evidence for a single -spin asymmetry in two -pion semi ... 15/giordano.pdf · evidence for a...

Francesca GiordanoFrancesca GiordanoUniversitUniversità degli studi di Ferraraà degli studi di Ferrara

INFN INFN sezsez. . di Ferraradi Ferrara

HERMES@DESYHERMES@DESY

EvidenceEvidence forfor a a SingleSingle--SpinSpin

AsymmetryAsymmetry in in twotwo--pionpion

SemiSemi--Inclusive DIS on a Inclusive DIS on a

transverselytransversely polarizedpolarized hydrogenhydrogen

targettarget

F.GiordanoQCD N06, 15 June 2006

Electron beam (27.5 Electron beam (27.5 GeV/cGeV/c) on a fixed polarized H) on a fixed polarized H--targettarget

∆∆∆∆∆∆∆∆p/pp/p ~ 1~ 1--2%2%

Electron identification efficiency ~ 98Electron identification efficiency ~ 98--99%99%

HERMES SPECTROMETERHERMES SPECTROMETER


HERMES RICHHERMES RICH

1 1 1 1 1 1 1 1 GeV/cGeV/c

DUAL-RADIOTOR RING

IMAGING CHERENKOV


TRANSVERSITYTRANSVERSITY

Since the transversity is a chiral-odd function, it cannot be probed in Inclusive

Deep Inelastic Scattering, but has to be

coupled to another chiral-odd function.

Semi Inclusive Deep Inelastic

Scattering (SIDIS): transversity is coupled to a chiral-odd

fragmentation function;


Semi Inclusive Deep Inelastic ScatteringSemi Inclusive Deep Inelastic Scattering

11--pion production pion production 22--pion productionpion production

scatterin

g planehadron plane

z xyk0q�S kP�hPh? Ph ST∑

⋅

⋅+∝ ⊥⊥

q

qqhT

qShTUT HhM

PkeS I ,1,1

2ˆ

)sin( φφσ ( )qq

q

qSRTUT HheS,1,1

2sinsin ⋅+∝ ∑⊥ φφθσ

φφφφφφφφhh

φφφφφφφφSS

scatterin

g planetwo−hadron plane

z xyk0qPh 2R �S kPP1 P2�R(= �R?)ST

π−

π+

θ

CMS frame

Ph

φφφφφφφφR R

φφφφφφφφSS


Semi Inclusive Deep Inelastic ScatteringSemi Inclusive Deep Inelastic Scattering

22--pion productionpion production

( ) qq

q

qSRTUT HheS ,1,1

2sinsin ⋅+∝ ∑⊥ φφθσ

Collinear physics: the relative momentum of the pion-pair has a transverse component RT even

after the integration over the transverse momentum of the pion-

pair Ph

A completely independent method to extract h1.

BUT: poorer statistics!!

scatterin

g planetwo−hadron plane

z xyk0qPh 2R �S kPP1 P2�R(= �R?)ST

π−

π+

θ

CMS frame

Ph

φφφφφφφφR R

φφφφφφφφSS


( )| |

( ) ( )( ) ( )θφφθφφ

θφφθφφσσ

θφφ,,

,,1,

SRSIDISSRSIDIS

SRSIDISSRSIDIS

TUU

UTSRUT

NN

NN

S=A

+++

+−+≡+

⊥↓

⊥↑

⊥↓

⊥↑

⊥

Event topologyEvent topology

85.01.0

6.0023.0

1

4

22

22

<<

≤≤

≥

≥

bj

bj

y

x

GeVQ

GeVW

Kinematical rangeKinematical range

∆E [ GeV ]

co

un

ts

0.60 < mππ < 0.95 GeV

0

200

400

600

800

1000

-2 0 2 4 6 8 10 12 14 16

PionsPions identified with RICHidentified with RICH

All possible combination of All possible combination of

detected detected pionspions were includedwere included

for each eventfor each event

%70|| ≥TS

GeVMMME PPx 22/)(22 >−≡∆

GeV/cP 1 >π


Partial wave expansionPartial wave expansion

( )

qqq

qqSRq

UTDf

HhA

,1,1

,1,1sinsin~

∑∑ + θφφ

21 zzz +=



( )

qqq

qqSRq

UTDf

HhA

,1,1

,1,1sinsin~

∑∑ + θφφ

21 zzz += ( ) ( )2,

1

2,

1 ,cos, h

pp

h

spMzHMzH θ+

The contribution to the Asymmetry is

due to interference of different

partial waves of the final state ππππ++++ππππ−−−−

),,( 2

1 θhMzH



( )

