Mapping the dominant regions of the phase space associated with $c \bar c$ production relevant for the Prompt Atmospheric Neutrino Flux

TL;DR

This paper maps the key kinematic regions influencing high-energy prompt atmospheric neutrino flux, highlighting the importance of ultra-small parton momentum fractions and large center-of-mass energies beyond current collider capabilities.

Contribution

It provides a detailed analysis of the dominant phase space regions for charm production affecting the prompt neutrino flux, emphasizing the need to explore ultra-small x values and high energies.

Findings

Neutrino energies above 10^7 GeV are sensitive to energies beyond LHC.

Production regions involve very small parton momentum fractions (x ~ 10^-8 to 10^-5).

The study highlights the potential of neutrino flux data to constrain QCD models.

Abstract

We present a detailed mapping of the dominant kinematical domains contributing to the prompt atmospheric neutrino flux at high neutrino energies by studying its sensitivity to the cuts on several kinematical variables crucial for charm production in cosmic ray scattering in the atmosphere. This includes the maximal center-of-mass energy for proton-proton scattering, the longitudinal momentum fractions of partons in the projectile (cosmic ray) and target (nucleus of the atmosphere), the Feynman $x_F$ variable and the transverse momentum of charm quark/antiquark. We find that the production of neutrinos with energies larger than $E_{\nu} >$ 10$^7$ GeV is particularly sensitive to the center-of-mass energies larger than the ones at the LHC and to the longitudinal momentum fractions in the projectile 10$^{-8}$ $< x <$ 10$^{-5}$. Clearly, these are regions where we do not control the parton, in particular gluon, densities. We also analyse the characteristic theoretical uncertainties in the charm production cross section coming from its QCD modelling. The precision data on the prompt atmospheric neutrino flux can efficiently constrain the mechanism of heavy quark production and underlying QCD dynamics in kinematical ranges beyond the reach of the current collider measurements.