Abstract
We calculate one loop y t 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 \( \left\{{\widehat{\alpha}}_{\mathrm{ew}},{\widehat{M}}_Z,{\widehat{G}}_F,{\widehat{m}}_t,{\widehat{m}}_h\right\} \) 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.
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Hartmann, C., Shepherd, W. & Trott, M. The Z decay width in the SMEFT: y t and λ corrections at one loop. J. High Energ. Phys. 2017, 60 (2017). https://doi.org/10.1007/JHEP03(2017)060
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DOI: https://doi.org/10.1007/JHEP03(2017)060