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Measuring the Fifth Structure Function in � �� � � ��� � �
G.P.Gilfoyle, R. Burrell, K. Greenholt, University of Richmond
1. Introduction and Background.
2. Event Selection and Corrections.
3. Extracting the Fifth Structure Function.
4. Measuring the Background Structure Functions
5. Preliminary Comparison with Theory.
6. Conclusions.
Introduction - 1� Goal: Measure the imaginary part of the LT interference term of
� � � � ��� � ��� to test the hadronic model at low ��� (� � �� � � �! �� ).
Scattering Plane
e’Reaction Plane
eθpq
θ( , q )ω
q
e
φ
p
pq
� Use the out-of-plane
production to extract
the fifth structure function.
� Cross section:
"�# $"% "& ' "& () *,+ ) * -. * /.
* - /0 12 3 45 �. * / / 0 12 76 3 45 �. 8 * � - / 2 9: 3 45 �
Introduction - 2; Asymmetry
<>= ?@ A B�C DEGF BIH DEB!C DEKJ BLH DE M BON PQB PJ BQ A R!ST U V WXY J Z R!ST U V W XY F
Subscripts - V WX . Superscripts - beam helicity.
; Analyze data from the E5 run period in Hall B.
– Recorded about 2.3 billion triggers, [�\ A ]^_ Z `^ ] a�b c d e!f g\ .
– Dual target cell with liquid hydrogen and deuterium.
Event Selection and CorrectionsFor electrons: Good CC, EC, SC status h h ij , k h i j , l h ij , lmn m i j
Energy-momentum match j o pq r stvu j ow p xy z{ z|} xj o pq r st~ j oj �
Reject pions k h k� � j owj j and � s� k � q r
EC track coordinates fiducial ��� h � l h �� w � r � � h� l hu �j � �q �j
EC fiducial No tracks withinwj h� of the end of a strip
Egiyan threshold cut st � �q w� ~ q o� ��� k h m �� k l�� � � �� j oj j w
Electron fiducial Same method as D. Protopopescu, et al., CLAS-Note 2000-007.
Quasi-elastic scattering j o � q � k � � � � w oj � k �
Select target u w w o r h � x� � xu � oj h �
Momentum corrections Pitt (CLAS-Note 2001-018) and elastic-scattering methods
For protons: Proton fiducial cut Same method as R. Nyazov and L.Weinstein, CLAS-NOTE 2001-013.
k s vertex cut �� � � k �u � � � s� � m� � � � � w o r h �
Momentum corrections Pitt (CLAS-Note 2001-018) method
For neutrons: Missing mass cut j o �� � k ��� � � � � � j o �q � k ��
Beam charge asymmetry: 2.6 GeV, reversed field: j o � � p � �j oj j j �
2.6 GeV, normal field: j o � �� � �j oj j j �
4.2 GeV, normal field j o � � � � �j oj j j �
Radiative corrections: EXCLURAD Adding helicity dependent model
Beam polarization: All Runs j o � p � �j oj w �
¡¢ £ ¤¥ ¦�§ Moments Analysis For ¨ ©ª
Recall
«¬ ® « ¯° « ± ° « ¯ ±³² ´µ ¶· ¸¹º ° « ± ± ² ´ µ ¶�» · ¸¹ º ° ¼ «¾½ ¯ ± µ¿ À ¶· ¸¹º
Let
Áµ¿ À · ¸¹Â ¬ ® ÃÄ ÅÄ «Æ¬ µ¿ À · ¸¹ÈÇ ·
ÃÄ ÅÄ «È¬ Ç ·
®É¬ µ¿ À ·Ê
Ë ¬
® Ì «¾½ ¯ ±
» ¶ « ¯° « ±ºÍ ÌÎ
½ ¯ ±»
For a sinusoidally-varying component to the acceptance
Áµ¿ À · ¸¹Â ¬ ® Ìν ¯ ±
» ° Ï ÐÑ Ñso
Áµ¿ À · ¸¹Â ÒÔÓ Áµ¿ À · ¸¹Â Å ® Î ½ ¯ ± Õ À Ö Áµ¿ À · ¸¹Â Ò ° Áµ¿ À · ¸¹Â Å ® » Ï ÐÑ Ñ
×ØÙ Ú ÛÜÝ Þ Moments Analysis For ß àá
Recall
