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Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
Transversity (transverse spin and transverse motion)
Transversity distributions – (some) theory
Transversity distributions - experiments
Transverse Single Spin Asymmetries (how to test a Quantum Field Theory)
Spin and k┴ dependent parton distributions (TMD)
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
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
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
+–– –
++ +
+ +
+ =),( 2Qxq),( 2Qxq
+– =),( 2Qxq
),( 2QxqT
|| 2
1 iin helicity basis
–+
+ – ),( 2
1 Qxh decouples from DIS
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
Helicity conservation in pQCD or QED
qq ,
qq ',
qqqq E
mO q
''
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
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
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
D. De Florian, G.A. Navarro and R. Sassot, hep-ph/0506326
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
–+
+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
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
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
/2 / 22121 sQxsMxxxxx LFF
llqq *
plenty of spin effects
h1 in Drell-Yan processes
p p
Q2 = M2
qT
qL
l+
l–γ*
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
q q
q qqqqq
TTTTxqxqxqxqe
xhxhxhxheaA
)()()()(
)()()()(ˆ
dd
dd
21212
211121112
h1 from
)cos(2 cos1
sin
ˆdˆd
ˆdˆdˆ
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 small
smaller s would help Martin, Schäfer, Stratmann, Vogelsang
Barone, Calarco, Drago
22 GeV 100 GeV 200 Ms
3102
Xllpp at RHIC
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
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
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
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
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
s=30 GeV2 s=45 GeV2
s=210 GeV2s=900 GeV2
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
s=30 GeV2 s=45 GeV2
s=210 GeV2s=900 GeV2
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
data from CERN WA39, π N processes, s = 80 GeV2
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
h1 x Collins from SIDIS processes
Spin effect comes from fragmentation of a transversely polarized quark pq
φ Sqp┴
)ˆˆ( ),(2
1
),(),(
/
//
ppSpz
pzDpzD
qqqhN
qhqh
initial q spin is transfered to final q',
which fragments
'll
Sq
Sq’p┴
)sin()ˆˆ( '' Shqq ppS
x
y
ΦSΦh
q
q’
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
)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[d
)sin( ]d[d 2)sin(
Sh
UTShA
Collins function
some data available from HERMES, first extraction of Collins functions: W. Vogelsang and F. Yuan (assuming Soffer-saturated h1)
transversity
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
fit to HERMES data on)sin( Sh
UTA
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
Extraction of Collins functions from HERMES + BELLE data
P1 depends on
)( )(
)( )(
21
2)1(
1)1(
zDzD
zDzD NN
(talk by Matthias)
M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin,
in preparation
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
Fits to HERMES Collins data, preliminary results
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
Fits to BELLE Collins data, preliminary results
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
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 T (higher-twist transversity
distribution)
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
S
p
p'
– pPTθ
θsinPpS T
NA
– p'
6;
5;
4;
3;
2;
1;
MMMMMM
Single Spin Asymmetry in elastic scattering. Example:
6 independent helicity amplitudes
)()(Im2 426315NA
'' qqqq
z
y
xTransverse
SSA
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
S
p
p'
– pPTθ
– p'
z
y
xΦS Φ
for a generic configuration:
)sin(PPpS STT
NA
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
0NA needs helicity flip + relative phase
–+
++
Im x
+
++
+
sq
N E
mA at quark level
large SSA observed at hadron level
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
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
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
Unweighted Collins moment: Unweighted Sivers moment:
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
X
p
S
+ –
Brodsky, Hwang, Schmidt model for Sivers function
q q
diquark diquark
)sin(PPpS STT
needs k┴ dependent quark distribution in p↑: Sivers function
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
p┴ = PT – z k┴ + O(k┴2/Q2)
Sivers asymmetry in SIDIS
)ˆˆ( ),(2
1
),(),(
/
//
kpSkxf
kxfkxf
pq
N
pqpq
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin hep-ph/0501196 (PRD 71, 074006) and hep-ph/0507181
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
Deuteron target hdhupd
N
pu
NUT DDffA Sh
4 //
)sin(
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
First p┴ moments of extracted
Sivers functions, compared with
models
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
Predictions for COMPASS, hydrogen target
0.4 ≤ zh ≤ 1 0.2 ≤ PT ≤ 1 GeV/c 0.02 ≤ xB ≤ 1
Q2 > 1 (GeV/c)2 W2 > 25 GeV2 PT > 0.1 GeV/c Eh > 4 GeV 0.2 < zh < 0.9 0.1 < y < 0.9
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
Predictions for K production at HERMES
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
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
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
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