Selected Recent Results on Parton Distribution and Fragmentation

Functions

Klaus Rith Moriond QCD March 19, 2009

Klaus Rith

University of Erlangen-Nürnberg & DESY

Main HERMES research topics:

Origin of nucleon spin

Details of nucleon structure

HERA longitudinally polarized 27.6 GeV e+/e- beam

Kinematics: 0.02<x<0.7, 1.0 GeV2<Q2<15 GeV2

RICH:

Hadron: ~ 98%, K ~ 88% , P ~ 85%

Polarized and unpolarized internal gas target (spin flip every 90 s)

1995-2000: longitudinal target polarization, 2002-2005: transverse target pol.

2006-2007: unpolarized H, D targets + Recoil Detector

Data taking: summer 1995 – June 30, 2007

HERMES Spectrometer

e

2

Complete description of nucleon by quark momentum and spin distri-butions at leading-twist: 3 kT-integrated distribution functions

(DF)

Unpolarised DF

Helicity DF Transversity DFq(x) f1

q (x)

q(x) g1

q(x)

q(x) h1

q(x)

well known

First glimpse

known

HERMES 1995-2000 HERMES 2002-2005

Leading-twist Parton Distributions

3

h1

f1

g1

Quark distribution functions

Sivers DF (T-odd)

Boer-Mulders DF

Transversity DF

(chiral-odd)

(chiral-odd)

Transverse Momentum Dependent DFs

Fragmentation functions (FF)D1 Dq

h = ‚normal‘ FF, H1

= spin-dependent Collins FF (chiral-odd)

4

Leading hadron originates with large probability from struck quark

Dqh(z):= Fragmentation function (FF)

z = Eh/

zq2q(x)

Dqh(z)

ALL (x,z) zq

2 q(x) Dqh(z)

q

q

Targets: H, D ; h = ±, K±, p (identified with RICH)

Measure hadron asymmetries

Quark Distributions from SIDIS

K+

K-

Flavor tagging

x = Q2/(2M) = fraction of nucleon‘s longitudinal momentum carried by struck quark

= E - E‘, Q2 = -q2 = -(l – l ‘)2

q(x) = quark number density

5

PRD 71 (2005) 012003

u quarks: large positive polarisation

d quarks: negative polarisation

d(x) - 0.4 u(x)

x

Sea quarks (u, d, s): polarisation compatible with 0.

Quark Helicity Distributions q(x)

HERMES

6

Inputs:

Multiplicities for K+ and K- from unpolarized deuteron d2ND

DIS/dxdQ2 = KU(x,Q2)[5 Q(x) + 2S(x)]

where Q(x) = u(x)+u(x)+d(x)+d(x) and S(x) = s(x) + s(x)

d2NDK/dxdQ2 = KU(x,Q2)[Q(x)DQ

K(z)dz + S(x) DSK(z)dz]

where DQK(z) = 4Du

K(z)+DdK(z) and DS

K(z) = 2DsK(z)

A1,D d2NDIS/dxdQ2 = KLL(x,Q2)[5Q(x) + 2S(x)]

A1,DKd2NK/dxdQ2 = KLL(x,Q2)[Q(x)DQ

K(z)dz + S(x) DS

K(z)dz]

Inclusive and K+, K- asymmetries from polarized deuteron

The Strange Sea: S(x), S(x)

7

S(x) from CTEQ6L with DQ

K(z)dz & DSK(z)dz as

free parameters (dotted) does not fit the data

S(x) much softer than assumed by current PDFs (mainly based on NX)

P.L. B666 (2008) 466

dNK Q(x)DQK(z)dz + S(x) DS

K(z)dz DQ

K(z)dz dNDIS 5 Q(x) + 2 S(x) 5 =

x > 0.3

Take DSK(z)dz = 1.27 0.13 from de Florian

et al.

S(x) from Kaon Multiplicities

( )

8

S = 0.037 0.019(stat.) 0.027(syst.)

compared

to S = - 0.085 0.013(stat.) 0.012(syst.) from inclusive data and SU(3)Large negative contribution from low x?

S(x) from Kaon Asymmetries

P.L. B666 (2008) 466

9

Amplitude has 2 components:

2sin( + S)hUT ~ h1

q(x)H1q(z)

U: unpol. e-beamT: transv. pol. Target

Transversity DF

Collins FF

2sin( - S)hUT~ f1Tq(x) D1

q(z)

Unpolarised FF

Sivers DF(Requires non-vanishing orbital angular momenta Lq of quarks)

z = Eh/

Transverse Azimuthal Angular Asymmetries

10

Collins Amplitudes

2sin( + S)hUT ~ h1q(x) H1

q(z)

First measurement of non-zero Collins effect

Both Collins fragmentation function and transversity distribution function are sizeableSurprisingly large - asymmetry

Possible source: large contribution (with opposite sign) from unfavored fragmentation, i.e. u -

H1

,disf - H1

,fav

N/q U L T

U f1 h1

L g1 h1L

T f1T g1T h1 h1T

Transversity DF

Collins FF

11

Experimental evidence for orbital angular momentum Lq of quarks

But: Quantitative contribution of Lq to nucleon spin still unclear

First observation of non-zero Sivers distribution function in DIS

2sin( - S)hUT ~ f1Tq(x) D1

q(z)

