Current and future constraints on heavy New Physics from $\tau$ weak dipole moments

Abstract

We study the weak magnetic and electric dipole moments of the $\tau$ lepton as precision tests of the Standard Model (SM) and probes of heavy New Physics (NP). We present an updated SM prediction for the $\tau$ weak magnetic dipole moment at one loop, including a careful assessment of theoretical uncertainties from electroweak scheme dependence. Working within the SM Effective Field Theory, we derive comprehensive current constraints on the $\tau$ dipole operators from a combination of observables: the $\tau$ weak and electromagnetic dipole moments, high-mass Drell-Yan tails at the LHC, $Z$ partial decay widths, and the electron electric dipole moment. Finally, we assess the prospects of measuring the SM value of the $\tau$ weak magnetic moment at the FCC-$ee$ Tera-$Z$ run, and project the sensitivities of the leading observables to heavy NP at FCC-$ee$ and HL-LHC, incorporating informed assumptions about improvements of systematic uncertainties. We find that the $\tau$ weak dipole moments are already among the leading probes of the $\tau$ dipole operators, and will become increasingly dominant at future colliders.

30 pages, 4 figures, 4 tables. V2: Updated to match published version