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Theoretical Overview of Spin Physics

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Title: Theoretical Overview of Spin Physics


1
Theoretical Overview of Spin Physics
  • Feng Yuan
  • RBRC, Brookhaven National Laboratory

2
Outline
  • I wont be able to cover everything for spin
    physics, just a few highlights
  • See relevant experimental talks in this
    conference
  • R. Seid, A. Hillenbrand , R. Fatemi, S.
    Procureur, K.O. Eyser

3
Introduction--Spin Crisis
  • Proton is a spin ½ particle it should be carried
    by its constituents, mostly by quarks, because of
    success of the Quark Model
  • EMC 1988
  • Spin Crisis--- proton spin carried by quark
    spin is rather small (1 12 24)

4
Summary of DIS data
(doesnt yet include new COMPASS results)
L. De Nardo (HERMES)
5
Where is the rest of the proton spin
  • Gluon spin?
  • Orbital motion?

6
Ultimate goal spin sum rule
Gluon spin
Orbital Ang. Momen
Quark spin
Transverse Spin
Longitudinal Spin
DVCS, FF, …
7
Where are the experiments
  • Current running
  • Lepton-nucleon scattering HERMES, COMPASS, JLAB
  • Polarized proton-proton scattering, RHIC
  • Future facilities
  • Polarized electron-proton colliders eRHIC
  • Polarized fixed target pp JPAC
  • Polarized p\bar p scattering GSI-FAIR

8
Where we can get gluons
Inclusive DIS
LO
NLO
… gluons are sub-dominant.
9
Current understanding of Mg from evolution of
DIS data
Measurement of ?g a major emphasis at RHIC
10
In hadronic collisions (RHIC) …
LO
… gluons are leaders.
11
Do we trust our theory at RHIC?
  • Although the general factorization theorem
    exists, its validation depends on how large the
    hard scale in the process
  • It is very promising that at RHIC energy region,
    the collinear factorization works well

12
at RHIC
See more in Fatemi and Eysers talks
13
Mg from ep scattering (Hermes and Compass)
  • Inclusive hadron prodution
  • Hadron pair production
  • Heavy quark pair production
  • (see more in the following talk by S.
    Procureur)

14
Generalized Parton Distributions (extract the
quark orbital motion)
  • Motivated by studying nuclear spin physics
  • A new type of parton distributions contains
    much more information than any other nuclear
    observables been considered so far
  • It depends on three variables xthe parton
    momentum fraction tthe momentum transfer ?the
    skewness
  • It can be measured in experiments
  • --Deeply Virtual Compton scattering exclusive
    meson production (HERMES,JLAB,COMPASS,…)

Muller 1994, Ji 1996, Radyushkin 1996
15
GPDs link many observables
D. Hasch_at_SPIN2004
16
Quarks 3-d imagine via x- filters (Wigner
functions)
Ji 03 Belitsky, Ji, Yuan 03
Beam direction
z
x
y
low x
moderate x
high x
17
Single Transverse-Spin Asy. (SSA)
  • SSAs have long history, from late 70 and 80
    they are large at forward rapidity in hadronic
    reactions recent activities in various
    experiments (HERMES,COMPASS,RHIC,JLAB)
  • It challenged researchers to understand this in
    QCD, because the naïve parton model failed to
    explain the large SSAs
  • SSA in hard partonic process is proportional to
    ?smq/Q (Kane et al, PRL41, 1978)
  • It requires the hadron heliciy flip (through,
    e.g., the Lq) and final/initial state interaction
    phasese to generate large SSAs

18
Two mechanisms beyond the naïve parton model
  • Spin-dependent transverse momentum dependent
    Sivers function
  • Sivers 90
  • Brodsky, Hwang, Schmidt, 02
  • Collins 02 Belitsky, Ji, Yuan, 02
  • Twist-3 quark-gluon correlations (coll.)
  • Efremov-Teryaev, 82, 84
  • Qiu-Sterman, 91,98

S?
k?
P
19
Unifying the Two Mechanisms (PT dependence of DY)
  • At low Pt, the non-perturbative TMD Sivers
    function will be responsible for its SSA
  • When Pt Q, purely twist-3 contributions
  • For intermediate P, ?QCDltlt Ptltlt Q, we should see
    the transition between these two
  • An important issue, at PtltltQ, these two should
    merge, showing consistence of the theory

(Ji, Qiu, Vogelsang, Yuan, hep-ph/0602239)
20
Factorization Arguments
Reduced diagrams for different regions of the
gluon momentum along P, P, and soft
Collins-Soper 81
21
Summary and outlook
  • Spin physics is very exciting at present, because
    of the ongoing experiments at RHIC,
    HERMES,COMPASS,JLAB, and future plan at
    eRHIC,JPAC,GSI-FAIR,…
  • Theoretical frameworks have been worked out for
    all relevant processes
  • Connecting different nuclear observables, such as
    Mq, MG, GPDs, TMDs, …

22
Ultimate goal spin sum rule
Gluon spin
Orbital Ang. Momen
Quark spin
Transverse Spin
Longitudinal Spin
DVCS, FF, …
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