Sivers Amplitudes Sivers

DFN/q U L T

U f1 h1

L g1 h1L

T f1T g1T h1 h1T

12

vv

vv

du

dT

uT

UTS ff

ff,

1,

1

,1

,1

4

42)sin(2

access to Sivers valence distribution

Transverse SSA for + - -

13

Azimuthal Asymmetries in Unpolarised SIDIS N/q U L T

U f1 h1

L g1 h1L

T f1T g1T h1 h1T

kT kT

sT

sT

hP

hP

112cos )ˆ)(ˆ(2

HhMM

pkphkhF

h

TTTTUU

C

Boer-Mulders DF

transversely polarised quarks in unpolarised nucleon

14

2cos(2h)

Azimuthal Asymmetries in Unpolarised SIDIS N/q U L T

U f1 h1

L g1 h1L

T f1T g1T h1 h1T

Cahn effect

kT

kT

hP

hP

1111cos

ˆˆ2Dfx

M

khHhx

M

ph

Q

MF T

h

TUU

C

Intrinsic transverse quark momentum

15

2cos(h)

1-photon exchange approximation: TAA forbidden

AN 0: Signature of

2-photon exchange

Compatible with zero !AN = O(10-3)

Transverse Azimuthal Asymmetry in DIS

(Spin-flip every 90 s)

16

Conclusions

HERMES made a first glimpse at various Transverse Momentum dependent parton Distribution functions

HERMES provides new constraints for S(x) at low Q2

TMDs offer a large amount of new information on the nucleon structure They need to be

explored in detail by the next generation of experiments at future high-luminosity e-N

facilities

17

Backups

3210 sin1

cos1

2cos LUUUUUUU dQ

dQ

ddd

1098 )3sin()sin()sin( UTSUTSUTS ddd

7654 cos1

sin1

2sin LLLLULUL dQ

ddQ

d

1211 sin1

)2sin(1

UTSUTS dQ

dQ

151413 )2cos(

1cos

1)cos( LTSLTSLTS d

Qd

Qd

d

I[h1H1┴]

Transversity & Collins

e

e

e

SL

N/q U L T

U f1 h1

L g1 h1L

T f1T g1T h1 h1T

I[f1TD1]

ST

Sivers

TMDs in SIDIS

3210 sin1

cos1

2cos LUUUUUUU dQ

dQ

ddd

1098 )3sin()sin()sin( UTSUTSUTS ddd

7654 cos1

sin1

2sin LLLLULUL dQ

ddQ

d

1211 sin1

)2sin(1

UTSUTS dQ

dQ

151413 )2cos(

1cos

1)cos( LTSLTSLTS d

Qd

Qd

d

ST

e

e

e

SL

N/q U L T

U f1 h1

L g1 h1L

T f1T g1T h1 h1T

I[g1TD1]┴

I[h1TH1┴]┴

I[h1LH1┴]┴

TMDs in SIDIS

kT kT

sT

sT

hP

hP

kT

kT

hP

hP

112cos )ˆ)(ˆ(2

HhMM

pkphkhF

h

TTTTUU

C

1111cos

ˆˆ2Dfx

M

khHhx

M

ph

Q

MF T

h

TUU

C

Cahn effect

Boer-Mulders effect

2coscos 2cos)(cos)( UUUU FyBFyC 2cosUUF

cosUUF

LUUTUUh

FyBFyAxxyQdPddzdydx

d,,

2

2

2

2

5

)()(2

1

TUUF , LUUF ,

Cahn and Boer-Mulders effect

First evidence for (transversity and) chiral-odd, naive-T-odd spin-dependent di-hadron fragmentation function

JHEP 06 (2008) 017

Transverse SSA for pion pairs

Explicit dependence on transverse momentum of Explicit dependence on transverse momentum of

hadronhadron P Ph┴ h┴

Convolution of two unknown functionsConvolution of two unknown functions

High statistical powerHigh statistical power

Trans. component of relative momentum survives Trans. component of relative momentum survives

integration over theintegration over the P Ph┴h┴ of pairof pair

Collinear kinematics (factorization, evolution)Collinear kinematics (factorization, evolution)

Simple product of unknown functionsSimple product of unknown functions

Limited statistical powerLimited statistical power

h1,q h1,q

Transverse SSA for pion pairs

Transverse quark spin + spin-dependent fragmentation

Azimuthal asymmetry ~ sin( + S)h h

h

q q

Left-right distribution asymmetry (due to orbital angular momentum) + final state interaction

Azimuthal asymmetry ~ sin( - S)h

COLLINS

SIVERS

anti-green remnant

green quark

Azimuthal angular asymmetries

H1h1

DF

1H

Need another chiral-odd object!

chiral odd fragmentationfunction

X'N hll SIDIS:

chiral-odd

?

chiral even!

Transversity Sq(pqxPh)

How to measure Transversity

Experimental evidence for orbital angular momentum Lq of quarks

But: Quantitative contribution of Lq to nucleon spin still unclear

First observation of non-zero Sivers distribution function in DIS

2sin( - S)hUT ~ f1Tq(x) D1

q(z) large!

Final result: K+ enhancement will be smaller, Q2 dependent?

Sivers Amplitudes Sivers

DFN/q U L T

U f1 h1

L g1 h1L

T f1T g1T h1 h1T

T

12

x vs z z vs Ph ┴ x vs Ph ┴

2-D Collins Moments for ±

x vs z z vs Ph ┴ x vs Ph ┴

2-D Sivers Moments for ±

Global fit

HERMES, COMPASS, BELLE

First extraction of transversity distribution

A. Prokudin at Transversity 2008

(ep->ehX)

(ed->ehX)

(ee->hhX)

Consistent picture

Also with new proton data from COMPASS

Extraction of Transversity

E. Boglione at Transversity 2008

Sivers Extraction

xf 1

T(x

)