âã ä â åæ â ç æ â å ç³è éê ëì íîï æ â ç ç è é ê ë�ð ì íî ï æ ñ â¾ò å ç êó ô ëì íîï
Let
õêó ô ì íîö ã ä ÷ø ùø âÆã êó ô ì íîÈú ì
÷ø ùø âÈã ú ì
äûã êó ô ìü
ý ã
ä þ â¾ò å ç
ð ë â åæ â çïÿ þ�
ò å çð
For a sinusoidally-varying component to the acceptance
õêó ô ì íîö ã ä þ�ò å ç
ð æ � �� �so
õêó ô ì íîö � � õêó ô ì íîö ù ä � ò å ç � ô � õêó ô ì íîö � æ õêó ô ì íîö ù ä ð � �� �� �
� � Results for � �� � � � � � ���
LTA
’
-0.15-0.1
-0.050
0.050.1
0.152=0.7-1.1 (GeV/c)2E=2.6 GeV, Q
Normal torus polarity
(GeV/c)mp0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
LTA
’
-0.4
-0.2
0
0.2
0.42=1.4-2.3 (GeV/c)2E=4.2 GeV, Q
Normal torus polarity
LTA
’
-0.04
-0.02
0
0.02
0.04
,e’p)n (Preliminary)ed(2=0.2-0.5 (GeV/c)2E=2.6 GeV, Q
Reversed torus polarity
Red - electron and proton fiducials on
Blue - fiducials off
Cou
nts
2000400060008000
100001200014000160001800020000 E=2.6 GeV
Normal torus polarity
2 (GeV/c)2Q0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Cou
nts
0
100
200
300
400
500E=4.2 GeVNormal torus polarity
Cou
nts
20406080
100120140160
310×d(e,e’p)n
E=2.6 GeVReversed torus polarity
���� � �� � � Moments Analysis For ! "#
Recall
$&% ' $ () $ * ) $ ( *,+ -. /0 123 ) $ * * + - . /54 0 12 3 ) 6 $87 ( * .9 : /0 123
Let
;.9 : 0 12< % ' => ?> $@% .9 : 0 12BA 0
=> ?> $B% A 0
'C% .9 : 0D
E %
' F $87 ( *
4 / $ () $ *3G FH
7 ( *4
For a sinusoidally-varying component to the acceptance
;.9 : 0 12< % ' FH7 ( *
4 ) I JK Kso
;.9 : 0 12< LNM ;.9 : 0 12< ? ' H 7 ( * O : P ;.9 : 0 12< L ) ;.9 : 0 12< ? ' 4 I JK K
Q�RS T UVW X Moments Analysis For Y Z[
Recall
\&] ^ \ _` \ a ` \ _ a,b cd ef ghi ` \ a a b c d e5j f gh i ` k \8l _ a dm n ef ghi
Let
odm n f ghp ] ^ qr sr \@] dm n f ghBt f
qr sr \B] t f
^u] dm n fv
w ]
^ x \8l _ a
j e \ _` \ aiy xz
l _ aj
For a sinusoidally-varying component to the acceptance
odm n f ghp ] ^ xzl _ a
j ` { |} }so
odm n f ghp ~N� odm n f ghp s ^ z l _ a � n � odm n f ghp ~ ` odm n f ghp s ^ j { |} }�� ��
Asymmetry Background Results
LTA
’
-0.15-0.1
-0.050
0.050.1
0.152=0.7-1.1 (GeV/c)2E=2.6 GeV, Q
Normal torus polarity
(GeV/c)mp0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
LTA
’
-0.4
-0.2
0
0.2
0.42=1.4-2.3 (GeV/c)2E=4.2 GeV, Q
Normal torus polarity
LTA
’
-0.04
-0.02
0
0.02
0.04
,e’p)n (Preliminary)ed(2=0.2-0.5 (GeV/c)2E=2.6 GeV, Q
Reversed torus polarity
Red - electron and proton fiducials on
Blue - fiducials off
Bac
kgro
und
Asy
mm
etry
-0.15
-0.1
-0.05
0
0.05
0.1
0.15 2.6 GeV, normal polarityred - efids, pfids onblue - fiducials off
(GeV/c)mp0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Bac
kgro
und
Asy
mm
etry
-0.4
-0.2
0
0.2
0.4 E=4.2 GeV, Normal torus polarity
Bac
kgro
und
Asy
mm
etry
-0.04-0.03-0.02-0.01
00.010.020.030.04
,e’p)ned(
E=2.6 GeV, Reversed torus polarity
Hartmuth Arenhoevel calculations of � ��
1. Numerical solution of the Schroedinger equation using some
parameterization of the NN interaction like the Paris potential
(NORMAL).
