Theoretical Overview of Spin Physics

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Theoretical Overview of Spin Physics

• Feng Yuan
• RBRC, Brookhaven National Laboratory

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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

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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)

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Summary of DIS data
(doesnt yet include new COMPASS results)
L. De Nardo (HERMES)
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Where is the rest of the proton spin

• Gluon spin?
• Orbital motion?

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

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Where we can get gluons
Inclusive DIS
LO
NLO
gluons are sub-dominant.
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Current understanding of Mg from evolution of
DIS data
Measurement of ?g a major emphasis at RHIC
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In hadronic collisions (RHIC)
LO
gluons are leaders.
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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

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at RHIC
See more in Fatemi and Eysers talks
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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)

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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
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GPDs link many observables
D. Hasch_at_SPIN2004
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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
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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

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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
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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)
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Factorization Arguments
Reduced diagrams for different regions of the
gluon momentum along P, P, and soft
Collins-Soper 81
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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,

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