EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 1 Spin dependence: theory and phenomenology Electromagnetic Interactions with Nucleons and

1 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece

Spin dependence: theory and phenomenology

Electromagnetic Interactions with Nucleons and Nuclei(EINN 2005)

6th European Research Conference September 21-24, 2005 - Milos, Greece

Mauro Anselmino Torino University

and INFN


Polarized DIS and helicity distributions, spin carried by quarks and gluons?

Spin dependent, k┴ unintegrated parton distributions: fundamental spin-k┴ correlations?

Transversity distributions, unknown

Transverse single spin asymmetries),,( 2,/, Qkxf Spsa

“Partonic spin cases”

),,( 2,/, QpzD saSh

Polarized fragmentation functions


What do we know, and how, about the proton structure?

WLE

E

MqE

'

2'd d

d4

2

Main source of information is DIS

l,s l’

q

p,S

X

L

W

θ

X

l’,E’

l,E,s p, S


parity conserving case (one photon exchange)

measuring dσ one extracts information on the structure functions F1, F2, g1 and g2

F1,2 related to q(x,Q2), g(x,Q2 ) quark, gluon distributions

g1 related to ∆q(x,Q2), ∆g(x,Q2) quark, gluon helicity distributions

qq

qppp

2ˆ

qp

Qx

2

2

)'(2'''2),',( llsimllgllllsllL

),()(

) ),(

),(ˆˆ

),(),,(

222

21

22

212

Qxgqp

pqSSqpQxg

qp

Sqi

QxFqp

ppQxF

q

qqgSqpW

qqq qqq ggg ggg


q

l’lL

Wq

p,S

X

QCD parton model


gCN

qqCeQxg gf

qq

q

1

2

1),( 22

1

gPP

PPQ

gQ gggq

qgqqs

2

)(

dln

d 2

2

...)(2

)()(),( )1(

20 xC

QxCxC i

sisi

...)(2

)()(),( )1(

20 xP

QxPxP ij

sijsij

coefficient functions

splitting functions

q

qq

),( ,d 21

Qyqy

xC

y

yqC

x s

QCD evolution



de Florian, Navarro, Sassot


Research Plan for Spin Physics at RHICFebruary 11, 2005

Figure 11: Left: results for Δg(x,Q2 = 5GeV2) from recent NLO analyses [1, 2, 36] of polarizedDIS. The various bands indicate ranges in Δg that were deemed consistent with the scalingviolations in polarized DIS in these analyses. The rather large differences among these bandspartly result from differing theoretical assumptions in the extraction, for example, regarding theshape of Δg(x) at the initial scale. Note that we show xΔg as a function of log(x), in orderto display the contributions from various x-regions to the integral of Δg. Right: the “net gluonpolarization” Δg(x,Q2)/g(x,Q2) at Q2 = 5 GeV2, using Δg of [2] and its associated band,and the unpolarized gluon distribution of [82].


Direct measure of Δg needed

xQxgQSqq gq

d ),()( )(1

0

22

1.0d ),(2

1 1

0

2 xQxSq

large pT di-hadron production in SIDIS,

high pT pions and jets at RHIC,

direct photon production at RHIC,

charm production at RHIC,

Small and large x behaviours, flavour decompositions, ….

qqg , qgqg gggg

qqg ccgg

gqgq LLSS2

1 longitudinal spin sum rule, not the whole story…

F. Tessarotto

R. De Vita


large pT di-hadron production in SIDIS


S

p

p'

– pPTθ

θsinPpS T

NA

– p'

5;

4;

3;

2;

1;

M

M

M

M

M

5 independent helicity amplitudes

)(Im 43215NA

pppp

z

y

x

Example:

Transverse single spin asymmetries in elastic scattering


0NA needs helicity flip + relative phase

–+

++

Im x

+

++

+

sq

N E

mA at quark level

but large SSA observed at hadron level!

