Relativistic meson-exchange currents in lepton-nucleus scattering V. Belocchi Universit`a degli Studi di Torino & INFN, Torino valerio.belocchi@unito.it Formalism When a lepton interacts with a nucleus two -or more- nucleons in the same interaction can be ejected, yielding to a np −nh process. This is a pure nuclear effect. Specifically, we focus on the 2p2h, based on RFG. The nuclear tensor contains matrix elements: wµν ∝⟨F| ˆJ2b† µ |2p2h⟩⟨2p2h| ˆJ2b ν |F⟩ with |F⟩the Fermi sphere and |2p2h⟩the 2p2h state. ˆJ2b µ is a two-body current, that is obtained following the Meson Exchange Currents (MEC) formalism. Subedi et al., Science 320, 1476 (2008) Meson Exchange Currents MEC for the EM-EW interaction, related to ∆resonance -a,b,c,d-, ’contact’ -e,f-, ’pion-in-flight’ -g- and ’pion-pole’ -h,i- currents. J2b µ is a fully relativistic two-body current, corresponding to the coupling of the virtual boson to a pair of nucleons exchanging a pion. It is derived from the Non-Linear σ-model Lagrangian in- vestigated in [1], where the ∆resonance is incorporated ad hoc. On the right exempla of direct and exchange many-body dia- grams, included in our computations, obtained combining two MEC currents. Inclusive process In an inclusive lepton-nucleus scattering only the outgoing lepton is detected: the 2p2h cross section is obtained including every possible hadronic final state with two ejected nucleons. Lepton-nucleus inclusive cross-section: d2σ dEe′dΩe′ = σ0 Lµν ν0 W µν A WA, L nuclear and leptonic tensor We described the 2p2h hadronic tensor in a RFG framework, hence: W µν (2p2h) = 1 4 V (2π)9 X s1,s2,s′ 1,s′ 2 t1,t2,t′ 1,t′ 2 Z hi<kF pi>kF dh1 dh2 dp1 dp2 δ4(p1 + p2 −h1 −h2 −˜q) wµν ˜q := (˜ω, q), ˜ω := ω −E2p2h s , for 12C ⇒E2p2h s = 40 MeV, kF = 228 MeV Integration over holes and particles momenta ⇒less non-vanishing hadronic contributions Results We tested our model with previous inclusive calculations for the electron [2] and for the CC neutrino [3] scattering. Double differential cross section for e 12C and νµ 12C, with quasi-elastic contribution evaluated using RFG nuclear model and the 2p2h, computed using MEC. Electron data are also shown, from archive 10.48550/arXiv.nucl −ex/0603032. Inclusive EW differential cross section as a function of the scattering angle and the energy transfer ω. Incident neutrino energy Eνµ = 550 MeV, corresponding to T2K ND flux peak. Semi-inclusive process J.M. Franco-Pati˜no, PhD Thesis (2024) In a semi-inclusive lepton-nucleus scattering an outgoing nu- cleon is detected in addition to the final lepton.We computed theoretical predictions for detected nucleon p1 lying on the scattering plane, ϕp1 = 0. Lepton-nucleus semi-inclusive cross-section: d6σ dωdΩe′dEmdΩp1 = p1Ep1 (2π)3σ0 Lµν ν0 W µν A(N) W µν A(N) := d W µν A dp1 Em = ω −Ep1 + mN Integration over holes and one particle only momenta ⇒numerous non-vanishing hadronic contributions Results Semi-inclusive predictions, with incident lepton energy E=478 MeV, energy transfer ω=263 MeV, momentum transfer q=303 MeV/c and proton scattering angle θp. Left: electron-carbon scattering, in violet the pion production threshold, data from [4]; right: CC muonic neutrino-carbon scattering, similar predictions can be found in J. Niewczas, PhD Thesis (2023). The isospin separation for ejected nucleons in final state is performed. Conclusion We computed the 2p2h contribution for the inclusive and semi-inclusive lepton-carbon scat- tering, showing preliminary weak predictions. In particular, we tested the EM-MEC formalism comparing with available semi-inclusive data focused in the ’dip’ region. For details, see [5]. Currently the 2p2h component of the cross section is simulated in event generators on the basis of inclusive calculations, necessarily relying on strong approximations. The model aims to provide a reliable description of neutrino-nucleus semi-inclusive 2p2h process, for which a complete microscopic and fully relativistic computation is still absent in t