By Richard D Field

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17mls llc 1'se ) pola ri zatio n sl. ('s . 27) results in a combin a tion of th e tra nsverse and longitudinal cross sections which I will label by the subscript L. 5) gives WerE -+ J-l+ J-l-) = aQ. 16). 31) shown in Fig. 3 the Born amplitude. 30) I would like to discuss techniques for summing over photon and gluon polarization states. 2) for helicity A = ±1. 4) The matrix element squared for any process with one real external photon / ,11 11 114' writt ~ Jl All ('2 . ' 0) . N lindy, IM I:! ~ )' >.

4) comes from the analytic continuati o n from the spacelike to the timelike region of q2. 11) for the real gluoll corrections, we arrive at (]'Mc(real) . ) + (]'JlfG(vrrtual = 20. 311' (]'o {11'2 -3 + 5 - 27 - 3211'2 + 11' 2} 42 C ll ll pl'''1 'J. 6 ) Both the log2(,B) and log(,B) terms cancel out in the sum leavin g a finite resu lt in the limit mg -+ O. Thus, the total rate for a virtual photon to decay into partons has the following perturbation series e+e- O"tot =0"0 (1 +-;+ a. ) .... 18) and A is the QCD perturbative parameter that sets the scale.

7) >. 6) provided Loo = L 33 . n) ( :auge invariance insures that this is indeed the case. 2 . 12) where A/,(x) is the electromagnetic current and (x) is an arbitrary rUllctioll must leave the results invariant . '2 . '2 . 2 . 9) is satisfied. 7) is equivalent to summing the two allowed helicity states. J £/'('\)£/1('\) >. 16) ' will work equally well, where '7 is an arbitrary gauge parameter (TJ Feynmap gauge, TJ = -1 is Landau gauge). =0 is ( ! lIpt"I ' 11'"l. 11 Itli (. 2 . <'I' ll(tl [('al massless photons.

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