Short-Range Correlations and Transverse Response Enhancement from Meson-Exchange Currents

TL;DR

The paper tackles the excess transverse strength observed in inclusive electron-nucleus scattering by examining short-range correlations (SRC) as a key ingredient in meson-exchange-current (MEC) effects on the 1p1h channel. It develops a microscopic framework in nuclear matter using the Bethe-Goldstone equation with the Granada $2013$ NN potential to generate correlated high-momentum pairs, and computes the interference between one-body and two-body MEC (seagull, pion-in-flight, and $\Delta$) in the transverse response. The main finding is that SRC induce a sizable, tensor-driven enhancement of the transverse $1p1h$ MEC response, with the dominant contribution arising from the $^3S_1$-$^3D_1$ channel, in qualitative agreement with correlated-basis-function results. When integrated into a SuSA-based hybrid model for $^{12}$C, the SRC-enhanced MEC contribution brings the calculated transverse response into closer agreement with data at low and intermediate momentum transfer, underscoring the importance of SRC and MEC in realistic descriptions of quasielastic scattering and neutrino-nucleus interactions.

Abstract

We investigate the role of short-range correlations (SRC) in the transverse nuclear response within the quasielastic peak region, focusing on the 1p1h channel. The calculation is performed in nuclear matter by solving the Bethe-Goldstone equation with the realistic Granada 2013 nucleon-nucleon potential, including both one-body and two-body meson-exchange currents (MEC) of seagull, pion-in-flight, and $Δ$ types. We find that MEC produce a sizable enhancement of the transverse response in the 1p1h channel when acting on correlated nucleon pairs with high-momentum components generated by SRC. This contrasts with the uncorrelated case, where MEC, dominated by the $Δ$ current, can even yield a negative effect. The results are consistent with previous findings based on the correlated basis function approach, supporting the interpretation that SRC play a central role in the transverse response enhancement from MEC.

Figures (5)

• Figure 1: Feynman diagrams illustrating the action of the two-body MEC on the high-momentum components of the correlated nucleon pair. The exchange contributions of the seagull and pionic (top), and $\Delta$ (bottom) currents are shown, where the photon is absorbed by the high-momentum intermediate legs generated by the correlation between nucleons $h$ and $k$.
• Figure 2: Comparison of the transverse 1p1h interference responses, obtained in the present calculation (left panels) for $^{12}$C, with those from the correlated basis function (CBF) calculation of Fabrocini Fab97 (right panels). The separate contributions from seagull (OB/C, red lines), pionic (OB/$\pi$, green lines), and $\Delta$ (OB/$\Delta$, black lines) currents are shown for momentum transfers $q=400$ MeV/c and $q=550$ MeV/c. In the left panels we show the results without (FG) correlations and total. In the right panels we show the results with Jastrow correlations only (J) and the total.
• Figure 3: Separate contributions to the interference transverse response of $^{12}$C for $q=380$ MeV/c, from different channels in the multipole expansion of the correlated wave function. Top panels: uncoupled channels with $S=0$ and $S=1$. Middle panels: coupled channels with $S=1$, $J=1$. Bottom panels: coupled channels with $S=1$, $J=2$. The dominant contribution clearly arises from the $^3S_1$--$^3D_1$ channel, showing the decisive role of tensor correlations in the nuclear medium.
• Figure 4: (Color online) Longitudinal response function of $^{12}$C for three values of the momentum transfer $q$ within the SuSA model. The model assumes factorization of the response into the single-nucleon contribution times the scaling function $f_L(\psi')$. Data are taken from Ref. Jou96Bod22.
• Figure 5: Transverse response of $^{12}$C in the hybrid model for different momentum transfers. The one-body (1b) contribution from SuSA is shown, together with the uncorrelated FG 1b–2b interference and the total including correlations. The inclusion of the correlation contribution produces a positive enhancement, bringing the theoretical prediction closer to the experimental data. Data are taken from Ref. Jou96Bod22.