Measurements of protons and charged pions emitted from ${\nu }_{\mu }$ charged-current interactions on iron at a mean neutrino energy of 1.49 GeV using a nuclear emulsion detector

This study conducted an analysis of muons, protons, and charged pions emitted from ${\nu }_{\mu }$ charged-current interactions on iron using a nuclear emulsion detector. The emulsion detector with a 65 kg iron target was exposed to a neutrino beam corresponding to $4.0\times {10}^{19}$ protons on target with a mean neutrino energy of 1.49 GeV. The measurements were performed at a momentum threshold of 200 $(50)\mathrm{MeV}/c$ for protons (pions), which are the lowest momentum thresholds attempted up to now. The measured quantities are the multiplicities, emission angles, and momenta of the muons, protons, and charged pions. In addition to these inclusive measurements, exclusive measurements such as the muon-proton emission-angle correlations of specific channels and the opening angle between the protons of $\mathrm{CC}0\pi 2p$ events were performed. The data were compared to Monte Carlo predictions and some significant differences were observed. The results of the study demonstrate the capability of detailed measurements of neutrino-nucleus interactions using a nuclear emulsion detector to improve neutrino interaction models.

Figure 1

Schematic view of the detector. The ECC bricks and Shifter are enclosed in a cooling shelter, which is placed in front of an INGRID module.

Figure 2

Structure of the ECC brick. Each ECC brick consists of 23 emulsion films interleaved with 22 iron plates.

Figure 3

Structure of the Shifter. The Shifter is composed of seven emulsion films mounted on three stages. Each stage is driven at a different speed along the $Y$ direction.

Figure 4

Exploded view of an INGRID module. The INGRID module comprises 11 scintillator planes interleaved with 9 iron plates.

Figure 5

Pion detection efficiency estimated using the MC simulation. Track angle is the angle with respect to the beam direction.

Figure 6

Proton detection efficiency estimated using the MC simulation. Track angle is the angle with respect to the beam direction. Blank bins in the region of momentum greater than $1\mathrm{GeV}/c$ and the backward direction denote that there are no events generated by the MC simulation.

Figure 7

Schematic view of the angular method of MCS measurement. In the figure, ${\theta }_i$ is the track segment angle and $\mathrm{\Delta }{\theta }_i$ is the angular difference in cell $i$.

Figure 8

Schematic view of the coordinate method of MCS measurement. In the figure, $\mathrm{\Delta }{y}_i$ is the positional displacement between track segments in cell $i$.

Figure 9

Relation between the reconstructed and true momenta of muons from the neutrino interactions in the MC simulation.

Figure 10

Relation between the reconstructed and true momenta of charged pions from the neutrino interactions in the MC simulation.

Figure 11

Relation between the reconstructed and true momenta of protons from the neutrino interactions in the MC simulation.

Figure 12

Top figure shows correlations between VPH and $p\beta$ of the tracks in the ECC bricks, primarily cosmic rays. The bottom figure shows the theoretical curves of the ionization loss in the emulsion film. The curves were calculated using the Bethe equation [58, 59, 60, 61].

Figure 13

Correlation between VPH and $p\beta$ of the data is shown. The PID between protons and charged pions is performed using the VPH and $p\beta$ of the tracks in the ECC bricks, whereas the muon ID is performed using track matching among the ECC bricks, Shifter, and INGRID.

Figure 14

Likelihood ratio distributions of protons and charged pions. The marker represents the data, and the histogram represents the MC simulation. The background includes ${\nu }_e$ and ${\overline{\nu }}_e$ interactions in the ECC bricks, neutrino interactions in the upstream wall of the detector hall and INGRID modules, and misconnected events between the ECC bricks, Shifter, and INGRID. The difference between the data and the MC simulation in the range of 0.1 to 0.9 reflect the difference between the observed and predicted numbers of protons and pions, as discussed in Sec. 6.

