Transcript QCD Factorization for Semi-Inclusive DIS

Transverse Partonic
Structure of the Proton
Feng Yuan
Lawrence Berkeley National Laboratory
RBRC, Brookhaven National Laboratory
4/6/2016
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90
00
2
(non)Universality
unify
Factorization
BJY Collins BHS
Mulders et al.
Collins
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Qiu-Sterman Jaffe-Ji
Sivers
CSS
Efremove-Teryav
Collins-Soper
Ralston-Soper
RHIC
RHIC
JLab
…
BELLE
COMPASS
HERMES
E704,pp to Pi
Bunce,Lambda
Transverse spin physics
Transverse spin physics

Goal
 Quark
transversity distributions
 Orbital motion of quarks and gluons?

Transverse partonic structure of proton
 Various
transverse momentum dependent physics
(additional information on nucleon structure)
 Sivers function (PDF)
 Collins function (FF)
…
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Transverse Momentum Dependent
Parton Distributions
Nucleon
Structure, connection to GPDs,
quantum phase space distribution
Single spin asymmetry phenomena
Nontrivial QCD dynamics, and
fundamental test of the factorization,
and the universality of PDFs, FFs,…
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Connection between TMD and GPD

Wigner distributions
Ji: PRL91,062001(2003)
After integrating over r, one gets TMD
After integrating over k, one gets
Fourier transform of GPDs
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Quantum Phase-Space Distributions of Quarks
Wp
u(k,r)
Probability to find a quark u in a
nucleon P with a certain
polarization in a position r and
momentum k
“Mother” Wigner distributions
FT
TMD PDFs fpu(x,kT),
TMD FFs Dup+(kT,z)
Measure momentum
transfer to quark
Direct info about
momentum distributions
IPDs Wpu(x,rT),…
PDFs fpu(x),…
FFs Dup+(z)
x=0
GPDs
Hpu(x,x,t),
GDAs
Fudp+(x,x)
Form Factors
F1pu(t),F2pu(t )..
GPD
Measure momentum
transfer to target
Direct info about
spatial distributions
Some PDFs same in exclusive and semi-inclusive analysis
H.Avakian, Nov 19, 2004
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TMD Distribution: the definition
Gauge Invariance requires the Gauge Link
Brodsky,Hwang,Schmidt 02’
Collins 02’
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Belitsky,Ji,Yuan
02’
Boer,Mulders,Pijlman, 03’
Polarized TMD Quark Distributions
Nucleon
Unpol.
Long.
Trans.
Quark
Unpol.
Long.
Trans.
Boer, Mulders, Tangerman
(96&98)
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Three classes in the view of a
quark model

S-wave
 Unpolarized,

helicity, transversity
S-P interference
 g_1T,h_1L
 f_1T^\perp,

h_1^\perp
P-P or S-D interference
 h_1T^\perp

Miller 07, Burkardt 07, Avakian et al 08.
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EIC Meeting 2008
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Lz≠0 Amplitude and Sivers
Function

All distributions can be calculated using
the wave function. Sivers function:
Lz=1
Lz=0

Similar expressions for others
Ji, Ma, Yuan, Nucl. Phys. B (2003)
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Where can we learn TMDs
Semi-inclusive hadron production in
deep inelastic scattering (SIDIS)
 Drell-Yan lepton pair production in pp
scattering
 Relevant e+e- annihilation processes
 Many others…

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EIC Meeting 2008
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Inclusive and
Semi-inclusive DIS
Inclusive DIS:
Q
Partonic Distribution depending on
the longitudinal momentum fraction
Semi-inclusive DIS:
Q
Probe additional information for parto
transverse distribution in nucleon
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Azimuthal Dependence in
SIDIS

Transverse Momentum Dependent (TMD)
Parton Distributions and Fragmentations
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SIDIS Cross Section
At leading power of 1/Q
The structure functions depend on Q2, xB, z, PhT
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Two major contributions

Sivers effect in the distribution
ST
kT
P

Collins effect in the fragmentation
(zk+pT)
(k,sT)

