Delia Hasch

Delia HaschDelia Hasch

Transversity & friends from Transversity & friends from

HERMESHERMES

International workshop on hadron and spectroscopy, Torino, Italy, 31. March – 02. April 2008

outlineoutline:

a very brief introduction

1 and 2 hadron production: transversity + Sivers fct.

theory meets experiments

longitudinally polarisedquarks and nucleons

transversely polarisedquarks and nucleons

unpolarised quarksand nucleons

quark structure of the nucleonquark structure of the nucleon

q q q

q: helicity-flip of both nucleon and quark

needs a chiral odd partner:q is chiral-odd

[also: h1q, Tq]

q

hqeqeqehXep zFFxq )()(

chiral-odd PDF

chiral-oddFF

chiral-even

chiral-odd fragmentation function acts as polarimeter of transverse quark polarisation

h

h

q q

Collins FF H1(z,kT

2) correlates transverse spin of fragmenting

quark and transverse momentum Ph of produced hadron h

left-right (azimuthal) asymmetry in the direction of the outgoing hadron

1hadron production: “1hadron production: “Collins-effect”Collins-effect”

our observable: single-spin azimuthal asymmetryour observable: single-spin azimuthal asymmetry

Sivers distribution function : distribution of unpolarised quarks in a transversely polarised nucleon describes spin-orbit correlations

another mechanism that produces single-spin azimuthal asymmetries:

is this observable unique?is this observable unique?

“ “Sivers-effect Sivers-effect ” ”

[Matthias Burkardt]

a non-zero Sivers fct. requires non-zero orbital angular momentum !

...

1)3sin()sin()sin(

QddσdσS UTSUTSUTST

polarised DISpolarised DIShh cross cross section section

.......1

)cos(

Q

S ST

UU

beam: target: SL ,ST ,...),,,,( h

h Pzyxdσ

q(x)

q(x)

LUUUUUUU dσQλdσ

Qdσdσ sin

1cos

12cos

LLLLLULULL dσ

QdσSλdσ

QdσS cos

1sin

12sin

polarised DISpolarised DIShh cross cross section section

.......1

)cos(

Q

S ST

,...),,,,( hh Pzyxdσ

1Hq

transversity

(Collins effect)

...1T11 LhDfHq

11 Hh ...1 He

1T1 Df

SIDIS with transversely polarised targets but not only…

LUUUUUUU dσQλdσ

Qdσdσ sin

1cos

12cos

q(x)

q(x)

LLLLLULULL dσ

QdσSλdσ

QdσS cos

1sin

12sin

...

1)3sin()sin()sin(

QddσdσS UTSUTSUTST

extraction of azimuthal amplitudesextraction of azimuthal amplitudes

UUUU)2cos()cos( fixed parameters for:

unbinned Maximum Likelihood fit

to the log of the weighted PDF :

definition of angles + asymmetries acc. to “Trento convention”

i

wi

iFL )(

)sin()sin(2)sin()sin(2[ S

h

UTSS

h

UTSP

1,,,...,)sin( S

h

UTSi PF

)2sin()2sin(2)3sin()3sin(2 S

h

UTSS

h

UTS

])sin()sin(2 S

h

UTS

…takes into account cross contamination of moments

[PRD70(2004),117504]

Collins asymmetriesCollins asymmetries

)()(δ 1 zHxq q )()(δ 1 zHxq qfirst time: transversity & Collins FF are non-zero!

