Measurements of the ${\nu }_{\mu }$ and ${\overline{\nu }}_{\mu }$-induced coherent charged pion production cross sections on ${}^{12}\mathrm{C}$ by the T2K experiment

We report an updated measurement of the ${\nu }_{\mu }$-induced, and the first measurement of the ${\overline{\nu }}_{\mu }$-induced coherent charged pion production cross section on ${}^{12}\mathrm{C}$ nuclei in the Tokai-to-Kamioka experiment. This is measured in a restricted region of the final-state phase space for which $p_{\mu ,\pi }>0.2\mathrm{GeV}$, $\cos ({\theta }_{\mu })>0.8$ and $\cos ({\theta }_{\pi })>0.6$, and at a mean (anti)neutrino energy of 0.85 GeV using the T2K near detector. The measured ${\nu }_{\mu }$ charged current coherent pion production flux-averaged cross section on ${}^{12}\mathrm{C}$ is $(2.98\pm 0.37(\mathrm{stat})\pm 0.31(\mathrm{syst}{)}_{-0.00}^{+0.49}({\mathrm{Q}}^2\text{model}))\times {10}^{-40}{\mathrm{cm}}^2$. The new measurement of the ${\overline{\nu }}_{\mu }$-induced cross section on ${}^{12}\mathrm{C}$ is $(3.05\pm 0.71(\mathrm{stat})\pm 0.39(\mathrm{syst}{)}_{-0.00}^{+0.74}({\mathrm{Q}}^2\text{model}))\times {10}^{-40}{\mathrm{cm}}^2$. The results are compatible with both the NEUT 5.4.0 Berger-Sehgal (2009) and GENIE 2.8.0 Rein-Sehgal (2007) model predictions.

Figure 1

Feynman diagram for coherent charged pion production from a neutrino off a nucleus. This is specific to the PCAC class of models. The square of the magnitude of the 4-momentum transfer to the nucleus is $|p_A{|}^2=|q-p_{\pi }{|}^2=|t|$.

Figure 2

The muon (left) and pion (right) kinematic distributions for the ${\nu }_{\mu }$ coherent signal events (top) and for all signal and background events (bottom). The straight lines indicate the restricted phase space; note no upper bound is set for the muon and pion momentum. Based on the NEUT Monte Carlo, 82.9% of the true COH events remain in the restricted phase space.

Figure 3

The muon (left) and pion (right) kinematic distributions for the ${\overline{\nu }}_{\mu }$ coherent signal events (top) and for all signal and background events (bottom). The straight lines indicate the restricted phase space; note no upper bound is set for the muon and pion momentum. Based on the NEUT Monte Carlo, 83.5% of the true COH events remain in the restricted phase space.

Figure 4

The ${\nu }_{\mu }$ (top) and ${\overline{\nu }}_{\mu }$ (bottom) COH selection, containing one muon and one charged pion, are shown in the VA (left) and $|t|$ (right) variables. The signal COH events for both selections concentrate in the low VA (less than 15 MeV) and low $|t|$ (less than $0.15{\mathrm{GeV}}^2$) region. The events with VA greater than 15 MeV are rejected. The events with $|t|$ greater than $0.15{\mathrm{GeV}}^2$ are used for background control. The stacked histogram shows the prefit simulation overlaid by data.

Figure 5

${\nu }_{\mu }$ data, nominal Monte Carlo simulation (prefit), and postfit Monte Carlo simulation comparisons in VA, $|t|$, ${\mathrm{Q}}^2$, $p_{\pi }$, and $\cos ({\theta }_{\pi })$ for the signal region. The stacked histograms represent the true reaction types of the events. The smaller postfit ${\chi }_{\mathrm{stat}}^2$ shows improved data and MC agreement in all five variables after the fit. The postfit ${\chi }_{\mathrm{stat}}^2$ for the VA distribution remains statistically incompatible to the data. The nominal MC was modified to reproduce the shapes seen in the data and used as a simulated data set. No significant bias in the total cross section extraction was observed (see text). Note that the fit does not consider these distributions, but only sees a single bin for the signal sample.

Figure 6

${\nu }_{\mu }$ data, nominal Monte Carlo simulation (prefit), and postfit Monte Carlo simulation comparisons in VA, $|t|$, ${\mathrm{Q}}^2$, $p_{\pi }$, and $\cos ({\theta }_{\pi })$ for the first sideband. The stacked histograms represent the true reaction types of the events. The postfit ${\chi }_{\text{stat}}^2$ are improved in general as a result of the RES and DIS background events being reweighted. The relatively larger VA and $p_{\pi }$ postfit ${\chi }_{\text{stat}}^2$ indicate lack of degrees of freedom in these two spaces.

Figure 7

${\nu }_{\mu }$ data, nominal Monte Carlo simulation (prefit), and postfit Monte Carlo simulation comparisons in VA, $|t|$, ${\mathrm{Q}}^2$, $p_{\pi }$, and $\cos ({\theta }_{\pi })$ for the second sideband. The stacked histograms represent the true reaction types of the events. Since this sideband is dominated by the DIS background events, the postfit ${\chi }_{\mathrm{stat}}^2$ is much improved after the fitter as a result of the DIS background events being reweighted.

Figure 8

${\overline{\nu }}_{\mu }$ data, nominal Monte Carlo simulation (prefit), and postfit Monte Carlo simulation comparisons in VA, $|t|$, ${\mathrm{Q}}^2$, $p_{\pi }$, and $\cos ({\theta }_{\pi })$ for the signal region. The stacked histograms represent the true reaction types of the events. The postfit ${\chi }_{\text{stat}}^2$ are not changed as much as in the ${\nu }_{\mu }$ case due to lower statistics. As with the ${\nu }_{\mu }$ case, only the VA distribution is statistically incompatible with the data. Note that the fit does not consider these distributions, but only sees a single bin for the signal sample.

Figure 9

${\overline{\nu }}_{\mu }$ data, nominal Monte Carlo simulation (prefit), and postfit Monte Carlo simulation comparisons in VA, $|t|$, ${\mathrm{Q}}^2$, $p_{\pi }$, and $\cos ({\theta }_{\pi })$ for the first sideband. The stacked histograms represent the true reaction types of the events. The postfit ${\chi }_{\text{stat}}^2$ are improved in general as a result of the RES background events being reweighted; however, the shape differences between the data and the MC in the VA and $|t|$ cannot be simply resolved by simple rescale of events.

Figure 10

The T2K ${\nu }_{\mu }$ (left) and ${\overline{\nu }}_{\mu }$ (right) CC-COH cross section measurement on C assuming $F(A)=A^{1/3}$. The measurement uncertainty shown is the quadratic sum of the statistical and systematic components. The $x$-axis error bar covers one standard deviation of the T2K flux around the mean (anti)neutrino energy of (0.85)0.85 GeV. The 2016 ${\nu }_{\mu }$ T2K result (same $E_{\nu }$ range, center point offset slightly for clarity of the figure) [19], and the MINERvA result [20] (for $E_{\nu }$ between 2–3 GeV) are also shown for comparison. Note the phase space between the different measurements are not exactly the same.