Measurement of polarized distribution functions at HERMES

Alessandra Fantoni(on behalf of the HERMES Collaboration)

•The spin puzzle & the HERMES experiment • Polarised quarks distributions•Transversity

13th International QCD Conference

Montpellier 03-07 July 2006

HERHERa a MEMEasurement of asurement of SSpin (DESY)pin (DESY)

180 Researchers from 30 Institutions of 12 Countries

Study of nucleon

structure

• double spin

asymmetries

(inclusive,

seminclusive)

• single spin asymmetries

(seminclusive,

transversity and

exclusive processes)

Data taking since 1995

The Nucleon Spin

gqsvvN ΔLΔLΔG)ΔqΔdu(2

1

2

1S

Polarised Deep Inelastic Scattering (DIS)

HERMES (√s=7 GeV): Q2max = 20 GeV2

Characteristiques of the HERMES experimentCharacteristiques of the HERMES experiment

Stern-Gerlach separation

• resolution: p/p~2%, <1 mrad• PID: leptons with ~98%, contam. <1% hadronsdual RICH: , K,p

2<Eh<15 GeV

27.5 GeV (e+/e-)

<Pb>~ 53±2.5 %

1H→ <|Pt|> ~ 85 %

2H→ <|Pt|> ~ 84 %

1H <|Pt|> ~ 74 %

gaseus atomic target, high polarisation, non diluited

hadron/positron separationcombining signals from: TRD-Calorimeter-Preshower-TRD-Calorimeter-Preshower-RICHRICH

Aerogel; n=1.03

C4F10; n=1.0014

hadron separationDual radiator RICH for , K, p

Particle Identification

K

Polarized quark distributionsInclusive DIS:Inclusive DIS:

22

11 η)Α(γ

Dγ1

Fg

σσ

σσA ||

),(2

1),( 2,22,

1 QxqCgCCeQxg npNSNSg

np

Measurements of g1 on p,d,p,d,33HeHe provides PDF through the Q2 evolution

||A

Polarised Structure Functions : g1

• g1 corrected for instrumental smearing (unfolded) and QED radiative effects

• measured on neutron (3He, 1995), proton and deuteron targets

• Better precision for g1n

from g1d-g1

p

Data can be used in NLO QCD fits to obtain polarized PDFs– Two methods will be used

g1 and QCD fit papers under preparation

g1(x) world data (at measured Q2) Measured Q2

Polarised semi-inclusive DIS

- ud

K- us

Flavor tagging

+ ud

f

fff zDdxz )()(q)(d hqh z=Eh/(EE’)

Partonic DistributionFunction (PDF)

FragmentationFunction

(FF)

Polarised Quark Distribution Functions

f

2hf

2f

2f

f

2hf

2f

2f

h21

h23

h21

h232h

1)Q(z,dzD)Q(x,qe

)Q(z,dzD)Q(x,Δqe

σσ

σσ)Q(x,A

known quantities

PolarisedPartonDistributionFunctions qf(x)=q+(x)-q-

(x)

Hadronic asymmetriesto be measured

)(

)()(

xq

xqxP

q

hq

Purity

Functions

A PQ����������������������������

Extract q by solving

Measured Asymmetries

Proton

Deuteron

1 ~ 0 ( )KA K us

statistics sufficient for 5 parameter fit:

( , , , , , 0)u d u d s s

Qu d su d s

��������������

[PRL92(2004), PRD71(2005)]u quarks: large positive polarisation

d quarks: negative polarisation

sea quarks (u, d, s, s):compatibile with 0

- - -

Polarised Quark Distribution FunctionsPolarised Quark Distribution Functions

First direct 5-flavor separation

of polarised PDFs

in measured range (0.023 – 0.6) :

0.002 0.043u 0.054 0.035d 0.028 0.034s

longitudinally polarisedquarks and nucleons

q(x): helicity difference

axial charge

known

q1h q1f

Nucleon quark structureNucleon quark structure

unpolarised quarksand nucleons

q(x): spin averaged

vector charge

well known

transversely polarisedquarks and nucleons

q(x): helicity flip

tensor charge

measuring !

