Electroweak Sphaleron with Dimension-6 Operators
  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.
