The singular behaviour of QCD amplitudes at two-loop order

Abstract

We discuss the structure of infrared singularities in on-shell QCD amplitudes at two-loop order. We present a general factorization formula that controls all the ǫ-poles of the dimensionally regularized amplitudes. The dependence on the regularization scheme is considered and the coefficients of the 1/ǫ 4 , 1/ǫ 3 and 1/ǫ 2 poles are explicitly given in the most general case. The remaining singlepole contributions are also explicitly evaluated in the case of amplitudes with a qq pair. † The RS that are mostly used in one-loop computations are the 't Hooft and Veltman scheme [22], the dimensional-reduction scheme [25] and the four-dimensional helicity scheme [26].

Two-loop QCD corrections to the heavy quark form factors: the vector contributions

“…The corresponding structure of massless two-loop QCD amplitudes has been predicted from non-abelian exponentiation in [35,36], and proven very valuable in the calculation of massless two-loop four-point amplitudes [37]. For QCD amplitudes involving massive quarks, the singularity structure is only understood at the one-loop level at present [38].…”

One-loop calculations in quantum field theory: From Feynman diagrams to unitarity cuts

“…In this Section we discuss the singular behavior of one-loop amplitudes [96,97]. Although this topic is interesting in its own right, the reason we present it here is a particular representation of color algebra employed in Ref.…”

“…Although this topic is interesting in its own right, the reason we present it here is a particular representation of color algebra employed in Ref. [97] to present singular limits of one-loop amplitudes in a simple way. This representation of the color algebra has the advantage that it treats the color degrees of freedom of quarks and gluons on the same footing.…”

“…[97]. The generalization to the case when massive particles are present is given at oneloop order in Ref.…”

The quark Regge trajectory at two loops

“…In Ref. [23] the divergent contribution is written in terms of the infrared singularity operators I (1) , I (2) and H (2) introduced by Catani [28] and the tree-and one-loop amplitudes. The finite remainder is given in terms of logarithms and polylogarithms with arguments −u/s, −t/s and u/t.…”