Intrinsic charm contribution to the prompt atmospheric neutrino flux

In this work we investigate the impact of intrinsic charm on the prompt atmospheric neutrino flux. The color dipole approach to heavy quark production is generalized to include the contribution of processes initiated by charm quarks. The prompt neutrino flux is calculated assuming the presence of intrinsic charm in the wave function of the projetile hadron. The predictions are compared with previous color dipole results which were obtained taking into account only the process initiated by gluons. In addition, we estimate the atmospheric ($\mathrm{conventional}+\text{prompt}$) neutrino flux and compare our predictions with the ICECUBE results for the astrophysical neutrino flux. Our results demonstrate that the contribution of the charm quark initiated process is non—negligible and that the prompt neutrino flux can be enhanced by a factor $\approx 2$ at large neutrino energies if an intrinsic charm component is present in the proton wave function.

Figure 1

Contributions to charm production at high energies and forward rapidities. (a) Contribution from gluon-initiated processes. (b) Contribution from charm in the initial state.

Figure 2

(a) Comparison between the BHPS and No IC predictions for the charm (lower red curves) and gluon (upper black curves) distributions. (b) Comparison between the BHPS and No IC predictions for the Feynman $x_F$ distributions considering $pp$ collisions at $\sqrt{s}=13\mathrm{TeV}$.

Figure 3

Energy dependence of the prompt neutrino flux, normalized by a factor $E_{\nu }^3$. (a) Comparison of our predictions with the results obtained in Refs. [18, 51] using the color dipole approach. The results derived in [18] considering different phenomenological saturation models for the dipole-proton scattering amplitude are represented by the cyan band. (b) Comparison of the No IC and BHPS predictions considering the gluon and charm contributions and only the gluon one in the calculation of the $x_F$ distribution.

Figure 4

(a) Comparison between the BPL and H3a models for the all-nucleon primary cosmic ray spectra. (b) Energy dependence of the prompt neutrino flux, normalized by a factor $E_{\nu }^3$, obtained using the BPL and H3a models as input in the calculations.

Figure 5

Energy dependence of the ratios between prompt neutrino fluxes. (a) Ratio between the flux calculated considering the gluon and charm channels (${\mathrm{\Phi }}_{g+c}$) and that derived assuming only the gluon channel (${\mathrm{\Phi }}_g$). (b) Ratio between the flux derived assuming the presence of this component (${\mathrm{\Phi }}_{\mathrm{BHPS}}$) with that calculated disregarding this component (${\mathrm{\Phi }}_{\mathrm{NoIC}}$).

Figure 6

Energy dependence of the prompt neutrino flux, normalized by a factor $E_{\nu }^2$, obtained considering the BPL model for the primary nucleon spectrum. (a) Comparison of our results with the predictions for the conventional neutrino flux derived in Ref. [10] and the astrophysical neutrino flux obtained in Ref. [3], which is represented by the cyan band. (b) Comparison between the predictions for the atmospheric ($\mathrm{conventional}+\text{prompt}$) neutrino fluxes and the astrophysical one.

Figure 7

(a) Comparison between the BPL and H3a predictions for the energy dependence of the atmospheric ($\mathrm{conventional}+\text{prompt}$) neutrino fluxes, normalized by a factor $E_{\nu }^2$. (b) Comparison between the BHPS predictions for the atmospheric ($\mathrm{conventional}+\text{prompt}$) neutrino flux with the results derived by Halzen and Willie (HW) [20] and by Laha and Brodsky (LB) [21]. Results derived using the H3a spectrum.