• asymmetries positive –

no surprise: u-quark

dominance and expect q>0

sinceq>0• large negative

asymmetries – ARE a

surprise: suggests the disfavoured CollinsFF being large and with oposite sign:

)()( fav,1

disfav,1 zHzH )()( fav,

1disfav,

1 zHzH

ep X

Collins asymmetriesCollins asymmetries

K

)()(δ 1 zHxq q )()(δ 1 zHxq qfirst time: transversity & Collins FF are non-zero!

ep KX

K+ amplitudes consistent with amplitudes as expected from u-quark dominance

K of opposite sign from (K is all-sea object)

more Collins asymmetriesmore Collins asymmetries

)()(δ 1 zHxq q )()(δ 1 zHxq qneutral pions: important ‘control’ asymmetry (isospin)

holds for all tw-2 and tw-3 DF in LO and NLO in s

more Collins asymmetriesmore Collins asymmetries

)()(δ 1 zHxq q )()(δ 1 zHxq qneutral pions:

results for the three pion charge states are consistent with isospin symmetry

holds for all tw-2 and tw-3 DF in LO and NLO in s

fulfilled!

neutral pions: important ‘control’ asymmetry (isospin)

spin-dependentspin-dependent fragmentationfragmentation

functionfunction

ee++ee--

extracting extracting transversitytransversity

e-

e+

Xee jet21jet

q

hqeqeqehXep zFFxq )()(

first glimpsefirst glimpse of transversity of transversityxd

(x)

xu

(x)

[Anselmino et al. PRD75(2007)]

xq(x) QSM

[Efremov,Goeke,Schweitzer PRD73(2006)]

q compare to a model calculation:

global, simultaneous fit:

first glimpsefirst glimpse of transversity of transversityxd

(x)

xu

(x)

[Anselmino et al. PRD75(2007)]

q

q

global, simultaneous fit:

compare to q:

first glimpsefirst glimpse of transversity of transversityxd

(x)

xu

(x)

[Anselmino et al. PRD75(2007)]

q

global, simultaneous fit:

• include new high statistic data

from BELLE and HERMES; identified

hadrons from COMPASS

looking forward:looking forward:

• awaiting proton results from

COMPASS extending to lower x

spin-orbit structurespin-orbit structure

Sivers function:

[Matthias Burkardt]

a non-zero Sivers fct. requires non-zero orbital angular momentum !

Sivers Sivers asymmetriesasymmetries

)()( 1T1 zDxf qq )()( 1T1 zDxf qq

are subtantial and positive:

• first unambiguous evidence for a non-zero T-odd distribution function in DIS

• a signature for quark orbital angular momentum !

Sivers Sivers asymmetriesasymmetries

)()( 1T1 zDxf qq )()( 1T1 zDxf qq

• SURPRISE: K amplitude 2.3±0.3 times larger than for

conflicts with usual expectations based on u-quark dominance

suggests substantial magnitude of the Sivers fct. for sea quarks

comparison to modelscomparison to models[Anselmino et al. PRD72(2005)]

kaon data suggest that sea quark contribution may be significant

excellent description of pion databut: cannot constrain sea predictions for kaons:

see talk from D’Alesio about choice of fragmentation functions

comparison to modelscomparison to models[Anselmino et al. PRD72(2005)]

kaon data suggest that sea quark contribution may be significant

excellent description of pion databut: cannot constrain sea predictions for kaons:

see talk from D’Alesio about choice of fragmentation functions

[M. Anselmino @PACSPIN07]

FF from [deFlorian, Sassot, Stratmann, arXiv:0703.242]

extracting theextracting the Sivers Sivers functionfunction

)()(A 1T1)sin

UTS zDxf qq( )()(A 1T1)sin

UTS zDxf qq(

crucial test of pQCD:

DYT1DIST1 )()( qq ff DYT1DIST1 )()( qq ff

ToDo:

@FAIR (GSI)

usual unpolarised fragmentation function

semi-inclusive 2-hadron semi-inclusive 2-hadron

productionproduction

Xepe

2-hadron asymmetries2-hadron asymmetries

),()(δ))sin(sin(~ 21 hq

SR MzHxq ),()(δ))sin(sin(~ 2

1 hq

SR MzHxq

UTA

UTA

interference fragmentation function between pions in s-wave and p-wave

• only relative momentum of hadron pair relevant

integration over transverse momentum of hadron pair simplifies factorisation (collinear!) and Q2 evolution

