The $Z$ decay width in the SMEFT: $y_t$ and $\lambda$ corrections at one loop

TL;DR

This paper computes one-loop corrections to Z decay widths in the SMEFT, revealing the complexity and parameter degeneracy in interpreting precision electroweak data at this order.

Contribution

It provides the first detailed calculation of y_t and lambda dependent one-loop SMEFT corrections to Z decay observables, highlighting parameter unboundedness issues.

Findings

Loop corrections are of order 1% to leading effects.

Number of SMEFT parameters exceeds measurable constraints at one loop.

Large numerical coefficients affect the size of loop effects.

Abstract

We calculate one loop $y_t$ and $\lambda$ dependent corrections to $\bar{\Gamma}_Z,\bar{R}_f^0$ and the partial $Z$ widths due to dimension six operators in the Standard Model Effective Field Theory (SMEFT), including finite terms. We assume $\rm CP$ symmetry and a $\rm U(3)^5$ 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 $\{\hat{\alpha}_{ew}, \hat{M}_Z, \hat{G}_F, \hat{m}_t, \hat{m}_h\}$ 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 $\sim\%$ to leading effects in the SMEFT, but we find multiple large numerical coefficients in our calculation at this order. We use a $\rm \overline{MS}$ scheme, modified for the SMEFT, for renormalization. Some subtleties involving novel evanescent scheme dependence present in this result are explained.