2. Additional components are then added to this starting point.
(a) Meson exchange currents (MEC).
(b) Isobar configurations (IC).
(c) Final state interactions (FSI).
3. Relativistic corrections (RC) are also made to the nucleon charge and
current densities.
4. In the figures to follow, all of the ingredients listed above are included
(KNP=6).
Comparison with Theory - Limiting Curves
Hartmuth Arenhoevel calculations
(GeV/c)mp0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
(GeV/c)mp0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
LTA
’
-0.15
-0.1
-0.05
-0
0.05
,e’p)ned(2=0.25-0.50 (GeV/c)2E=2.6 GeV, Q
Reversed torus polarity
2=0.35 (GeV/c)2red - KNP=6, Q
2=0.50 (GeV/c)2black - KNP=6, Q
(GeV/c)mp0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
(GeV/c)mp0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
LTA
’
-0.15
-0.1
-0.05
-0
0.05
,e’p)ned(2=0.6-1.1 (GeV/c)2E=2.6 GeV, Q
Normal torus polarity
red - KNP=6, 2=0.60 (GeV/c)2Q
black - KNP=6,2=1.10 (GeV/c)2Q
Cou
nts
2000400060008000
100001200014000160001800020000 E=2.6 GeV
Normal torus polarity
2 (GeV/c)2Q0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Cou
nts
0
100
200
300
400
500E=4.2 GeVNormal torus polarity
Cou
nts
20
4060
80100
120140
160310×
d(e,e’p)n
E=2.6 GeVReversed torus polarityred points - Arenhoevel
calculations
Comparison with Theory - � -Averaged Curves
Hartmuth Arenhoevel calculations
(GeV/c)mp0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
LTA
’
-0.15
-0.1
-0.05
-0
0.05
,e’p)ned(2=0.25-0.50 (GeV/c)2E=2.6 GeV, Q
Reversed torus polarity
averaged2red - KNP=6, Q
(GeV/c)mp0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
LTA
’
-0.15
-0.1
-0.05
-0
0.05
,e’p)ned(2=0.6-1.1 (GeV/c)2E=2.6 GeV, Q
Normal torus polarity
averaged2red - KNP=6, Q
Cou
nts
2000400060008000
100001200014000160001800020000 E=2.6 GeV
Normal torus polarity
2 (GeV/c)2Q0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Cou
nts
0
100
200
300
400
500E=4.2 GeVNormal torus polarity
Cou
nts
20
4060
80100
120140
160310×
d(e,e’p)n
E=2.6 GeVReversed torus polarityred points - Arenhoevel
calculations
Comparison with Theory - � -Averaged Curves
Jean-Marc Laget calculations
(GeV/c)mp0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
LTA
’
-0.15
-0.1
-0.05
-0
0.05
,e’p)ned(2=0.25-0.50 (GeV/c)2E=2.6 GeV, Q
Reversed torus polarity
red - JML calculation
(GeV/c)mp0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
LTA
’
-0.15
-0.1
-0.05
-0
0.05
,e’p)ned(2
=0.6-1.1 (GeV/c)2E=2.6 GeV, QNormal torus polarity
red - JML Calculation
(GeV/c)missp0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
(GeV/c)missp0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
LTA
’
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
E = 2.558 GeV, Laget calculations2black - 0.70 (GeV/c)
2red - 1.13 (GeV/c)2blue - 1.55 (GeV/c)
Conclusions� We observe a 4-6% dip in� � �� at �� � � � � � � ��� in the lower ���
data sets. At higher energy, we can’t draw conclusions because of the
large statistical uncertainties.
