Transcript DIS08-spin

High-Energy QCD
Spin Physics
Xiangdong Ji
Maryland Center for Fundamental Physics
University of Maryland
DIS 2008, April 7, 2008, London
Outline
 Why spin physics?
 Polarized parton distribution functions
 Spin structure of the proton,
Orbital angular momentum and
Generalized parton distributions (GPDs)
 Transverse single-spin asymmetries
 Conclusion
Why spin physics?
 Spin is a fundamental degree of freedom originated
from the space-time symmetry.
 Spin plays a critical role in determining the basic
structure of fundamental interactions.
 Test of a theory is not complete without a full test of
spin-dependent decays and scattering.
 Spin provides a unique opportunity to probe the inner
structure of a composite system (such as the proton)
and hence testing our ability to understand the working
of non-perturbative QCD.
Remarkable experimental progress in
QCD spin physics in the last 20 years
 Inclusive spin-dependent DIS




EMC, SMC, COMPASS
E142,E143,E154,E156
HERMES
Jlab-Hall A, B(CLAS)
 Semi-inclusive DIS


SMC, COMPASS
HERMES
 Polarized pp collisions

RHIC

PHENIX & STAR
Recent experimental progress
 Double-spin asymmetries in semi-inclusive processes
from HERMES & COMPASS
Talks by Korzenev, Robinet,
Stolarski, Jackson
Recent experimental progress
 Double spin asymmetry for pion production from
PHENIX and jet production from STAR (run 5+6)
(
Talks by Gagliardi, Hoffman, Aoki, Ellinghaus
Polarized Parton Distributions
Polarized PDFs
 When the proton (or neutron) is polarized, the quarks
and gluons are polarized as well,
 In the large Nc limit, the mass of the nucleon is order
Nc and spin is of order 1.

The polarized effect is relatively small, particularly for
the gluons of order Nc squared in the vacuum.
 Pol. PDF can be extracted from the experimental data
through global fits.
(NLO) Global fits
 Make some generic assumptions about the functional
form with a few parameters and fit them to data
 Many efforts in the past have been made





Gluck, Reya, Stratmann, Vogelsang (2001)
Blumlein and Bottcher (2003)
Leader, Sidorov, Stamenov (2006)
Hirai, Kumano, Saito (2006)
…..
 One of the most recent is the NLO fit by de Florian,
Sassot, Stratmann and Vogelsang (hep-ph/0804.0422)
in which pp collision jet data are first included.
(Technically challenging!)
DSSV PDF
Polarized sea distributions
RHIC spin asymmetries
DSSV spin content
 The gluon pol. is small, but the uncertainty is large (E.
Leader’s talk). Future data will improve this
Gluon polarization and chi-squared
Future improvement
 Sea-quark polarization


W production at RHIC
EIC
 Gluon pol.


Direct photon production
Higher precision in jet and pion
Spin Structure
of the Nucleon
The nucleon spin
 The driving question for QCD spin physics is where
the nucleon spin come from?
Spin budget of the proton
Total
proton spin = 1/2
25%
Quark spin measured
In DIS
“Dark” angular momentum?
75%
Spin of the proton in QCD
 The spin of the nucleon can be decomposed into
contributions from quarks and gluons
J  1/ 2  J q (  )  J g (  )
 Further decomposition of quark contribution
1
J q   [ (q v f  q s f )  Lqf ]
2
f
 Further decomposition of gluon contribution
J g  g  Lg
Infinite momentum frame
There is no analogous sum rule involving transversity!
Spin in asymptotic limit
 Scale evolution equation
 
 
2


J

  16,3n f

d  q
s


2
2
d ln   J g   2  9 16,3n f
 
 
2


J

 q


 J  2 
 g

 Asymptotic solution
1 3n f
1 16
J q   
, J g   
2 16  3n f
2 16  3n f
Roughly half of the angular momentum is carried by
gluons!
OAM must be important
Argument for large orbital motion
 Quarks are essentially massless. A relativistic quark
moving in a small region of space must have non-zero
orbital angular momentum. (MIT bag model)
 Finite orbital angular momentum is essential for




