Transcript Discussion Topics Spring 05

Parton Model & Parton Dynamics
Huan Z Huang
Department of Physics and Astronomy
University of California, Los Angeles
Department of Engineering Physics
Tsinghua University
Oct 2006 @ Tsinghua
Quantum Chromodynamics
QCD:
Field Theory of strong
interaction in matter
SUflavor(3) X SUcolor(3)
Confinement:
No free quarks, gluons
(so-called partons)
Color singlet
Hadrons:
meson
baryon
Scattering Process
Momentum Scale and Position Resolution
P Dx > hc ~ 200 MeV fm
Discoveries
Rutherford
Hofstadter
SLAC
FNAL
CERN
HERA
New Machine and Energy
Frontier  Discovery
• Exploring nuclear structure - elastic electron-nucleus scattering

Scattering of electron (Spin 1/2) on pointcharge charge (Spin 0): Mott cross-section

Take into account finite charge distribution:
12C
Form factor
Ignore recoil!
Hofstadter, 1953
Form Factors
 d   d 
2 2


  F (q )
 d   d  Mott
*
F (q )   e
2
f (r ) 
i q x / 
1
(2 )
3
f ( x)d x
F
(
q
)
e

2
3
i q  x / 
3
d q
Form Factors
Form Factors
Experimental Data
Charge Distribution
Data from Electron Scatterings!
How do we measure the neutron distribution?
Parton Scattering and Bjorken Limit
  p  q
2
2
Q2 = -q2
p


Q 
2
2
M    Q 
2
2
Bjorken Limit:
Q2,  infinite,
2 >> Q2 >> 2
  Q2/(2M) = xJ
2

Kinematic Variables
(momentum transfer)2
virtuality of *, Z0, W
 (size of the probe)-1
fraction of the proton
momentum carried by
the charged parton
fraction of the electron
energy carried by the
virtual photon
(inelasticity)
center of mass energy
of ep system
(mass)2 of * p
system
Exploring the Proton structure - inelastic ep scattering

Scattering of electron (Spin 1/2) on proton (Spin 1/2)
Scattering on pointlike objects: Quarks!
Deep-inelastic
scattering (DIS)
Nobel Prize 1990
Friedman, Kendall and Taylor
Structure Functions
• Structure function measurement: Formalism
– In terms of laboratory variables:
– Formulate this now in relativistic invariant quantities:
– Instead of W1 and W2, use: F1 and F2:
Longitudinal structure
function: FL
Parton Model Interpretation of F2
F1eN ( x)   qi ( x) z i2
i
F2eN ( x)  xF1eN ( x)
Isospin Symmetry
)
F2 Measurements
(small)
Neutrino Scattering
Sketch of Structure Function
Experimental Data
Scaling Region !
From Experimental Measurement to
Parton Distribution Function
Model Dependent Result !
Structure Function as a Function of x and Q2
Quark Structure Functions
Sea Quarks Dominate
Zd2/Zu2 ~ 1/4
u quark in p
d quark in n
dominate ?
Total Momentum in Quarks
Momentum Carried by u, d quarks:


  xd ( x)  d ( x) dx  0.18
1
Pu   x u( x)  u( x) dx  0.36
0
Pd
1
0
Proton: uud
Quarks carry ~50% of the momentum
Gluons ~ 50%
Interest in the low x Region
Saturation Region
Gluon pile up at fixed size until
gluons with strength
act like a hard sphere
Once one size scale is filled
Move to smaller size scale
Typical momentum scale
grows
Saturation in the Parton PDF
Saturation:
Low x region
Scale Q2 ~ GeV2
Saturation:
The saturation scale
changes in nuclei
~ A1/3
EMC Effect
Gluon EMC Effect
Not measured well
in electron or
muon scattering
experiments !
Why?
How to improve
the gluon
measurement?
Experimental Measurement from lepton
Scattering on Polarized Target
Fit Experimental Data for Spin
Structure Functions
u+
d–
sea –
gluon ?
Gluon Spin
@Q2 = 1.0 GeV2
Result Model-Dependent !
Spin Physics Program
The Spin Structure of the Proton:
½ = ½ SDq + DG + <L>
q  up, down and strange quarks
G  gluons
L  angular momentum of quarks and gluons
Experimentally:
1) total spin in quarks ~ 30%
2) sea quarks are polarized too
3) little info about the gluon polarization
4) even less know about <L> and how to measure <L>
RHIC Spin Physics
At RHIC we use polarized p+p collisions to study
1) Gluon spin structure function q+gq+
2) Sea quark spin structure function q+qW boson
3) Quark transverse spin distribution
Essential to measure photons, electrons and jets !
STAR: TPC and Electromagnetic CalorimeterLead/Plastic Scintillator sandwich,
Shower Max Detector for electron/hadron
separation.
Meson Spectroscopy
Baryon Spectroscopy
Where Does the Mass Come From?
QCD Masses Dominate !!
Proton Mass ~ 940 MeV
three quarks uud
each quark ~ 300 MeV
Pion two quarks: Mass ~ 140 MeV, spin=0
Rho meson (same quark content as pion):
Mass ~ 776 MeV
Very large component of the mass from Interactions
The Interaction energy strongly spin-dependent !
Proton Wave Function
1
1
 p ( J  , m j  )  2 3  uu (1,1)  d ( 1 2 , 1 2)  13  uu (1,0)  d ( 1 2 , 1 2)
2
2
 (1,0)    / 2
Proton and Neutron Wave Functions
Magnetic Moments
Magnetic Moments
n
p
2

3
Exp ~ -0.685
Magnetic Moments of Baryons
The END