The role of charm and unflavored mesons in prompt atmospheric lepton fluxes

TL;DR

The study probes the origin of prompt atmospheric leptons in the high-energy regime, focusing on intrinsic charm and light unflavored meson decays as sources of prompt muons and muon neutrinos. It implements intrinsic charm models in MCEq alongside standard hadronic inputs (Sibyll-2.3c, H3a) and confronts IceCube measurements of the high-energy muon flux and limits on prompt $\nu_\mu+\bar{\nu}_\mu$, revealing tensions that cannot be resolved by charm alone. By introducing a scaling factor for unflavored meson prompt production and fitting IC normalization, the authors show that modest IC contributions ($w_{c}^{\rm intr}\sim 10^{-4}-10^{-3}$) combined with enhanced unflavored production can better reconcile muon data with neutrino limits, though the required balance is model-dependent. The work underscores the need for improved hadronic interaction models and dedicated data on unflavored and heavy-flavor production, and suggests that energy- and zenith-angle-dependent flux ratios in future neutrino telescopes could help distinguish between IC-driven and unflavored-meson–driven scenarios.

Abstract

The all-sky very-high-energy ($10^4-10^6$ GeV) atmospheric muon flux measured by IceCube shows a spectral hardening at the highest energies, indicating the presence of a prompt component. IceCube has also measured the atmospheric muon neutrino flux at high energy. However, since this flux is dominated by astrophysical neutrinos, only an upper bound can be placed on the prompt atmospheric $ν_μ+\barν_μ$ contribution. In this work, we provide a new evaluation of the prompt atmospheric muon flux including an intrinsic charm component in the cosmic ray-air interactions. The latter enhances the forward production of $\bar{D}^0$, $D^-$, and $Λ_c$, which subsequently decay into final states containing muons and muon neutrinos. We show how the increase in the prompt muon flux due to intrinsic charm is accompanied by a corresponding enhancement in the prompt muon neutrino flux. We implement different intrinsic charm production models in MCEq to calculate the resulting lepton fluxes. We discuss the challenges of achieving predictions that are simultaneously consistent with both IceCube's high-energy atmospheric muon flux measurements and IceCube upper bound on the prompt muon neutrino flux, and we quantify the resulting discrepancies. As possible solutions, we explore scaling of the unflavored meson contributions to the prompt atmospheric muon flux to assess how such adjustments can reconcile these differences. The tensions emphasized in our work call for a refinement of the hadronic interaction models, especially the production of unflavored mesons, and for new experimental data sensitive to unflavored meson and heavy flavor production with reliable estimates of the associated uncertainties. We suggest that the energy and zenith angle dependence of muon and neutrino flux ratios from future neutrino telescope measurements may help to disentangle different scenarios.

Figures (19)

• Figure 1: The atmospheric ($\mu^+ + \mu^-$) flux and atmospheric ($\nu_\mu+\bar{\nu}_\mu$) flux, both scaled by $E^3$ and angle-averaged over zenith angles less than 60$^\circ$, from MCEqFedynitch:2018cbl using H3a cosmic ray flux model Gaisser:2011klf and Sibyll-2.3cRiehn:2017mfmFedynitch:2018cbl for interactions. The dashed lines show the prompt contributions, and the solid lines show the total contributions (conventional + prompt).
• Figure 2: Results for $E^3\phi(E)$ for $\mu^++\mu^-$ and $\nu_\mu+\bar{\nu}_\mu$ for zenith angle $\theta=0^\circ$ (vertical), showing the individual contributions of light, heavy and unflavored mesons, as determined by MCEq using the Sibyll-2.3c hadronic interaction model and the H3a cosmic ray flux model.
• Figure 3: Left: MCEq predictions for angle-averaged (up to zenith angle of $60^\circ$) conventional and prompt ($\mu^{+}+\mu^{-}$) flux, compared to the experimentally measured spectrum of high-energy muons using data for $\theta_{\rm zen}\leq 60^\circ$ from refs. Soldin:2023lbrSoldin:2018vakIceCube:2015wro. The unflavored and pQCD($c \bar{c}$) curves are nearly equal in the muon energy range shown in the figure. Right: Comparison of MCEq pQCD($c\bar{c}$) prompt ($\nu_\mu + \bar{\nu}_{\mu}$) flux with the upper limit on the prompt flux from the analysis of up-going muon tracks performed in Ref. IceCube:2016umi, which assumed a prompt neutrino energy spectrum with the same shape as in Enberg et al. PhysRevD.78.043005. The angle-averaged (up to zenith angle of $60^\circ$) conventional neutrino flux from MCEq is also shown. The prompt neutrino flux is isotropic in the energy range considered here. The cosmic ray all-nucleon flux model H3a and the hadronic interaction model Sibyll-2.3c are used as input of MCEq.
• Figure 4: $f_{h_c^{(intr}}$ of $D$ mesons and $\Lambda_c$ as a function of $x_{h_c}$ (see eq. \ref{['eq:dsdx-ic']}) using the Regge ansatz Kaidalov:1985jgKaidalov:2003wp with either $a_N=-0.5$ (Regge1) or $a_N=0$ (Regge2), and using the Hobbs, Londergan and Melnitchouk (HLM) approach Hobbs:2013bia (see text for details).
• Figure 5: As in \ref{['fig:average-flux-muon-neutrino']}, the angle-averaged atmospheric fluxes with $\theta_{\rm zen}\leq 60^\circ$. Left: Including intrinsic charm (IC) contribution with the weight $w_c^{\rm intr}=3.87\times10^{-3}$, the best-fit for the IceCube data IceCube:2015wro. The gray curve shows the sum of conventional and prompt $\mu^++\mu^-$ fluxes including intrinsic charm. Right: The prompt atmospheric muon neutrino flux including intrinsic charm contribution with $w^c_{\rm intr} =3.87\times10^{-3}$ and the upper limit on the prompt flux from IceCube IceCube:2016umi. The sum of perturbative and intrinsic charm contributions to the prompt $\nu_\mu+\bar{\nu}_\mu$ flux is shown with the gray curve.