arXiv subjects

G. Heinrich

Publications and source records attributed to G. Heinrich.

111 records · Page 7Linked to original sources

arXiv1999

Split dimensional regularization for the Coulomb gauge at two loops

We evaluate the coefficients of the leading poles of the complete two-loop quark self-energy Σ(p) in the Coulomb gauge. Working in the framework of split dimensional regularization, with complex regulating parameters σand n/2-σfor the energy and space components of the loop momentum, respectively, we find that split dimensional regularization leads to well-defined two-loop integrals, and that the overall coefficient of the leading pole term for Σ(p) is strictly local. Extensive tables showing the pole parts of one- and two-loop Coulomb integrals are given. We also comment on some general implications of split dimensional regularization, discussing in particular the limit σ\to 1/2 and the subleading terms in the epsilon-expansion of noncovariant integrals.

hep-th↗

arXiv1999

Reduction formalism for dimensionally regulated one-loop N-point integrals

We consider one-loop scalar and tensor integrals with an arbitrary number of external legs relevant for multi-parton processes in massless theories. We present a procedure to reduce N-point scalar functions with generic 4-dimensional external momenta to box integrals in (4-2ε) dimensions. We derive a formula valid for arbitrary N and give an explicit expression for N=6. Further a tensor reduction method for N-point tensor integrals is presented. We prove that generically higher dimensional integrals contribute only to order εfor N>=5. The tensor reduction can be solved iteratively such that any tensor integral is expressible in terms of scalar integrals. Explicit formulas are given up to N=6.

hep-ph↗

arXiv1998

The light-cone gauge and the calculation of the two-loop splitting functions

We present calculations of next-to-leading order QCD splitting functions, employing the light-cone gauge method of Curci, Furmanski, and Petronzio (CFP). In contrast to the `principal-value' prescription used in the original CFP paper for dealing with the poles of the light-cone gauge gluon propagator, we adopt the Mandelstam-Leibbrandt prescription which is known to have a solid field-theoretical foundation. We find that indeed the calculation using this prescription is conceptionally clear and avoids the somewhat dubious manipulations of the spurious poles required when the principal-value method is applied. We reproduce the well-known results for the flavour non-singlet splitting function and the N_C^2 part of the gluon-to-gluon singlet splitting function, which are the most complicated ones, and which provide an exhaustive test of the ML prescription. We also discuss in some detail the x=1 endpoint contributions to the splitting functions.

hep-ph↗