Top quark decay at next-to-leading order in the Standard Model Effective Field Theory

We consider top quark decay in the standard model effective field theory (SMEFT). We present a calculation of the total decay width and the $W$-boson helicity fractions at next-to-leading order (NLO) in SMEFT. Our result includes the complete set of contributing four-fermion operators in addition to QCD dipole operators and bottom-mass suppressed effects. We show that operators that first appear at NLO in the SMEFT can be bounded by the current data as well as future data from both a high-luminosity LHC and a potential ${e}^{+}{e}^{\ensuremath{-}}$ collider, demonstrating the importance of going beyond leading order when studying the SMEFT. We discuss technical aspects of our calculation that we believe will be useful in future higher-order studies of the SMEFT, in particular, the treatment of ${\ensuremath{\gamma}}_{5}$ in loop diagrams.