Applications of Perturbative QCD by Richard D Field

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By Richard D Field

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15). Namely, 20. 7. , q2 is spacelike). 7,:1) arrive at II l1 d . (]'MC ( vIrtual ) 20. { -log 2() = S(]'o {3 11' 3 log() (3 - 2'7 - 3211'2 + 11' 2} . , q2 timelike). 1) I need only keep the real part. 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.

J . fi . I /I) 11 11 (,? 12). l: iV('H (]' Mc (virtual) = (],v(virtual) + (]'s(virtual) 20. 11 . 1II) - - 2 3 \ 1111 11 cOIILa ins only infrared divergences. vi o l(' l, , 111,,,11' /, has dropped out. ~ . 7 Order as Correction - M G Scheme \ I II t he massive gluon scheme the order o. virtual corrections are givc II by ('I. 15). Namely, 20. 7. , q2 is spacelike). 7,:1) arrive at II l1 d . (]'MC ( vIrtual ) 20. { -log 2() = S(]'o {3 11' 3 log() (3 - 2'7 - 3211'2 + 11' 2} . , q2 timelike).

The origin of this divergence is clear. 24) . 39) where 823 is the angle between P2 and P3 and E2 and ware the energy of the outgoing quark and gluon, respectively. 5 (a) Dalitz plot for the "decay" of I. virtual photon with invariant mass Xi = 2EdQ. The shaded area is the allowed kinematic region. nd f3 = mi/Q2. ch carrying fractional energy the energy of the gluon goes to zero (w .... 0, "soft divergence") or when the outgoing quark and gluon become parallel (cos 023 .... 1, "parallel divergence").

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