Renormalization scheme dependence in a qcd cross section
McKeon, D. G. C.
Sherry, T. N.
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Chishtie, Farrukh; McKeon, D. G. C. Sherry, T. N. (2016). Renormalization scheme dependence in a qcd cross section. Physical Review D 94 (5),
The zero to four loop contribution to the cross section Re+e- for e(+)e(-) -&gt; hadrons, when combined with the renormalization group equation, allows for summation of all leading-log, next-to-leading-log, ..., next-to-next-to-next-to-leading-log perturbative contributions. It is shown how all logarithmic contributions to Re+e- can be summed and that Re+e- can be expressed in terms of the log-independent contributions, and once this is done, the running coupling a is evaluated at a point independent of the renormalization scale mu. All explicit dependence of Re+e- on mu cancels against its implicit dependence on mu through the running coupling a so that the ambiguity associated with the value of mu is shown to disappear. The renormalization scheme dependency of the &quot;summed&quot; cross section Re+e- is examined in three distinct renormalization schemes. In the first two schemes, Re+e- is expressible in terms of renormalization scheme-independent parameters tau(i) and is explicitly and implicitly independent of the renormalization scale mu. Two of the forms are then compared graphically both with each other and with the purely perturbative results and the renormalization group-summed next-to-next-to-next-to-leading-log results.