Seagull and pion-in-flight currents in neutrino-induced $1N$ and $2N$ knockout

Background: The neutrino-nucleus ($\nu A$) cross section is a major source of systematic uncertainty in neutrino-oscillation studies. A precise $\nu A$ scattering model, in which multinucleon effects are incorporated, is pivotal for an accurate interpretation of the data.

Purpose: In $\nu A$ interactions, meson-exchange currents (MECs) can induce two-nucleon ($2N$) knockout from the target nucleus, resulting in a two-particle two-hole (2p2h) final state. They also affect single nucleon ($1N$) knockout reactions, yielding a one-particle one-hole (1p1h) final state. Both channels affect the inclusive strength. We present a study of axial and vector, seagull and pion-in-flight currents in muon-neutrino induced $1N$ and $2N$ knockout reactions on ${}^{12}C$.

Method: Bound and emitted nucleons are described as Hartree-Fock wave functions. For the vector MECs, the standard expressions are used. For the axial current, three parametrizations are considered. The framework developed here allows for a treatment of MECs and short-range correlations (SRCs).

Results: Results are compared with electron-scattering data and with literature. The strengths of the seagull, pion-in-flight, and axial currents are studied separately and double differential cross sections including MECs are compared with results including SRCs. A comparison with MiniBooNE and T2K data is presented.

Conclusions: In the 1p1h channel, the effects of the MECs tend to cancel each other, resulting in a small effect on the double differential cross section. $2N$ knockout processes provide a small contribution to the inclusive double differential cross section, ranging from the $2N$ knockout threshold into the dip region. A fair agreement with the MiniBooNE and T2K data is reached.

Figure 1

The vector current diagrams considered in this paper. The boson $X$ can be either a $\gamma$ or a $W^{+}$ in this work. Diagram (a) shows the 1p1h channel in the impulse approximation (IA), diagrams (b), (d), (e), and (g) are the 1p1h and 2p2h seagull diagrams; and (c) and (f) are the pion-in-flight diagrams. The $p$ and $h$ denote the single-nucleon particle and hole states.

Figure 2

Diagrams considered in the axial charge density ${\widehat{\rho }}_A^{\left[2\right],axi}$ derived in Ref. [34], $A_1$ denotes the $A_1$ meson.

Figure 3

The correction of the MECs on the 1p1h responses for ${}^{12}C({\nu }_{\mu },{\mu }^{-})$ at three different $q$.

Figure 4

The ${}^{12}C({\nu }_{\mu },{\mu }^{-}{N}_a{N}_b)$ cross section ($N_a=p,N_b=p^{\prime },\text{n}$) at $E_{{\nu }_{\mu }}=750$ MeV, $E_{\mu }=550$ MeV, ${\theta }_{\mu }={15}^{\circ }$, and proton kinetic energy $T_p=50$ MeV for in-plane kinematics. The bottom plot shows the (${\theta }_a,{\theta }_b)$ regions with $P_{12}<300$ MeV/$c$.

Figure 5

Semiexclusive ${}^{12}C({\nu }_{\mu },{\mu }^{-}p)$ cross section for in-plane kinematics for $E_{{\nu }_{\mu }}=750$ MeV, $E_{\mu }=550$ MeV, and three muon scattering angles. The bottom panel shows the (${\theta }_p,E_m$) area with $P_{12}<300$ MeV/$c$ for ${\theta }_{\mu }={15}^{\circ }$.

Figure 6

The 1p1h and 2p2h MEC response functions $W_{CC}$ and $W_T$ for ${}^{12}C(e,e^{\prime })$ for three values of $q$. The dotted blue line is the contribution of the sea+pif currents, only present in the $W_T$ response. The solid black lines are the 1p1h+2p2h results from [52]; the data sets are from Refs. [53, 54].

Figure 7

The 2p2h MEC response function $W_T$ for ${}^{12}C(e,e^{\prime })$ for three values of $q$. The contributions of the seagull and pion-in-flight currents are shown separately. The solid black lines are the sea+pif results from [52].

Figure 8

The transverse 1p1h and 2p2h responses for ${}^{12}C(e,e^{\prime })$ at $q=500$ MeV/$c$ with only seagull currents. The solid (dashed) black lines are the 1p1h (2p2h) results from Ref. [55].

Figure 9

The Coulomb and transverse 1p1h and 2p2h responses for ${}^{12}C({\nu }_{\mu },{\mu }^{-})$ at $q=500$ MeV/$c$ with only seagull and axial currents. The solid (dashed) black lines are the 1p1h (2p2h) results from Ref. [55].

Figure 10

The 1p1h and 2p2h response functions $W_{CC}$ and $W_T$ for ${}^{12}C({\nu }_{\mu },{\mu }^{-})$ for three values of $q$. The three different axial currents are compared for $W_{CC}$. In the 1p1h calculations IA+MEC the axial current “axi” was used.

Figure 11

Detail of the $W_T$ 2p2h response of Fig. 10. The contributions of the seagull and pion-in-flight currents are shown separately.

Figure 12

The $\omega$ dependence of the ${}^{12}C({\nu }_{\mu },{\mu }^{-})$ cross section for $E_{{\nu }_{\mu }}=750$ MeV and three different values for the lepton scattering angle ${\theta }_{\mu }$. The top panels show the 1p1h and 2p2h cross sections. The bottom panels show the 2p2h part of the cross section, separating the contributions of SRCs and MECs.

Figure 13

MiniBooNE CCQE-like flux-folded double differential cross sections per target neutron for ${}^{12}C({\nu }_{\mu },{\mu }^{-})$. The solid line is the incoherent sum of the CRPA, MEC, and SRC contributions. Data are from Ref. [58], the experimental error bars represent the shape uncertainties, flux uncertainties are not included.

Figure 14

T2K flux-folded double differential cross sections per target nucleon for ${}^{12}C({\nu }_{\mu },{\mu }^{-})$. The solid line is the incoherent sum of the CRPA, MEC, and SRC contributions. The experimental error bars represent the shape uncertainties, flux uncertainties are not included. (a) Inclusive T2K data from Ref. [62]. (b) $\mathrm{CC}0\pi$ T2K data from Ref. [63].