partons and bjorken scaling - university of...
TRANSCRIPT
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)