Strangeness and Spin in Fundamental Physics

Mauro Anselmino: The transverse spin structure of the nucleon Delia Hasch: The transverse spin structure of the nucleon – exp.Elliot Leader: The longitudinal spin structure of the nucleonWerner Vogelsang: QCD spin physics in hadronic interactionsNaohito Saito: Spin Physics at RHIC - experiment Raimondo Bertini: Spin physics with strangeness

Spin lectures

Spin seminars Robert Jaffe: Gluon spin basics

Harut Avakian: Spin Physics at JLabMariaelena Boglione: The first way to transversity

Varenna, June 19-29, 2007

–

Parton transverse motion, spin-k┴

correlation, orbiting? )()()( xqxqxqT

frame c.m. * sin p)Φ(ΦPA SπTT PpS

Transverse single spin asymmetries in SIDIS, experimentally observed (D. Hasch)

z

y

xΦSΦπ

X

p

S

PT

in collinear configurations there cannot be (at LO) any PT

Xhp *

Mauro Anselmino: The transverse spin structure of the nucleon - II

About partonic intrinsic motion and SSA

Estimate of transverse motion of quarks

TMDs: spin-intrinsic motion correlations in distribution and fragmentation functions

Sivers and Collins functions; SSA in SIDIS

Coupling Collins function and Transversity

What do we learn from Sivers functions?

The full structure of TMDs in SIDIS

p p

Q2 = M2

qT

qL

l+

l–*

Plenty of theoretical and experimental evidence for transverse motion of partons within nucleons and

of hadrons within fragmentation jets

GeV/c 0.2 fm 1 pxuncertainty principle

gluon radiation

±1

± ±k┴

Partonic intrinsic motion

qT distribution of lepton

pairs in D-Y processes

Hadron distribution in jets in e+e– processes

pT distribution

of hadrons in SIDIShXp *

Parton Model with intrinsic motion

Assume: struck parton carries 4-momentum k

k

P

k’

02 k

) ,0 ,0 ,( 00 PPP

);,();,(ˆd);,(d 222 QzDQyQxf hq

lqlq

q qlhXlp

pkk

factorization holds at large Q2, and

QCDT kP Ji, Ma, Yuan

zqP

PPz h

h

pkP zT

observables at

:

Q

kO

SIDIS in parton model with intrinsic k┴

xxB

Elementary Mandelstam variables:

The on shell condition for the final quark

implies

cos1

21)(ˆ 2 y

Q

ksxkls

cos

1

21)1( )(ˆ 2

yQ

kysxklu

22)(ˆ Qllt

neglecting terms one has

hB zzxx

cos1)2(4)1(1ˆˆˆ 2

2

422 yy

Q

ky

y

Qusd lqlq

“Cahn effect”

hh

lhXlp

ΦBAΦ

cosd

d

pkP zT

assuming:

one finds:

with

clear dependence on (assumed to be constant)and

Find best values by fitting data on Φh and PT dependences

EMC data, µp and µd, E between 100 and 280 GeV

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

Large PT data explained by

NLO QCD corrections

EMC data

How does intrinsic motion help with SSA?One can introduce spin-k┴ correlation in the Parton Distribution Functions (PDFs) and in the parton Fragmentation Functions (FFs)

