Gerald A' Miller

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Model Independent Nucleon results
Gerald A. Miller University of Washington
Everything that rises, Martin Puryear
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Outline

• Phenomenological considerations
• proton is not round.
• Model independent
• neutron charge density,
• proton magnetization
• shape of proton
• Experimental progress-Jefferson lab INT program
  Jlab-12 Fall 09

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Naive Model of Nucleon

• Proton 2 u, 1 d, Neutron 2 d, 1 u
• Confined quarks move with zero orbital angular
  momentum

Spin Crisis Quarks carry only 30 of proton
spin three ideas- u,d quarks surrounded by s
s gluons carry angular momentum quarks
carry orbital angular momentum
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Definitions
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Expectations- Pre Jlab
Jlab
QF2 /F1
GE/GM
GE/GM
QF2/F1
Q2
Q2
Proton
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Old Interpretation of GE(Q2) is Fourier
transform of charge density
This is correct in non-relativistic physics

• invariant same in initial and final frame

Relativity ? is frame dependent, initial and
final wave functions have different momentum OLD
interpretation of Sachs wrong
-
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Why relativity if Q2 ltltM2

• QCD- photon hits ¼ massless quarks
• No matter how small Q2 is, there
• is a boost correction / Q2
• GE n Q2 (s d3r r2?2C/(mq)2)

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Need relativistic 3-quark model Implement
Relativity-Light Cone Cooordinates
Time xc t z x0x3 Evolve
p-(p0-p3) Space x-ct-zx0-x3 Momentum
pp0p3 Bjorken variable Transverse position
b, momentum p Separate internal and cm
coordinates
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Relativistic formalism-kinematic subgroup of
Poincare

• Lorentz transformation transverse velocity v

k- such that k2 not changed
Transverse boosts act like non-relativistic
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Impulse Approximation 1995
Frank, Jennings, Miller 95
g
Correct wave function includes PQCD, Feynman
mechanisms
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Ratio of Pauli to Dirac Form Factors 1995 theory,
data 2000
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Relativistic Model Explanation
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Model exists

• lower components of Dirac spinor
• orbital angular momentum
• shape of proton?? Wigner Eckart
• no quadrupole moment
• spin dependent densities SDD
• non-relativistic example

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?
s r
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Shapes of the proton
three vectors n, K, S
MODEL , HOW TO MEASURE?
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Model Independent Densities and Shapes
Phys.Rev.Lett.99112001,2007 charge
density arxiv0711.0972 magnetization
density arXiv0708.2297 nucl-th in PRC- shape
Model independent charge densities using form
factors- magnetization density of proton Model
independent shape of proton from (e, p ? e, ?
X)
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What is charge density at the center of the
neutron?

• Neutron has no charge, but charge density need
  not vanish
• Is central density positive or negative?

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n p ?-
4? r2?n(r)
TTM
One gluon exchange also givespositive central
charge density
Today- model independent information
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Generalized Parton Distribution
A0, t(p-p)2 -Q2 -
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Hq(x,0)q(x) (PDF)
transverse center of mass R
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Burkardt
Integrate on x, Left sets x-0 qy(0,b)
q(0,b) DENSITY right 2 Dim. Fourier T. of F1
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RESULT
Soper 77
(2?)2
Density
Two dimensional Fourier Transform
?Q2/4M2
? GM ¼ GE at low Q2
For neutron
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neutron
proton
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hep-ex/0602017
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Results
BBBA
Kelly
Negative
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GeV2
G
GeV2
Negative F1 means central density negative
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Neutron Interpretation

-
b
Why ?
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Shapes of the proton

• Relate spin dependent density SDD to experiment

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Field theoretic SDD

• Probability to have momentum K, and spin
  direction n

Matrix elements depend on three vectors n, K, S
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Transverse Momentum Distributions TMDs

• xK/P
• Mulders Tangerman 96

?i?5 ??i ?0 ?i
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Relate SDD to TMD

• SDD depend on Kx, Ky , Kz equal time
  correlation function
• TMD depend on x, Kx , Ky ?0 tz correlation
  function
• Integrate SDD over Kz --gt t0,z0
• Integrate TMD over x ! ?0, t0,z0
• Result non-spherical nature of proton related to
  h1T?

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Transverse spin-dependent densities
n
n
S
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Measure e, p ? e, ? X
ST
e
?
e
Cross section has term proportional to cos 3?
Boer Mulders 98
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Summary of SDD

• SDD are closely related to TMDs
• If h1T? is not 0, proton is not round.
  Experiment can show
• proton aint round.

The Proton
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Spares follow
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Spin density operator d(r-rp) s . n
PRB65, 144429

• Canted ferromagnetic structure of UNiGe high
  magnetic fields
• Neutron magnetic scattering
• Neutron, B, crystal

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Summary of density

• Model independent information on charge density

• Central charge density of neutron is negative
• Pion cloud at large b

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Charge symmetry u in proton is d in neutron, d
in proton is u in neutron ?u?p?n/2 ?d?p2?n
?p4/3?u-1/3 ?d