Erratum: Zero‐Field Splitting, One‐ and Two‐Center Coulomb‐Type Integrals

Dimensionally Regulated One-Loop Integrals

We describe methods for evaluating one-loop integrals in 4−2 dimensions. We give a recursion relation that expresses the scalar n-point integral as a cyclicly symmetric combination of (n− 1)point integrals. The computation of such integrals thus reduces to the calculation of box diagrams (n = 4). The tensor integrals required in gauge theory may be obtained by differentiating the scalar integra...

Scalar one-loop integrals for QCD

We construct a basis set of infra-red and/or collinearly divergent scalar oneloop integrals and give analytic formulas, for tadpole, bubble, triangle and box integrals, regulating the divergences (ultra-violet, infra-red or collinear) by regularization in D = 4− 2ǫ dimensions. For scalar triangle integrals we give results for our basis set containing 6 divergent integrals. For scalar box integr...

One-Loop Tensor Integrals in Dimensional Regularisation

We show how to evaluate tensor one-loop integrals in momentum space avoiding the usual plague of Gram determinants. We do this by constructing combinations of nand (n− 1)-point scalar integrals that are finite in the limit of vanishing Gram determinant. These non-trivial combinations of dilogarithms, logarithms and constants are systematically obtained by either differentiating with respect to ...

Erratum

A Calculational Formalism for One-Loop Integrals

We construct a specific formalism for calculating the one-loop virtual corrections for standard model processes with an arbitrary number of external legs. The procedure explicitly separates the infrared and ultraviolet divergences analytically from the finite one-loop contributions, which can then be evaluated numerically using recursion relations. Using the formalism outlined in this paper, we...