Effects of squared four-fermion operators of the Standard Model Effective Field Theory on meson mixing

TL;DR

This paper investigates how squared four-fermion operators in SMEFT influence meson mixing, emphasizing the importance of including dimension-8 operators for accurate phenomenological analyses beyond leading-order effects.

Contribution

It provides a detailed analysis of the renormalization of dimension-6 operators and highlights the significance of dimension-8 operators in meson mixing phenomenology.

Findings

Bounds on Wilson coefficients of dimension-6 operators derived

Large Yukawa contributions significantly impact meson mixing

Dimension-8 operators are essential for comprehensive SMEFT analyses

Abstract

The Standard Model Effective Field Theory (SMEFT) is a universal way of parametrizing New Physics (NP) manifesting as new, heavy particle interactions with the Standard Model (SM) degrees of freedom, that respect the SM gauged symmetries. Higher order terms in the NP interactions possibly lead to sizable effects, mandatory for meaningful phenomenological studies, such as contributions to neutral meson mixing, which typically pushes the scale of NP to energy scales much beyond the reach of direct searches in colliders. I discuss the leading-order renormalization of double-insertions of dimension-6 four-fermion operators that change quark flavor by one unit (i.e., $ | \Delta F | = 1 $, $ F = $ strange-, charm-, or bottom-flavor), by dimension-8 operators relevant to meson mixing (i.e., $ | \Delta F | = 2 $) in SMEFT. Then, I consider the phenomenological implications of contributions proportional to large Yukawas, setting bounds on the Wilson coefficients of operators of dimension-6 via the leading logarithmic contributions. Given the underlying interest of SMEFT to encode full-fledged models at low energies, this work stresses the need to consider dimension-8 operators in phenomenological applications of dimension-6 operators of SMEFT.