Richard D Field's Applications of Perturbative QCD PDF

By Richard D Field

ISBN-10: 0201142953

ISBN-13: 9780201142952

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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.

3) for these terms give finite contributions when integrating over Xl. 5) We can replace the /3 and /3 2 terms by a 6-function and arrive at d(T dXI = 2a. 6) using f3 1 - - dXI = -log(/3), o 1 - Xl 1 - f3 1 --log(l - Xl) dXI = o 1- Xl 1 1 xI) } . 8) / Vi ,I,111i1

31 is, of course, gauge invariant. 31) yields 1 dl7E 2a. 33) The order a. 32) over the kinematically allowed range of Xl and X2 . 34) or in terms of Xi (1 - xd(l- x2)(1 - X3) = O. 37) is shown in Fig. 5. 32) becomes 2 a. 38) and we are left with a problem that will occur over and over as we perform perturbative QeD calculations. 32) diverges as Xl or X2 goes to 1 and l7(real) is infinite. 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.

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Applications of Perturbative QCD by Richard D Field


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