Improved constraint on the MINERvA medium energy neutrino flux using $\bar{\nu}e^{-} \!\rightarrow \bar{\nu}e^{-}$ data

Processes with precisely known cross sections, like neutrino-electron elastic scattering (<math display="inline"><mi>ν</mi><msup><mi>e</mi><mo>-</mo></msup><mo stretchy="false">→</mo><mi>ν</mi><msup><mi>e</mi><mo>-</mo></msup></math>) and inverse muon decay (<math display="inline"><mrow><msub><mrow><mi>ν</mi></mrow><mrow><mi>μ</mi></mrow></msub><msup><mrow><mi>e</mi></mrow><mrow><mo>-</mo></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>-</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub></mrow></math>) have been used by <math display="inline"><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">I</mi><mi mathvariant="normal">N</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mi>ν</mi><mi mathvariant="normal">A</mi></mrow></math> to constrain the uncertainty on the neutrinos at the main injector (NuMI) neutrino beam flux. This work presents a new measurement of neutrino elastic scattering with electrons using the medium energy <math display="inline"><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>μ</mi></msub></math>-enhanced NuMI beam. A sample of 578 events after background subtraction is used in combination with the previous measurement on the <math display="inline"><msub><mi>ν</mi><mi>μ</mi></msub></math> beam and the inverse muon decay measurement to reduce the uncertainty on the <math display="inline"><msub><mi>ν</mi><mi>μ</mi></msub></math> flux in the <math display="inline"><msub><mi>ν</mi><mi>μ</mi></msub></math>-enhanced beam from 7.6% to 3.3% and the <math display="inline"><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>μ</mi></msub></math> flux in the <math display="inline"><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>μ</mi></msub></math>-enhanced beam from 7.8% to 4.7%.