� The ���� ¡¢ £¤¥ technique works well including the subtraction of the two
different beam helicities to eliminate acceptance effects.
� The background asymmetry is sensitive to the fiducial cuts for the
reversed torus polarity running conditions, but not for the normal torus
polarity running (within statistics).
� At low missing momentum � � , the calculations by Arenhoevel and
Laget reproduce the data, but diverge (they’re too negative) above
�� ¦ � § � � � � � . The dip we observe in� � �� is not well understood.
� The source of the background asymmetry is under investigation.
dependence of ¨ ©ª at the Quasi-elastic Peak
(GeV/c)mp0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
(GeV/c)mp0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
-0.1
-0.05
0
0.05
0.1
0.15
’LTA
corr2.56n, efid, p
black - 1.04 < W < 1.12
red - 0.96 < W < 1.04
green - 0.88 < W < 0.96
(GeV/c)mp0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
(GeV/c)mp0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
-0.1
-0.05
0
0.05
0.1
0.15corr2.56n, efid, p
green - 0.88 < W < 0.96
blue - 0.80 < W < 0.88
black - 0.72 < W < 0.80
’LTA
W(GeV)0.6 0.7 0.8 0.9 1 1.1 1.2
W(GeV)0.6 0.7 0.8 0.9 1 1.1 1.2
Eve
nts
0
20
40
60
80
100
120
140
160
310×
2.56 GeV, normal polarity
blackredgreenbluepurple
« dependence of ¬ ® at the Quasi-elastic Peak
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70 0.1 0.2 0.3 0.4 0.5 0.6 0.7-0.15
-0.1
-0.05
-0
0.05
0.1
0.15
0.2
2.6 GeV, normal polarity2 < 0.98 GeV20.90 < MM
Quasielastic
’LTA
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70 0.1 0.2 0.3 0.4 0.5 0.6 0.7-0.15
-0.1
-0.05
-0
0.05
0.1
0.15
0.2
2.6 GeV, normal polarity2 < 0.92 GeV20.84 < MM
Quasielastic
’LTA
(GeV/c)mp0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
(GeV/c)mp0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.15
-0.1
-0.05
-0
0.05
0.1
0.15
0.2
2.6 GeV, normal polarity < 0.8620.78 < MM
red - fiducials onblue - fiducials offQE kinematics
’LTA
Fifth Structure Function Asymmetry for ¯ °± ² ³ ²µ´ ¶ ·�¸
¹ Measured º¼» ½¾ for the ¿ ÀÁ  à » Ä ÅÇÆ
reaction for the E5 running period.
¹ See a dip in º » ½¾ at ÄÈ É Ê Ê Ë Â Ì Í�Î
in the lower �Рdata.
¹ Background asymmetry extracted for
each set of running conditions. We see
significant difference for reversed
torus polarity running.
¹ Existing calculations from Arenhoevel
and Laget diverge from the data at Ä È Ñ Ê Ò Ë Â Ì Í�Î .
LTA
’
-0.15-0.1
-0.050
0.050.1
0.152=0.7-1.1 (GeV/c)2E=2.6 GeV, Q
Normal torus polarity
(GeV/c)mp0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
LTA
’-0.4
-0.2
0
0.2
0.42=1.4-2.3 (GeV/c)2E=4.2 GeV, Q
Normal torus polarity
LTA
’
-0.04
-0.02
0
0.02
0.04
,e’p)n (Preliminary)ed(2=0.2-0.5 (GeV/c)2E=2.6 GeV, Q
Reversed torus polarity
Red - electron and proton fiducials on
Blue - fiducials off
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