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

Abstract

We present a complete and independent set of dimension-7 operators in the low\nenergy effective field theory (LEFT) where the dynamical degrees of freedom are\nthe standard model five quarks and all of the neutral and charged leptons. All\noperators are non-Hermitian and are classified according to their baryon\n($\\Delta B$) and lepton ($\\Delta L$) numbers violated. Including\nHermitian-conjugated operators, there are in total $3168$, $750$, $588$, $712$\noperators with $(\\Delta B,\\Delta L)=(0,0)$, $(0,\\pm 2)$, $(\\pm 1,\\mp 1)$, $(\\pm\n1,\\pm 1)$ respectively. We perform the tree-level matching with the standard\nmodel effective field theory (SMEFT) up to dimension-7 (dim-7) operators in\nboth LEFT and SMEFT. As a phenomenological application we study the effective\nneutrino-photon interactions due to dim-7 lepton number violating operators\nthat are induced and much enhanced at one loop from dim-6 operators that in\nturn are matched from dim-7 SMEFT operators. We compare the cross sections of\nvarious neutrino-photon scattering with their counterparts in the standard\nmodel and highlight the new features. Finally we illustrate how these effective\ninteractions could arise from ultraviolet completion.\n