The Z decay width in the SMEFT: yt and \u03bb corrections at one loop

Abstract

We calculate one loop yt and λ dependent corrections to {overline{Gamma}}_{mathrm{Z}},{overline{R}}_f^0 and the partial Z widths due to dimension six operators in the Standard Model Effective Field Theory (SMEFT), including finite terms. We assume CP symmetry and a U(3)5 symmetry in the UV matching onto the dimension six operators, dominantly broken by the Standard Model Yukawa matrices. Corrections to these observables are predicted using the input parameters left{{widehat{alpha}}_{mathrm{ew}},{widehat{M}}_Z,{widehat{G}}_F,{widehat{m}}_t,{widehat{m}}_hright} extracted with one loop corrections in the same limit. We show that at one loop the number of SMEFT parameters contributing to the precise LEPI pseudo-observables exceeds the number of measurements. As a result the SMEFT parameters contributing to LEP data are formally unbounded when the size of loop corrections are reached until other data is considered in a global analysis. The size of these loop effects is generically a correction of order ∼ % to leading effects in the SMEFT, but we find multiple large numerical coefficients in our calculation at this order. We use a overline{mathrm{MS}} scheme, modified for the SMEFT, for renormalization. Some subtleties involving novel evanescent scheme dependence present in this result are explained.