QMeS-Derivation: Mathematica package for the symbolic derivation of functional equations

Four-quark scatterings in QCD I

“…Moreover, these regulators with shape functions such as (G.2) are then taken for computational convenience: The shape function decays rapidly for large spatial momenta and hence facilitates the computation of the loop integrals, as is the fact that it is infinitely differentiable. The lack of the latter property is a numerical obstruction for the use of non-analytic regulators such as the flat regulator (45). In any case, while the present results are obtained within the specific choice (44).…”

“…with the flat shape function (45). As discussed in Section 4.2.1, for more advanced approximations smooth regulators are more convenient both computationally as well as in the context of optimised fRG flows.…”

“…We use the functional renormalisation group approach to QCD, in which the evolution of the full effective action of QCD is described by its functional flow equation for the effective action Γ k [Φ] where k is an infrared cutoff scale that regularises the infrared propagation of all fields, for recent reviews see [43,44]. Including dynamical hadronisation, the flow equation reads [5,45],…”