mauro anselmino, prague, august 1, 2005 hadron structure and hadron spectroscopy transversity...

Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy

Transversity (transverse spin and transverse motion)

Transversity distributions – (some) theory

Transversity distributions - experiments

Transverse Single Spin Asymmetries (how to test a Quantum Field Theory)

Spin and k┴ dependent parton distributions (TMD)


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


+–– –

++ +

+ +

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

+– =),( 2Qxq

),( 2QxqT

|| 2

1 iin helicity basis

–+

+ – ),( 2

1 Qxh decouples from DIS


Helicity conservation in pQCD or QED

qq ,

qq ',

qqqq E

mO q

''


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


D. De Florian, G.A. Navarro and R. Sassot, hep-ph/0506326


–+

+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


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

/2 / 22121 sQxsMxxxxx LFF

llqq *

plenty of spin effects

h1 in Drell-Yan processes

p p

Q2 = M2

qT

qL

l+

l–γ*


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


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


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 preparation


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

Spin effect comes from fragmentation of a transversely polarized quark pq

φ Sqp┴

)ˆˆ( ),(2

1

),(),(

/

//

ppSpz

pzDpzD

qqqhN

qhqh

initial q spin is transfered to final q',

which fragments

'll

Sq

Sq’p┴

)sin()ˆˆ( '' Shqq ppS

x

y

ΦSΦh

q

q’


)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 Matthias)

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


Alternative accesses to transversity

Inclusive Λ production and measure of Λ polarization

)()(1 zDxhP T (transverse fragmentation function)

Two pion production: l p↑ → π π X

),()(dd 1 pzqxh I (interference

fragmentation function)

Vector meson production: l p↑ → ρ X

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

(generalized fragmentation function)

Inclusive hadronic production: p p↑ → π X

),()(dd/1

pzDxh

q

N

Single Spin Asymmetry in D-Y processes

),()(dd 11 pzhxh T (higher-twist transversity

distribution)


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

xTransverse

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:


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


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


Predictions for COMPASS, hydrogen target

0.4 ≤ zh ≤ 1 0.2 ≤ PT ≤ 1 GeV/c 0.02 ≤ xB ≤ 1

Q2 > 1 (GeV/c)2 W2 > 25 GeV2 PT > 0.1 GeV/c Eh > 4 GeV 0.2 < zh < 0.9 0.1 < y < 0.9


Predictions for K production at HERMES


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


The spin story goes on .......

Polarization data has often been the graveyard of fashionable theories. If theorists had their way, they might just ban such measurements altogether out of self-protection.

J.D. BjorkenSt. Croix, 1987

mauro anselmino, prague, august 1, 2005 hadron structure and hadron spectroscopy transversity...

Documents

gev2h1 x collins

hermes collins data

belle collins data

p p xsingle spin asymmetry

transversity transverse

small x att

relative phase x

h1simple q2 evolution