Magnetic moment of the proton.
g2 structure function
Asymmetric momentum-dependent parton distribution
in a transversely polarized nucleon
…
Total quark angular momentum
 The total angular momentum is related to the GPDs by
the following sum rule
1
J q  lim  dxx[ H q ( x, t ,  )  Eq ( x, t ,  )]
t 0 2



Where E and H are GPDs defined for unpolarized
quarks.
Contribution from H is related to the momentum
fraction carried by quarks.
E is similar to Pauli form factor F2, can best be
determined with a trans. pol. target.
Talk by D. Mueller
DVCS with transversely
polarized target from HERMES & Jlab
Talk by P. Haegler
Looking forward
 Jlab 12 GeV upgrade
A comprehensive program to study GPDs
Vanderhaeghen et al.
Vanderheaghen et al
 EIC
D. Hasell, R. Milner et al.
EIC: 5 GeV e on 50 GeV proton: Much large range possible….
Transverse Single-Spin
Asymmetries
Session talks by F. Yuan, Radici, Lu, Mulders
Goldstein, Sozzi, Ogawa, Videbaek, Fields, Melis,
Tanaka
Transverse-Spin Related Distributions
 Transversity distribution q(x) or h(x) (twist-2)


the density of transversely polarized quarks in a
transversely polarized nucleon
chirally-odd
 Sivers function qT(x, kT) (twist-2 at small k)


Asymmetric distribution of quarks with T-momentum kT
in a transversely polarized nucleon
T-odd, depends on ISI/FSI
 Twist-3 quark-gluon correlation functions

Polarized gluons!
 Related Fragmentation functions
What have we learned from data?
 SSA in PP scattering is large,
even at RHIC energy.
Consistent with twist-3
expectation.
 SSA in eP scattering is large at
HERMES, becomes small at
COMPASS.


The Collins function is
consistent with e+e- data,
but with interesting/strange
charge dependence.
(Ogawa)
Siver’s function has
interesting flavor
dependence.
Talk by Ogawa
First extraction of transversity
 From semi-inclusive DIS asymmetry measured by
HERMES &COMPASS (Anselmino et al, 2007)
A unified picture for SSA
 In DIS and Drell-Yan processes, SSA depends on Q
and transverse-momentum PT


At large PT, SSA is dominated by twist-3 correlation
effects (Afremov& Teryaev, Qiu & Sterman)
At moderate PT, SSA is dominated by the kTdependent parton distribution/fragmentation functions
 Ji, Qiu, Vogelsang, & Yuan, Phys.Rev.Lett.97:082002,2006
The two mechanisms at intermediate PT generate the
same physics! However, this does not generalize to
higher order in 1/Q (Bacchetta et al, 0803.0227)
Baccetta’s talk
Future Challenge?
 PQCD & Factorization?


Is PT =1-2 GeV high enough to use pQCD ? (a twist-3
effect, scaling, maybe ok for total cross section.)
Is the peculiar flavor dependence in HERMES data due to
non-perturbative physics? Or imprecise data? (g2)
 Transverse-spin effort small at high energy?



Jaffe & Saito, QCD selection rule (1996)
Vogelsang & others, small double asymmetry for Drell-Yan
PAX collaboration at GSI, PP-bar scattering at lower energy
 The ultimate goal?


Can one extract transversity to a good precision?
Can one calculate TMD & Twist-3 correlations?
Conclusion
 We have learned a lot about pol. PDF in the last 20
years. The quantitative gluon and sea quark
polarizations need high-precision measurement.
 Significant orbital angular momentum contribution to
the spin of the proton. Must find way to expose them.
DVCS and other related process are unique way to do
this (GPDs).
 Much theoretical progress has been made in
understanding the physical mechanisms of single spin
asymmetries. It yet becomes the useful tool to learn
about the spin structure of the nucleon.