Electroweak vacuum stability and finite quadratic radiative corrections

TL;DR

This paper investigates how finite quadratic radiative corrections influence electroweak vacuum stability within the Standard Model, especially considering the MSSM as a UV completion, revealing potential cancellations at multi-TeV scales and implications for the hierarchy problem.

Contribution

It introduces a method to compute the SM cutoff in the context of multiple scales in the MSSM, linking quadratic corrections to finite threshold effects and providing new constraints on the MSSM's Focus Point scenario.

Findings

Quadratic corrections can cancel at multi-TeV scales, not just Planck scale.

Matching conditions constrain the MSSM's Focus Point solution.

Finite threshold contributions are equivalent to quadratic corrections in the SM.

Abstract

If the Standard Model (SM) is an effective theory, as currently believed, it is valid up to some energy scale $\Lambda$ to which the Higgs vacuum expectation value is sensitive throughout radiative quadratic terms. The latter ones destabilize the electroweak vacuum and generate the SM hierarchy problem. For a given perturbative Ultraviolet (UV) completion, the SM cutoff can be computed in terms of fundamental parameters. If the UV mass spectrum involves several scales the cutoff is not unique and each SM sector has its own UV cutoff $\Lambda_i$. We have performed this calculation assuming the Minimal Supersymmetric Standard Model (MSSM) is the SM UV completion. As a result, from the SM point of view, the quadratic corrections to the Higgs mass are equivalent to finite threshold contributions. For the measured values of the top quark and Higgs masses, and depending on the values of the different cutoffs $\Lambda_i$, these contributions can cancel even at renormalization scales as low as multi-TeV, unlike the case of a single cutoff where the cancellation only occurs at Planckian energies, a result originally obtained by Veltman. From the MSSM point of view, the requirement of stability of the electroweak minimum under radiative corrections is incorporated into the matching conditions and provides an extra constraint on the Focus Point solution to the little hierarchy problem in the MSSM. These matching conditions can be employed for precise calculations of the Higgs sector in scenarios with heavy supersymmetric fields.