A complete algebraic reduction of one-loop tensor Feynman integrals

Understand

We set up a new, flexible approach for the tensor reduction of one-loop Feynman integrals.

• The 5-point tensor integrals up to rank R=5 are expressed by 4-point tensor integrals of rank R-1, such that the appearance of the inverse 5-point Gram determinant is avoided.
• The 4-point tensor coefficients are represented in terms of 4-point integrals, defined in $d$ dimensions, $4-2\epsilon \le d \le 4-2\epsilon+2(R-1)$, with higher powers of the propagators.
• They can be further reduced to expressions which stay free of the inverse 4-point Gram determinants but contain higher-dimensional 4-point integrals with only the first power of scalar propagators, plus 3-point tensor coefficients.