Franz Gross

The shape of the nucleonFrascati Workshop on Nucleon Form Factors (N05)

October 13, 2005

Franz GrossJLab and W&M

Outline: I. BackgroundII. The modelII. Parameters and results

III. Discussion and implications

*This talk is based on a modified version ofJLAB-THY-04-39 (under review by PRD) by FG and Peter Agbakpe.

Franz Gross

Background

Beautiful new data from JLab, Mainz and other labs on the formfactors

Lots of excitement about the decrease in the ratio Rp = GEp/GMpwith Q2

Enter Jerry Miller, John Ralston, and the Jlab workshop of May2002• Deformed protons !!!!• lack of helicity conservation !!!!• USA Today, Science News !!!• Great discovery !!!!

Whats going ON !!!?

*G. Miller, Phys. Rev. C 68, 022201(R) (2003)

*

Franz Gross

"The proton is the simplest thing around, and it is not spherical," says physicist Charles Glashausser ofthe Rutgers University campus in Piscataway, N.J. The neutron, the uncharged partner-particle to theproton in the nucleus of atoms, also is built of quarks, he notes.

Physicists thrown for a loop ; New insight on protons changes the shape of things;[FINAL Edition]Dan Vergano. USA TODAY. McLean, Va.: Sep 23, 2002. pg. D.07

Copyright USA Today Information Network Sep 23, 2002Science and education

The humble proton, an atomic particle with mysteries long thought solved, turns out to have a hiddensecret, scientists report.

Experimental results released this year by the Department of Energy's Jefferson Lab in Newport News,Va., have upturned the normally placid world of nuclear physics with the suggestion that protons, thepositively charged particles found in the center of every atom, aren't round. Instead, they seemsomewhat elliptical.

The round proton has been a staple of textbooks for 40 years, tied to the theory that protons andneutrons are built of three smaller particles called "quarks" slowly bubbling inside their interiors.What difference does it make whether protons are round or elliptical? Plenty, physicists say. Adjustmentsin protons and neutrons could affect scientific understanding of the magnetic "spin" of atoms. Scientistshope to use "spintronics" in future computers and tiny "nano-scale" devices. Understanding thefundamental shape of particles will affect those application's success.

At a Jefferson Lab meeting in May, about 60 nuclear physicists met to debate the "crisis," in the words ofphysicist John Ralston of the University of Kansas, over the odd shape of the proton.At the May meeting, a consensus emerged that Einstein's theory of special relativity, which explains howthings moving near the speed of light have smooshed lengths and increased mass, seemed the likeliestexplanation for the weird experiment results.

"The new thing we've figured out is that quarks are moving around inside the proton at relativistic (nearspeed of light) speeds," says physicist Gerald Miller of the University of Washington- Seattle. Quarksmoving at those speeds simply elongate the particle's electromagnetic shape, Miller says. In a paper inthe journal Physical Review C, he outlines how quarks moving at high speeds, about 90% of the speedof light, stretch out protons.

Franz Gross

WHAT'S GOING ON?

A spin 1/2 object cannot have a quadrupole deformation!

(Unless it is deformed in the sense of the transition nuclei, described byBohr and Mottelson.* In this case there will be rotational bands and largeelectromagnetic transition rates, not seen.)

Talking about such things could make the field look foolish, or we couldwaste our time arguing about what we mean. It matters (confusion andethics).

To remove the danger of making a mistake about shapes, we MUSTbe sure rotational invariance is treated exactly.

(The light-front formalism does not.)

Can the data be explained using standard physics?

*See: Buchmann and Henley, PRC 63,015202 (2001)

Franz Gross

The Model

Franz Gross

The nucleon consists of 3 constituent quarks (CQ) with a size, mass,and form factor given by the dressing of the quark in the sea ofgluons and qq pairs.

