Convergence and gauge dependence properties of the resummed one loop quark quark scattering amplitude in perturbative QCD

for quark-quark scattering is derived by diagrammatic resummation of the one-loop amplitude using an arbitary covariant gauge. Except for the particular choice of gauge parameter

\xi = -3, \alpha_s^{eff}

is found to increase with increasing scale as

\ln Q

or

\ln^2 Q

. For

\xi = -3, \alpha_s^{eff}

decreases with increasing

Q

and satisfies a renormalisation group equation. Experimental measurements of

\alpha_s

indicate, however, that in this case,

\alpha_s^{eff}

is convergent only for scales

\le

300 GeV.

Note:

28 pages, 5 tables, 5 figures. v3 The one-loop amplitudes in Section 2 are recalculated using dimensional regularisation, and several errors in the on-shell calculation of Reference[1] are pointed out. v4 one figure removed one added. Three tables and new text in Section 5 added. Published version

12.38.t
12.38.Bx
12.38.Cy
quark quark: scattering amplitude
quantum chromodynamics: perturbation theory
Feynman graph: higher-order
transformation: gauge
renormalization group
strong interaction: coupling constant
asymptotic freedom

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Figures(0)

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