Electroweak Sphaleron with Dimension-6 Operators

TL;DR

This paper investigates how dimension-6 operators, representing new physics at the TeV scale, influence sphaleron energy and baryon-number violation rates, affecting electroweak baryogenesis scenarios.

Contribution

It provides a numerical analysis of the impact of dimension-6 operators on sphaleron energy using the Newton-Kantorovich method, highlighting their potential to alter baryon-number washout conditions.

Findings

Dimension-6 operators can change sphaleron energy by a few percent.

The sign of the operator coefficient determines increase or decrease in sphaleron energy.

Effects are proportional to $m_W^2 / \Lambda^2$, where $\Lambda$ is the new physics scale.

Abstract

New physics at the TeV scale can affect the dynamics of the electroweak phase transition in many ways. In this note, we evaluate its impact on the rate of baryon-number violation via sphaleron transitions. We parameterize the effect of new physics with dimension-6 operators, and we use the Newton-Kantorovich method to numerically solve the resulting equations of motion. Depending on the sign of the coefficient of the dimension-6 operators, their presence can either increase or decrease the sphaleron energy at the level of a few percent, parametrically of order $m_W^2 / \Lambda^2$ where $\Lambda$ is the scale suppressing the dimension-6 operator. The baryon-number washout condition, typically written as $v_c / T_c > 1$, is directly proportional to the sphaleron energy, and we discuss how the presence of dimension-6 operators can affect electroweak baryogenesis.