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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)
2
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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4
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
23
(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
27
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
32
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
35
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
36
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