Mauro Anselmino, Como, September 7, 2005

Transversity 2005 1

Transversity (transverse spin and transverse motion)

Towards transversity distributions: theory and experiments

Transverse Single Spin Asymmetries

Spin and k┴ dependent parton distributions (TMD)

(unravelling the spin-orbital motion of partons?)

Collins mechanism

Sivers mechanism

),,( 2,/, Qkxf Spsa

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 2

Parton distributions

are fundamental leading-twist quark distributions

quark distribution – well known

quark helicity distribution – known

transversity distribution – unknown

all equally important

related to

positivity bound

qq , and 1h (or ) , qq T

qqq

qqq

qqqT

q qq 5

chiral-even

qT qq 5 related to chiral-odd

qqqT ||2

ggg gluon helicity distribution – poorly known

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 3

+–– –

++ +

+ +

+ =),( 2Qxq),( 2Qxq

+– =),( 2Qxq

),( 2QxqT

|| 2

1 iin helicity basis

–+

+ – ),( 2

1 Qxh decouples from DIS (no quark helicity flip)

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 4

h1 must couple to another chiral-odd function. For example: D-Y, pp → l+l– X, and SIDIS, l p → l π X, processes

++ –

++

–

+ –

–– +

–

+ –

h1 x h1

h1 x Collins function

J. Ralston and D.Soper, 1979 J. Cortes, B. Pire, J. Ralston, 1992

J. Collins, 1993

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 5

–+

+1 –1

2 g

1

No gluon contribution to h1

simple Q2 evolution

Q2 = 25 GeV2 Q02

= 0.23 GeV2

V. Barone, T. Calarco, A. Drago

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 6

Elementary LO interaction:

3 planes: plane ┴ polarization vectors,p-γ* plane, l+l– γ* plane

)( )()( )(1

9

42121

2

212

2

2

2

xqxqxqxqexxsMdxdM

daaaa

aa

F

sqxsMxxxxx LFF /2 / 22121

llqq *

plenty of spin effects

p p

Q2 = M2

qT

qL

l+

l–γ*

h1 in Drell-Yan processes

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 7

q q

q qqqqq

TTTTxqxqxqxqe

xhxhxhxheaA

)()()()(

)()()()(ˆ

dd

dd

21212

211121112

h1 from

)cos(2 cos1

sin

ˆdˆd

ˆdˆdˆ

2

2

TTa

RHIC energies:

small x1 and/or x2

h1q (x, Q2) evolution much slower than

Δq(x, Q2) and q(x, Q2) at small x

ATT at RHIC is very small

smaller s would help Martin, Schäfer, Stratmann, Vogelsang

Barone, Calarco, Drago

22 GeV 100 GeV 200 Ms

3102

Xllpp at RHIC

talk by A. Mukherjee

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 8

h1 from

)()(

)()(ˆ

)()()()(

)()()()(ˆ

21

2111

21212

211121112

xuxu

xhxha

xqxqxqxqe

xhxhxhxheaA uu

TT

q q

q qqqqq

TTTT

22 GeV 2 GeV 21030 MsGSI energies: large x1,x2

one measures h1 in the quark valence region: ATT

is estimated to be large, between 0.2 and 0.4

at GSIXllpp

PAX proposal: hep-ex/0505054

Talks by M. Contalbrigo, N. Nikolaev, M. Maggiora

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 9

Energy for Drell-Yan processes

"safe region": /JMM

s

M J /2

QCD corrections might be very large at smaller values of M:

yes, for cross-sections, not for ATT K-factor almost spin-independent

Fermilab E866 800 GeV/c

H. Shimizu, G. Sterman, W. Vogelsang and H. Yokoya, hep-ph/0503270

V. Barone et al., in preparationtalks by M. Guzzi, A. Bianconi

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 10

s=30 GeV2 s=45 GeV2

s=210 GeV2s=900 GeV2

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 11

s=30 GeV2 s=45 GeV2

s=210 GeV2s=900 GeV2

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 12

data from CERN WA39, π N processes, s = 80 GeV2

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 13

h1 x Collins from SIDIS processes

Asymmetry in the fragmentation of a transversely polarized quark

pq

φ Sqp┴

)ˆˆ( ),(2

1

),(),(

/

//

ppSpzD

pzDpzD

qqqh

N

qhqh

initial q spin is transferred to final q', which fragments

'll

Sq

Sq’p┴

)sin()ˆˆ( '' Shqq ppS

x

y

ΦSΦh

q

q’

“Trento conventions”

(Fundamental QCD property? D. Sivers)

q

hqh

N HMz

pD 1/

2

Amsterdam notations

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 14

)sin( ),()/(]y)-(1[1 )(

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

dd

/22

/2

/

21

2

Sh

q pqpqq

q qh

Nqq

hN

pzDxyxfe

pzDxyyxhe

A

neglecting intrinsic motion in partonic distributions:

]d[d

)sin( ]d[d 2)sin(

Sh

UTShA

Collins function

some data available from HERMES, first extraction of Collins functions: W. Vogelsang and F. Yuan (assuming Soffer-saturated h1)

transversity

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 15

fit to HERMES data on)sin( Sh

UTA

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 16

Extraction of Collins functions from HERMES + BELLE data

P1 depends on

)( )(

)( )(

21

2)1(

1)1(

zDzD

zDzD NN

(talk by R. Seidl)

M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin,

in preparation

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 17

Fits to HERMES Collins data, preliminary results

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 18

Fits to BELLE Collins data, preliminary results

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 19

HERMES + BELLE: Collins function is not zero

Theory: probably universal Collins, Metz

Models: few, in disagreement Amrath, Bacchetta, Metz,

Kundu, Mulders, …

assumes h1 = ∆q

disfavoured Collins functions = 0

pion-quark vertex ? loop?

Talk by. A. Bacchetta

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 20

X

p

Alternative accesses to transversity

Inclusive Λ production and measure of Λ polarization

)()(1 zDxhP Ttransverse fragmentation function

COMPASS analysis in progress

qqT DDD

Talk by A. Ferrero

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 21

Two pion production:

),()(dd 1 pzqxh I interference

fragmentation function

Xpl

ISRUT qhA )sin(~ 11HqI

Talks by P. van der Nat, M. Radici

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 22

Vector meson production:

),()()( ,0,1110 pzDxhV

(generalized fragmentation function)

Inclusive hadronic production:

),()(dd/1

pzDxhq

N

Single Spin Asymmetry in D-Y processes

),()(dd 11 pzhxh

(Boer-Mulders distribution)

Talk by F. Murgia

Xpl

Xpp

q

pq

N hM

kf 1/

Talks by D. Boer, G. Goldstein, M. Radici

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 23

S

p

p'

– pPTθ

θsinPpS T

NA

– p'

6;

5;

4;

3;

2;

1;

MMMMMM

Single Spin Asymmetry in elastic scattering. Example:

6 independent helicity amplitudes

)()(Im2 426315NA

'' qqqq

z

y

x

Transverse SSA

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 24

S

p

p'

– pPTθ

– p'

z

y

xΦS Φ

for a generic configuration:

)sin(PPpS STT

NA

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 25

0NA needs helicity flip + relative phase

–+

++

Im x

+

++

+

sq

N E

mA at quark level

large SSA observed at hadron level

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 26

BNL-AGS √s = 6.6 GeV 0.6 < pT < 1.2

E704 √s = 20 GeV 0.7 < pT < 2.0

STAR-RHIC √s = 200 GeV 1.1 < pT < 2.5

E704 √s = 20 GeV 0.7 < pT < 2.0

SSA, pp → πX

Xpp

Xpp 0

Xpp

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 27

Unweighted Collins moment: Unweighted Sivers moment:

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 28

Transverse Λ polarization in unpolarized p-Be scattering at Fermilab

XNp

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 29

pppp pppp

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 30

X

p

S

+ –

Brodsky, Hwang, Schmidt model for Sivers function

q q

diquark diquark

)sin(PPpS STT

needs k┴ dependent quark distribution in p↑: Sivers function

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 31

p┴ = PT – z k┴ + O(k┴2/Q2)

Sivers asymmetry in SIDIS

)ˆˆ( ),(2

1

),(),(

/

//

kpSkxf

kxfkxf

pq

N

pqpq

qTpq

N fM

kf

1/

2

Amsterdam notations

talk by A. Prokudin

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 32

M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin hep-ph/0501196 (PRD 71, 074006) and hep-ph/0507181

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 33

Deuteron target hdhupd

N

pu

NUT DDffA Sh

4 //

)sin(

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 34

First p┴ moments of extracted Sivers

functions, compared with models

M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin

data from HERMES and COMPASS

qTq

N ff )1(1

)1(

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 35

SSA in p↑p → π X

fit to AN with Sivers effects alone

maximized value of AN

with Collins effects alone

E704 data, E = 200 GeV

U. D’Alesio, F. Murgia M.A, M. Boglione, U. D’Alesio, E. Leader, F. Murgia

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 36

HERMES + E704: Sivers function is not zero

Theory: not quite universal

J. Collins, a “QCD theorem”

Models: few, in fair agreement

Spin-k┴ partonic correlations in nucleonsTalks by M. Burkardt

D. Sivers, X. Artru

YD

qTSIDIS

qT ff

11

dT

uT ff 11

chiral models, A. Drago, P. Pobilytsa

qqTf

1M. Burkardt

Sum rules: talk by O. Teryaev

Talk by A. Baccheta

Mauro Anselmino, Como, September 7, 2005

Transversity 2005 37

Looking forward to an interesting workshop, thanks!