qqq

qqSRq

UTDf

HhA

,1,1

,1,1sinsin~

∑∑ + θφφ

21 zzz += ( ) ( )2,

1

2,

1 ,cos, h

pp

h

spMzHMzH θ+

The contribution to the Asymmetry is

due to interference of different

partial waves of the final state ππππ++++ππππ−−−−

),,( 2

1 θhMzH

))1cos3(cos( ,1

2

,1,1,1 4/1pp

q

sp

qqqqDDDf −++∑ θθ sp ppss pp,


First step: linear approximationFirst step: linear approximation

))1cos3(4/1cos(

)cossin(sin)sin(~

,1

2

,1,1,1

,

,1

,

,1,1

pp

q

sp

qqqq

pp

q

sp

qqSRq

UTDDDf

HHhA

−++

++

∑∑ ⊥

θθ

θθθφφ

qqq

pp

q

sp

qqSRq

UTDf

HHhA

,1,1

,

,1

,

,1,1 )2sin(sin)sin(~

∑∑ ++⊥ θθφφ

First step: neglect denominator partial wave expansion

spss pp, pp


))1cos3(4/1cos(

)cossin(sin)sin(~

,1

2

,1,1,1

,

,1

,

,1,1

pp

q

sp

qqqq

pp

q

sp

qqSRq

UTDDDf

HHhA

−++

++

∑∑ ⊥

θθ

θθθφφ

qqq

pp

q

sp

qqSRq

UTDf

HHhA

,1,1

,

,1

,

,1,1 )2sin(sin)sin(~

∑∑ ++⊥ θθφφ

First step: linear approximationFirst step: linear approximation

First step: neglect denominator partial wave expansion

ss pp, sp pp


Linear fitLinear fit

)2sinsin()sin(sin)sin( θθφφ θφφ

bAaA SR

UTUT SR+++= +⊥

⊥

The The azimuthalazimuthal moments are extracted from Amoments are extracted from AUTUT using a 2using a 2--dimensional dimensional χχχχχχχχ22 fitfit

compatible with zerocompatible with zero




bAaA SR

UTUT SR+++= +⊥

⊥


q

q

qq

sp

q

q

qq

UTDfe

HheA SR

,11

2

,

,11

2

sin)sin(~∑∑+⊥ θφφ





bAaA SR

UTUT SR+++= +⊥

⊥


ExtraExtra--terms like the ones below do not influence the value of the extrterms like the ones below do not influence the value of the extracted momentsacted moments

θφφ sincos,sin ⊥RS


q

q

qq

sp

q

q

qq

UTDfe

HheA SR

,11

2

,

,11

2

sin)sin(~∑∑+⊥ θφφ

THE EXTRACTED VALUES OF THE MOMENTSARE NOT INFLUENCED BY THE

PRESENCE OF THIS TERM IN THE FIT FUNCTION


Results with linear fitResults with linear fit

∑∑

∝+⊥

q q

q

q

q

sp

q

q

q

UTDfe

HheA SR

,11

2

,

,11

2

sin)sin( θφφ



∑∑

∝+⊥

q q

q

q

q

sp

q

q

q

UTDfe

HheA SR

,11

2

,

,11

2

sin)sin( θφφ

Significant sinusoidal Significant sinusoidal

behavior!behavior!


∑∑

∝+⊥

q q

q

q

q

sp

q

q

q

UTDfe

HheA SR

,11

2

,

,11

2

sin)sin( θφφ


)(003.0)(009.0040.0sin)sin(

syststatSR

UTA ±±=+⊥ θφφ

First evidence of a TFirst evidence of a T--odd and odd and

chiralchiral--odd odd dihadrondihadron

fragmentation functionfragmentation function

(it can be measured at Belle!)(it can be measured at Belle!)


MMππππππππππππππππ--dependencedependence

POSITIVE ASYMMETRY in the whole range of Mππππππππ-mass



POSITIVE ASYMMETRY in

the whole range of Mππππππππ-mass

No evidence of the signNo evidence of the sign--change at the change at the ρρ0 0 mass mass

predicted by predicted by

Jaffe et alJaffe et al..

(Phys.Rev.Lett.80,1166(1998))(Phys.Rev.Lett.80,1166(1998))



POSITIVE ASYMMETRY in

the whole range of Mππππππππ-mass

Different models don’t predictDifferent models don’t predict

a sign change of the asymmetry around the a sign change of the asymmetry around the ρρρρ0000 mass

Radici et al. Radici et al.

