Sphalerons and the electroweak phase transition in models with higher scalar representations
Amine Ahriche (The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, I-34014, Trieste, Italy, Fakultät für Physik, Universität Bielefeld, 33501, Bielefeld, Germany, Department of Physics, University of Jijel, PB 98, Ouled Aissa, DZ-18000, Jijel, Algeria); Talal Chowdhury (SISSA, Via Bonomea 265, 34136, Trieste, Italy); Salah Nasri (Department of Physics, UAE University, P.O. Box 17551, Al-Ain, United Arab Emirates)
In this work we investigate the sphaleron solution in a SU(2) × 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, θ 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 > η , is relaxed with respect to the doublet case, i.e. η < 1.
