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

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.