“Hammer” events, neutrino energies, and nucleon-nucleon correlations

Background: Accelerator-based neutrino oscillation measurements depend on observing a difference between the expected and measured rate of neutrino-nucleus interactions at different neutrino energies or different distances from the neutrino source. Neutrino-nucleus scattering cross sections are complicated and depend on the neutrino beam energy, the neutrino-nucleus interaction, and the structure of the nucleus. Knowledge of the incident neutrino energy spectrum and neutrino-detector interactions are crucial for analyzing neutrino oscillation experiments. The ArgoNeut liquid argon time projection chamber (lArTPC) observed charged-current neutrino-argon scattering events with two protons back-to-back in the final state (“hammer” events) which they associated with short-range correlated (SRC) nucleon-nucleon pairs. The large volume MicroBooNE lArTPC will measure far more of these unique events.

Purpose: Determine what we can learn about the incident neutrino energy spectrum and/or the structure of SRC from hammer events that will be measured in MicroBooNE.

Methods: We simulate hammer events using two models and the well-known electron-nucleon scattering cross section. In the first model the neutrino (or electron) scatters from a moving proton, ejecting a ${\pi }^{+}$, and the ${\pi }^{+}$ is then absorbed on a moving deuteron-like $np$ pair. In the second model the neutrino (or electron) scatters from a moving nucleon, exciting it to a $\mathrm{\Delta }$ or $N^{*}$, which then de-excites by interacting with a second nucleon: $\mathrm{\Delta }N\to pp$.

Results: The pion production and reabsorption process results in two back-to-back protons each with momentum of about 500 MeV/$c$, very similar to that of the observed ArgoNeut events. These distributions are insensitive to either the relative or center-of-mass momentum of the $np$ pair that absorbed the $\pi$. In this model, the incident neutrino energy can be reconstructed relatively accurately using the outgoing lepton. The $\mathrm{\Delta }p\to pp$ process results in two protons that are less similar to the observed events.

Conclusions: ArgoNeut hammer events can be described by a simple pion production and reabsorption model. The hammer events that will be measured in MicroBooNE can be used to determine the incident neutrino energy but not to learn about SRC. We suggest that this reaction channel could be used for neutrino oscillation experiments to complement other channels with higher statistics but different systematic uncertainties.

Figure 1

Pictorial diagram of electron induced two-proton knockout, $A(e,e^{\prime }pp)$. (a) The electron scatters from a first nucleon, which emits a pion, typically after resonance excitation (not shown). The pion is absorbed by two nucleons, which are detected. (b) The electron scatters from a first nucleon, exciting it to a resonance, which de-excites via $\mathrm{\Delta }N\to pp$. The diagrams for the corresponding charged current neutrino interactions $A(\nu ,\mu pp)$ would replace the incident electron with a neutrino, the outgoing electron with a muon, and the exchanged virtual photon with a $W$.

Figure 2

The invariant mass of the initial proton plus vector boson (e.g., the virtual photon) expected for hammer events in MicroBooNE. Black solid line: $\pi$ production and reabsorption model; blue dashed line: $\mathrm{\Delta }N\to pp$ model.

Figure 3

The four-momentum transfer squared, $Q^2$, plotted versus the energy transfer $\nu$ expected for hammer events in MicroBooNE.

Figure 4

The cosine of the opening angle of the two final state protons in the laboratory system expected for hammer events in MicroBooNE. The black solid histogram corresponds to the pion production and reabsorption model and the blue dashed histogram corresponds to the $\mathrm{\Delta }N\to pp$ model. The opening angle distribution was almost identical for the two different center of mass momentum distributions of the NN pair absorbing the $\pi$.

Figure 5

The momentum of the two protons in the laboratory frame, sorted into the slower proton and faster proton as expected for hammer events in MicroBooNE. The histograms peaked at $p_p\approx 0.4$ GeV/$c$ correspond to the slower proton and the histograms peaked at $p_p>0.5$ to 0.6 GeV/$c$ correspond to the faster proton in the event. The solid black large-bin histogram corresponds to the pion production and reabsorption model and the dashed blue small-bin histogram corresponds to the $\mathrm{\Delta }N\to pp$ model.

Figure 6

The transverse missing momentum of the muon plus two final state protons in the laboratory system expected for hammer events in MicroBooNE. The black solid histogram corresponds to the pion production and reabsorption model and the blue dashed histogram corresponds to the $\mathrm{\Delta }N\to pp$ model.

Figure 7

The fractional error (top) and standard deviation (bottom) of the distribution of the reconstructed beam energy $(E_{\mathrm{rec}}-E_{\nu })/E_{\mathrm{rec}}$ vs the reconstructed beam energy for four ways to calculate the invariant mass of the struck nucleon as described in the text: (left) for the $\pi$ production and reabsorption model calculated and (right) for the $N\mathrm{\Delta }\to pp$ model. The labels QE (blue circles), $\mathrm{\Delta }$ (black squares), $pp$ mass (red triangles), and $pp$ energy (red inverted triangles) refer to the four models of the invariant mass of the struck nucleon described in the text. The label ArgoNeut (green open circles) refers to $E_{\nu }=E_{\mu }+T_{p1}+T_{p2}+T_{A-2}+30$ MeV as used in Ref. [12].