Quasi-Elastic (QE) Region
For the neutrino energy between 0.1 GeV and 1 GeV, the Quasi-Elastic (QE) process dominates the neutrino-nucleus reactions. This process is very important in the long-baseline experiments such as at T2K, because the neutrino-oscillation experiments must reconstruct the neutrino energy by selecting events from the charged current (CC) QE process.
The spectral function of nuclei  is known to be a key to calculating the QE process and pion productions in the neutrino-nucleus reactions with accuracy. The nuclear spectral functions P(p,E) is the probability of removing a nucleon of momentum p from ground state of the nucleus leaving the residual nucleus with excitation energy E.
A current issue in the spectral function approach is to better understand effects of 2p-2h (2-particle-2-hole) configuration and/or MEC (meson-exchange current) in the QE process. This subject has been raised by several recent experiments on the QE cross section measurement . The data seem to indicate a considerable contribution from 2p-2h and/or MEC effects, and have motivated active theoretical studies  including us.
 O. Benhar, N. Farina, H. Nakamura, M. Sakuda, and R. Seki, Phys. Rev. D 72, 053005 (2005).
 R. Gran et al. (K2K), Phys. Rev. D 74 052002 (2006); A.A. Aguilar-Arevalo et al. (MiniBooNE), Phys. Rev. Lett. 100, 032301 (2008); ibid Phys.Rev.D 81 092005 (2010); V. Lyubushkin et al. (NOMAD), Eur. Phys. J. C 63 355 (2009).
 M. Martini, M. Ericson, G. Chanfray, and J. Marteau, Phys. Rev. C 80 065501 (2009); J. Nieves, I. Ruiz Simo, and M.J. Vicente Vacas, Phys. Lett. B 707 72 (2012).
Resonance (RES) Region
The neutrino-nucleus reactions in the Resonance (RES) region are multi-channel reactions, where the single-pion and double-pion production cross sections become comparable, and η and kaon productions also take place with smaller cross sections. A particular feature in this region is the appearance of the nucleon excitations (N*), which can exist only as unstable resonances in the reaction processes. One must deal with this kind of complecated multichannel and multiresonance reactions to describe the neutrino-nucleus interactions in the RES region.
An ideal approach is to extend a unitary dynamical coupled-channels (DCC) model , which was originally developed to study the N* resonances through the π- and γ-induced πN, ηN, ππN, KΛ, and KΣ production reactions in the RES region and successfully manages complications associated with the multichannel and multiresonance nature of the reactions. A first application of the DCC model to the neutrino-induced meson production reactions at forward angle limit has been made, by invoking Partially Conserved Axial Current (PCAC) hypothesis .
The current DCC model for the neutrino reaction is limited to only the forward kinematics. In this project, we will extend the model so that we can analyze the neutrino reaction of all kinematics in the RES region.
 H. Kamano, S.X. Nakamura, T.-S.H. Lee, and T. Sato, arXiv:1305.5341;
A. Matsuyama, T. Sato, and T.-S.H. Lee, Phys. Rep. 439, 193 (2007).
 H. Kamano, S.X. Nakamura, T.-S.H. Lee, and T. Sato, Phys. Rev. D 86, 097503 (2012).
Deep Inelastic Scattering (DIS) Region
The Deep Inelastic Scattering (DIS) region of neutrino-nucleus reactions corresponds to the kinematical conditions of Q2 ≥ 1 GeV2 and W2 ≥ 4 GeV2, and the cross sections or structure functions are described by the parton model.
The neutrino-nucleus cross section via the charged current is characterized by the three nuclear structure functions FA1, FA2, and FA3, which are expressed in terms of the nuclear parton distribution functions (NPDFs), fAi, i=u,d,s,...). The NPDFs have been extracted by a global analysis of experimental data on lepton-nucleus DIS and Drell-Yan processes with nuclear targets .
Neutrino DIS data interested in this project can be included in the global analysis for extracting the NPDFs. However, one should be careful that nuclear modification data such as FA2 / FD2, where D indicates the deuteron, are not available in the neutrino scattering. Recently, there are some discussions on possible differences between nuclear modifications of charged-lepton and neutrino reactions.
M. Hirai, S. Kumano, and M. Miyama, Phys. Rev. D 64, 034003 (2001); M. Hirai, S. Kumano, and T.-H. Nagai, Phys. Rev. C 70, 044905 (2004); ibid, 76, 065207 (2007); M. Hirai, S. Kumano, and K. Saito, AIP Conf. Proc. 1189, 269 (2009).