Quasielastic neutrino charged-current scattering off ${}^{12}\mathrm{C}$: Effects of the meson exchange currents and large nucleon axial mass

The quasielastic scattering of muon neutrino and electrons on a carbon target are analyzed using the relativistic distorted-wave impulse approximation (RDWIA). We also evaluate the contribution of the two-particle and two-hole meson exchange current ($2p\text{−}2h$ MEC) to electroweak response functions. The nuclear model dependence of the (anti)neutrino cross sections is studied within the RDWIA+MEC approach and RDWIA model with the large nucleon axial mass. It is shown that the results for the squared momentum transfer distribution $d\sigma /d{Q}^2$ and for invariant mass of the final hadronic system distribution $d\sigma /dW$ obtained within these models are substantially different.

Figure 1

(a) Longitudinal and (b) transverse response functions at $\left|\mathbf{q}\right|=300$ MeV/$c$ versus energy transfer $\omega$ for electron scattering on ${}^{12}C(e,e^{\prime })$. The solid line is the the RDWIA + MEC results, the dashed line is the contribution from the $NN$-correlated pairs in (a) and the contribution from the RDWIA in (b). The dash-dotted line in (b) is the $2p\text{−}2h$ MEC contributions. The data points are from Refs. [23, 24].

Figure 2

Same as in Fig. 1, but the longitudinal and transverse responses at $\left|\mathbf{q}\right|=400$ MeV/$c$ are shown in (a), (c) and at $\left|\mathbf{q}\right|=380$ MeV/$c$ in (b), (d). As shown in the key the data points are from Refs. [23, 24].

Figure 3

Same as in Fig. 2, but at $\left|\mathbf{q}\right|=550$ MeV/$c$ and $\left|\mathbf{q}\right|=570$ MeV/$c$.

Figure 4

Inclusive cross section versus energy transfer $\omega$ for electron scattering on ${}^{12}\mathrm{C}$. The solid line is the RDWIA + MEC results, the dashed line is the $2p\text{−}2h$ MEC contributions, and the dashed-dotted line is the contribution from the RDWIA. The data are from Ref. [60] (filled triangles), Ref. [23] (filled squares), Ref. [61] (filled circles). In Ref. [60] data are for the electron beam energy $E=1500$ MeV, and scattering angle $\theta =11.{95}^{\circ },\theta =13.{54}^{\circ }$; in Ref. [23] data are for $E=680$ MeV and $\theta ={36}^{\circ }$; in Ref. [61] data are for $E=500$ MeV and $\theta ={60}^{\circ }$.

Figure 5

Same as in Fig. 4, but the data are from Ref. [62] (open circle) for the electron beam energy $E=730$ MeV and $\theta =37.1^{\circ }$; Ref. [23] (filled squares) for $E=560$ MeV and $\theta ={60}^{\circ }$ and $E=620$ MeV and $\theta ={60}^{\circ }$; Ref. [63, 64] for $E=2130$ MeV and $\theta ={16}^{\circ }$.

Figure 6

Inclusive cross section (top) and ratios $R\left(MEC\right)$ and $R(M_A=1.35)$ (bottom) vs the muon energy for neutrino and antineutrino scattering on ${}^{12}\mathrm{C}$ and for incoming neutrino energy ${\varepsilon }_{\nu }=2$ GeV. In the top panels the solid line is the RDWIA+MEC calculation, the dash-dotted line is the RDWIA ($M_A=1.35$ GeV) calculation, whereas the dashed and dotted lines are the $\mathrm{RDWIA}(M_A=1.03$ GeV) and MEC contributions to the RDWIA+MEC cross sections. In the bottom panel the solid and dashed lines are the $R\left(MEC\right)$ and $R(M_A=1.35)$ ratios, respectively.

Figure 7

Same as in Fig. 6, but for $d\sigma /d{Q}^2$ cross section vs the $Q^2$.

Figure 8

Same as in Fig. 6, but for $d\sigma /dW$ cross section vs the $W$.

Figure 9

Total cross sections for QE and QE+MEC scattering of muon neutrino (top) and antineutrino (bottom) on ${}^{12}\mathrm{C}$ as a function of incoming (anti)neutrino energy. Data points for different targets are from Refs. [47, 48, 67, 68, 69, 70, 71]. Also shown are predictions of the RDWIA+MEC (solid line), $\mathrm{RDWIA}(M_A=1.35$ GeV) (dashed line), $\mathrm{RDWIA}(M_A=1.03$ GeV) (dash-dotted line), and $2p\text{−}2h$ MEC (dotted line).