Partons and Bjorken Scaling

Wesley KetchumPhysics 363 Presentation

05-21-08

Overview

Electron-Proton Elastic Scattering

Electron-Proton Inelastic Scattering

Stanford Linear Accelerator

Bjorken Scaling at High Energies assuming partons

Callan-Gross Relation

Elastic Scattering Theory

Proton recoils against incident electron

Known proton has some internal structure before quark model

Not simple Mott/Rutherford scattering of point particles

Hide ignorance by showing it as blob in Feynman diagram

Represented in scattering amplitude/diff. cross section with unknown functions K1 and K2, which are functions of momentum transfer

Kick it up a notch

At higher electron energies, inelastic scattering can occur

Hadrons produced in process

Following similar thinking for elastic case (blob masking ignorance) get differential cross section---looks similar to elastic case, but now unknown functions (W1 and W2) dependent on two variables

Now some assumptions

Can give values for K1 and K2 based on elastic scattering with point proton

Gives K1 = -Qp2 q2; K2 = 4 Qp2 M2

Assume proton made up of pointlike parts with spin 1/2---partons

Describe parton W’s from previous equation, which can be re-expressed in terms of momentum fraction

Get total W’s using probability distribution and integrating over partons

And we get?Two functions dependent only on x---momentum transfer dependence fades away with very large q2 but not large x

Termed Bjorken scaling (Bjorken and others did it in 67, with help from Feynman)

Good for q2> 1 (GeV)2 and q*p> 3 (GeV)2

Why is this important?

Direct test for model of proton as made up of partons

If parton model true, then Bjorken scaling should happen

Callan-Gross Relation

Callan and Gross related Bjorken’s scaline functions based on whether partons were spin 0 or spin 1/2

2xF1(x)/F2(x) = 0 for spin 0

2xF1(x)/F2(x) = 1 for spin 1/2

Note that according to our derivation, we got the latter result

Experiment?

SLAC started up in 1966, and did deep inelastic scattering experiments

Jerome Friedman, Henry W. Kendall, and Richard E. Taylor won Nobel prize in 1990 for work verifying parton model

...

Cross Section

Callan Gross Relation

References

J. D. Bjorken, Phys. Rev. 163, 1767 (1967)

J. D. Bjorken, Phys. Rev. 179, 1547 (1969)

J. D. Bjorken, and E. A. Paschos, Phys. Rev. 185, 1975 (1969)

C. G. Callan, and David J. Gross, Phys. Rev. Letters 22, 156 (1969)

Richard P. Feynman, Phys. Rev. Letters 23, 1415 (1969)David Griffiths, Introduction to Elementary Particle Physics, pp. 262-273, John Wiley and Sons Press, 1987.

M. Gell-Mann, Phys. Letters 8, 214 (1964)