• however cross section becomes very complicated (depends on 9! variables)

models for 2-hadron models for 2-hadron asymmetriesasymmetries

M (GeV)

[Bacchetta, Radici PRD74(2006)]

pythia:

[Jaffe et all, PRL80(1998)]

),(cos),(

)cos,,(2,

12,

1

21

MzHMzH

MzHppsp

),(cos),(

)cos,,(2,

12,

1

21

MzHMzH

MzHppsp

0

due to interference 0

model for H1<|q (Mhh)

combined with various

models for q(x)

2-hadron asymmetries2-hadron asymmetries

Xepe

),()(δ 1 MzHxq q ),()(δ 1 MzHxq q

• BOTH: transversity and interference fragmention function are non-zero ! [arXiv:0803.2367]

models for 2-hadron models for 2-hadron asymmetriesasymmetries

M (GeV)

[Bacchetta, Radici PRD74(2006)]

model calculation for H1<|q (z)

combined with various models for q(x)

pythia:

[Jaffe et all, PRL80(1998)]

ruled outruled out

shape compares shape compares wellwell

0

2-hadron asymmetries2-hadron asymmetries

• first evidence for non-zero first evidence for non-zero interference FFinterference FF

• this kind of interference effect is a very this kind of interference effect is a very

promising way to access promising way to access q @RHICq @RHIC

q(x) from SIDIS pp ee-

• BELLE plans to measure it !BELLE plans to measure it !

),()(~ 1 MzHxq q

where do we stand ?where do we stand ?precision of data for identified hadrons adequate for quantitative extraction of flavour dependence of both transversity and Sivers fct

where do we stand ?where do we stand ?

more to come:more to come:

precision of data for identified hadrons adequate for quantitative extraction of flavour dependence of both transversity and Sivers fct

T

1/7/07@ 1:09:56 am

where do we stand ?where do we stand ?

more to come:more to come:

precision of data for identified hadrons adequate for quantitative extraction of flavour dependence of both transversity and Sivers fct

PT-weighted Collins and Sivers asymmetries

model-independent interpretation of asymmetries

requires control of acceptance effects (more @transversity08)

Boer-Mulders fct. via <cos(2)>, <kT> via Cahn-effect <cos>

requires control of acceptance effects (more @transversity08)

<cos(S)>LT : access to tw-2 fct. g1T ; other AUT moments

T

inclusive pion photoproduction AUT (“E704 effect”)

stay tuned !

BACKUP SLIDESBACKUP SLIDES[courtesy of A. Bacchetta]

Sivers Sivers asymmetriesasymmetries

)()( 1T1 zDxf qq )()( 1T1 zDxf qq

neutral pions:

results for the three pion charge states are consistent with isospin symmetry

contributions from VMcontributions from VM

AUT of VM prod.n and decay distributions not yet available for a

correction …

resolving the convolution resolving the convolution

integralintegral

pT weighted asymmetries:

what about the Pwhat about the PT T weighted weighted

asymmetries?asymmetries?MC study of acceptance effects:gmc_trans: generator for transversity + TMDs

Collins asymmetriesunweighted

[L. Pappalardo, PhD Thesis University Ferrara]

what about the Pwhat about the PT T weighted weighted

asymmetries?asymmetries?MC study of acceptance effects:gmc_trans: generator for transversity + TMDs

Collins asymmetriesweighted

[L. Pappalardo, PhD Thesis University Ferrara]

what about the Pwhat about the PTT weighted weighted

asymmetries?asymmetries?acceptance depends strongly on PT:

<pT>=<kT>=0.38, constant

what about the Pwhat about the PTT weighted weighted

asymmetries?asymmetries?solutions under study:solutions under study:

very promising more details @transversity08, Ferrara, May 28-31

multiplicities compared to multiplicities compared to theorytheory

[deFlorian,Sassot,Stratmann arXiv:0708.0769]

new FF from combined NLO analysis of single-inclusive hadron production in ee, pp and DIS