ST (PXkT)
~pTXsT
Other contributions…
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Universality of the Collins
Fragmentation
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Collins effects in e+e
Reliable place to extract the information on
the Collins fragmentation function
Belle Col.,
PRL 06
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Collins asymmetry in pp collisions
Collins Fragmentation function
Quark transversity distribution
FY, arXiv:0709.3272 [hep-ph]
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Simple model a la Collins 93
Phase information in the vertex
or the quark propagator
Collins-93
e+e- annihilation
Semi-inclusive DIS
Hadron in a jet in pp
Universality of the Collins Function!!
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One-gluon exchange (gauge link)?
Metz 02, Collins-Metz 02:
Gamberg-Mukherjee-Mulders, 08
Universality of the Collins function!!
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Similar arguments for pp collisions
By using the Ward
Identity:
same Collins fun.
Conjecture: the Collins function will be the same as e^+e^- and SIDIS
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Key observations
Final state interactions DO NOT
provide a phase for a nonzero SSA
 Eikonal propagators DO NOT contribute
to a pole
 Ward identity is applicable to warrant
the universality arguments

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Sivers effect is different
It is the final state interaction
providing the phase to a nonzero SSA
 Ward identity is not easy to apply
 Non-universality in general
 Only in special case, we have
“Special Universality”

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DIS and Drell-Yan

Initial state vs. final state interactions
*
Drell-Yan
*
DIS
HERMES

“Universality”: fundamental QCD prediction
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Experiment SIDIS vs Drell Yan
HERMES Sivers Results
RHIC II Drell Yan Projections
0
0
Markus Diefenthaler
DIS Workshop
Munich, April 2007
0.1
0.2
0.3 x
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http://spin.riken.bnl.gov/rsc/
Study QCD dynamics at different
PT Region



Integrate out PT (w/o weight)
-- normal factorization, similar to inclusive
DIS
Large PT (>>QCD)
-- hard gluon radiation, can be calculated from
perturbative QCD
Low PT (~QCD)
-- nonperturbative information: TMD
factorization formula
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A unified picture for SSA

In DIS and Drell-Yan processes, SSA depends
on Q and transverse-momentum P
 At
large P, SSA is dominated by twist-3
correlation effects
 At moderate P, SSA is dominated by the
transverse-momentum-dependent parton
distribution/fragmentation functions

The two mechanisms at intermediate P
generate the same physics!
Ji-Qiu-Vogelsang-Yuan,Phys.Rev.Lett.97:082002,2006
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A difficulty at next-leadingpower (1/Q)

Mismatch at low and high transverse
momentum SIDIS at 1/Q


Bacchetta-Boer-Diehl-Mulders, 0803.0227
The factorization needs to be carefully
examined at this order
 Earlier


works indicates possible problems
Afanasev-Carlson, PRD, 2006
Gamberg-Hwang-Metz-Schlegel, PLB, 2006
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Final PT Distribution

PT dependence
Sivers function at low Pt
Qiu-Sterman Twist-three
Which is valid for all Pt range
 SSA is suppressed by 1/Pt at large Pt

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Extend to all other TMDs: large
Pt power counting
kt-even distributions have the same
dependence on kt
 kt-odd distributions are suppressed at
large kt
 Power Counting Rule

kt-even: 1/kt2
kt-odd: 1/kt4
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SIDIS cross sections at large Pt
1/Pt2
1/Pt4
1/Pt3
1/Pt5
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Transition from Perturbative region
to Nonperturbative region?

Compare different region of PT
Nonperturbative TMD
Perturbative region
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pp scattering experiments

RHIC and RHIC II
 Collins
effects, quark transversity
 Drell-Yan, quark Sivers
 Heavy flavor, gluon Sivers

JPARC (pp collision at low energy)
 Drell-Yan,

quark Sivers effects
GSI-FAIR (ppbar collision)
 Drell-Yan,
quark transversity
 Quark Sivers effects
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Summary
We are in the early stages of a very
exciting era of transverse spin physics
studies, where the future JLAB, RHIC,
and EIC experiments will certainly play
very important roles
 We will learn more about QCD dynamics
and nucleon structure from these
studies, especially for the quark orbital
motion
 More work needs to be done

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
Quark distribution is deformed when nucleon is
transversely polarized, because of the orbital motion
y
x

This deformation will lead to a single transverse spin
asymmetry (SSA), because of final state interactions
y
z
Burkardt, 2003
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Semi-Inclusive DIS


Transverse Momentum Dependent (TMD)
Parton Distributions and Fragmentations
Novel Single Spin Asymmetries
U: unpolarized beam
T: transversely polarized target
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What’s Single spin asymmetry?
Transverse plane
Final state particle is
Azimuthal symmetric
Single Transverse Spin
Asymmetry (SSA)
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SSAs in Modern era : RHIC, JLab,
HERMES, …
STAR
Central rapidity!!
BRAHMS
Large SSA continues at DIS ep
and collider pp experiments!!
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Naïve parton model fails

