Single-spin asymmetrieswith 2 hadron fragmentation:

The Measurement

Paul Bastiaan van der Nat (NIKHEF)On behalf of the HERMES collaboration

Layout:Introduction

Results

Interpretation

Transversity workshop - Trento – p.1/16

The holy grail

� � � � � �Characteristics of

��� :

leading twist -> on equal footing with��� and � �

chiral-odd -> can NOT be probed in inclusive DIS

Solution: couple

� to chiral-odd fragmentation function

Two options: 1 or 2 particle semi-inclusive DIS

Transversity workshop - Trento – p.2/16

Single Spin Asymmetry

��� � ��� � ����longitudinally polarized deuterium target

���� ���� � ��� ���! � "# ���� � �$ " #&%' ( ) " * ���� � � $ " *% ' (" # ���� � � $ " #+%' ( � " * ���� � � $ " *+%' (

Transversity workshop - Trento – p.3/16

Asymmetries -Theory

A. Bacchetta, M. Radici, PRD 69, 0740XX (2004)

� ,� - . �0/ �21 354 ���� � � �76 � � 8 9� � : �0/ �21 354 ��76 � ; �=< < < �

� ,�� - : �0/ �21 354 ���� � � ; � � 8 9� � � � >@? 9 �

A$B � C target spin defined w.r.t. virtual photon

Transversity workshop - Trento – p.4/16

Asymmetries - Experiment

��� D � ,�� ) 1 354 EGF � ,� target spin define d w.r.t. beam

target spin w.r.t. virtual photon

HJI KHIHML H@N

OQP

R1 3 4 EGF S � R � TVU W � ) / S D XZY X [\

��� - : �0/ �21 354 ���� � � ; � � 8 9� � � � > ? 9 � � . , �/ �1 3 4 ���� � �; � 8 9�

if

8 9� ]� X

:

� C 2 hadron fragmentation can probe transversity!

Transversity workshop - Trento – p.5/16

Interference FF

R2^_ 1 E Sa` X � C 8 9�b c c� drops out!

8 9� �0d!e ^_ 1 Ee �f f �� 8 9�b g c� �0d!e � f f � � ^_ 1 E 8 9�b c c� �0d e � f f �

CM

h i

h j kmln

m(GeV)

sinδ

0sin

δ 1sin

(δ0-

δ 1)

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0

0.2

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0.6

0.5 0.6 0.7 0.8 0.9 1

Jaffe et al. [hep-ph/9709322]:

8 9�b g c� �0d e � f f �� 1 3 4 oqp 1 354 o � 1 354 � oqp ) o � � 8 9�b g c r� �0d �

s�t (

s�u ) v S(P)-wave phase shifts

� w � �f f � 8 9�b g c r� �d �

x y z|{} might depend stongly on

~=� �

Transversity workshop - Trento – p.6/16

The HERMES Experiment

1

0

2

-1

-2

� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �

� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �

m

LUMINOSITY

CHAMBERSDRIFT

FC 1/2

TARGETCELL

DVC

MC 1-3

HODOSCOPE H0

MONITOR

BC 1/2

BC 3/4 TRD

PROP.CHAMBERS

FIELD CLAMPS

PRESHOWER (H2)

STEEL PLATE CALORIMETER

DRIFT CHAMBERS

TRIGGER HODOSCOPE H1

0 1 2 3 4 5 6 7 8 9 10

RICH270 mrad

270 mrad

MUON HODOSCOPEWIDE ANGLE

FRONTMUONHODO

MAGNET

m

IRON WALL

e+

27.5 GeV

140 mrad

170 mrad

170 mrad

140 mrad

MUON HODOSCOPES

SILICON

Forward acceptance spectrometer: 40 mrad

� O � � ��

mrad

Tracking: 57 tracking planes:

s� � � x � ��� ��� �� � ��

,

s O � ��� �

mrad

Transversity workshop - Trento – p.7/16

Analysis method

Fitting method:

z|{} �� ��� � � � � �� �� � � fit withx y � � �0� � � x � t � � u �  ¢¡ � � £ u ¤¥ � � � � � �

z ¦ §©¨ ª{}Weighting method:

z ¦ §©¨ ª{} � « ¬­¯®u �  ¢¡ � ­� « °­¯®u �  ¡ � ­u± � � �� � � �Used fitting method for released resultsx y less sensitive to detector acceptance

Transversity workshop - Trento – p.8/16

Results

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0

0.02

0.04

0.06

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

AU

L

sin

φ R⊥

Mππ [GeV]

ρ0

sys. unc. = 0.007x > 0.023 <x> = 0.074

<z> = 0.48

ed→

→ e' h+h- XHERMES PRELIMINARY

sin

φ R⊥

first measurement everof

� ² ³µ´ ¶a· ¸��small asymmetries

Transversity workshop - Trento – p.9/16

¹-dependence

Attempt to study º and d -dependence:� ² ³µ´ ¶»· ¸�� ¼ � � º � 8 9�b g c� �d e f f � � � Y Y Y �-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

AU

Lsi

nφ R

⊥

ρ0

sys. unc. = 0.0070.023 < x < 0.046

<x> = 0.036<z> = 0.45 0.046 < x < 0.076

<x> = 0.059<z> = 0.49 x > 0.076

<x> = 0.13<z> = 0.50

ed→

→ e' h+h- X HERMES PRELIMINARY

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

ρ0

sys. unc. = 0.0070.023 < x < 0.046

<x> = 0.036<z> = 0.45 0.046 < x < 0.076

<x> = 0.059<z> = 0.49 x > 0.076

<x> = 0.13<z> = 0.50

ed→

→ e' h+h- X HERMES PRELIMINARY

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

Mππ [GeV]