Using the spectator theory, the nucleon is described by a 3-CQvertex function with two of the CQ on shell

Confinement insures that this vertex function is zero when all threequarks are on shell (i.e. there is no 3q scattering)

The nucleon wave function (1)

Γ××

Γ×

×× = 0

p

ps P Ψα = 1m − p − iε

⎛

⎝⎜⎞

⎠⎟αβ

Γβ P, ps( )

Hence, model Ψ directly

Franz Gross

Spin-isospin structure of the NR nucleon wave function

• Assume a simple, fully symmetric S state spatial wave function• Then spin-flavor wave function is fully symmetric

in operator form

Relativistically

The nucleon wave function (2)

p ↑ =12

Φ0 + 12( )Φ0 + 1

2( ) +Φ1 + 12( )Φ1 + 1

2( ){ } red = spinblue = flavor

fs =12

ξ0 χs⎡

⎣⎤⎦ ξ0 χ

f⎡⎣

⎤⎦ −13

σ ⋅ξ1 χs⎡

⎣⎤⎦ τ ⋅ξ1 χ

f⎡⎣

⎤⎦

⎧⎨⎩

⎫⎬⎭

(0,0) diquark (1,1) diquark

χ12 =

10

⎛⎝⎜

⎞⎠⎟

χ− 12 =01⎛⎝⎜

⎞⎠⎟

Ψα =12uα P, s( ) ξ0 χ

f⎡⎣

⎤⎦ψ00 P, ps( ){+13γ 5η( )αβ uβ P, s( ) τ ⋅ξ1 χ

f⎡⎣

⎤⎦ψ11 P, ps( )⎫⎬

⎭

Franz Gross

Relativistic wave function, including spin-flavor structure

when P = 0, this reduces to the nonrelativistic form

choose and to be spherical in the rest frame (i.e. theydepend only on the magnitude of ps only)

The nucleon wave function (3)

Ψ00 Ψ11

(1,1) diquark

(0,0) diquarkΨα =

12uα P, s( ) ξ0 χ

f⎡⎣

⎤⎦ψ00 P, ps( ){+13γ 5η( )αβ uβ P, s( ) τ ⋅ξ1 χ

f⎡⎣

⎤⎦ψ11 P, ps( )⎫⎬

⎭

Ψ00 ≡N0

β1 + 2 1+κ 2 − 2( ) β2 + 2 1+κ 2 − 2( ) NR⎯ →⎯⎯

N0

β1 +κ2( ) β2 +κ

2( )

Ψ11 =1

1+ 23κ

2 Ψ00 NR⎯ →⎯⎯

N0

β1 +κ2( ) β2 +κ

2( )

κ =psms

Franz Gross

xx

= 3P+ P−

P± = P ± 12 q Q2 = −q2

Relativistic impulse approximation for the form factors

In the spectator theory, the photon couples to the off-shell quark, andbecause of the symmetry, the coupling to all three quarks is 3 times thecoupling to one

J Iµ = u P+ , λ '( ) 3

2d 3ps

(2π )32Es (ps )∫ jI

µ ψ 00 P+ , ps( )ψ 00 P− , ps( ){

− 19γ νγ 5τ j jI

µτ jγ5γ ν 'Δνν 'ψ 11 P+ , ps( )ψ 11 P− , ps( )} u P− , λ( )

quark currentswith form factors

integrate overthe (on-shell)spectator threemomentum sum over the vector diquark, using

ηνην 'η∑ ≡ Δνν ' = −gνν ' +

psν psν 'ms2

x~ 3

approximate the two spectator quarksby a single diquark with a fixed mass

Franz Gross

Quark form factors include vector dominance and a pion cloud

The quark currents are

jIµ = f1 γ

µ + f2iσ µνqν2M

, fi = fi+ + τ 3 fi−

f1± = 1

3 f1u 16 f1d f2± = 1

2 µu f2u ± µd f2d( )

the quark form factors have 9 parameters:

f1+ = e+1− λ

1+Q02

Λ1+2

+ λ

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

f2 ± = µ±1

1+Q02

Λ2±2

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

f1− = e−1− λ − λπ

1+Q02

Λ1−2

+λπ

1+Q02

Λπ2

⎛⎝⎜

⎞⎠⎟2 + λ

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

pion cloud

VDM terms

Franz Gross

Normalization and shape

To find the shape and normalization, compute JI0(q=0).

