Muon-neutrino-induced charged-current cross section without pions: Theoretical analysis

We calculate the charged-current cross sections obtained at the T2K near detector for ${\nu }_{\mu }$-induced events without pions in the final state. The method used is quantum-kinetic transport theory. Results are shown first, as a benchmark, for electron-inclusive cross sections on ${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$ to be followed with a detailed comparison with the data measured by the T2K Collaboration on ${\mathrm{C}}_8{\mathrm{H}}_8$ and ${\mathrm{H}}_2\mathrm{O}$ targets. The contribution of 2p2h processes is found to be relevant mostly for backward angles; their theoretical uncertainties are within the experimental uncertainties. Particular emphasis is then put on a discussion of events in which pions are first created but then reabsorbed. Their contribution is found to be essential at forward angles.

Figure 1

Inclusive cross sections for interactions of electrons with ${}^{12}\mathrm{C}$ for an incoming energy of 680 MeV and a scattering angle of 60 deg as a function of energy transfer $\omega$. The individual curves give the contributions of the subprocesses QE scattering, 2p2h interactions, $\mathrm{\Delta }$ resonance contributions, contributions of higher lying resonances $N^{*}$, and the $1\pi$ background contributions. The curves labeled “inmed $\mathrm{\Delta }$” give results of calculations in which the in-medium spectral function of the $\mathrm{\Delta }$ resonance from Ref. [49] was used. The data are taken from the arXiv for quasielastic electron-nucleus scattering data [50].

Figure 2

Inclusive cross sections for interactions of electrons with ${}^{16}\mathrm{O}$. The electron energies and scattering angles are given below each figure. The individual curves give the contributions of the subprocesses QE scattering, 2p2h interactions, $\mathrm{\Delta }$ resonance contributions, contributions of higher lying resonances $N^{*}$, the $1\pi$ background contributions, and finally those from deep inelastic scattering. The data are taken from the arXiv for quasielastic electron-nucleus scattering data [50]. (a) $E=0.7$ GeV, $\theta =32$ deg; (b) $E=0.737$ GeV, $\theta =37.1$ deg; (c) $E=0.88$ GeV, $\theta =32$ deg; (d) $E=1.080$ GeV, $\theta =32$ deg; (e) $E=1.2$ GeV, $\theta =32$ deg; and (f) $E=1.5$ GeV, $\theta =32$ deg.

Figure 3

Muon momentum distributions per nucleon in the various angular bins as used by the T2K analysis [13] for a C target. The top dash-dot-dotted curve gives the fully inclusive cross section. The solid (red) curves give the total cross section for events with 0 pions in the outgoing channel. The dotted (green) curves give the cross sections for QE + 2p2h alone; the dash-dotted (blue) curve gives the 2p2h contribution alone.

Figure 4

Muon momentum distributions per nucleon for 0-pion events in the various angular bins used by the T2K analysis [13] for a ${\mathrm{C}}_8{\mathrm{H}}_8$ target. The solid (red) curves give the total cross section per nucleon for events with 0 pions in the outgoing channel for the isospin $\mathcal{T}=1$ 2p2h contribution. The dotted (green) curves give the cross sections for QE + 2p2h alone; the dash-dotted (blue) gives the 2p2h contribution alone. The data are taken from Ref. [13].

Figure 5

Muon momentum distributions per nucleon in the various angular bins as used by the T2K analysis [14] for an ${\mathrm{H}}_2\mathrm{O}$ target. The solid (red) curves give the total cross section per nucleon for events with 0 pions in the outgoing channel. The dotted (green) curves give the cross section without the stuck-pion events and the dash-dotted (blue) curves give the contribution of the 2p2h excitations.

Figure 6

Comparison of GiBUU results (steplike solid curve) with the ${\mathrm{H}}_2\mathrm{O}$ 0-pion data from Ref. [14]. The (green) dotted curve gives the cross section per nucleon for 0-pion events from QE and 2p2h processes only. The (blue) dash-dotted line gives the contributions from 2p2h processes.