Speaker
Description
We discuss the existence of Landau-pole-free renormalization group trajectories in the Minkowskian version of the Curci-Ferrari model as a function of a running parameter q^2 associated to the four-vector q at which renormalization conditions are imposed, and which can take both spacelike (q^2 < 0) and timelike (q^2 > 0) values. We discuss two possible extensions of the infrared-safe scheme defined in a previous work for the Euclidean version of the model, which coincide with the latterin the space-like region upon identifying Q^2 ≡ −q^2 with the square of the renormalization scale in that reference. The first extension uses real-valued renormalization factors and leads to a flow in the timelike region with a similar structure as the flow in the spacelike region (or in the Euclidean model), including a non-trivial fixed point as well as a family of trajectories bounded at all scales by the value of the coupling at this fixed point. Interestingly, the fixed point in the timelike region has a much smaller value of λ ≡ g^2 N/16π^2 than the corresponding one in the spacelike region, a value close to the perturbative region λ ≤ 1. In this real-valued infrared-safe scheme, however, the flow cannot connect the timelike and spacelike regions. It is thus not possible to deduce what is the relevant timelike flow trajectory from the sole knowledge of a spacelike flow trajectory. To try to cure this problem, we investigate a second extension of the Euclidean IR-safe scheme which allows for complex-valued renormalization factors. We discuss under which conditions these schemes can make sense and study their ability to connect spacelike and timelike flow trajectories. In particular, we investigate to which types of timelike trajectories the perturbative spacelike trajectories are mapped into.
