Sphalerons and the Electroweak Phase Transition in Models with Higher Scalar Representations

Abstract

In this work we investigate the sphaleron solution in a $SU(2)\times U(1{)}_X$ gauge theory, which also encompasses the Standard Model, with higher scalar representation(s) ($J^{(i)},X^{(i)}$). We show that the field profiles describing the sphaleron in higher scalar multiplet, have similar trends like the doublet case with respect to the radial distance. We compute the sphaleron energy and find that it scales linearly with the vacuum expectation value of the scalar field and its slope depends on the representation. We also investigate the effect of $U(1)$ gauge field and find that it is small for the physical value of the mixing angle, ${\theta }_W$ and resembles the case for the doublet. For higher representations, we show that the criterion for strong first order phase transition, $v_c/T_c>\eta$, is relaxed with respect to the doublet case, i.e. $\eta <1$.

arXiv comment20 pages, 5 figures & 1 table, published version

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• Electroweak Baryogenesis with Vector-like Leptons and Scalar Singlets
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• Dual electroweak phase transition in the two-Higgs-doublet model with the $S_3$ discrete symmetry
• Scattering Entanglement Entropy and Its Implications for Electroweak Phase Transitions
• Exploring CP-violation in $Y=0$ inert triplet with real singlet
• Sphaleron in the Higgs Triplet Model
• Phase transitions, anomalous baryon number violation and electroweak multiplet dark matter
• Electroweak phase transition with radiative symmetry breaking in Type-II seesaw with inert doublet