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Strongly electroweak phase transition with $U(1)_{L_μ-L_τ}$ gauged non-zero hypercharge triplet

Shilpa Jangid, Anirban Biswas, Seong Chan Park

TL;DR

This work extends the Standard Model by adding three hypercharge-carrying scalar triplets charged under $U(1)_{L_\mu-L_\tau}$ and studies their impact on vacuum stability, perturbativity, and the electroweak phase transition. The two-loop renormalization-group analysis shows vacuum stability up to the Planck scale, while perturbativity breaks near $10^{12}$ GeV, rendering the model an effective theory above that scale. The triplets contribute to the finite-temperature potential in a way that induces a strongly first-order electroweak phase transition, with several benchmark points predicting gravitational waves in the LISA and BBO bands. These benchmarks also imply testable collider signatures and deviations in the Higgs trilinear coupling, linking early-Universe dynamics to near-future experimental probes. Overall, the model provides a coherent framework for stable electroweak vacuum, strong EWPT, and GW phenomenology within a well-defined effective-field-theory regime.

Abstract

This article considers three non-zero hypercharge triplets as an extension of the Standard Model Higgs doublet. Under extra $U(1)_{L_μ-L_τ}$ symmetry, the triplets are charged. We examine the stability of the electroweak vacuum at the two-loop and tree-levels. The two-loop $β$-functions are found to be capable of satisfying the vacuum stability up to the Planck scale. On the other hand, only up to $10^{12}$ GeV can the perturbative unitarity be satisfied because of the increase in the positive influence from triplet degrees of freedom. For the strongly electroweak first-order phase transition, the parameter space permitted by the Planck scale stability is examined. Because the triplet degrees of freedom contribute sufficiently to the cubic term, the model satisfies the strongly first order phase transition for the triplet bare mass parameters up to the TeV scale. For all mass ranges, it is found that this model predicts a strongly first-order phase transition until the degrees of freedom are heavy enough to separate from the thermal bath. The gravitational wave signatures are tested at the benchmark places that fulfill the strongly first-order phase transition. The measurable frequency range of the LISA and BBO experiments also turns out to contain the benchmark points permitted by Planck scale stability, strongly first-order phase transition.

Strongly electroweak phase transition with $U(1)_{L_μ-L_τ}$ gauged non-zero hypercharge triplet

TL;DR

This work extends the Standard Model by adding three hypercharge-carrying scalar triplets charged under and studies their impact on vacuum stability, perturbativity, and the electroweak phase transition. The two-loop renormalization-group analysis shows vacuum stability up to the Planck scale, while perturbativity breaks near GeV, rendering the model an effective theory above that scale. The triplets contribute to the finite-temperature potential in a way that induces a strongly first-order electroweak phase transition, with several benchmark points predicting gravitational waves in the LISA and BBO bands. These benchmarks also imply testable collider signatures and deviations in the Higgs trilinear coupling, linking early-Universe dynamics to near-future experimental probes. Overall, the model provides a coherent framework for stable electroweak vacuum, strong EWPT, and GW phenomenology within a well-defined effective-field-theory regime.

Abstract

This article considers three non-zero hypercharge triplets as an extension of the Standard Model Higgs doublet. Under extra symmetry, the triplets are charged. We examine the stability of the electroweak vacuum at the two-loop and tree-levels. The two-loop -functions are found to be capable of satisfying the vacuum stability up to the Planck scale. On the other hand, only up to GeV can the perturbative unitarity be satisfied because of the increase in the positive influence from triplet degrees of freedom. For the strongly electroweak first-order phase transition, the parameter space permitted by the Planck scale stability is examined. Because the triplet degrees of freedom contribute sufficiently to the cubic term, the model satisfies the strongly first order phase transition for the triplet bare mass parameters up to the TeV scale. For all mass ranges, it is found that this model predicts a strongly first-order phase transition until the degrees of freedom are heavy enough to separate from the thermal bath. The gravitational wave signatures are tested at the benchmark places that fulfill the strongly first-order phase transition. The measurable frequency range of the LISA and BBO experiments also turns out to contain the benchmark points permitted by Planck scale stability, strongly first-order phase transition.

Paper Structure

This paper contains 13 sections, 35 equations, 3 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Model setup
  3. Stability Conditions
  4. Two-loop stability
  5. Electroweak phase transition
  6. Experimental constraints
  7. Direct and indirect searches:
  8. Higgs trilinear coupling:
  9. Scope of the present work:
  10. Conclusion
  11. Acknowledgement
  12. Two-loop $\beta$-functions for dimensionless couplings
  13. Scalar Quartic Couplings

Figures (3)

  • Figure 1: Parameter space satisfying the tree-level stability conditions given in \ref{['stability']} in \ref{['fig:treestab']}(a)-(c)-(e) and same stability conditions using running couplings with two-loop $\beta$-functions in \ref{['fig:treestab']}(b)-(d)-(f) .
  • Figure 2: Minima of the potential as a function of temperature in GeV, where $h_1$ is the background field for the SM Higgs doublet and $h_2, h_3$ and $h_4$ are the background fields for the Higgs triplets.
  • Figure 3: GW signatures for the benchmark points permitted by strongly first-order phase transition and vacuum stability at the Planck scale. For BP2-BP5, the gravitational wave intensity peaks at about $10^{-3}$ Hz, whereas for BP1, it peaks at about $0.01$ Hz. For every benchmark point, the GWs intensity is within the observable frequency range of the BBO and LISA studies. For every BP, the GWs intensity is less intense for the corresponding LIGO detectable range.