Contribution of two-particle–two-hole final states to the nuclear response

The excitation of two-particle–two-hole final states in neutrino-nucleus scattering has been advocated by many authors as the source of the excess cross section observed by the MiniBooNE Collaboration in the quasielastic sector. We analyze the mechanisms leading to the appearance of these final states and illustrate their significance through the results of accurate calculations of the nuclear electromagnetic response in the transverse channel. A novel approach, allowing for a consistent treatment of the amplitudes involving one- and two-nucleon currents in the kinematical region in which the nonrelativistic approximation breaks down, is outlined, and its preliminary results are reported.

Figure 1

Transverse response function of ${}^4\mathrm{He}$, obtained within the approach of Ref. [18]. The shaded area shows the results of the full calculation, with the associated uncertainty arising from the inversion of the Euclidean response, while the dotted line has been obtained including the one-nucleon current only. The dot-dashed line represents the response computed neglecting the interference term, the contribution of which is displayed by the dashes. The data are taken from Ref. [13].

Figure 2

Sum rule of the electromagnetic response of carbon in the transverse channel. The dashed line shows the results obtained including the one-nucleon current only, while the solid line corresponds to the full calculation. The dot-dashed line represents the sum rule computed neglecting the interference term, the contribution of which is displayed by the dotted line. The results are normalized so that the dashed line approaches unity as $\left|\mathbf{q}\right|\to \infty$. Monte Carlo errors bars are not visible on the scale of the figure.

Figure 3

Cross section of the process $e+{}^{12}\mathrm{C}\to e^{\prime }+X$ at beam energy $E_e=961$ MeV and electron scattering angle ${\theta }_e=37.5^{\circ }$, computed using Eq. (17) with the spectral function of Ref. [20]. The solid line shows the results of the full calculation, while the breakdown into 1p1h and 2p2h contributions is illustrated by the dot-dashed and dashed lines, respectively.

Figure 4

Electron-carbon cross section obtained from Eq. (17) using relativistic (solid line) and nonrelativistic (dashed line) kinematics. The experimental data are from Ref. [23].

Figure 5

Relative momentum distribution of a nucleon pair in isospin-symmetric nuclear matter at equilibrium density.

Figure 6

Electromagnetic response of carbon in the transverse channel, at momentum transfer $\left|\mathbf{q}\right|=570$ MeV. The solid line represents the results of the full calculation, whereas the dashed line has been obtained including only amplitudes involving the one-body current. The contributions arising from the two-nucleon current are illustrated by the dot-dashed and dotted lines, corresponding to the pure two-body current transition probability and the interference term, respectively. The experimental data are taken from Ref. [28].