Higgs Potential from Instantons

TL;DR

This work proposes that the Higgs potential is partly shaped by instanton dynamics in a hidden confining SU(N) sector, activated via a dimension-6 operator that couples $H^\dagger H$ to the hidden gauge field. The resulting potential combines an exponential instanton term with a quartic, producing an electroweak minimum whose location is given by the Lambert $W_0$ function. Phenomenologically, deviations in the Higgs self-couplings, especially the cubic coupling for $M\lesssim 3$ TeV, offer a potential signal, while the running of the quartic coupling preserves stability within the EFT. Cosmologically, the hidden sector undergoes a first-order confinement transition near $T\sim \mu_0$, potentially generating gravitational waves, with suppressed collider access to hidden states due to small mixing with the Higgs. The paper also explores UV completions and a Twin Higgs-inspired realization, and connects the framework to ideas about field-space endpoints.

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.

Figures (5)

• Figure 1: Value of the Higgs self coupling parameter $\lambda$ which yields the experimentally determined Higgs vev and mass, as a function of the mass $M$ where the new physics is expected to set in.
• Figure 2: The cubic and quartic couplings of the Higgs boson in the scenario presented in this work are represented by the solid magenta and dark blue curves, respectively. The dashed green and light blue lines represent, respectively, the corresponding SM self coupling predictions of the Higgs boson. As the mass scales gets higher, the parameters in our model approach their SM values.
• Figure 3: The Higgs potential parameter $\mu_0$ vs. $M$.
• Figure 4: Running of $\lambda$ for three values of $M$. The dark blue, green and light blue curves correspond to $M=2,4,6$ TeV, respectively. The vertical, dashed lines represent the mass scale with the same color coding. Above this respective scale the explicit UV completion needs be taken into account because the EFT assumption is no longer valid.
• Figure 5: Feynman diagram generating the effective operator \ref{['dim-6']} after integrating out the heavy dark scalar $S$ and fermion $\psi$ running in the loop.