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The Partonic The Partonic Transverse-spin Transverse-spin

Structure of the ProtonStructure of the Proton

Marco Radici Pavia

The Partonic Structure of Hadrons

ECT* (Trento), 9-14 May 2005

Barone, Drago, Ratcliffe, Phys. Rep. 359 (2002) 1 orBarone and Ratcliffe, Transverse Spin Physics (World Scientific, 2003)

In collaboration with: A. Bacchetta (Univ. Regensburg) A. Bianconi (Univ. Brescia)

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Examples of large SSA

Ex.: Heller et al., P.R.L. 41 (‘78) 607

Ex.: Adams et al., STAR P.R.L. 92 (‘04) 171801

Airapetian et al., HERMES P.R.L. 94 (’05) 012002

Ex.: Conway et al., E615 P.R. D39 (‘89) 92

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helicity basis transverse basis

But helicity flip suppressed in QCD

collinear factorization + ~ massless quark spinors= § 1

) transverse spin effects (! SSA) suppressed in QCD

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We need transverse spin distribution (transversity)

it completes the parton structure of N at leading twist

DDistribution FFunction in quark-N helicity basis (Jaffe)

suppressed in inclusive DIS

struct. functionanalogue in Parton Model

F1 g1 ?

• helicity = chirality at leading twist ) helicity flip , chiral-odd

dynamical breaking of chiral symmetry?

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Properties of transversity

• h1(x,Q2) = g1(x,Q2) in nonrelativistic theory because [boost , rotation] = 0

difference ) information on relativistic dynamics of quarks in hadrons

• no h1 for gluons ) no mixing with gluons in evolution contrary to helicity g1

) non-singlet evolution of h1 for quarks

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cont’ed

• tensor charge (1st moment of h1) has anomalous dimension 0

• tensor charge is C-odd ) does not couple to quark-antiquark, gluons..

singlet DF ) more valence quark-like content of h1 ? Place to test CQM ?

• from lattice: f h1f = 0.562 § 0.088 (Aoki et al.)

• inequalities: |h1(x)| f1(x) (positivity) ; |2h1(x)| f1(x) + g1(x) (Soffer)

• nonsinglet axial charge (1st moment of g1) does not depend on scale Q2

better place to test evolution

• several model calculations

but QCDSF : g1 » h1

(Schierholz et al.)

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suppressed in inclusive DIS: how to extract transversity ?

search for chiral-odd partner of h1 constraint: leading twist process

initial state polarized Drell-Yan (DY) :

final state semi-inclusive

DIS :

annihilation :

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presumably h1 for antiquarks in p is small ! use antiprotons: HESR@GSI

ATT small (NLO) by Soffer inequality (Martin, Schaefer, Stratmann, Vogelsang ’98

Barone, Calarco, Drago, ‘97)

search for transversity in double polarized DY : p"p" ! l+l - X(historically the 1st: Ralston & Soper ’79)

Collins-Soper frame: qT(*) in (xz) plane

only transversity involved, no other unknowns, but

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semi-inclusive production :

which mechanism ?!

e p" ! e’ + X

p p" ! + XE704RHIC

semi-inclusive process ? polarization of quark

intuitively search for ? polarized final hadrons

Double Spin Asymmetry (DSA)

depolarization (spin transfer coefficient)

HESR@GSI can help in selecting models:

DeGrand & Miettinen ’81Andersson et al. ’79Dharmaratna & Goldstein ’90Anselmino et al. ’91....

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in seminclusive DIS {pq, q, kq} not all collinear

) transfer q " not to h " final hadron (DSADSA), but to orbital motion of h

) SSA SSA with intrinsic Ph? dependence not integrated ) Collins effect

asymmetry insin / k £ Ph ¢ ST

chiral-odd Collins function H1?(z, kT) :

extract it at e+e- facilities (Belle@RHIC)

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Technical slide ! DIS : ep" ! e’hX

Collins effect

leading twist:

S 0,

convolution

keep d enoughdifferential

(C = h+S) to break the convolution F […]

need

(Boer & Mulders ’98)

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new TMD functions (s dkT ! 0) ! new spin effectsleading twist ! number density interpretation

kPhT

Sivers

Collins

polarized PFF

kPhT

Boer-Mulders

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Superposition of effects : take reaction

observe ? momenta

in final state

explain SSA data with Collins effect

in initial state Sivers effect

third possibility :

in initial state Boer ‘99

generalized factorization scheme

complete proof not yet available

search for effects ! SSA , but surviving s dkT

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Collins effect

2 hadron semi-inclusive processe p" ! e’ (1 2) X p p" ! (1 2) X ..

! asymmetry in the azimuthal orientation of pair plane with respect to some reference plane survives s dkT

suggested for the first time by Collins, Heppelmann & Ladinski, 1994 but no twist analysis nor quantitative calculations (see also Ji 1994) then Jaffe, Jin, Tang 1998 ! suggestion of SSA from interference of ( ) partial wavesand Bianconi, Boffi, Jakob, M.R., 2000 ! complete twist-2 analysis and first model calculation

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Interference Fragmentation Functions for q ! (h1,h2) X with unpolarized h1,h2

hadronic tensor

Ph=P1+P2

R=(P1-P2)/2

functions of ( z, / z1/z1+z

2 , Mh

2, kT2, kT ¢ RT ) ! ( z, , Mh

2 )

( twist-2 Bianconi, Boffi, Jakob, M.R., 2000 ; twist-3 Bacchetta, M.R., 2004)(18)

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Color gauge invariance ? (Boer, Mulders, Pijlman, 2003)

insert all unsuppressed A- gluons and AT gluons at n+=-1 makes the nonlocal q-q correlator color gauge invariantinsert also all AT gluons makes the nonlocal q-g-q correlator color gauge invariant

leading-twist projections are semipositive definite in Dirac space ! probabilistic interpretation

(Bacchetta and M.R., 2004)

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quark chiral basis : P§ PR/L with P§=½ ¨ § PR/L= ½ (1 § 5)

( ) - ´ q’q = ½

bounds :

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RT

e p" ! e’ (h1h2) X

leading-twist dleading-twist d

- no specific weight for

- collinear factorization

- no admixture with other effects

unknownmost general !

