Neutrino Induced Charged Current Coherent Pion Production for Constraining the Muon Neutrino Flux at DUNE

We study neutrino induced charge current coherent pion production ($ν_μ\text{CC-Coh}π$) as a tool for constraining the neutrino flux at the Deep Underground Neutrino Experiment (DUNE). The neutrino energy and flavor in the process can be directly reconstructed from the outgoing particles, making it especially useful to specifically constrain the muon neutrino component of the total flux. The cross section of this process can be obtained using the Adler relation with the $π$-Ar elastic scattering cross section, taken either from external data or, as we explore, from a simultaneous measurement in the DUNE near detector. We develop a procedure that leverages $ν_μ\text{CC-Coh}π$ events to fit for the neutrino flux while simultaneously accounting for relevant effects in the cross section. We project that this method has the statistical power to constrain the uncertainty on the normalization of the flux at its peak to a few percent. This study demonstrates the potential utility of a $ν_μ\text{CC-Coh}π$ flux constraint, though further work will be needed to determine the range of validity and precision of the Adler relation upon which it relies, as well as to measure the $π$-Ar elastic scattering cross section to the requisite precision. We discuss the experimental and phenomenological developments necessary to unlock the $ν_μ\text{CC-Coh}π$ process as a "standard candle'' for neutrino experiments.