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By Richard D Field

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L- pair with a quark-antiquark pair as in Fig. 3 Born amplitude for the "decay" of a virtual photon into a quarkantiquark pair. from the sum over the three quark colors and the factor e~, where eq is the charge of the quark q in units of the electric charge e. Assuming that quarks turn into hadrons with unit probability one arrives at the famous parton model prediction for the ratio of the total cross section e+ e- -+ hadrons to the total cross section for e+ e- -+ p+ p-. 16) i=1 where the sum is over all quark pairs that can be produced at the given center-of-mass energy of Q.

16) 3, where dN-PI d N -P2 (271")N-I(2Et) (271")N-1(2E2) N d -P3 ( )N 6N( ) (271")N-1( 2E3) 271" q - PI - P2 - P3 . 17) I have chosen the axis to be in the direction of particle 1 with z = cos 0 12 , where 0 12 is the relative angle between particle 1 and particle 2, and all decay particles have been taken to be massless. 20) when N = 4 and as before we cannot integrate d 2R3 any further without knowing the matrix element since, in general, it will depend on Xl and X2. 10) we define a dimension I 88 stroll ll.

The 10g(j3) = 10g(xI/j3) . 43) is tough . 12), Li~(x), is defi ll ed ill ApJl( 'lIdi x I';. '111) p, IV" S • O'mCrE -+ qijg ) = 2a. 37r 0'0 { 2log2() {J + 3 log () {J 2 + 37r + '5} 2 ' where again terms that vanish in the limit {J -+ 0 have been dropp d. 50) has a term that diverges like log2 ({J) as (3 • () which comes from the region in which both Xl and X2 approach 1. here is a term that diverges like log({J) and there are terms that a r fillil,, · IIH (J -+ O. As Q increases this cross section increases like log(Q).

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