Single-spin asymmetries in two hadron production of polarized deep

inelastic scattering at HERMES

Tomohiro KobayashiTokyo Institute of Technology

for the HERMES collaboration

Second Joint Meeting of the Nuclear Physics Divisions of APS and JPS, Hawaii (Sep. 22nd, 2005 Session JE-9)

Contents• The HERMES experiment• Quark distribution functions• Single-spin asymmetry in 2-hadron semi-inclusive DIS• Conclusion and outlook

HERMES experiment at DESY

positron (electron) beam

27.6 [GeV]

current ~ 30[mA]

Xepe

Transversely polarized hydrogen target 　(2002~2005)

polarization ~ 75[%]

HERA Target magnet

ＨＥＲＭＥＳ Spectrometer

• acceptance : 40 mrad ≦ 220 mrad≦• Tracking resolution ： P/P = (0.7-1.3)% 、 = 0.6 mrad• PID ： Hodoscope 、 Calorimeter 、 TRD and RICH Lepton ID efficiency > 97%, Hadron contamination < 1% Hadron ID(K, P) at 2‐15 GeV/c

e+ beam

27.6GeV

8m

Internal gas targetH(pol) 、 D （ pol ）、He 、 Ne 、 Kr 、 Xe

unknownchiral odd

Quark distribution functions

Quark momentum distribution:

Quark Helicity:

Quark Transversity:

At leading twist

)()(2

1)(

)()(

xqxqxq

xqxq

• quark’s relativistic nature

• positivity bound :

　 Soffer bound ：

)()( xqxq

)(xq

)(xq

)(xq:)(xq

quark spin

proton spin

Access to transversity

chiral odd Need another chiral odd objects.

Transversity couples to …• Collins fragmentation function (FF)• 2-hadron interference FF• Polarized Lambda FF• Spin-1 FF :

:)(xq

Inclusive DIS Semi-inclusive DIS

Not accessible accessible

)(xq

Single-spin asymmetry of 2-hadron production

Azimuthal single-spin asymmetries

hpXPPkepke )()()()( 21

)()(sin)sin(~ 1 zHxqSR

Transversity Interference FF (chiral odd)

describes interference between different production channels of pion pairs

)(1 zH

),,( SRUTA

(data taken in 2002…2004)

can be extracted using measured by e+ e- collider, BELLE

)( xq )(1 zH

DISDIS

DISDIS

NNNN

NNNN

S SRSR

SRSR

T /),,(/),,(

/),,(/),,(1

beam spin target spin

: s-p wave interference in scattering theory

R. L. Jaffe, Xuemin Jin, and Jian Tan, Phys. Rev. Lett. 80, 1166 (1998)

P. Estabrooks and A. D. Martin, Nucl. Phys. B79, 301 (1974)

)()sin(sinsin),( ',11010

2,1 zHMzH spsp

scatteringnp using analysisshift phase

FF ceInterferen of dependenceM

),(cos),(),cos,( 2,1

2,1

21 MzHMzHMzH ppsp

1H

dependenceM

Partial wave expansion

Sign of the phase shift changes at

0 MM

might depend strongly on MUTA

Spectator model for fragmentation

M. Radici et al., hep/ph-0110252

No strong dependence.M

),(cos),(),cos,( 2,1

2,1

21 MzHMzHMzH ppsp

Partial wave expansion

Single-spin asymmetry in 2-hadron production

Single-spin asymmetries

First observation of transverse asymmetries in interference process

1sin)sin(~ qHA SRUT

(no binning)

)sin(10 SRaa

Fit

with

SystStat1 003.0009.0040.0 　a

009.0040.0

006.0000.0

1

0

a

a

1sin)sin(~ qHSR

AUT

01 Hq

Single-spin asymmetry in 2-hadron production

Single-spin asymmetries

Amplitude of the asymmetry modulation

Positive asymmetry is observed around 0 MM

sin)sin(10 SRaa

Asymmetry is fitted with

1sin)sin( aA SR

UT

Single-spin asymmetry in 2-hadron production

If we look at dependence,M M( : invariant mass of pion pair)

Spectator model for fragmentation

Marco Radici at Como, 7 - 10 Sept 2005

),(cos),(),cos,( 2,1

2,1

21 MzHMzHMzH ppsp

Partial wave expansion

Conclusion

ConclusionConclusion• Single-spin asymmetry in production is measured with transversely polarized hydrogen target at HERMES.

