Higgs Potential from Instantons

Abstract

We propose that the Higgs potential, a key element in our understanding of Nature, is partially generated by the instantons of new confining dynamics, perhaps from a hidden sector. In this picture, while the Higgs itself is a fundamental field, it controls the strength of the non-perturbative interactions that give rise to its potential. We examine a simple setup in which this instanton contribution is augmented by a quartic term, which is sufficient for a realistic electroweak symmetry breaking mechanism. The minimum of the potential is given by the Lambert $W_0$ function, with these assumptions. We discuss the predictions of this model and how it may be tested through measurements of the Higgs self coupling. Given the connection with non-trivial dynamics, one may also consider the prospects of accessing hidden sector states at colliders; this seems to be typically challenging in our setup. Symmetry restoration in the early Universe in this scenario is briefly examined. We also comment on the possible connection of our general setup with recent work on the physics of field space end points.