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Register a new userMeson-exchange currents and superscaling analysis with relativistic effective mass of quasielastic electron scattering from $^{12}$C
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We reanalyze the scaling properties of inclusive quasielastic electron scattering from $^{12}$C by subtracting from the data the effects of two-particle emission. A model of relativistic meson-exchange currents (MEC) is employed within the mean field theory of nuclear matter, with scalar and vector potentials that induce an effective mass and a vector energy to the nucleons. A new phenomenological quasielastic scaling function is extracted from a selection of the data after the subtraction of the 2p-2h contribution. The resulting superscaling approach with relativistic effective mass (SuSAM*) can be used to compute the genuine quasielastic cross section without contamination of the 2p-2h channel that can then be added separately to obtain the total quasielastic plus two-nucleon emission response.
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We present a global analysis of the inclusive quasielastic electron scattering data with a superscaling approach with relativistic effective mass. The SuSAM* model exploits the approximation of factorization of the scaling function $f^*(psi^*)$ out of the cross section under quasifree conditions. Our approach is based on the relativistic mean field theory of nuclear matter where a relativistic effective mass for the nucleon encodes the dynamics of nucleons moving in presence of scalar and vector potentials. Both the scaling variable $psi^*$ and the single nucleon cross sections include the effective mass as a parameter to be fitted to the data alongside the Fermi momentum $k_F$. Several methods to extract the scaling function and its uncertainty from the data are proposed and compared. The model predictions for the quasielastic cross section and the theoretical error bands are presented and discussed for nuclei along the periodic table from $A=2$ to $A=238$: $^2$H, $^3$H, $^3$He, $^4$He, $^{12}$C, $^{6}$Li, $^{9}$Be, $^{24}$Mg, $^{59}$Ni, $^{89}$Y, $^{119}$Sn, $^{181}$Ta, $^{186}$W, $^{197}$Au, $^{16}$O, $^{27}$Al, $^{40}$Ca, $^{48}$Ca, $^{56}$Fe, $^{208}$Pb, and $^{238}$U. We find that more than 9000 of the total $sim 20000$ data fall within the quasielastic theoretical bands. Predictions for $^{48}$Ti and $^{40}$Ar are also provided for the kinematics of interest to neutrino experiments.
We review some recent progress in the study of electroweak interactions in nuclei within the SuSAv2-MEC model. The model has the capability to predict (anti)neutrino scattering observables on different nuclei. The theoretical predictions are compared with the recent T2K $ u_mu-^{16}$O data and good agreement is found at all kinematics. The results are very similar to those obtained for $ u_mu-^{12}$C scattering, except at low energies, where some differences emerge. The role of meson-exchange currents in the two-particle two-hole channel is analyzed in some detail. In particular it is shown that the density dependence of these contributions is different from what is found for the quasielastic response.
The experimental data from quasielastic electron scattering from $^{12}$C are reanalyzed in terms of a new scaling variable suggested by the interacting relativistic Fermi gas with scalar and vector interactions, which is known to generate a relativistic effective mass for the interacting nucleons. By choosing a mean value of this relativistic effective mass $m_N^* =0.8 m_N$, we observe that most of the data fall inside a region around the inverse parabola-shaped universal scaling function of the relativistic Fermi gas. This suggests a method to select the subset of data that highlight the quasielastic region, about two thirds of the total 2,500 data. Regardless of the momentum and energy transfer, this method automatically excludes the data that are not dominated by the quasielastic process. The resulting band of data reflects deviations from the perfect universality, and can be used to characterize experimentally the quasielastic peak, despite the manifest scaling violation. Moreover we show that the spread of the data around the scaling function can be interpreted as genuine fluctuations of the effective mass $M^* equiv m^*_N/m_N sim 0.8 pm 0.1$. Applying the same procedure we transport the scaling quasielastic band into a theoretical prediction band for neutrino scattering cross section that is compatible with the recent measurements and slightly more accurate.
The present study is focused on the superscaling behavior of electron-nucleus cross sections in the region lying above the quasielastic peak, especially the region dominated by electroexcitation of the Delta. Non-quasielastic cross sections are obtained from all available high-quality data for Carbon 12 by subtracting effective quasielastic cross sections based on the superscaling hypothesis. These residuals are then compared with results obtained within a scaling-based extension of the relativistic Fermi gas model, including an investigation of violations of scaling of the first kind in the region above the quasielastic peak. A way potentially to isolate effects related to meson-exchange currents by subtracting both impulsive quasielastic and impulsive inelastic contributions from the experimental cross sections is also presented.
We develop a model of relativistic, charged meson-exchange currents (MEC) for neutrino-nucleus interactions. The two-body current is the sum of seagull, pion-in-flight, pion-pole and $Delta$-pole operators. These operators are obtained from the weak pion-production amplitudes for the nucleon derived in the non-linear $sigma$-model together with weak excitation of the $Delta(1232)$ resonance and its subsequent decay into $Npi$. With these currents we compute the five 2p-2h response functions contributing to $( u_l,l^-)$ and $(overline{ u}_l,l^+)$ reactions in the relativistic Fermi gas model. The total current is the sum of vector and axial two-body currents. The vector current is related to the electromagnetic MEC operator that contributes to electron scattering. This allows one to check our model by comparison with the results of De Pace {em et al.,} Nuclear Physics A 726 (2003) 303. Thus our model is a natural extension of that model to the weak sector with the addition of the axial MEC operator. The dependences of the response functions on several ingredients of the approach are analyzed. Specifically we discuss relativistic effects, quantify the size of the direct-exchange interferences, and the relative importance of the axial versus vector current.
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