spin and k ┴ dependent parton distributions
DESCRIPTION
Spin and k ┴ dependent parton distributions. - a closer look at the nucleon structure -. (with the help of antiprotons). integrated partonic distributions the missing piece, transversity partonic intrinsic motion (TMD) spin and k ┴ : transverse Single Spin Asymmetries - PowerPoint PPT PresentationTRANSCRIPT
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Spin and k┴ dependent parton distributions
Mauro Anselmino, ECT* Trento, 04/07/2006
- a closer look at the nucleon structure -
integrated partonic distributions
the missing piece, transversity
partonic intrinsic motion (TMD)
spin and k┴: transverse Single Spin Asymmetries
SSA in SIDIS and p-p, p-pbar inclusive processes
conclusions
(with the help of antiprotons)
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K┴ integrated parton distributions
quark distribution – well known
quark helicity distribution – known
transversity distribution – unknown
all equally important
related to
positivity bound
qqq
qqq
qqqT
q qq 5
chiral-even
qT qq 5 related to chiral-odd
qqqT ||2
ggg gluon helicity distribution – poorly known
are fundamental leading-twist quarkqq , and 1h (or ) , qq T distributions depending on longitudinal momentum fraction x
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),( 2Qxq ),( 2Qxq
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de Florian, Navarro, Sassot
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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].
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+–– –
++ +
+ +
+ =),( 2Qxq),( 2Qxq
+– =),( 2Qxq
),( 2QxqT
|| 2
1 iin helicity basis
–+
+ – ),( 2
1 Qxh decouples from DIS (no quark helicity flip)
The missing piece, transversity
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h1 must couple to another chiral-odd function. For example
++ –
++
–
+ –
–– +
–
+ –
h1 x h1
h1 x Collins function
J. Ralston and D.Soper, 1979 J. Cortes, B. Pire, J. Ralston, 1992
J. Collins, 1993
XlplXllpp SIDIS, and , Y,D
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–+
+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
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First ever “transversity”, according to Gary Goldstein, QCD-N06, Villa Mondragone, June 15, 2006
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Elementary LO interaction:
3 planes:
)( )()( )(1
9
42121
2
212
2
2
2
xqxqxqxqexxsMdxdM
daaaa
aa
F
sqxsMxxxxx LFF /2 / 22121
llqq *
plenty of spin effects
p p
Q2 = M2
qT
qL
l+
l–
h1 in Drell-Yan processes
*
plane plane, * llp , on vectorspolarizati to plane
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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
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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
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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
M. Guzzi, V. Barone, A. Cafarella, C. Corianò and P.G. Ratcliffe
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s=30 GeV2 s=45 GeV2
s=210 GeV2s=900 GeV2
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s=30 GeV2 s=45 GeV2
s=210 GeV2s=900 GeV2
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data from CERN WA39, π N processes, s = 80 GeV2
H. Shimizu, G. Sterman, W. Vogelsang and H. Yokoya
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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┴
qT distribution of lepton pairs in D-Y processes
Partonic intrinsic motion
p p
Q2 = M2
qT
qL
l+
l–*
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pT distribution of hadrons in SIDIS
Xhp *
Hadron distribution in jets in e+e– processes
Large pT particle production in hXpN
Transverse motion is usually integrated, but
there might be important spin-k┴ correlations
pxp
k┴
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spin-k┴ correlations? orbiting quarks?
Transverse Momentum Dependent distribution functions
Space dependent distribution functions (GPD)
),( kxq
),( bxq
k
?
b
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M. Arneodo et al (EMC): Z. Phys. C 34 (1987) 277
),(ˆd ),(d 22 QzDQxf hq
lqlq
lhXlp
Unpolarized SIDIS, )]([ 0sO
qp
Qx
2
2
22 qQ
pl
qpy
in collinear parton model
222 )1(1ˆˆˆd yuslqlq thus, no dependence on azimuthal angle Фh at zero-th order in pQCD
the experimental data reveal that
hhhXlhlq ΦCΦBAΦ 2coscosd/ˆd
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Cahn: the observed azimuthal dependence is related to the intrinsic k┴ of quarks (at least for small PT values)
These modulations of the cross section with azimuthal angle are denoted as “Cahn effect”.
