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.