QED and QCD interactions conserve helicity, up to corrections )/( EmO q


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


“Sivers moment”

XlNl

dd

ddNA

)dd(d d

)sin()dd(d d2

)sin(2

S

S

)sin(

S

UTSSA


“Collins moment”

dd

ddNA

XlNl

)dd(d d

)sin()dd(d d2

)sin(2

S

S

)sin(

S

UTSSA


Transverse Λ polarization in unpolarized p-Be scattering at Fermilab

XNp


pppp pppp

“The largest spin effect ever seen by any human”, S. Brodsky, Como 2005


)sin(PPpSA STTN

need k┴ dependent quark distribution in p↑

z

y

xΦSΦπ

X

p

S

PT

Transverse single spin asymmetries in SIDIS

Sivers mechanism

or p┴ dependent fragmentation of polarized quark Collins mechanism

(talk by G. Schnell)


X

p

S

+ –

Brodsky, Hwang, Schmidt model for Sivers function

q q

diquark diquark


p┴ = PT – z k┴ + O(k┴2/Q2)

Sivers asymmetry in SIDIS

)ˆˆ( ),(2

1

),(),(

/

//

kpSkxf

kxfkxf

pq

N

pqpq

pSk┴

φq


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


Collins mechanism for SSA

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’

(Fundamental QCD property? D. Sivers)


)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[ddd

)sin( ]d[ddd 2)sin(

Sh

ShSh

UTShA

Collins function

First extraction of Collins functions from HERMES data: 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

jets theinside pions of onsdistributi azimuthal twothe

between is that , and ofspin thebetween event,by event n,correlatio

qq


Fits to HERMES Collins data, preliminary results


Fits to BELLE Collins data, preliminary results M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin, in preparation


qTpq

N fM

kf

1/

2

pSk┴

φq

pq

φ Sqp┴

)ˆˆ( ),(2

1

),(),(

/

//

ppSpzD

pzDpzD

qqqh

N

qhqh

)ˆˆ( ),(2

1

),(),(

/

//

kpSkxf

kxfkxf

pq

N

pqpq

Amsterdam group notations

q

hqh

N HMz

pD 1/

2

spin-k┴ correlations – Trento conventions

Sivers function Collins function

YD

qTSIDIS

qT ff

11


q

pq

N hM

kf 1/

p

Sqk┴

φq

pq

φSΛp┴

)ˆˆ( ),(2

1

),(2

1),(

/

//

ppSpzD

pzDpzD

qq

N

qhq

)ˆˆ( ),(2

1

),(2

1),(

/

//

kpSkxf

kxfkxf

qpq

N

pqpq

Amsterdam group notations

qTq

N DMz

pD

1/

spin-k┴ correlations

Boer-Mulders function polarizing f.f.


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


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 5chiral-even

qT qq 5 related to chiral-odd

qqqT ||2

ggg gluon helicity distribution – poorly known

ggg gluon distribution ~ known


+–– –

++ +

+ +

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

+– =),( 2Qxq

),( 2QxqT

|| 2

1 iin helicity basis

–+

+ – ),( 2

1 Qxh decouples from DIS (no quark helicity flip)


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


–+

+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

sqxsMxxxxx LFF /2 / 22121

llqq *

plenty of spin effects

h1 in Drell-Yan processes

p p

Q2 = M2

qT

qL

l+

l–γ*


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

s = 210 GeV2 is best energy (talk by P. Reimer at workshop)


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


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 (Boer-Mulders function)

(problematic)


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

Spin is one of the most fundamental concepts in physics, deeply rooted in Poincare invariance and

hence in the structure of space-time itself. All elementary particles we know today carry spin,

among them the particles that are subject to the strong interactions, the spin-1/2 quarks and the

spin-1 gluons. Spin, therefore, plays a central role also in our theory of the strong interactions, Quantum Chromodynamics (QCD), and to

understand spin phenomena in QCD will help to understand QCD itself.

RHIC proposal 2005

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EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 1 Spin dependence: theory and phenomenology Electromagnetic Interactions with Nucleons and