Mauro Anselmino, Como, September 7, 2005 Transversity 2005 1 Transversity (transverse spin and transverse motion) Towards transversity distributions: theory.

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


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


Transversity 2005 3

+–– –

++ +

+ +

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

+– =),( 2Qxq

),( 2QxqT

|| 2

1 iin helicity basis

–+

+ – ),( 2

1 Qxh decouples from DIS (no quark helicity flip)


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


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


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


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


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


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


Transversity 2005 10

s=30 GeV2 s=45 GeV2

s=210 GeV2s=900 GeV2



s=30 GeV2 s=45 GeV2

s=210 GeV2s=900 GeV2



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



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



)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



fit to HERMES data on)sin( Sh

UTA



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



Fits to HERMES Collins data, preliminary results



Fits to BELLE Collins data, preliminary results



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



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



Two pion production:

),()(dd 1 pzqxh I interference

fragmentation function

Xpl

ISRUT qhA )sin(~ 11HqI

Talks by P. van der Nat, M. Radici



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



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



S

p

p'

– pPTθ

– p'

z

y

xΦS Φ

for a generic configuration:

)sin(PPpS STT

NA



0NA needs helicity flip + relative phase

–+

++

Im x

+

++

+

sq

N E

mA at quark level

large SSA observed at hadron level



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



Unweighted Collins moment: Unweighted Sivers moment:



Transverse Λ polarization in unpolarized p-Be scattering at Fermilab

XNp



pppp pppp



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



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



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



Deuteron target hdhupd

N

pu

NUT DDffA Sh

4 //

)sin(



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(



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



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



Looking forward to an interesting workshop, thanks!

Mauro Anselmino, Como, September 7, 2005 Transversity 2005 1 Transversity (transverse spin and transverse motion) Towards transversity distributions: theory.

Documents

transversity slide

mauro anselmino

transversity distributions

known slide

drago slide

preparation slide

bacchetta slide

ferrero slide