llpp

Transversity via Drell-Yan processes

Physics with polarized antiprotons at GSI-PAX

TTA direct access to transversity

Transverse Single Spin Asymmetries

QCD “theorem”: (Sivers)D-Y = – (Sivers)DIS

Time-like e.l.m. form factors

SSA in 1F

Elastic processes

SLSSLLNNN AAA AA , , ,,

NA

2Fform factors and vs.

spin misteries like in pp ?

M. Anselmino, Milano, May 4, 2005

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. Bjorken

St. Croix, 1987

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

–++ –

),( 21 Qxh decouples from DIS

h1 must couple to another chiral-odd function. For example: D-Y, pp → μ+μ- 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

Elementary LO interaction:

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

)( )()( )(1 94

21212

212

2

2

2

xqxqxqxqexxsMdxdM

daaaa

aa

F

/2 / 22121 sQxsMxxxxx LFF

*qq

plenty of spin effects

q q

q qqqqqTTTT xqxqxqxqe

xhxhxhxheaA

)()()()(

)()()()(ˆ

dddd

21212

211121112

h1 from

)cos(2 cos1

sinˆdˆdˆdˆdˆ 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 smallsmaller s would help Martin, Schäfer, Stratmann, Vogelsang

Barone, Calarco, Drago

22 GeV 100 GeV 200 Ms3102

Xllpp at RHIC

h1 from

)()(

)()(ˆ)()()()(

)()()()(ˆ

21

2111

21212

211121112

xuxuxhxha

xqxqxqxqe

xhxhxhxheaA uu

TT

q q

q qqqqqTTTT

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

Energy for Drell-Yan processes

"safe region": /JMM

sM 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

s=30 GeV2 s=45 GeV2

s=210 GeV2s=900 GeV2

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

J/ψq q

q

l+

l–

l+

l–

all vector couplings, same spinor structure

and, at large x1, x2

measure ATT also in J/ψ resonance region

llXJpp /

/2

/2

))((

JJ

Vl

Vq

MiMMvuguvg

2

) )((M

vueuveq

q

*

*/ ˆˆ TT

JTT aa

)()()()(

)()()(

)()()(ˆ

21

2111

212

21112

xuxuxhxh

xqxqg

xhxhgaA uu

qVq

q qqVq

TTTT

M. A., V. Barone, A. Drago and N. Nikolaev

Single Spin Asymmetries (and their partonic origin)

pq

Pqπ

k┴Collins effect = fragmentation of polarized quark

depends on Pq· (pq x k┴)

P

pk┴

Sivers effect = number of partons in polarized proton depends on P · (p x k┴)

q

pk┴

Boer-Mulders effect = polarization of partons in unpolarized proton depends on Pq · (p x k┴)

qPq

Collins: chiral-odd

Sivers: chiral-even

Boer-Mulders: chiral-odd

These effects may generate SSA

d dd d

NA

BNL-AGS √s = 6.6 GeV 0.6 < pT < 1.2 p↑p

E704 √s = 20 GeV 0.7 < pT < 2.0 p↑p

STAR-RHIC √s = 200 GeV 1.1 < pT < 2.5 p↑p

E704 √s = 20 GeV 0.7 < pT < 2.0 p↑p

SSA, pp → πX

SSA, SIDIS

Transversity and SSA in Drell-Yan processes

)cos(2 sin cos1d 22unp

),(),( 221111

kxhkxh

Boer-Mulders functions

)sin( sin2SNA

),(),( 221111

kxhkxh

extract these unknown chiral-odd functions from unpolarized cross-section

combine above measurement with measurement of AN to obtain information on h1

This AN expected of the order of a few percentsA. Bianconi, M. Radici

D. Boer, 1999

GSIat processes in SSA Other pp

)(),( 2111Y-D xfkxfA TN

Sivers function usual parton distribution

Direct access to Sivers function

test QCD basic result: DIS1Y-D1 )()( TT ff J. Collins

qqTDXpp

N DfA )( 1

usual fragmentation function

process dominated by no Collins contribution

ccqq

same process at RHIC is dominated by ccgg

Electromagnetic form factors

Jμem

p p'

)()'(||' pupupJp em

qQFmQF p )(2/)( 2

22

1

21 FFGE 21 FFGM F1(0) = F2(0) = 1

Κ = 1.79

22 4/ pmQ

In pQCD

41

QF6

2 QF

JLAB: F2/F1 ~ 1.25 GeV/Qdifficult to separate F1,F2 or

GE,GM

p p̄

In time-like region GE and GM may have relative phases

P l+

l-

θL

SN

there may be a SSA: σN - σ –N

σN + σ –N= Ay = Py

1

/||sin||)cos1()Im()2sin(

2222

*

EM

MEy GG

GGA

Py can be very large: predictions depend strongly on model assumptions for F2/F1

Unexpected spin effects in pp elastic scattering

larger t region can be explored in pp

pppppppp

Unexpected large polarization in pppp

What about pppp ?

Conclusions

ATT in D-Y processes at GSI energies: highway to transversity

AN and SSA: many effects expected and test of QCD theorem: (Sivers)D-Y = – (Sivers)DIS

…the transverse-spin asymmetries whose measurement is suggested for these experiments, are remarkably insensitive to shifts in the overall normalization. In summary, perturbative corrections appear to make the cross sections larger independently of spin.

They would therefore make easier the study of spin asymmetries, and ultimately transversity distributions. (G. Sterman et al.)

Exploration and separation of proton form factors, spin results from new time-like region

Spin asymmetries in proton-antiproton elastic processes: as mysterious as in proton-proton?