ρ0

sys. unc. = 0.0070.023 < x < 0.046

<x> = 0.036<z> = 0.45 0.046 < x < 0.076

<x> = 0.059<z> = 0.49 x > 0.076

<x> = 0.13<z> = 0.50

ed→

→ e' h+h- X HERMES PRELIMINARY

no strong º-dependence observed

statistics doesn’t allow finer binningTransversity workshop - Trento – p.10/16

½-dependence

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0

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0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

AU

Lsi

nφ R

⊥

ρ0

sys. unc. = 0.0070 < z < 0.52

<x> = 0.070<z> = 0.38 0.52 < z < 1

<x> = 0.081<z> = 0.64

ed→

→ e' h+h- X HERMES PRELIMINARY

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

Mππ [GeV]

ρ0

sys. unc. = 0.0070 < z < 0.52

<x> = 0.070<z> = 0.38 0.52 < z < 1

<x> = 0.081<z> = 0.64

ed→

→ e' h+h- X HERMES PRELIMINARY

d � ¾ f f¿

no strong d -dependence observed

no more than two bins possible

0

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1

0 0.5 1 1.5 2 2.5 3 3.5Mππ [GeV]

z

Transversity workshop - Trento – p.11/16

comparison to model prediction

Model by Jaffe et al.:

predicts mass dependence

NO statements on size/signof the asymmetry

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0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1Mhh [GeV]

sin

δ 0sin

δ psi

n(δ

0-δ p

)

Fit data with: À Á Âà à ÄÆÅ ÇÈ É Á Â Ã Ã ÄµÊ Ç Â

by extracting ÇÈ & Ç Â a qualitative comparisoncan be made to the model prediction

Transversity workshop - Trento – p.12/16

comparison to model prediction

ÇÈ Ë ÌZÍ Ì Î Ì Ï ÌÍ ÌÐÑ

Ç Â ËÓÒ ÌÍ Ì ÌÔ Ï ÌÍ Ì Ì Î

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0

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0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

AU

L

sin

φ R⊥

Mππ [GeV]

ρ0

sys. unc. = 0.007x > 0.023 <x> = 0.074

<z> = 0.48

ed→

→ e' h+h- XHERMES PRELIMINARY

sin

φ R⊥

hint of a sign change atthe Õ Ö mass

À Á Âà à ÄÆÅ ÇÈ É Á Â Ã Ã ÄµÊ Ç Â

Transversity workshop - Trento – p.13/16

×-dependence

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0

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0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

AU

Lsi

nφ R

⊥

ρ0

sys. unc. = 0.0070.023 < x < 0.046

<x> = 0.036<z> = 0.45 0.046 < x < 0.076

<x> = 0.059<z> = 0.49 x > 0.076

<x> = 0.13<z> = 0.50

ed→

→ e' h+h- X HERMES PRELIMINARY

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

ρ0

sys. unc. = 0.0070.023 < x < 0.046

<x> = 0.036<z> = 0.45 0.046 < x < 0.076

<x> = 0.059<z> = 0.49 x > 0.076

<x> = 0.13<z> = 0.50

ed→

→ e' h+h- X HERMES PRELIMINARY

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

Mππ [GeV]

ρ0

sys. unc. = 0.0070.023 < x < 0.046

<x> = 0.036<z> = 0.45 0.046 < x < 0.076

<x> = 0.059<z> = 0.49 x > 0.076

<x> = 0.13<z> = 0.50

ed→

→ e' h+h- X HERMES PRELIMINARY

higher Ø: hint of sign change atÕ Ö according to Jaffe’s modelÇÈ Á Ø Ä0Ù Ú È Á Ø Ä ?-0.2

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-0.1

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0

0.05

0.1

0.15

0.2

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14xbj

c1

Transversity workshop - Trento – p.14/16

Û-dependence

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0

0.02

0.04

0.06

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

AU

Lsi

nφ R

⊥

ρ0

sys. unc. = 0.0070 < z < 0.52

<x> = 0.070<z> = 0.38 0.52 < z < 1

<x> = 0.081<z> = 0.64

ed→

→ e' h+h- X HERMES PRELIMINARY

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

Mππ [GeV]

ρ0

sys. unc. = 0.0070 < z < 0.52

<x> = 0.070<z> = 0.38 0.52 < z < 1

<x> = 0.081<z> = 0.64

ed→

→ e' h+h- X HERMES PRELIMINARY

sign change at Õ Ö according toJaffe’s model for low d

ÇÈ Á0d Ä Ù Ü Ý�Þ ß cÈ Á0d e Ã Ã Ä ?-0.2

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-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.2 0.3 0.4 0.5 0.6 0.7 0.8z

c1

x > 0.023x > 0.046

Transversity workshop - Trento – p.15/16

Conclusions & Outlook

Conclusions:

Presented first measurement of

à á â©ã äæå çèé

Asymmetries of order ê ë ì

, but also consistent with zeroí=î î -dependence consistent with model by Jaffe et al.

Comparison with model prediction hints at ï and ð dependenceñ ò sensitive to

ó�ô õ ï ö÷ øúù ûüô õ ðý í=î î ö

?

Outlook to

à á â ã äå çèþ :

comparable uncertainty:

L polarized target ÿ ê8M DIS eventsT polarized target ÿ ê4M DIS events?

� à � � � �� ÿ � àdominated by statistical uncertainty

much larger transverse target polarization ÿ ê1/0.045 ñ ë ë

times bigger!

Transversity workshop - Trento – p.16/16