Electroweak vacuum stability and finite quadratic radiative corrections

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.

36 pages, 5 figures; v2: logarithm corrections included, figures improved, references added

References in corpus (5)

• Higgs Mass and Unnatural Supersymmetry
• The lifetime of the electroweak vacuum and sensitivity to Planck scale physics
• The Effective Theory of the Light Stop Scenario
• Maximally Natural Supersymmetry
• Focus Point in the Light Stop Scenario

Cited by in corpus (9)

• Detectable Gravitational Waves from Very Strong Phase Transitions in the General NMSSM
• Black Hole Shadow in Symmergent Gravity
• Neutrino seesaw models at one-loop matching: Discrimination by effective operators
• Emergent Gravity as the Eraser of Anomalous Gauge Boson Masses, and QFT-GR Concord
• Natural Supersymmetry from Extra Dimensions
• Electroweak phase transition triggered by fermion sector
• The hierarchy problem and fine-tuning in a decoupling approach to multi-scale effective potentials
• Dynamical Emergence of the Universe into the False Vacuum
• Gauge mediation with light stops