Sphaleron in the Higgs Triplet Model

The Higgs triplet model (HTM) extends the Standard Model (SM) by one complex triplet scalar (also known as the type-II seesaw model), offering a simple and viable way to account for nonzero neutrino masses. On the other hand, the nontrivial couplings of the triplet to the gauge fields and to the SM Higgs field are expected to influence the topological vacuum structure of the SM, and consequently, the energy and the field configuration of the electroweak sphaleron. The sphaleron process plays a crucial role in dynamically generating the baryon asymmetry of the Universe. In this work, we study the vacuum structure of the gauge and Higgs fields and calculate the saddle-point sphaleron configuration in the HTM. The coupled nonlinear equations of motion of the sphaleron are solved using the spectral method. We find the inclusion of the triplet scalar could in principle significantly change the sphaleron energy compared with the SM. Nevertheless, at zero temperature, the current stringent experimental constraint on the vacuum expectation value of the triplet suppresses the difference. Interestingly, we find that there still exists some narrow parameter space where the sphaleron energy can be enhanced up to $30\%$ compared with the SM case.