Positivity bounds on Minimal Flavor Violation

TL;DR

This paper investigates how positivity bounds on higher-dimensional operators in the Standard Model Effective Field Theory constrain the Yukawa couplings and CKM matrix within models that implement Minimal Flavor Violation, finding limited constraints at leading order.

Contribution

It analyzes the impact of positivity bounds on flavor structures in MFV models, revealing that these bounds mainly constrain Yukawa couplings when coefficients are natural, but not the CKM matrix at leading order.

Findings

Positivity bounds do not constrain CKM entries at leading order.

Yukawa couplings could be bounded if coefficients are natural.

Flavor-blind factors leave the Yukawa sector largely unconstrained.

Abstract

From general analyticity and unitarity requirements on the UV theory, positivity bounds on the Wilson coefficients of the dimension-8 operators composed of 4 fermions and two derivatives appearing in the Standard Model Effective Field Theory have been derived recently. We explore the fate of these bounds in the context of models endowed with a Minimal Flavor Violation (MFV) structure, models in which the flavor structure of higher dimensional operators is inherited from the one already contained in the Yukawa sector of the Standard Model Lagrangian. Our goal is to check whether the general positivity bounds translate onto bounds on the Yukawa coefficients and/or on elements of the CKM matrix. MFV fixes the coefficients of dimension-8 operators up to some multiplicative flavor-blind factors and we find that, in the most generic setup, the freedom left by those unspecified coefficients is enough as not to constrain the parameters of the renormalizable Yukawa sector. On the contrary, the latter shape the allowed region for the former. Requiring said overall coefficients to take natural $\mathcal{O}(1)$ values could give rise to bounds on the Yukawa couplings. Remarkably, at leading order in an expansion in powers of the Yukawa matrices, no bounds on the CKM entries can be retrieved.