By Richard D Field
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Extra resources for Applications of Perturbative QCD
Example text
G . ~) Itlld where L is large. For small k, C(k) is approximately equal to one. bllt. at. rge k it behaves like 1/k 2 causing the integrals to converge. In the massive gluon scheme the infrared divergences are handled by r\ ' pl acing 1/k 2 by 1/(k 2 - m~) in the gluon propagator. Both the infrar d Iwd 1IItravioiet divergences can be treated simultaneously by the replacem ent. :\) fo r the gluon propagator. 5) and where for simplicity I have set 7J = 0 (Feynman gauge). 6) -+ 0 have been dropped.
8. 8 . 1 2) being dimensionless. The "dimensional regularization mass", rnD, plays a n analogous role to the gluon mass , rn g , in the massive gluon regularizatio n scheme. 8) gives r(~) aty;'; --;. qij) == 0'0 = 3ae~ Q r(N ~ 2) or 2 0'0 = 3ae q Q (Q2 )N/2-2 47rrnb . 30) when { = o. To evaluate the three-body decay of a virtual photon into a quark, antiquark, and a gluon we proceed in an analogous manner. 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 .
L . Rosner, "Hadron Spectra and Quarks," Am. J. Phys. 49 (10),954 (1981). F . D. , 1984. , 1983. P. , 1981. References 1. N. L. Mill, Phys. Rev. 96, 191 (1954) . 2. F. D. , 1984. 3. W . G. Roberts, Physics Reports 120, 275 (1985) . 4. W. De Boer, SLAC-PUB-4428, invited talk at the xth Warsaw Symposium on Elementary Particle Physics, Kazimierz, Poland, May 25-29, 1987. / C IIAP'I' En 2 Electron-Positron Annihilations: Total Rate to Hadrons 15 10 <;1. t,loI II ld,,' III. ('d oi>j,·(' t,. ntly bing cr atcd and til n die after living the time allowed them by th e un certainty principle.
