Measurement of the neutrino neutral-current elastic differential cross section on mineral oil at $E_{\nu }\sim 1\mathrm{GeV}$

We report a measurement of the flux-averaged neutral-current elastic differential cross section for neutrinos scattering on mineral oil (${\mathrm{CH}}_2$) as a function of four-momentum transferred squared, $Q^2$. It is obtained by measuring the kinematics of recoiling nucleons with kinetic energy greater than 50 MeV which are readily detected in MiniBooNE. This differential cross-section distribution is fit with fixed nucleon form factors apart from an axial mass $M_A$ that provides a best fit for $M_A=1.39\pm 0.11\mathrm{GeV}$. Using the data from the charged-current neutrino interaction sample, a ratio of neutral-current to charged-current quasielastic cross sections as a function of $Q^2$ has been measured. Additionally, single protons with kinetic energies above 350 MeV can be distinguished from neutrons and multiple nucleon events. Using this marker, the strange quark contribution to the neutral-current axial vector form factor at $Q^2=0$, $\Delta s$, is found to be $\Delta s=0.08\pm 0.26$.

Figure 1

Neutrino flux at the MiniBooNE detector for different types of neutrinos as a function of their energy as reported in [9, 25].

Figure 2

Fraction of prompt hits versus the total number of tank PMT hits for beam-unrelated data and NCE MC events reconstructed under an electron hypothesis. The error bars correspond to the root mean square of the distributions.

Figure 3

Log-likelihood ratio between electron and proton event hypotheses for MC-generated NCE scattering events and beam-unrelated data. Both histograms are normalized to unit area. Events with $\ln ({\mathcal{L}}_e/{\mathcal{L}}_p)<0.42$ are selected for the analysis.

Figure 4

Reconstructed nucleon kinetic energy spectra for the data and MC after the NCE event selection and a uniform fiducial volume cut of $R<4.2\mathrm{m}$ are applied. All MC distributions are normalized to the number of POT).

Figure 5

The MiniBooNE NCE ($\nu N\to \nu N$) flux-averaged differential cross section on ${\mathrm{CH}}_2$ as a function of $Q_{\mathrm{QE}}^2=2m_N\sum _i{T}_i$, where we sum the true kinetic energies of all final state nucleons produced in the NCE interaction. The blue dotted line is the predicted spectrum of NCE-like background which has been subtracted out from the total NCE-like differential cross section.

Figure 6

MiniBooNE NCE/CCQE cross section ratio on ${\mathrm{CH}}_2$ as a function of $Q_{\mathrm{QE}}^2$. The NUANCE MC prediction is plotted for two assumptions of parameters: the black solid line for $M_A=1.23\mathrm{GeV}$ and $\kappa =1.022$ [13] and the blue dotted line for $M_A=1.35\mathrm{GeV}$ and $\kappa =1.007$ [26]. $\Delta s$ is assumed to be zero in both of these cases. Both cross sections in the ratio are per target nucleon—there are $14/6$ times more target nucleons in the numerator than in the denominator. The error bars represent both statistical and all systematic uncertainties (excluding flux errors) taken in quadrature.

Figure 7

MiniBooNE NCE-like/CCQE-like cross-section ratio on ${\mathrm{CH}}_2$ as a function of $Q_{\mathrm{QE}}^2$ with total error. The color code for the histograms is the same as in Fig. 6.

Figure 8

${\chi }^2$ tests performed on the NCE reconstructed nucleon kinetic energy distribution for MC with different $M_A$ values of 1.35, 1.23, and 1.02 GeV. The ${\chi }^2$ values are 27.1, 29.2, and 41.3 for 49 degrees of freedom (DOF), respectively. The distributions are normalized to POT.

Figure 9

The proton/muon cut based on the $\ln ({\mathcal{L}}_{\mu }/{\mathcal{L}}_p)$ variable, which is the log-likelihood ratio of muon and proton event hypotheses. The left part of the cut is used for the analysis. The histograms are normalized to POT.

Figure 10

The proton/neutron cut based on the fraction of prompt hits with the corrected time between 0 and 5 ns. The right part of the cut is used for the analysis. The histograms are normalized to POT.

Figure 11

The angle between the reconstructed nucleon direction and the incident beam direction for data and MC after the NCE, proton/muon, and proton/neutron cuts. All distributions are POT-normalized. Events with ${\theta }_p<60°$ are used in the analysis.

Figure 12

The ratio of $\nu p\to \nu p/\nu N\to \nu N$ as a function of the reconstructed energy for data and MC with $\Delta s$ values as labeled.

Figure 13

Fits to the data using MC templates for the in-tank and dirt events in $Z$ for different reconstructed energy bins. The “total MC before the fit” is a sum of the in-tank and dirt templates, which are absolutely (POT) normalized.

Figure 14

Combined dirt energy correction fit from $Z$, $R$, and energy distributions. Errors for $Z$ and $R$ are statistical from the minimization fitting these distributions. The error for the energy distribution is the largest systematic uncertainty resulting from the optical model of the mineral oil.

Figure 15

Efficiency corrections $C_{\nu p,H}$, $C_{\nu p,C}$, and $C_{\nu n,C}$ versus $Q_{\mathrm{QE}}^2$ for different NCE processes (as labeled).