Positivity bounds in the Standard Model effective field theory beyond tree level

TL;DR

This paper investigates the stability of positivity bounds in the Standard Model effective field theory beyond tree level, revealing violations and constraints due to quantum corrections and operator mixing.

Contribution

It provides the first computation of renormalisation mixing of dimension-eight operators and analyzes their impact on positivity bounds in SMEFT.

Findings

Some positivity bounds are violated in simple Standard Model extensions.

Renormalisation mixing can drive operators out of positivity bounds.

Dimension-six induced running respects positivity bounds.

Abstract

Focusing on four-Higgs interactions, we analyse the robustness of tree-level-derived positivity bounds on Standard Model effective field theory (SMEFT) operators under quantum corrections. Among other results, we demonstrate that: (i) Even in the simplest extensions of the Standard Model, e.g. with one new scalar singlet or with a neutral triplet, some positivity bounds are strictly violated; (ii) the mixing of the dimension-eight operators under renormalisation, which we compute here for the first time, can drive them out of their positivity region; (iii) the running of the dimension-eight interactions triggered by solely dimension-six terms respects the positivity bounds. Our results suggest, on one hand, that departures from positivity within the SMEFT, if ever found in the data, do not necessarily imply the breaking of unitarity or causality, nor the presence of new light degrees of freedom. On the other hand, they lead to strong constraints on the form of certain anomalous dimensions.