assuming collinear fragmentation, φ = Φh
)0 ,sin ,cos( kkk
2
2
cos12
1ˆQ
ky
Q
ksxs O
2
2
cos1
21)1( ˆ
Q
k
yQ
kyxsu O
hhh
lhXlq
ΦCΦBAusΦ
2coscosˆˆd
ˆd 22
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SIDIS with intrinsic k┴
kinematics according to Trento conventions (2004)
);,();,(ˆd);,(d 222 QpzDQkyQkxf hq
lqlq
q qlhXlp
factorization holds at large Q2, and QCDT kP Ji, Ma, Yuan
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The situation is more complicated as the produced hadron has also intrinsic transverse momentum with respect to the fragmenting parton
k
kz
p
TP
px
hp
Qk /neglecting terms of order one has
kzpPT
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assuming:
one finds:
with
clear dependence on (assumed to be constant)and
Find best values by fitting data on Φh and PT dependences
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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
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Large PT data explained by NLO QCD corrections
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dashed line: parton model with unintegrated distribution and fragmentation functions solid line: pQCD contributions at LO and a K factor (K = 1.5) to account for NLO effects
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ccdab
pbgqqdcba
pa Dff //,,,,,
/ ˆd d
PDF FF pQCD elementary
interactions
ab
c
0DX
X
f
f
(collinear configurations)Xpp 0factorization theorem
p
p
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The cross section
uts ˆ ,ˆ ,ˆ elementary Mandelstam variables
uts , , hadronic Mandelstam variables
uxtxzsxx baba
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Xpp 0
RHIC data GeV 200s
Xpp
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FNAL data, PLB 73 (1978)
F. Murgia, U. D’Alesio
Xpp 0 GeV 20soriginal idea by Feynman-Field
GeV 8.0 k k no
a b
c
0D
X
X
ff
non collinear configurations
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S
p
p'
– pPTθ
θsinPpSdd
ddT
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: elastic scattering
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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
Single spin asymmetries at partonic level. Example: '' qqqq
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BNL-AGS √s = 6.6 GeV 0.6 < pT < 1.2
E704 √s = 20 GeV 0.7 < pT < 2.0
E704 √s = 20 GeV 0.7 < pT < 2.0
experimental data on SSA
Xpp
Xpp
observed transverse Single Spin Asymmetries
dd
ddNA
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STAR-RHIC √s = 200 GeV 1.1 < pT < 2.5
AN stays at high energies ….
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Transverse Λ polarization in unpolarized p-Be scattering at Fermilab
XNp
dd
ddP
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pppp pppp
dd
ddNA
dd
ddNNA
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“Sivers moment”
XlNl
dd
ddNA
)dd(d d
)sin()dd(d d2
)sin(2
S
S
)sin(
S
UTSSA
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“Collins moment”
dd
ddNA
XlNl
)dd(d d
)sin()dd(d d2
)sin(2
S
S
)sin(
S
UTSSA
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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
Sivers function Collins function
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q
pq
N hM
kf 1/
p
Sqk┴
φq
pq
φSΛp┴
)ˆˆ( ),(2
1
),(2
1),(
/
//
ppSpzD
pzDpzD
N
qhq
)ˆˆ( ),(2
1
),(2
1),(
/
//
kpSkxf
kxfkxf
qpq
N
pqpq
Amsterdam group notations
qTq
N DMz
pD
1/ 2
spin-k┴ correlations
Boer-Mulders function polarizing f.f.
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8 leading-twist spin-k┴ dependent distribution functions
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M.A., U.D’Alesio, M.Boglione, A.Kotzinian, A Prokudin
from Sivers mechanism)sin( S
UTA
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Deuteron target hdhupd
N
pu
NUT DDffA Sh
4 //
)sin(
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The first and 1/2-transverse moments of the Sivers quark distribution functions. 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
kkdxf q
Tq
T
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
kkdf q
Tq
T
),( )( 1
2)2/1(1
kxfM
kkdxf q
Tq
T
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fit to HERMES data on)sin( Sh
UTA
W. Vogelsang and F. Yuan
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Hadronic processes: the cross section with intrinsic k┴
factorization is assumed, not proven in general; some progress for Drell-Yan processes, two-jet production, Higgs
production via gluon fusion (Ji, Ma, Yuan; Collins, Metz; Bacchetta, Bomhof, Mulders, Pijlman)
intrinsic k┴ in distribution and fragmentation functions and in elementary interactions
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The polarized cross section with intrinsic k┴
A
aa
SAa ,/'
badcM ,;,ˆ
CC
ccD
,
, '
helicity density matrix of parton a inside polarized hadron A
pQCD helicity amplitudes
product of fragmentation amplitudes
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E704 data, E = 200 GeV
fit to AN with Sivers effects alone
maximized value of AN
with Collins effects alone
M.A, M. Boglione, U. D’Alesio, E. Leader, F. Murgia
SSA in p↑p → π X
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Maximised (i.e., saturating positivity bounds) contributions to AN
quark Sivers contribution
gluon Sivers contribution
Collins contribution
Special channels available with antiprotons – Results from U. D’Alesio
Xpp
dd
ddNA
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Xllpp
Predictions for AN in D-Y processes
Sivers function from SIDIS data, large asymmetry and cross section expected
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XDpp at PAX, contrary to RHIC, dominates the
ccqq channel:
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SSA in p↑p → D X
only Sivers effect: no transverse spin transfer in
dominance of gluonic channel, access to gluon Sivers function
QQggQQqq ,
maxNA
assuming saturated Sivers
function
papa
N ff //2
)rapidities denote 8.3 ,2 ,1 ,0
:lines thin , :lines(thick QQqqQQgg
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predictions based on Sivers functions
extracted from fitting E704 data
maximised contributions from h1 times B-M, not suppressed by phases
channels dominating and gqqqqg
dd
ddNA
Xpp
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predictions based on Sivers functions from E704 data Xpp ,0,
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Conclusions
Polarized antiprotons are the only way to access directly the transversity distribution: optimum energy at s 200 ≈ GeV2
Unintegrated (TMD) distribution functions allow a much better description of QCD nucleon structure and hadronic interactions
(necessary for correct differential distribution of final state particles, (Collins, Jung, hep-ph/0508280)
k┴ is crucial to understand observed SSA in SIDIS and pp interactions; antiprotons will add new information and allow further
test of our understanding
Spin-k┴ dependent distribution and fragmentation functions: towards a complete phenomenology of spin asymmetries
Open issues: factorization, QCD evolution, universality, higher perturbative orders, …