$τ$-lepton pair spin in proton-proton LHC collisions for anomalous dipole moments

Abstract

The spin correlations in the pair of $τ$ leptons produced in the high-energy proton-proton collisions are studied. The invariant mass of the $τ$-lepton pair is chosen close to $Z$-boson mass, in these conditions $Z$-boson exchange gives the dominant contribution to the Drell-Yan mechanism. The interaction of $Z$ boson with $τ$ lepton, in addition to the Standard Model couplings, can include weak anomalous magnetic and electric dipole moments (or form-factors) of the $τ$ lepton. Dependence of elements of the $pp$ spin-correlation matrix on the weak anomalous moments is determined for various regions of the rapidity of the $τ$-lepton pair. Based on this calculation, we construct a semi-realistic observable built on the momenta of pions in the $τ^\mp \to π^\mp ν_τ$ and $τ^\pm \to ρ^\pm ν_τ\to π^\pm π^0 ν_τ$ decay channels, and show that this observable can be sensitive to the weak anomalous dipole moments.