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

Understand

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.