$\mu^-\mu^+\to {\nu_\mu}\bar{\nu}_\mu t\bar{t}H$ amplitudes in the Feynman-diagram gauge

TL;DR

This paper analyzes the $^-^+ o u_ar{ u}_ tar{t}H$ process within SMEFT, highlighting how the Feynman-diagram gauge makes the dominance of weak boson fusion diagrams and high-energy behavior more transparent, especially with CP-violating couplings.

Contribution

It demonstrates the advantages of using the Feynman-diagram gauge over the unitary gauge for analyzing high-energy processes with dimension-6 SMEFT operators and CP violation.

Findings

Feynman-diagram gauge clearly shows weak boson fusion dominance.

High-energy behavior is governed by dimension-6 operators.

Differences between gauges affect the visibility of certain process features.

Abstract

We study the process $\mu^-\mu^+\to {\nu_\mu}\bar{\nu}_\mu t\bar{t}H$ with complex CP violating $ttH$ couplings in the SMEFT with a dimension-6 operator. When the amplitudes are expressed in the Feynman-Diagram gauge, the dominance of the total cross section via the weak boson fusion diagrams is manifest. The high energy behaviour is dictated by the higher-dimensional vertices in the dimension-6 SMEFT operator. These properties are not manifest in the unitary gauge because of subtle cancellation among diagrams.