X

pS

k

Only possible (scalar) correlation is

)( kpS

)ˆˆ( ),(),(

)ˆˆ( ),(2

1),(),(

1/

//,/

kpS

kpSkS

kxfM

kkxf

kxfkxfxf

qTpq

pq

Npqpq

TMDs: Sivers function

Boer-Mulders function

)ˆˆ( ),(2

1),(

2

1

)ˆˆ( ),(2

1),(

2

1),(

1/

///,

kps

kpsks

qq

pq

qpq

Npqpq

kxhM

kkxf

kxfkxfxfq

)ˆˆ( ),(

),(

)ˆˆ( ),(2

1 ),(),(

1/

//,/

pps

ppsps

qqq

hqh

qqqh

Nqhqh

pzHMz

ppzD

pzDpzDzDq

Collins function

)ˆˆ( ),(

),(2

1

)ˆˆ( ),(2

1 ),(

2

1),(

1/

///,

ppS

ppSpS

qq

Tqh

qq

Nqhq

pzDMz

ppzD

pzDpzDzD

Polarizing fragmentation function

Sivers effect in SIDIS

)ˆˆ( ),(2

1),(),(

/// ,

kpSk kxfkxfxfpq

Npqpq

),(),(ˆ),(,/

,

pkk zDydxfd hqq pq

),(),(ˆd)ˆˆ(),(/

pkkpS zDykxf

ddhqq pq

N

)sin( S

qTpq

N fM

kf

1/

2

q

hq

lqlq

pqSh

Shhq

lqlq

Spq

N

q Sh

Sh

ShShΦΦUT

pzDdQ

dkxfddΦdΦ

ΦΦpzDdQ

dΦkxfddΦdΦ

dddΦdΦ

ΦΦdddΦdΦA Sh

),(ˆ

),(

)sin( ),(ˆ

)sin( ),(

][

)sin(] [ 2

2/2

2/

2

)sin(

k

k

)ˆˆ( ),(2

1

),(),(

/

//

kpS

k

kxf

kxfxf

pq

N

pqpq

kPp zT

qTpq

N fM

kf

1/

2

Brodsky, Hwang, Schmidt model for Sivers function

X

p

S

)sin( ST TPPpS

+ –

q q

diquark

diquark

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

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

Fit of HERMES data on)sin( S

UTA

Deuteron target hd

hupd

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

),( 4

/

2

)1(1

)1(

kxfm

kkd

ff

pq

N

p

qTq

N

hep-ph/0511017

?11d

Tu

T ff

The first and 1/2-transverse moments of the Sivers quark distribution functions, defined in Eqs. (3, 9), as extracted in Refs. [20, 21, 23]. The fits were constrained mainly (or solely) by the preliminary HERMES data in the indicated x-range. The curves indicate the 1-σ regions

of the various parameterizations.

),( )( 12)2/1(

1

kxf

M

kdxf q

Tq

T k

M. Anselmino, M. Boglione, J.C. Collins, U. D’Alesio, A.V. Efremov, K. Goeke, A. Kotzinian, S. Menze, A. Metz, F. Murgia, A. Prokudin, P. Schweitzer, W. Vogelsang, F. Yuan

),( 2

12

22)1(

1

kxf

M

kdf q

Tq

T k

Spin effect comes from fragmentation of a transversely polarized quark

)ˆˆ( ),(2

1

),(),(

/

//

pps

p

qqqhN

qhqh

pz

pzDzD

initial q spin is transfered to final q', which

fragments

)sin()ˆˆ( '' Shqq pps

q

q’

Collins effect in SIDIS

)ˆˆ( ),(),( //

ppsp qqqh

N

qh

N pzzD

x

y

CΦ

SΦ hΦ

qs

qs

ll

TP

][

)sin( ]d[d 2)sin(

dddΦdΦ

ΦΦdΦdΦA

Sh

ShShΦΦUT

Sh

),( ),(ˆ

)sin(),(ˆ

),(

//22

/212

)sin(

q pqpq

lqlq

Sh

q Shqh

Nlqlq

qSh

ΦΦUT

pzDkxfdQ

dddΦdΦ

ΦΦzDdQ

dkxhddΦdΦ

A Sh

k

pk

lqlqlqlq ddd ˆˆˆ

),(),(ˆd),(/1

pk zDykxhdd

qh

N

q q

Collins effect in SIDIS couples to transversity, seminar of E. Boglione for combined

extraction

fit to HERMES data on)sin( Sh

UTA

W. Vogelsang and F. Yuan

Soffer-saturated h1 ||2 1 qqh

A. V. Efremov, K. Goeke and P. Schweitzer(h1 from quark-soliton model)

COMPASS measured Collins and Sivers asymmetries for positive (●) and negative (○) hadrons

dhuhpd

N

pu

NUT DDffA Sh

////

)sin( 4

small values due to

deuteron target:

cancellation between u and d contributions

dh

N

uh

NduUT DDhhA Sh

//11)sin( 4

S

kp̂

k

number density of partons with longitudinal

momentum fraction x and transverse momentum k┴, inside a proton with spin S

0),( ,/2 a pa xfddx kkk S

M. Burkardt, PR D69, 091501 (2004)

What do we learn from the Sivers distribution?

),(ˆ 2

ˆ cosˆ sin

)ˆˆ( ),(ˆ2

1),(ˆ

/

2

//2

kxfkdkdx

kxfkxfddx

pa

NSS

pa

Npa

a

ji

kpSkkk

Total amount of intrinsic momentum carried by partons of flavour a

for a proton moving along the +z-axis and polarization vector

jiS ˆ sinˆ cos SS

S

ak

)sin()ˆˆ( SkpS

GeV/c ˆ cosˆ sin 13.0

GeV/c ˆ cosˆ sin 14.003.002.0

0.050.06-

jik

jik

SSd

SSu

uk

dk? 0

du kk

Sivers functions extracted from AN data in Xpp give also opposite results,

with

036.0 032.0 du kk

Numerical estimates from SIDIS dataU. D’Alesio

Sivers function and proton anomalous magnetic momentM. Burkardt, S. Brodsky, Z. Lu, I. Schmidt

Both the Sivers function and the proton anomalous magnetic moment are related to correlations of proton wave functions with opposite helicities

? ),( 1

0 /

2qpq

N Ckxfddx k

in qualitative agreement with large z data:

d

uΦΦ

UT

ΦΦ

UT

S

S

A

A

) sin(

) sin(

APA,

aka,

The leading-twist correlator, with intrinsic k┴, contains several other functions .....

8 leading-twist spin-k┴ dependent distribution functions

Courtesy of Aram Kotzinian

Polarized SIDIS cross section, up to subleading order in 1/Q

Kotzinian, NP B441 (1995) 234

Mulders and Tangermann, NP B461 (1996) 197

Boer and Mulders, PR D57 (1998) 5780

Bacchetta et al., PL B595 (2004) 309

Bacchetta et al., JHEP 0702 (2007) 093

SIDISLAND