Description of $\nu$ and $\overline{\nu }$ scattering within quantum hadrodynamic theory

In this paper we develop a model to describe $\nu$ and $\overline{\nu }$ scattering in the GeV region by nuclei within a nuclear matter quantum hadrodynamics approach that is fully relativistic. We simplify it as much as possible, keeping the most relevant effects and trying to describe the greatest number of observables. We introduce explicitly the effect of ground-state correlations through a momentum distribution calculated perturbatively, and also final-state interactions using a perturbed nucleon propagator dressed by a relativistic self-energy containing nucleon-nucleon and $\mathrm{\Delta }$-nucleon correlations. Also, primary $\mathrm{\Delta }$ excitations are considered within a consistent approach. All these mentioned effects are built on together, into the Lehmann representation of the propagator. Within our model we take into account the effect of 2p2h and 3p3h excitations in addition to the quasielastic 1p1h ones, needed to describe the experimental data. The obtained results are promising, showing that the model works quit well and thus putting to disposal a simple but powerful approach developed within the context of nuclear matter field theory.

Figure 1

QE 1p1h response for $\nu$ scattering. For $\overline{\nu }$ scattering we change $n,p,W^{+}\to p,n,W^{-}$. Here, the $W$ boson emitted from the weak vertex is absorbed by $N=n,p$ from the 0p0h component of GS and excited above the Fermi level.

Figure 2

Self-energy contributions in the QHDI. With dashed lines we indicate the scalar (s) and vector (v) meson exchange.

Figure 3

2p2h and 3p3p final states from FSI and GSC contributions are shown. (a) 1p1h excitation generated on the 0p0h GS component and then FSI generate an additional ph pair; (b) and (c) the action on a 2p2h GS component. In (b) hole or particle scattering leads to 2p2h final states while in (c) an additional 1p1h excitation is produced to get 3p3h final states. Interference contributions between excitation amplitudes from (a) and (b) are not shown.

Figure 4

Pion series modifying $\pi$ propagation in nuclear matter.

Figure 5

Contribution to ${\mathrm{\Sigma }}_N$ that lead to 2p1h contribution. In (a) the TPE not correlated are shown, while in (b) TPE correlated with an intermediate $\mathrm{\Delta }$ excitation are depicted. At lowest order $\mathrm{\Pi }$ indicates a ph bubble.

Figure 6

$\mathrm{\Delta }\mathrm{h}$ primary excitation where the $\mathrm{\Delta }$ decays into 2p1h and 3p2h configurations. The interference amplitude from 2p2h contributions in (a) with those in Fig. 3 coming from FSI are not shown.

Figure 7

Left (right) panel double differential cross section for $\nu (\overline{\nu }$) scattering at certain $\cos {\theta }_{\mu }(\cos {\theta }_{{\mu }^{+}}$) selected bins. With dotted lines QE 1p1h response within the RHA is indicated. Dashed lines indicate QE 1p1h + 2p2h (coming from FSI and GSC). Finally full lines also include the $\mathrm{\Delta }h$ excitations that decay into 2p2h and 3p3h final states. Data are obtained from the MiniBooNE experiment of Refs. [12, 13].

Figure 8

Left (right) panel double differential cross section for $\nu (\overline{\nu }$) scattering at certain $T_{\mu }(T_{{\mu }^{+}}$) selected bins. Descriptions of lines and data are the same as in Fig. 7.

Figure 9

Total unfolded and folded $d\sigma /d{Q}^2$ cross sections. Descriptions of the lines and data are the same as in Fig. 7.

Figure 10

Ratio of total unfolded cross sections of neutrinos over antineutrinos for the QE 1p1h(dashed) approach and full with QE+npnh contributions (full lines).