{hel3}},</math>
			\|}

			(1.20)

			where <math>FC^{hel1,hel2}</math> (<math>FC^{hel4,hel3}</math>) represents the Faraday cup counts observed for the original helicity 1 and 2 states (the complement helicity 3 and 4 states).

			{\| border="0" style="background:transparent;" align="center"
			\|-
			\|
			[[File:FC_ChargeAsymmetry_282101RunNumber_14_23HelPairs_03_12_12.png\|400px]]
			\|}<br>

			Fig. 1.14: 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>

	EG1b data sets, with the same half wave plate, target type, target polarization, and beam torus have been combined. The beam charge asymmetries have been calculated for the each run group and are listed in Table 1.2.		EG1b data sets, with the same half wave plate, target type, target polarization, and beam torus have been combined. The beam charge asymmetries have been calculated for the each run group and are listed in Table 1.2.
	~~A1−4 × 10−4 A2−3 × 10−4~~
			{\| border="1" style="text-align: center;" align="center"
	Run Group		\|-
	Half wave ~~plane~~(HWP)		\|Run Group \|\| Half wave plate(HWP) \|\| <math>A_{1-4} \times 10^{-4}</math> \|\| <math>A_{2-3} \times 10^{-4}</math>
	~~28100 – 28105~~		\|-
	+1		\| 28100 - 28105 \|\| +1 \|\| <math>5.88 \pm 34.40</math> \|\| <math>4.03 \pm 34.36</math>
	~~28106 – 28115~~		\|-
	-1		\| 28106 - 28115 \|\| -1 \|\| <math>7.53 \pm 22.30</math> \|\| <math>8.28 \pm 22.30</math>
	~~28145 – 28240~~		\|-
	+1		\| 28145 - 28240 \|\| +1 \|\| <math>31.70 \pm 7.99</math> \|\| <math>30.40 \pm 7.99</math>
	~~28242 – 28284~~		\|-
	-1		\| 28242 - 28284 \|\| -1 \|\| <math>49.6 \pm 10.8</math> \|\| <math>47.9 \pm 10.8</math>
	~~28286 – 28324~~		\|-
	+1		\| 28286 - 28324 \|\| +1 \|\| <math>36.3 \pm 11.6</math> \|\| <math>37.0 \pm 11.5</math>
	~~28325 – 28447~~		\|-
	-1		\| 28325 - 28447 \|\| -1 \|\| <math>21.1 \pm 13.4</math> \|\| <math>22.2 \pm 13.4</math>
	~~28449 – 28479~~		\|-
	+1		\| 28449 - 28479 \|\| +1 \|\| <math>-11.6 \pm 16.5</math> \|\| <math>-21.6 \pm 16.5</math>
			\|}
	~~5~~.88 ± 34.40 7.53 ± 22.30 31.70 ± 7.99 49.~~6 ± 10.8 36.3 ± 11.6 21~~.1 ~~± 13.4 −11~~.6 ~~± 16.5~~
	~~4.03 ± 34~~.36 8~~.28 ± 22.30 30.40 ± 7.99~~ 47.9 ± 10.8 37.0 ± 11.5 22.2 ± 13.4 ~~−21~~.6 ± 16.5		'''Table 1.2''': Run Group versus Beam Charge Asymmetry.






	Table 1.2: Run Group versus Beam Charge Asymmetry.

	==Electron Asymmetry==		==Electron Asymmetry==

Didbtama: /* Pion Identification */

2013-06-20T16:46:06Z

Pion Identification

← Older revision		Revision as of 16:46, 20 June 2013
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	Charged pions are identified using a coincidence hit in the drift chamber		Charged pions are identified using a coincidence hit in the drift chamber
	and Time-of-Flight (ToF) counter. Pions are separated from the other charged		and Time-of-Flight (ToF) counter. Pions are separated from the other charged
	particles by looking at the particle momentum versus the ~~<math>\beta</math>~~ distribution. The		particles by looking at the particle momentum versus the β distribution. The
	particle velocity, ~~<math>\beta~~ = v~~</math>~~ , is calculated from the difference of the RF time and the c		particle velocity, β = v , is calculated from the difference of the RF time and the c
	time-of-flight measurement in the ToF system with the path length from the		time-of-flight measurement in the ToF system with the path length from the

	vertex to the ToF counters. The mass of the charged particle can be identified by combining the particle’s ~~<math>\beta</math>~~ with the particle momentum obtained from the track measured by the drift chamber in the known magnetic field. The particle mass in a magnetic field is given as		vertex to the ToF counters. The mass of the charged particle can be identified by combining the particle’s β with the particle momentum obtained from the track measured by the drift chamber in the known magnetic field. The particle mass in a magnetic field is given as

	{\| border="0" style="background:transparent;" align="center"		{\| border="0" style="background:transparent;" align="center"
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	\|}<br>		\|}<br>
	'''Fig. 1.8''': The charged particle momentum versus <math>\beta</math> distribution. The pion and proton bands are clearly separated.		'''Fig. 1.8''': The charged particle momentum versus <math>\beta</math> distribution. The pion and proton bands are clearly separated.

	~~{\| border="0" style="background:transparent;" align="center"~~
	\|-
	\|
	~~[[File:PionMomentumvsMass.png\|400px]]~~
	~~\|}<br>~~
	'''Fig. 1.9''': The charged particle momentum versus mass squared distribution for the<math>\vec{e}p \rightarrow \vec{e}^{\prime}\pi^+n</math> electroproduction process. The bands around zero and one represent pions and protons respectively [5].

	=Event Reconstruction Efficiency=		=Event Reconstruction Efficiency=