CP Violation in Rare Lepton-Number-Violating $W$ Decays at the LHC

Abstract

Some models of leptogenesis involve a quasi-degenerate pair of heavy neutrinos $N_{1,2}$ whose masses can be small, $O(\mathrm{GeV})$. Such neutrinos can contribute to the rare lepton-number-violating (LNV) decay $W^{\pm }\to {\ell }_1^{\pm }{\ell }_2^{\pm }(q^{\prime }\bar{q}{)}^{\mp }$. If both $N_1$ and $N_2$ contribute, there can be a CP-violating rate difference between the LNV decay of a $W^{-}$ and its CP-conjugate decay. In this paper, we examine the prospects for measuring such a CP asymmetry $A_{\mathrm{CP}}$ at the LHC. We assume a value for the heavy-light neutrino mixing parameter $|B_{\ell N}{|}^2=10^{-5}$, which is allowed by the present experimental constraints, and consider $5\mathrm{GeV}\le M_N\le 80\mathrm{GeV}$. We consider three versions of the LHC -- HL-LHC, HE-LHC, FCC-hh -- and show that small values of the CP asymmetry can be measured at $3\sigma$, in the range $1\%\lesssim A_{\mathrm{CP}}\lesssim 15\%$.

Comments: 19 pages, 2 figures, (i) we have made the motivation more generic, so that it refers to any leptogenesis model that contains a quasi-Dirac pair of almost-degenerate neutrinos, not just the nuMSM,(ii) we focus only on the l^- l^- (q' qbar)^+ final state, since it is purely LNV (the trilepton final state has both LNV and LNC contributions). We have also added references and corrected typos."