M. Goodsell: The Higgs mass and infra-red catastrophes

In theories defined by high-energy boundary conditions (such as supersymmetry), the Higgs mass is a prediction. On the other hand, in the Standard Model, it is an input, that we need to use to calculate the Higgs quartic coupling, to predict the cubic coupling and also to test for vacuum stability. However, since the Higgs is a scalar, its mass is very sensitive to those of other particles such as the top quark -- or any new physics (hence we have a hierarchy problem) but this also means that we need to calculate as many loop corrections as we can in order to obtain accurate results. Once we reach two loops, however, we find a technical "Catastrophe" associated with the would-be Goldstone Bosons of the W and Z bosons: in Landau gauge their masses vanish, and this leads to infra-red divergences in the amplitudes. I will show how this problem can be avoided for general renormalisable field theories, with applications in the Standard Model and several popular extensions (such as the NMSSM), and describe how the results have been implemented in the public code SARAH. 

On the other hand, when we consider that the scale of new physics might be high, we need a method of making predictions for the Higgs mass (or predictions for the properties of the high-energy theory's stability) using the Standard Model as an effective field theory. These calculations are beset by a similar but worse infra-red problem, in that the infra-red divergences appear already at one-loop order. I will briefly describe some work in progress to show the relation between the two problems and how to solve the latter, so far at one-loop order.