(Phys.Rev.D65,074031(2002))(Phys.Rev.D65,074031(2002))


WORK IN PROGRESS…WORK IN PROGRESS…


In progress….In progress….

))1cos3(4/1cos(

)cossin(sin)sin(~

,1

2

,1,1,1

,

,1

,

,1,1

pp

q

sp

qqqq

pp

q

sp

qqSRq

UTDDDf

HHhA

−++

++

∑∑ ⊥

θθ

θθθφφss pp, sp pp



)sin()sin(

SR

SR

UTUT AaA φφφφ ++=⊥

+⊥

11--DIMENSIONAL LINEAR FIT DIMENSIONAL LINEAR FIT

(INTEGRATED OVER(INTEGRATED OVER θθθθθθθθ))

))1cos3(4/1cos(

)cossin(sin)sin(~

,1

2

,1,1,1

,

,1

,

,1,1

pp

q

sp

qqqq

pp

q

sp

qqSRq

UTDDDf

HHhA

−++

++

∑∑ ⊥

θθ



)sin()sin(

SR

SR


+⊥

11--DIMENSIONAL LINEAR FIT DIMENSIONAL LINEAR FIT

(INTEGRATED OVER(INTEGRATED OVER θθθθθθθθ))

∑∑

∝+⊥

q q

q

q

q

sp

q

q

q

UTDfe

HheA SR

,11

2

,

,11

2

)sin( φφ


))1cos3(4/1cos(

)cossin(sin)sin(~

,1

2

,1,1,1

,

,1

,

,1,1

pp

q

sp

qqqq

pp

q

sp

qqSRq

UTDDDf

HHhA

−++

++

∑∑ ⊥

θθ


ss pp,


Can we integrate over Can we integrate over θθθθθθθθ ??

If 2-π pair are isotropicallydistributed in the phase-space

θ-distribution is proportional to sinθ:

A CUT ON THE MOMENTA BIASES

SIGNIFICANTLY THE θθθθ DISTRIBUTION!!0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0 0.5 1 1.5 2 2.5 3θ [rad]

no

rmal

ized

co

un

ts

Pπ > 3 GeV/c

Pπ > 2 GeV/c

Pπ > 1 GeV/c

)sin()sin(

SR

SR


+⊥

>>>>>>>>>>>>>>>>>>>>>>>>


)sin(coscos1

)2sinsin(2

sin)sin(

SRdc

bAA

SR

UT

UT φφθθ

θθθφφ

+++

+=

⊥

+⊥

NONNON--LINEAR FIT:LINEAR FIT:


ss pp,))1cos3(4/1cos(

)cossin(sin)sin(~

,1

2

,1,1,1

,

,1

,

,1,1

pp

q

sp

qqqq

pp

q

sp

qqSRq

UTDDDf

HHhA

−++

++

∑∑ ⊥

θθ



)sin(coscos1

)2sinsin(2

sin)sin(

SRdc

bAA

SR

UT

UT φφθθ

θθθφφ

+++

+=

⊥

+⊥

NONNON--LINEAR FIT:LINEAR FIT:∑∑

−

+ ∝⊥

q

pp

qq

q

q

q

sp

q

q

q

UTDDfe

HheA SR

)( ,14/1,11

2

,

,11

2

sin)sin( θφφ


))1cos3(4/1cos(

)cossin(sin)sin(~

,1

2

,1,1,1

,

,1

,

,1,1

pp

q

sp

qqqq

pp

q

sp

qqSRq

UTDDDf

HHhA

−++

++

∑∑ ⊥

θθ


ss pp, pp


Conclusion Conclusion

•• For the first timeFor the first time a nona non--zero Single Spin Asymmetry zero Single Spin Asymmetry (SSA) is measured in two(SSA) is measured in two--pionpion production;production;

••The measured SSA allows to probe The measured SSA allows to probe transversitytransversity in 2in 2--pion SIDIS and is the first evidence for a nonpion SIDIS and is the first evidence for a non--zero zero chiralchiral--

odd interference fragmentation function;odd interference fragmentation function;

•• No evidence of a sign change of SSA at No evidence of a sign change of SSA at ρρ00 mass;mass;

••A nonA non--linear fit is in progress to take into account all linear fit is in progress to take into account all the partialthe partial--wave terms; wave terms;

•• 2005 data will double current statistics;2005 data will double current statistics;

THANK YOU!!!THANK YOU!!!

evidence for a single -spin asymmetry in two -pion semi ... 15/giordano.pdf · evidence for a...

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