Charge Density of the Neutron
Charge Density of the Neutron
Charge Density of the Neutron
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<strong>Charge</strong> <strong>Density</strong> <strong>of</strong> <strong>the</strong> <strong>Neutron</strong><br />
Gerald A. Miller<br />
University <strong>of</strong> Washington<br />
arXiv:0705.2409<br />
What do form factors really measure?
What is charge density at <strong>the</strong><br />
center <strong>of</strong> <strong>the</strong> neutron?<br />
<strong>Neutron</strong> has no charge, but charge density<br />
need not vanish<br />
Is central density positive or negative?
TTM<br />
4π r 2 ρ n (r)<br />
One gluon exchange also gives<br />
positive central charge density
Enough models- models models- Today<br />
model independent independent<br />
information
Outline<br />
Electromagnetic form factors<br />
Light cone coordinates, kinematic<br />
subgroup<br />
GPDs + Bit <strong>of</strong> math<br />
Two dimensional Fourier transf. transf.<br />
<strong>of</strong> F gives ρ(b), (b), Soper ’77 77<br />
1 Data analysis, Interpretation
Definitions<br />
Old Interpretation- Breit frame<br />
G E is helicity flip matrix element <strong>of</strong> J 0<br />
2
Interpretation <strong>of</strong> Sachs - G (Q E 2 Interpretation <strong>of</strong> Sachs - GE(Q (Q ) is 2 ) is<br />
Fourier transform <strong>of</strong> charge density<br />
Correct non-relativisticaly<br />
φ invariant under Galilean transformation<br />
--<br />
φ is frame dependent,<br />
interpretation <strong>of</strong> Sachs wrong
Why relativity if Q2 ¿ M2 Why relativity if Q 2 ¿ M2 QCD- QCD photon hits ≈ massless<br />
quarks<br />
No matter how small Q 2 is, <strong>the</strong>re<br />
is a boost correction that is ∝ Q2 F ∼ Q 1 2<br />
RN<br />
2 (|ψ| (| 2 +C/(m qRN) 2 )
Light Light cone cone coordinates<br />
coordinates
Relativistic formalism-<br />
kinematic subgroup <strong>of</strong> Poincare<br />
Lorentz transformation –transverse transverse<br />
velocity v<br />
k - such that k 2 not changed<br />
Just like non-relativistic
Generalized Parton Distribution<br />
A + =0, t=(p-p’) 2 = -Q 2 =-
H q (x,0)=q(x) (PDF)<br />
transverse center <strong>of</strong> mass R
Burkardt<br />
Integrate on x, Left: sets x - =0 q + † (0,b) q+ (0,b)<br />
DENSITY; right 2 Dim. Fourier T. <strong>of</strong> F 1
<strong>Density</strong><br />
RESULT<br />
τ=Q 2 /4M 2<br />
(2π) 2<br />
Soper ‘77
hep-ex/0602017
Results<br />
Kelly<br />
BBBA<br />
Negative
Negative F 1<br />
means central<br />
density negative<br />
GeV<br />
G<br />
2<br />
GeV 2
<strong>Neutron</strong> Interpretation<br />
0.005<br />
1<br />
0.5<br />
0.1<br />
0.05<br />
0.01<br />
-<br />
+<br />
b<br />
0 1 2 3 4 5 6<br />
? π - at short distance ?
<strong>Neutron</strong> Form Factors in LFCBM<br />
Miller 2002<br />
These give negative F 1
<strong>Charge</strong> symmetry: u in proton is d in<br />
neutron, d in proton is u in neutron<br />
ρ u =ρ p -ρ n /2 ρ d =ρ p -2ρ n<br />
ρ p =4/3ρ u -2/3 ρ d
?Quark interpretation?<br />
b=0, high transverse momentum, low<br />
Bjorken x<br />
low x, sea<br />
u u<br />
-<br />
u is suppressed by Pauli principal,<br />
Signal & Thomas
Summary<br />
Model independent information on charge<br />
density<br />
• Central charge density <strong>of</strong><br />
neutron is negative<br />
• Pion cloud at large b
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