Figure 15

Mis-PID rate distributions of charged pions and protons. The top figure shows the rate of pions, whereas the bottom figure shows the rate of protons. In these measurements, the momentum in the horizontal axis is expressed by $p\beta$, because the PID process uses $p\beta$ estimated by MCS measurements.

Figure 16

Event display of a ${\nu }_{\mu }$-iron CC interaction candidate. The left-hand side of the figure shows the event display in the ECC brick, while the right-hand side shows the event display both in the ECC bricks and in INGRID. On the left-hand side, with their colors representing the track segment and their width indicating the VPH. On the right-hand side, the lines from the ECC bricks are the ECC tracks extrapolated to INGRID, with the blue line representing a muon candidate and the pink and green lines representing protonlike and pionlike tracks, respectively. The width of the lines indicates the VPH. The red markers represent hits and their sizes represent deposited photoelectrons in INGRID.

Figure 17

Neutrino flux uncertainties are due to hadron production and neutrino beamline optics uncertainties.

Figure 18

Systematic uncertainties of the charged pion and the proton multiplicities. The left-hand side of the figures shows the uncertainties of the charged pion multiplicity, whereas the right-hand side shows the uncertainties of proton multiplicity. Statistical uncertainty of our data is also shown for comparison.

Figure 19

Systematic uncertainties of the muon, charged pion, and proton kinematics. The figures in each column show the uncertainties in the muon, charged pion, and proton kinematics. The left-hand side of the figures shows the uncertainty of the emission angle distribution, whereas the right-hand side shows the uncertainty of the momentum distribution. Statistical uncertainty of our data is also shown for comparison.

Figure 20

Systematic uncertainties of the opening angle between two protons of $\mathrm{CC}0\pi 2p$ events. Statistical uncertainty of our data is also shown for comparison.

Figure 21

Results of charged pion and proton multiplicities. The left-hand side of the figures shows the charged pion multiplicity, while the right-hand side shows the proton multiplicity. In the rightmost bin of the pion (proton) distribution, all events with a multiplicity above three pions (five protons) are contained.

Figure 22

Emission angles and momenta of muons, charged pions, and protons. The top figures show the muon results, whereas the middle and bottom show the charged pion and proton results, respectively. The left-hand side of the figures shows the emission angle distributions and the right-hand side shows the momentum distributions. In the rightmost bin of the muon momentum distribution, all events with momenta greater than $5\mathrm{GeV}/c$ are contained. In the rightmost bins of the pion and proton momentum distributions, all events with momenta greater than $1.4\mathrm{GeV}/c$ are also contained. The range 70°–110° in the pion and proton emission angle distributions cannot be reliably measured, and the errors are not shown.

Figure 23

Correlations between emission angle and momentum for muons, charged pions, and protons. The top figure shows that of the muons, while the bottom shows pions and protons, respectively. In the rightmost bin of the muon distribution, all events with momenta greater than $5\mathrm{GeV}/c$ are contained. In the rightmost bins of the pion and proton distributions, all events with momenta greater than $1.4\mathrm{GeV}/c$ are also contained. The data are represented by marker points, and the MC predictions are represented by a two-dimensional histogram. Colors in the histogram represent the number of events predicted by the MC simulation.

Figure 24

Correlations between emission angles of muons and protons. The top half of the figures shows the correlation of $\mathrm{CC}N\pi N^{\prime }p$ events, while the bottom half shows those of $\mathrm{CC}0\pi 1p$ and $\mathrm{CC}1\pi 1p$ events, respectively. The data are represented by marker points, and the MC predictions are represented by a two-dimensional histogram. Colors in the histogram represent the number of events predicted by the MC simulation.

Figure 25

Opening angle between two protons of $\mathrm{CC}0\pi 2p$ events. Back-to-back protons are represented by $\cos \theta =-1$, whereas protons emitted in the same direction are represented by $\cos \theta =1$.