If the underlying scattering mechanism is
hard, the naïve parton model generates a
very small SSA: (G. Kane et al, 1978),
 It

is in general suppressed by αSmq/Q
We have to go beyond this naïve picture
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Two mechanisms in QCD

Spin-dependent transverse momentum
dependent (TMD) function
S
k
T
 Sivers
T
Sivers function ~ ST (PXkT)
90
.
P
 Brodsky,Hwang,Schmidt, 02 (FSI)
 Gauge Property: Collins 02;Belitsky-Ji-Yuan,NPB03
Boer-Mulders-Pijlman,03
 Factorization: Ji-Ma-Yuan,PRD04;Collins,Metz,04

Twist-3 quark-gluon correlations (coll.)
 Efremov-Teryaev,
82, 84
 Qiu-Sterman, 91,98
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What can we learn from SSA

Quark Orbital Angular Momentum
e.g, Sivers function ~ the wave function
amplitude with nonzero orbital angular
momentum!
Vanishes if quarks only in s-state!
Ji-Ma-Yuan, NPB03
Brodsky-Yuan, PRD06
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Take Drell-Yan as an example
(with non-zero transverse momentum q?)

We need a loop to generate a phase
+
+
+
+
-
Kane et al., hard parton model
+
+
-
Twist-three Correlations
Efremov-Teryaev, 82, 84
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Qiu-Sterman, 91,98
Further factorization (q?<<Q)

The collinear gluons dominate
q?<<Q
Twist-three Correlations
Efremov-Teryaev, 82, 84
Qiu-Sterman, 91,98
Transverse Momentum Dependent
distributions
Sivers, 90, Collins, 93,02
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Brodsky-Hwang-Schmidt,02
Ji-Qiu-Vogelsang-Yuan,06
Quantum Phase Space Distribution

Wigner operator

Wigner distribution: “density” for quarks having
position r and 4-momentum k (off-shell)
a la Saches
7-dimensional distribtuion
No known experiment can measure this!
Custom-made for high-energy
processes


In high-energy processes, one cannot measure k =
(k0–kz) and therefore, one must integrate this out.
The reduced Wigner distribution is a function of six
variables [r,k=(k+ k)].
 After integrating over r, one gets transversemomentum dependent parton distributions
 Alternatively, after integrating over k, one gets a
spatial distribution of quarks with fixed
Feynman momentum k+=(k0+kz)=xM.
Collins from HERMES


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Large, positive p+ asymmetries:
no surprise from u-quark
dominance
Large, negative p asymmetries:
first a surprise, now understood
by large, negative disfavored
Collins function
Collins from COMPASS
PRL 94, 202002 (2005) and Nucl.Phys.B765:31-70,2007

Smaller asymmetries than in proton case
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First extraction of
Collins functions and
transversity
distributions from
fitting HERMES +
COMPASS + BELLE
data
By Anselmino et al.,
PRD 75 (07)
Comparison with some models
[1] Soffer et al. PRD 65 (02)
[4] Wakamatsu, PLB 509 (01)
[2] Korotkov et al. EPJC 18 (01)
[5] Pasquini et al., PRD 72 (05)
[3] Schweitzer et al., PRD 64 (01)
[6] Anselmino et al., PRD 75 (07)
Non-universality: Dijet-correlation at
RHIC

Proposed by Boer-Vogelsang


Initial state and/or final state interactions?







Pheno. studies: Vogelsang-Yuan 05;
Bomhof-Mulders-Vogelsang-Yuan 07
Bacchetta-Bomhof-Mulders-Pijlman: hep-ph/0406099, hepph/0505268, hep-ph/0601171, hep-ph/0609206
Qiu-Vogelsang-Yuan, arXiv:0704.1153; 0706.1196
Collins-Qiu, arXiv:0705.2141
Voglesang-Yuan, arXiv:0708.4398
Collins, arXiv:0708.4410
Bomhof-Mulders, arXiv:0709.1390
Factorization? Universality?
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The asymmetry could be related to that in DIS, only
at the leading order (one-gluon exchange),

qTDIS--- Sivers function from DIS
qt--- imbalance of the dijet
Hsivers depends on subprocess
Qiu,Vogelsang,Yuan, 07
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This simple picture does not hold for
two-gluon exchanges
Vogelang-Yuan, 0708.4398;
Qiu,Collins, 0705.4121;
Collins, 0708.4410
Similar calculations can be
Shown for QCD
4/6/2016
Integrated over transverse
momentum
DPN Meeting 2007
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