Chiral realization and direct nucleon-decay contributions of the SMEFT dimension-7 operator O_{\bar{e}ddDd}

Develop the chiral perturbation theory realization for the low-energy effective field theory operators induced by the Standard Model Effective Field Theory dimension-7 baryon-number-violating derivative operator O^{prst}_{\bar{e}ddDd}, and compute their direct contributions to two-body nucleon decays into a light pseudoscalar meson and a lepton, so that these effects can be incorporated into phenomenological constraints.

Background

Among the dimension-7 baryon-number-violating operators in SMEFT, the derivative operator O_{\bar{e}ddDd} matches at the electroweak scale onto low-energy operators with a derivative acting on quark fields. To calculate nucleon decay rates within chiral perturbation theory, one must realize these quark-level operators in the chiral Lagrangian.

In this work, the authors note that the chiral realization for O_{\bar{e}ddDd}-induced operators is not available in the literature. Consequently, they omit its direct contributions to nucleon decay amplitudes and instead infer constraints on its Wilson coefficients only through renormalization-group mixing with other operators. Completing the missing chiral matching would allow inclusion of these direct effects in the phenomenology.