Neutrino flux predictions for the NuMI beam

Knowledge of the neutrino flux produced by the Neutrinos at the Main Injector (NuMI) beamline is essential to the neutrino oscillation and neutrino interaction measurements of the MINERvA, $\mathrm{MINOS}+$, NOvA and MicroBooNE experiments at Fermi National Accelerator Laboratory. We have produced a flux prediction which uses all available and relevant hadron production data, incorporating measurements of particle production off of thin targets as well as measurements of particle yields from a spare NuMI target exposed to a 120 GeV proton beam. The result is the most precise flux prediction achieved for a neutrino beam in the one to tens of GeV energy region. We have also compared the prediction to in situ measurements of the neutrino flux and find good agreement.

Figure 1

The number of interactions per ${\nu }_{\mu }$ passing through MINERvA as a function of the neutrino energy in the LE beam configuration. The lines show the different categories of interactions for which we apply constraints and uncertainties based on hadron production data: “nucleon-A” refers mainly to nucleons interacting in material that is not carbon [20], and “meson inc.” refers to mesons interacting on any material in the beamline.

Figure 2

A summary of the hadron production data from NA49 and its application in the analysis to predict the thin target flux. The markers show the location of NA49’s measurements of the invariant cross section for $pC\to {\pi }^{+}X$ interactions as a function of the produced pion’s kinematics in the ($x_F$, $p_T$) plane. The marker types correspond to statistical uncertainties $<2.5\%$ (filled circle), $<5\%$ (open circle) and $>5\%$ (plus). The color scale shows the data/MC ratio $f_{\text{Data}}/f_{\mathrm{MC}}$ applied in Eq. (2) to correct the simulation. The topographical contours indicate the number of $pC\to {\pi }^{+}X$ interactions leading to ${\nu }_{\mu }$ in MINERvA in the LE beam. From inner to outer these are at 75%, 50%, 25%, 10%, and 2.5% of the peak value. The upper axis shows the approximate energy of a ${\nu }_{\mu }$ produced by a pion at the corresponding $x_F$.

Figure 3

A summary of the hadron production data from MIPP and its application to predict the thick target flux. The markers show the bin center of MIPP’s measurements of ${\pi }^{+}$ yields from 120 GeV protons interacting with a NuMI target. The upper $p_T$ bins extend to $2\mathrm{GeV}/\mathrm{c}$ but the markers are drawn at $0.8\mathrm{GeV}/\mathrm{c}$. The marker types correspond to statistical uncertainties $<2.5\%$ (filled circle), $<5\%$ (open circle) and $>5\%$ (plus). The color scale shows the data/MC ratio applied to correct the simulation. The topographical contours indicate the number of ${\pi }^{+}$ exiting the target that lead to ${\nu }_{\mu }$ in MINERvA in the LE beam. From inner to outer these are at 75%, 50%, 25%, 10%, and 2.5% of the peak value. The upper axis shows the approximate energy of a ${\nu }_{\mu }$ produced by a pion at the corresponding $p_z$. The region around $p_z\approx 5\mathrm{GeV}/\mathrm{c}$ corresponds to a gap in MIPP’s acceptance, which resulted in increased statistical errors in some kinematic bins and the inability to measure yields in others.

Figure 4

A summary of the material traversed by ${\pi }^{+}$ parents of ${\nu }_{\mu }$ incident on MINERvA in the LE beam configuration. This material accounting is used to compute the impact that uncertainties on hadron absorption cross sections have on the flux.

Figure 5

Uncertainties on the NuMI low energy ${\nu }_{\mu }$ thin target flux that originate from the different hadron interaction categories described in the text. The label nucleon-A refers mainly to nucleons interacting in material that is not carbon [20], and meson inc. refers to mesons interacting on any material in the beamline; “target abs.” and “other abs.” refer to absorption in the target (C) and other materials (Al, He, Fe).

Figure 6

Uncertainties on the NuMI low energy ${\nu }_{\mu }$ thick target flux that originate from the different hadron interaction categories described in the text. The label nucleon-A refers mainly to nucleons interacting in material that is not carbon [20], and meson inc. refers to mesons interacting on any material in the beamline; target abs. and other abs. refer to absorption in the target (C) and other materials (Al, He, Fe).

Figure 7

Beam geometry and focusing uncertainties on the ${\nu }_{\mu }$ flux at MINERvA in the LE beam configuration. The sources of uncertainty are described in the text.

Figure 8

The predicted thin target ${\nu }_{\mu }$ flux at the MINERvA detector for the low energy, ${\nu }_{\mu }$ focused, beam configuration. The ratio plot shows the effect of correcting the flux simulation using thin target hadron production and attenuation data as described in the text. The error band includes uncertainties due to hadron interactions, beam geometry and beam focusing.

Figure 9

The predicted thick target ${\nu }_{\mu }$ flux at the MINERvA detector for the low energy, ${\nu }_{\mu }$ focused, beam configuration. The ratio plot shows the effect of correcting the flux simulation using thick and thin target hadron production and attenuation data as described in the text. The error band includes uncertainties due to hadron interactions, beam geometry and beam focusing.

Figure 10

Ratios of flux predictions. (a) The flux predicted using data from thick target experiments divided by the flux prediction that uses only thin target data. (b) The thin and thick target flux predictions divided by the in situ flux measured using the low-$\nu$ technique. The error bands on each curve account for uncertainties in the numerator and denominator, including the effect of significant correlations between the thick and thin target predictions.