Upper Limit on Forward Charm Contribution to Atmospheric Neutrino Flux

We revisit the calculation of charm particle production in hadron collisions, focusing on the production of charm particles that carry a large fraction of the momentum of the incident proton. In the case of strange particles, such a component is familiar from the abundant production of $K^+\Lambda$ pairs. Modern collider experiments have no coverage in the very large rapidity region where the forward pair production dominates. While forward charm particles are produced inside the LHC beampipe, they dominate the high-energy atmospheric neutrino flux in underground experiments because long-lived pions and kaons interact before decaying into neutrinos. The fragmentation of the spectator quark in the partonic subprocesses $qc \rightarrow qc$ and $gc \rightarrow gc$ is responsible for the forward component of charm production in perturbative QCD. We use this phenomenological framework to construct a charm cross section that saturates available accelerator and cosmic ray data, i.e., it represents an upper limit on the normalization of the charm cross section that cannot be reliably calculated because the charm mass is much smaller than the center-of-mass energy. Where the highest energy IceCube observations are concerned, we conclude that the upper limit on the flux of neutrinos from forward charm production may dominate the much-studied central component. It may therefore also represent a significant contribution to the TeV atmospheric neutrino flux but cannot accommodate the PeV flux of high-energy cosmic neutrinos observed by IceCube, or even the excess of events observed in the 30 TeV energy range.