Precision Measurements of the Electroweak Mixing Angle in the Region of the Z pole

Abstract

We review the current status and techniques used in precision measurements of the effective leptonic weak mixing angle ${\sin }^2{\theta }_{\mathrm{eff}}^{\ell }$ (a fundamental parameter of the Standard Model (SM)) in the region of the Z pole with emphasis on hadron colliders. We also build on these techniques to extract the most precise single measurement to date of ${\sin }^2{\theta }_{\mathrm{eff}}^{\ell }$ from a new analysis of the published forward-backward asymmetry ($A_{\mathrm{FB}}$) in Drell-Yan dielpton production in proton-proton collisions at a center of mass energy of 13 TeV measured by the CMS collaboration at the large hadron collider. The uncertainty in ${\sin }^2{\theta }_{\mathrm{eff}}^{\ell }$ published by CMS is dominated by uncertainties in Parton Distribution Functions (PDFs), which are reduced by PDF profiling using the dilepton mass dependence of $A_{\mathrm{FB}}$. Our new extraction of ${\sin }^2{\theta }_{\mathrm{eff}}^{\ell }$ from the CMS values of $A_{\mathrm{FB}}$ includes profiling with additional new CMS measurements of the $W$-boson decay lepton asymmetry, and W/Z cross section ratio at 13 TeV. We obtain the most precise single measurement of ${\sin }^2{\theta }_{\mathrm{eff}}^{\ell }$ to date of 0.23156$\pm$0.00024, which is in excellent agreement with the SM prediction of 0.23161$\pm$0.00004. We also discuss outlook for future measurements at the LHC including more precise measurements of ${\sin }^2{\theta }_{\mathrm{eff}}^{\ell }$, a measurement of ${\sin }^2{\theta }_{\mathrm{eff}}^{\ell }$ for b-quarks in the initial state, and a measurement of the running of ${\sin }^2{\theta }^{\overline{\mathrm{MS}}}(\mu )$ up to 3 TeV.

Comments: 14 pages, 12 figures, 4 tables, to be submitted to Physics Reports collection of papers on Electroweak Precision Measure- ments, edited by Costas Vellidis, Franco Bedeschi, Michael Ramsey-Musolf, Doreen Wackeroth, and Ashutosh Kotwal