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Production of muonic kaon atoms at high-energy colliders

Xiaofeng Wang, Zebo Tang, Zhangbu Xu, Chi Yang, Wangmei Zha, Yifei Zhang

Abstract

We develop a framework for the formation of exotic muonic kaon atoms ($μK$) 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, $\mathrm{BR}(D^{0}\!\to(μK)ν_μ)=2.29\times10^{-10}$, is implemented in a ROOT-based code to estimate yields at RHIC, LHC, and STCF. We show quantitatively that $μK$ 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 $μK$ atoms is within reach.

Production of muonic kaon atoms at high-energy colliders

Abstract

We develop a framework for the formation of exotic muonic kaon atoms () in semileptonic decays, using the effective weak Hamiltonian, a helicity-based treatment of the leptonic current, and a nonrelativistic bound-state projection. The resulting branching ratio, , is implemented in a ROOT-based code to estimate yields at RHIC, LHC, and STCF. We show quantitatively that 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 decays in LHC high-luminosity collisions indicate that the first observation of atoms is within reach.
Paper Structure (14 sections, 36 equations, 2 figures, 2 tables)

This paper contains 14 sections, 36 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Theoretical Framework and Methodology
  3. Free semileptonic decay amplitude for $D^0\to K^-\mu^+\nu_\mu$
  4. Bound-state projection for $D^0\to (K\mu)_{\rm atom}\nu_\mu$
  5. Yield estimates at STCF, RHIC, and the LHC
  6. Dissociation in detector material and observable signatures
  7. Results and Discussion
  8. Branching ratios for atomic channels
  9. Production yields at RHIC, the LHC, and STCF
  10. Comparison with coalescence production in heavy-ion collisions
  11. $K\mu$ atoms as a probe of primordial low-$p_T$ muons
  12. Experimental feasibility
  13. Summary
  14. Acknowledgments

Figures (2)

  • Figure 1: Exponential-function fits to the STAR direct virtual-photon $p_T$ spectrum STAR:2016use are used to extrapolate into the low-$p_T$ region where no direct experimental measurements exist.
  • Figure 2: Schematic dependence of the $\pi$--$\mu$ yield ratio $1/f_{\mu/\pi}$ as a function of the coalescence radius $r_0$. The cyan band shows the value of $1/f_{\mu/\pi}$ and its $1\sigma$ interval derived from the direct virtual-photon spectrum in Fig. \ref{['fig:mu_extrap']}, where extrapolation into the low-$p_T$ region introduces significant uncertainty. The blue band represents the constraint on $r_0$ from the $K$--$\pi$ correlation analysis STAR:2003cqe. The purple band indicates a projected yield and $1\sigma$ interval obtained by combining an assumed $(K\mu)_{\rm atom}$ yield with Eq. \ref{['eq:coal']} and an assumed $\pm10\%$ uncertainty. The overlap of the three bands provides a strong combined constraint on the primordial muon yield.