Single Spin Asymmetry

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or extracted self consistently also from p-p collisions (Bacchetta, M.R. 2004 )

p p" ! ( ) X

p p ! ( )C ( )D X

contains also

same as for gluons

available for spin ½ hadronotherwise chiral-odd ! g for spin ¸ 1

? from e+e- ! ( )jet 1 ( )jet 2 X (Artru, Collins ‘96; Boer, Jakob, M.R. ‘03)

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e+e- ! (+ -)jet 1 (+ -)jet 2 X

leading twist

(Boer, Jakob, Radici, ’03)

“Artru-Collins” azimuthal asymmetry

same as in SIDIS

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(Jaffe, Jin, Tang, ’98)

X | , Xih , X| ~ |( )L=0ih( )L=1| + |( )L=1ih( )L=0|

T-odd structure from interference of L=0 ( ! ) and L=1 ( ! )

fragmentation in helicity basis collinear ep" ! e’ (+-) X

collinear factorization ok, but not general !

IFF(z,(cos),Mh2) = n IFFn (z,Mh

2) Pn (cos)

2h c.m. frame

|RT| = |R|(M1,M2,Mh) sin

= a(M1,M2,Mh) + b(M1,M2,Mh) cos

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q’q = ½

n … Pn (cos)

(A. Bacchetta and M.R., 2003)

s-p interference

(Jaffe)

(24)

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0 0

0 0 0

0 0

0 0 0

0 0 0

0 0

0 0 0

0 0 0 0

s p,+1 p,0 p,-1

s

p,+1

p,0

p,-1

(Jaffe)

spin 1 !

(Bacchetta Mulders)

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ep" ! e’ (+ -) X at leading twist

(Jaffe, Jin, Tang, 1998)

• no calculation of qI (z)• , stable particles• interference from - phase shifts only

(Radici, Jakob, Bianconi, 2002)

uncertainty band from:

• different fp / fs strength ratio• f1(x), h1(x) from spectator model• f1(x), h1(x)=g1(x) from GRV98 & GRSV96

• f1(x), h1(x) = (f1+g1)/2 from “ “

spectator model

spectator model

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New model calculation (A. Bacchetta and M.R., in preparation)

spectator model in :

off-shell spectator :

p wave: resonant 0 ! +-

partial-wave analysis

s wave: coherent sum of direct production and

resonant f0 ! +-

plus incoherent

s d0 ! + - 0

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Parameters and fit of event distribution

form factor

PDGm, ,mf0, f0, m,

fit [GeV]

PRELIMINARY

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spectator model ! flavor symmetry

PRELIMINARY

f1, h1 from spectator model

f1, h1=g1 from GRV98 & GRSV96

( “ “ ) x 2

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Double polarized Drell-Yan with antiprotons

c.m. energy

invariant mass

parton momenta

DIS regime

factorization

for specific M,leading twist

low ! high scollider mode for HESR@GSIat present:

2 M ranges explored: Y 9 ¸ M ¸ 4 J/ (GeV)J/ 2.5 ¸ M ¸ 1.5 ( “ )

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Monte-Carlo simulation (A. Bianconi and M.R., hep-ph/0504261)

events for +- Drell-Yan pairs distributed with cross section

NLLA QCD corrections(compensate in DSA?)

factorized leptonsqT dependence (Anassontzis et al. 1988)

/ d0

PDF(x,M2) da

violation of Lam-Tung sum rule

Collins-Soper frame: qT(*) in (xz) plane

N.B. S1, S2 randomly distributed in Collins-Soper frame

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cuts: s=200 GeV2 ; 4<M<9 GeV ; qT>1 GeV/c ; 60o< <120o ; ST=50%

sample: 80.000 events ! 40.000 ! 17.000

(A. Bianconi and M.R., hep-ph/0504261)

0.08. . 0.4

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unambiguous extraction of h1(x) seems possible

statistical error bars from 20 repetitions

cuts: s=200 GeV2 ; 4<M<9 GeV ; qT>1 GeV/c ; 60o< <120o ; ST=50%

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cuts: s=200 GeV2 ; 1.5<M<2.5 GeV ; qT>1 GeV/c ; 60o< <120o ; ST=50%

sample: 80.000 events ! 40.000 ! 17.000

(A. Bianconi and M.R., hep-ph/0504261)

0.01. . 0.03

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unambiguous extraction of h1(x) seems possible

cuts: s=200 GeV2 ; 1.5<M<2.5 GeV ; qT>1 GeV/c ; 60o< <120o ; ST=50%

statistical error bars from 20 repetitions

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Conclusions

• interpretation of future 2 semi-inclusive data in terms of collinear fragmentation via IFF seems reasonable and feasible; work in progress…

• extraction of transversity via IFF more convenient with respect to Collins effect

• HESR@GSI will probably offer anther tool: collinear fully polarized Drell-Yan with antiprotons

Transverse spin physics without transverse momentais a real option

Transverse spin physics without transverse momentais a real option