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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Definitions
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old helicity conservation
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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
Correct in non-relativistic physics, Galilei
invariance of wave function ?
Relativity ? is frame dependent, initial final
wave functions have different momentum OLD
interpretation of Sachs wrong
QCD- photon hits massless quarks. No matter how
small Q2, there is boost correction GEn Q2
((d3r r2?2C/(mq)2)
-
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Need relativistic 3-quark model Implement
Relativity-Light Front 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
Transverse boosts act like non-relativistic
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Impulse Approximation 1995
Frank, Jennings, Miller 95
g
carry orbital angular momentum
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Ratio of Pauli to Dirac Form Factors 1995
Frank,Jennings, Miller theory, data 2000
Model flat curve due to orbital ang. mom.
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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
Central charge density of the neutron?

Neutron has no charge, but charge density need
not vanish Is central density positive or
negative? Pion cloud effect- positive One gluon
exchange-positive Today model independent
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The Density
transverse center of mass R
Burkardt
b is distance from cm, R0
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Generalized Parton Dist. GPD
0 skewness
Hq(x,0)q(x) (PDF)
Burkardt
transverse center of mass R
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Burkardt
Integrate on x, Left sets x-0 q(0,b)2
DENSITY right 2 Dim. Fourier T. of F1
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RESULT
Soper 77
(2?)2
Density
Two dimensional Fourier Transform
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Form factor parameterizations
Kelly PRC70,068202
hep-ex/0602017
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Results
BBBA
Kelly
Negative
Phys.Rev.Lett.99112001,2007
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GeV2
G
GeV2
Negative F1 means central density negative
Phys.Rev.Lett.99112001,2007
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Neutron Interpretation

-
b
Why ? In proton u(x) dominates at high x
b0, in neutron d at b0, Miller Arrington
arXiv0806.3977 
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(No Transcript)
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Shapes of the proton

• Relate spin dependent density SDD to experiment
• Phys.Rev.C76065209,2007

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Field theoretic SDD

• Probability for momentum K, and spin direction
  n. Matrix elements depend on three vectors n, K,
  S

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
• Result non-spherical nature of proton related to
  h1T?

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Model-Transverse spin-dependent densities
n
n
S
Lattice SDD not zero, proton not round,
Scheirholtz
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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 is not 0, proton is not round.
  Experiment can show
• proton aint round.

The Proton
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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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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
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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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Relativistic Model Explanation