Influence of short-range correlations in neutrino-nucleus scattering

Background: Nuclear short-range correlations (SRCs) are corrections to mean-field wave functions connected with the short-distance behavior of the nucleon-nucleon interaction. These SRCs provide corrections to lepton-nucleus cross sections as computed in the impulse approximation (IA).

Purpose: We want to investigate the influence of SRCs on the one-nucleon ($1N$) and two-nucleon ($2N$) knockout channels for muon-neutrino induced processes on a ${}^{12}\mathrm{C}$ target at energies relevant for contemporary measurements.

Method: The model adopted in this work corrects the impulse approximation for SRCs by shifting the complexity induced by the SRCs from the wave functions to the operators. Due to the local character of the SRCs, it is argued that the expansion of these operators can be truncated at a low order.

Results: The model is compared with electron-scattering data, and two-particle two-hole responses are presented for neutrino scattering. The contributions from the vector and axial-vector parts of the nuclear current as well as the central, tensor, and spin-isospin parts of the SRCs are studied.

Conclusions: Nuclear SRCs affect the $1N$ knockout channel and give rise to $2N$ knockout. The exclusive neutrino-induced $2N$ knockout cross section of SRC pairs is shown and the $2N$ knockout contribution to the QE signal is calculated. The strength occurs as a broad background which extends into the dip region.

Figure 1

Graphical presentation of a 2p2h excitation induced by SRCs (dashed area) with distortion effects (dashed lines) from the $A-2$ spectator nucleons. The boson $X$ can be either a ${\gamma }^{*}$ or a $W^{+}$ in this work.

Figure 2

Diagrams considered in the 1p1h calculations reported in this paper. The left diagram shows the 1p1h channel in the IA and the right diagram shows the SRC corrections (dashed oval).

Figure 3

The $\omega$ dependence of the longitudinal ($W_{CC}$) and transverse ($W_T$) responses for the 1p1h contribution to ${}^{12}\mathrm{C}(e,e^{\prime })$. Results are shown for three values of the momentum transfer $q$. The data are from Refs. [59, 60].

Figure 4

Diagrams considered in the $2N$ knockout calculations.

Figure 5

The ${}^{12}\mathrm{C}$(${\nu }_{\mu },{\mu }^{-}{N}_a{N}_b)$ cross section ($N_a=\mathrm{p},N_b={\mathrm{p}}^{\prime },\mathrm{n}$) at $E_{{\nu }_{\mu }}=750\mathrm{MeV},E_{\mu }=550\mathrm{MeV},{\theta }_{\mu }={15}^{\circ }$ and $T_{\mathrm{p}}=50\mathrm{MeV}$ for in-plane kinematics. The bottom plot shows the (${\theta }_a,{\theta }_b)$ regions with $P_{12}<300\mathrm{MeV}/\mathrm{c}$.

Figure 6

Semi-exclusive ${}^{12}\mathrm{C}({\nu }_{\mu },{\mu }^{-}\mathrm{p})$ cross section for $E_{{\nu }_{\mu }}=750$ MeV, $E_{\mu }=550$ MeV, and three muon scattering angles for in-plane kinematics (${\varphi }_p=0^{\circ }$). The bottom panel shows the (${\theta }_p,E_m$) area with $P_{12}<300$ MeV/$c$ for ${\theta }_{\mu }={15}^{\circ }$.

Figure 7

The $\omega$ dependence of the ${}^{12}\mathrm{C}(e,e^{\prime })$ cross section at $E_e=680$ MeV and ${\theta }_{e^{\prime }}={60}^{\circ }$. The results are compared with data from Ref. [59].

Figure 8

The 2p2h SRC response functions $R_{CC}$ and $R_T$ for ${}^{12}\mathrm{C}({\nu }_{\mu },{\mu }^{-})$ at $q=400$ MeV/$c$. The contributions of the three different SRC types ($\mathrm{SRC}=c+t\tau +\sigma \tau$) are shown for the vector (V) and axial (A) parts of the nuclear current.

Figure 9

Same as Fig. 8. The contributions of the initial $pn$ and $nn$ pairs are shown for the three different SRC types.

Figure 10

The computed $\omega$ dependence of the ${}^{12}\mathrm{C}({\nu }_{\mu },{\mu }^{-})$ cross section for $E_{{\nu }_{\mu }}=750$ MeV and three different values for the lepton scattering angle ${\theta }_{\mu }$. The top panels show the combined 1p1h and 2p2h cross sections. The middle panels show the correction of the SRCs on the 1p1h cross section and the bottom panels show the 2p2h SRC part of the cross section.