• This is the first observation of transverse target spin asymmetry in interference process.

• modulation of is observed at 4 sigma level.

• Positive asymmetry is observed for measured invariant mass range. ( =0.25 - 2.0 [GeV/c2])

,

,

)sin( SR UTA

01 Hq

SystStat 003.0009.0040.0sin

)sin(

　

SRUTA

M

Outlook

OutlookOutlook• 4~5 M more DIS events are expected in 2005, compared to 3.5 M DIS events in 2002~2004.

backup

Event selection

Kinematic cuts : ≥ 1 GeV2

≥ 4 GeV2

≥ 0.023 0.1 < < 0.85 > 2.5 GeV (for DIS lepton) > 1 GeV (for Hadron)

> 2 GeV, whereE

p

p

y

x

W

Q

track

track

2

2

p

px

M

MME

2

22

Xeep SIDIS events with at least pion pair( ) appeared were analyzed.

,

To cut exclusive channel.

Data set : 2002~2004

Evaluate

DISDIS

DISDIS

/),,(/),,(

/),,(/),,(1),,(

NNNN

NNNN

SA

SRSR

SRSR

TSRUT

UTA

0.54.75 TSwhere is the average target polarization. ( )TS

,...sin)sin(~ 11 HhSR

What is measured

sin)sin(ofdependence SRUTAM

Positive asymmetry is observed around 0 MM

sin)sin(10 SRaa

Asymmetry is fitted with

1sin)sin( aA SR

UT

binning :0.25, 0.40, 0.55, 0.77, 2.0 [GeV]

M

Single-spin asymmetry in 2-hadron production

M : invariant mass of pion pair

spectrumM

With or without cut]GeV[2.0E

p

px

M

MME

2

22

spectrumz

With or without cut]GeV[2.0E

p

px

M

MME

2

22

double spin asymmetry

Beam polarization don’t affect to the asymmetry

sin)sin(sin)sin( SRSR cba

Fit

for both beam polarization.

11sin)sin(~ HhA SRUT

Beam polarization (%)

0Pfor 012.0040.0

0Pfor 011.0041.0

beam

beam

sin)sin(

bA SRUT

No double spin asymmetry

Polarized cross section for 2 hadron SIDIS

GAgHhA LULR

~11

sin

GCfeHA RLU

~11

sin

2 hadron semi-inclusive DIS

Single spin asymmetries

11)sin( HhA SR

UT

)~

(sin 112 aaqqaaqq

LRq

qUL GAgHhed

aaqqaaqqR

qqLU GCfHeed 1112 ~sin

(...)sin)sin( 112

Saaqq

SRq

qUT BHhed

Polarized cross section for 2 hadron SIDIS

2 hadron semi-inclusive DIS

Gfz

eHM

M

Q

RyWed

DxfM

MH

M

RH

zh

Q

MyV

HhM

RyB

Sed

Ggz

HhM

M

Q

RyVSed

hHM

MD

z

f

Q

RyVDfyAed

h

xRe

qqLU

Th

o

h

hS

hSR

qqUT

Lh

xLR

qqUL

h

xR

qqUU

~1sinsin)(

sin~1

sin)(

sin)sin()(

~1sin)(sin

~sincos)()(

112

1)1(

12

2

21

11

2

112

11

112

yyyWyyyV

yyB

yyyA

12122

12

12

)()()(

)(

)(

In Wandzura-Wilzcek approx.,function with tilde vanish.