Abstract
In a series of two papers, we make a comparative analysis of the performance of conventional perturbation theory to analyze electroweak phase transition in the real triplet extension of Standard Model ($\Sigma$SM). In Part I (this paper), we derive and present the high-$T$ dimensionally reduced effective theory that is suitable for numerical simulation on the lattice. In the sequel (Part II), we will present results of the numerical simulation and benchmark the performance of conventional perturbation theory. Under the assumption that $\Sigma$ is heavy, the resulting effective theory takes the same form as that derived from the minimal standard model. By recasting the existing non-perturbative results, we map out the phase diagram of the model in the plane of triplet mass $M_\Sigma$ and Higgs portal coupling $a_2$. Contrary to conventional perturbation theory, we find regions of parameter space where the phase transition may be first order, second order, or crossover. We comment on prospects for prospective future colliders to probe the region where the electroweak phase transition is first order by a precise measurement of the $h\rightarrow\gamma\gamma$ partial width.
Highlights
Explaining the origin of the observed baryon asymmetry of the Universe, characterized by the baryon-to–entropy density ratio [1], YB ≡ ρB=s 1⁄4 ð8.61 Æ 0.09Þ × 10−11; remains an outstanding problem at the interface of highenergy and nuclear physics with cosmology
Without further information, we are unable to assess the strength of the phase transition relevant for baryogenesis. (ii) For a given value of the physical triplet scalar mass, there is a minimum value of the portal coupling that accommodates a first-order transition
The zero Matsubara modes of these scalar fields are classified as light d.o.f. This hierarchy of scales in the high-T limit is illustrated in Fig. 1 and motivates us to pass through a series of threedimensional effective field theories, obtaining a DR3EFT involving just the light d.o.f., which is most readily simulated on the lattice for a nonperturbative study of the electroweak phase transition (EWPT)
Summary
Explaining the origin of the observed baryon asymmetry of the Universe, characterized by the baryon-to–entropy density ratio [1], YB ≡ ρB=s 1⁄4 ð8.61 Æ 0.09Þ × 10−11; remains an outstanding problem at the interface of highenergy and nuclear physics with cosmology. Assuming the triplet Σ is heavy or superheavy (defined in Sec. III below) where it is integrated out, we utilize the results of existing lattice computations for the DR3EFT in which the Higgs boson is the only dynamical scalar to analyze the nature of the single-step transition to the Higgs phase. III below) where it is integrated out, we utilize the results of existing lattice computations for the DR3EFT in which the Higgs boson is the only dynamical scalar to analyze the nature of the single-step transition to the Higgs phase While this case cannot address the viability of the two-step EWSB scenario since the Σ has been integrated out, it does provide one arena in which to compare with the corresponding perturbative calculations. A listing of matching relations among the various DR3EFTs is provided in the Appendixes
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