6 research outputs found
A Feynman integral in Lifshitz-point and Lorentz-violating theories in R<sup>D</sup> âš R<i><sup>m</sup></i>
We evaluate a 1-loop, 2-point, massless Feynman integral ID,m(p,q) relevant for perturbative field theoretic calculations in strongly anisotropic d=D+m dimensional spaces given by the direct sum RD âš Rm . Our results are valid in the whole convergence region of the integral for generic (noninteger) codimensions D and m. We obtain series expansions of ID,m(p,q) in terms of powers of the variable X:=4p2/q4, where p=|p|, q=|q|, p Đ RD, q Đ Rm, and in terms of generalised hypergeometric functions 3F2(âX), when X<1. These are subsequently analytically continued to the complementary region Xâ„1. The asymptotic expansion in inverse powers of X1/2 is derived. The correctness of the results is supported by agreement with previously known special cases and extensive numerical calculations