Production of muonic kaon atoms at high-energy colliders

Abstract

We develop a framework for the formation of exotic muonic kaon atoms ($K\mu$) in semileptonic $D^{0}$ decays, using the effective weak Hamiltonian, a helicity-based treatment of the leptonic current, and a nonrelativistic bound-state projection. The resulting branching ratio, $\mathrm{BR}(D^{0} \to (K\mu )\nu_{\mu})=2.29\times10^{-10}$, is implemented in a ROOT-based code to estimate yields at RHIC, LHC, and STCF. We show quantitatively that $K\mu$ atoms-also produced through coalescence in the quark-gluon plasma (QGP)-provide a sensitive probe of low-momentum primordial muons and early time electromagnetic radiation, offering complementary constraints in an otherwise unexplored phase space for thermal dilepton and photon emission. Newly estimated dissociation cross sections in detector material indicate that secondary-vertex reconstruction should be experimentally feasible, allowing clean experimental identification of the atoms. Projected yields from QGP coalescence in LHC and RHIC heavy-ion collisions, and from $D^{0}$ decays in LHC high luminosity $p+p$ collisions indicate that the first observation of $K\mu$ atoms is within reach.