Theory Seminar

Fermion traces without evanescence

by Nikolai Zerf

Main/2-313 - 313 (Main)

Main/2-313 - 313


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I am going to talk about a dimensionally continued regularization method that can deal with intrinsically integer dimensional tensors (like $\gamma_5$ in d=4 dimensions) in fermion traces, and does not require symmetry restoring finite counterterms like the 't Hooft-Veltman or Larin prescription. Such a regulator is required for calculations involving multiple $\gamma_5$'s at the multi-loop level. Here it is not feasible anymore to restore intrinsically integer dimensional symmetries by hand. In very basic steps I will recall the basic properties of fermion traces from a group theoretical perspective and explain why a continuous d dimensional algebra cannot pick up certain so called non-naive contributions that are present in integer dimensions only. I will show that evanescent contributions prevent $\gamma_5$ from freely anti-commuting in continuous d-dimensional fermion traces and thus break four dimensional symmetries. The obtained insight will be applied in the evaluation of the VVA anomaly in d=4. If  time permits it, I will comment on recent evaluations of SM \beta-functions at the four loop level. The talk will be based on arXiv:1911.06345 [hep-ph].