Extending low energy effective field theory with a complete set of dimension-7 operators

TL;DR

This paper systematically classifies all dimension-7 operators in low energy effective field theory involving standard model particles, performs matching with SMEFT, and explores phenomenological implications like neutrino-photon interactions.

Contribution

It provides a complete set of dimension-7 operators in LEFT, including their classification, matching with SMEFT, and phenomenological applications, which was not previously available.

Findings

Classified 3168, 750, 588, 712 operators by baryon and lepton number violation.

Performed tree-level matching between LEFT and SMEFT up to dimension-7.

Analyzed neutrino-photon interactions induced by dimension-7 operators and compared with Standard Model predictions.

Abstract

We present a complete and independent set of dimension-7 operators in the low energy effective field theory (LEFT) where the dynamical degrees of freedom are the standard model five quarks and all of the neutral and charged leptons. All operators are non-Hermitian and are classified according to their baryon ($\Delta B$) and lepton ($\Delta L$) numbers violated. Including Hermitian-conjugated operators, there are in total $3168$, $750$, $588$, $712$ operators with $(\Delta B,\Delta L)=(0,0)$, $(0,\pm 2)$, $(\pm 1,\mp 1)$, $(\pm 1,\pm 1)$ respectively. We perform the tree-level matching with the standard model effective field theory (SMEFT) up to dimension-7 (dim-7) operators in both LEFT and SMEFT. As a phenomenological application we study the effective neutrino-photon interactions due to dim-7 lepton number violating operators that are induced and much enhanced at one loop from dim-6 operators that in turn are matched from dim-7 SMEFT operators. We compare the cross sections of various neutrino-photon scattering with their counterparts in the standard model and highlight the new features. Finally we illustrate how these effective interactions could arise from ultraviolet completion.