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