q1g

nxhxgxfx T1

5151L1Tw2Corr Sγγ)(γ)(S)(

2

1)(

Single helicity flip

NOT allowed in e.m. & strong interactions

Peculiarities of Transversity q

Double helicity flip

chiral-odd DF

chiral-odd DF x chiral-odd FF

“Collins” FF

DIS + SIDIS cross section

LUUUUUUU dσQλdσ

Qdσdσdσ sin

1cos

12cos

LLLLLULULL dσ

QdσλSdσ

QdσS cos

1sin

12sin

UTSUTSUTSUTST d

QddσdσS )2sin(

1)3sin()sin()sin(

.....)3sin()2cos(1

)cos(

LTSLTSLTST ddσ

QdσS

11 Hh

(Collins)

1T1 Df

(Sivers)

Relativistic nature of quark. In absence of relativistic effects h1(x)=g1(x)Q2 -evolution. Unlike for g1

p(x), the gluon doesn’t mix with quark in h1

p (x)

High sensitivity to the valence quark polarization q and q have opposite sign.

_

Tensor charge: first moment of h1. Calculable by lattice QCD.

Chiral-odd Distribution Function

•Chiral-even naïve T-odd DF

•Related to parton orbital momentum

•Violates naïve universality of PDF

- Different sign of in DY

t1f

t1fPeculiarity of

Transversity asymmetryTransversity asymmetry [PRL94(2005)][PRL94(2005)]

)()(q 1coll zHxA )()(q 1coll zHxA

)()( 1T1siv zDxfA )()( 1T1siv zDxfA

transversity x Collins FF

Sivers DF x FF unpolarised

Sivers DF connected to quark angular momentum

)sin(A)sin(A SSiversUTS

CollinsUT

),(N),(N||

1),(A

SS

),(N

1

),(N

1

TS

hUT

SS

i ihi ih PP

S

q

q1

q1

2qs (z)H(x)he)(....sin

q

q1

q1T

2qs (z)D(x)fe)(....sin

No other assumption necessary !!

Separation DF and FF weighting the events with their

phT

Angles and Asymmetries DefinitionsConvolution Integral on initial quark

transverse momentum pT and final k T

Bi-dimensional fit of A(, s)

TTransversity Asymmetriesransversity Asymmetries [PRL94(2005)][PRL94(2005)]

positivo e negativo

)()(q)( 1Scoll zHxA )()(q)( 1Scoll zHxA )()()( 1T1Ssiv zDxfA )()()( 1T1Ssiv zDxfA

•Significant non zero asymmetries

•A+>0, A-<0

•|A| > |A| ?

•Possible evidence

fav1,disf1, HH

•First measurement of naïve T-odd DF in DIS

• ?

•.

0L0A:π qsinφUT

DYDIS ff )()( 11

Ferving activities

STAR

PHENIX

Hall A

CLAS

COMPASS

BELLE

TTransversity Asymmetries on Kaonsransversity Asymmetries on Kaons )()(q)( 1Scoll zHxA )()(q)( 1Scoll zHxA )()()( 1T1Ssiv zDxfA )()()( 1T1Ssiv zDxfA

•No Significant non zero amplitudes

•Systematic uncertainty: PID, Acceptance, Smearing, Unpolarised cosine moments

•A k+ > 0, Ak-≈ 0

•Systematic uncertainty: PID, Acceptance, Smearing, Unpolarised cosine moments

TTransversity Asymmetries on Kaons-ransversity Asymmetries on Kaons-

PionsPions )()(q)( 1Scoll zHxA )()(q)( 1Scoll zHxA )()()( 1T1Ssiv zDxfA )()()( 1T1Ssiv zDxfA

•Ak+ consistent with A+

• u quarks dominance

• Collins FF similar for and k ?

•Ak+ larger than A+ in some bins

• u quarks dominance

• Sea quarks contribution to Sivers moment important ?

ConclusionsConclusions• Polarised Structure Functions:

1. Precise and complete measurement of g1

• Polarised Quark Distributions:

1. First complete separation of pPDFs w/o assumption on sea

polarization

2. No hint of negative strange sea

• Transversity:

1. First measurements of Collins and Sivers moments for pions in

SIDIS

2. First measurements of Collins and Sivers moments for kaons in

SIDIS

3. 2005 data will double the statistics

4. Collins function estimation will allow extraction

of the transversity distribution

5. Sivers function will be extracted in the next

few years at HERMES