After some algebra:

J I0 (q = 0) = 1

2 1+ τ 3( )δλ 'λd 3ps

(2π )32Es (ps )∫ ψ 00

2 P, ps( )

= 12 1+ τ 3( )δλ 'λ

d 3κ(2π )32Es (κ )∫

N02

β1 − 2 + 2Es (κ )( )2 β2 − 2 + 2Es (κ )( )2

spherical shape

correct normalization

Franz Gross

The Parameters and Results

Franz Gross

Results: Overview

The form factors data is fit with 11 parameters:• 1 asympotic value of the f1 quark form factors, λ• 2 nucleon wave function parameters β1 and β2

• 2 quark anomalous moments µu and µd

• 2 pion cloud parameters, the strength λπ , and its range, Λπ

• 4 vector monopole dominance scales for the four quark formfactors, Λi±

• 11 total

The the model automatically normalizes GEp(0) = 1 and GEn(0) = 0, byadjusting the normalization constant (not a parameter) N0

The fit constrains the nucleon anomalous moments and the nucleonradii to their experimental values, assuring realistic low Q2

properties/

The other 7=11-4 parameters are determined my minimizing χ2.

Franz Gross

The parameters

0.7961.0862.217−0.8232.772

0.2310.5911.6851.1270.069

β1 β2 µu µd Λ1+ Λ1− Λ2+ Λ2− λπ Λπ

χ 2

datum = 1.32, λ = 0.156, N02 = 149.8, rp

2 = 0.780, rn2 = −0.113

rp2 (exp) = 0.780(25), rn

2 (exp) = −0.113(7)

Fit to the data

φ0 ≡N0

β1 + 2 1+κ 2 − 2( ) β2 + 2 1+κ 2 − 2( ) Nonrelativistic⎯ →⎯⎯⎯⎯N0

β1 +κ2( ) β2 +κ

2( )

φ1 =1

1+ 23κ

2 φ0 Nonrelativistic⎯ →⎯⎯⎯⎯N0

β1 +κ2( ) β2 +κ

2( )f1+ Q2( ) = 1− λ( ) 1

1+Q02

Λ1+2

⎛⎝⎜

⎞⎠⎟+ λ f1

− Q2( ) = 1− λ − λπ( ) 1

1+Q02

Λ1−2

⎛⎝⎜

⎞⎠⎟+

λπ

1+Q02

Λπ2

⎛⎝⎜

⎞⎠⎟+ λ

f2± Q2( ) = 1

1+Q02

Λ2±2

⎛⎝⎜

⎞⎠⎟

Franz Gross

The quark form factors

f1+

f2+

f1−

f2−

Franz Gross

The magnetic form factors

Both magnetic form factors are similar in shape. Better data forGMn a must! Pion cloud essential to explain GMn

fit with pion cloudno pion cloudrefit with NO pion cloud

Franz Gross

The charge form factors

The fits to the charge from factors are both excellent. Again thepion cloud is essential to the desciption of GEn

Prediction: GEp will change sign at Q2 ~ 8 GeV2

fit with pion cloudno pion cloudrefit with NO pion cloud

Franz Gross

The F2/F1 puzzle for the proton

QF2p/F1p is indeed flat, but this is an accident; The asymptotic valuewill not be reached until Q2 ~ 100 GeV2.

Rmag =QF2 p (Q

2 )κ p F1p (Q

2 )

Franz Gross

Comparisons (light front theory)

G. A. Miller, Phys. Rev. C 66, 032201(R) (2002)

F. Cardarelli and S. Simula, Phys. Rev. C 62, 065201 (2000)

Franz Gross

Comparisons (vector dominance)

Bijker and Iachello, Phys. Rev. C 69, 068201 (2004)Original model (IJL, 1973) fails, and new fit gives different predictionfor GEp !!

Lomon, Phys. Rev. C 66, 045501 (2002), gives similar result for GEP

Franz Gross

Discussion and Implications

The data do not require the proton to be deformed!• This is forbidden by quantum mechanics (unless there are rotational bands).• This model is a counter example to claims that the data cannot be explained

by a spherical proton

The data do give interesting new information about the CQ formfactors, and tell us about the proton wave function.

The model is so simple that it can be used to study many phenomenanear the quark-hadron transition

Predictions• GEp will change sign near Q2 ~ 8 GeV2

• GMn will be larger than the older data suggests

What does this problem teach us about over-selling science?

Franz Gross

END