CERN Accelerating science

Top: nuclear transparency of $^{12}$C (ratio of a number of events without FSI to all events) depending on the position of the neutrino interaction inside the nucleus, simulated with INCL. The y-coordinate is averaged out to the 5 slices. The direction of the Z-axis corresponds to the neutrino direction. The center of the coordinate system is in the center of the nucleus. Bottom: nuclear transparency of $^{12}$C simulated with INCL and NuWro. The direction of the Z-axis corresponds to the outgoing proton direction. The center of the coordinate system is in the center of the nucleus. The solid lines are digitized from~\cite{Pandharipande:1992zz}.

Top: nuclear transparency of $^{12}$C (ratio of a number of events without FSI to all events) depending on the position of the neutrino interaction inside the nucleus, simulated with INCL. The y-coordinate is averaged out to the 5 slices. The direction of the Z-axis corresponds to the neutrino direction. The center of the coordinate system is in the center of the nucleus. Bottom: nuclear transparency of $^{12}$C simulated with INCL and NuWro. The direction of the Z-axis corresponds to the outgoing proton direction. The center of the coordinate system is in the center of the nucleus. The solid lines are digitized from~\cite{Pandharipande:1992zz}.

Missing energy profile extracted from the hole spectral function of Carbon~\cite{BENHAR1994493}. The area under the "SF profile" distribution is normalized to one. The highlighted area, labelled "$1p_{3/2}$", represents the expected contribution of valence nucleons, as described in the text.

Top: excitation energy of the nuclear remnant after neutrino interactions. "SF" is the calculation in the pure PWIA approach, while "SF+INCL" is the result after the cascade, as described in the text. Bottom: excitation energy of the nuclear remnant after neutrino interactions for $169.5 < p_m < 174.5$~MeV, as presented in Ref.~\cite{VanDerSteenhoven:1988um}. Data are digitalized from Ref.~\cite{VanDerSteenhoven:1988um}. The s-shell contribution is approximated with a linear fit. The first three peaks were included in the model, while the next three were neglected.

Top: excitation energy of the nuclear remnant after neutrino interactions. "SF" is the calculation in the pure PWIA approach, while "SF+INCL" is the result after the cascade, as described in the text. Bottom: excitation energy of the nuclear remnant after neutrino interactions for $169.5 < p_m < 174.5$~MeV, as presented in Ref.~\cite{VanDerSteenhoven:1988um}. Data are digitalized from Ref.~\cite{VanDerSteenhoven:1988um}. The s-shell contribution is approximated with a linear fit. The first three peaks were included in the model, while the next three were neglected.

Proton momentum before (left) and after (right) FSI in CCQE events with T2K neutrino energy flux. Top: INCL, middle: INCL + ABLA, bottom: NuWro SF. The shape of proton momentum before FSI is by definition identical for INCL and NuWro cascades. The 0 proton channel in NuWro includes muon only and pion and neutron production. There is no cluster production in NuWro.

Proton momentum before (left) and after (right) FSI in CCQE events with T2K neutrino energy flux. Top: INCL, middle: INCL + ABLA, bottom: NuWro SF. The shape of proton momentum before FSI is by definition identical for INCL and NuWro cascades. The 0 proton channel in NuWro includes muon only and pion and neutron production. There is no cluster production in NuWro.

Proton momentum before (left) and after (right) FSI in CCQE events with T2K neutrino energy flux. Top: INCL, middle: INCL + ABLA, bottom: NuWro SF. The shape of proton momentum before FSI is by definition identical for INCL and NuWro cascades. The 0 proton channel in NuWro includes muon only and pion and neutron production. There is no cluster production in NuWro.

Proton momentum before (left) and after (right) FSI in CCQE events with T2K neutrino energy flux. Top: INCL, middle: INCL + ABLA, bottom: NuWro SF. The shape of proton momentum before FSI is by definition identical for INCL and NuWro cascades. The 0 proton channel in NuWro includes muon only and pion and neutron production. There is no cluster production in NuWro.

Proton momentum before (left) and after (right) FSI in CCQE events with T2K neutrino energy flux. Top: INCL, middle: INCL + ABLA, bottom: NuWro SF. The shape of proton momentum before FSI is by definition identical for INCL and NuWro cascades. The 0 proton channel in NuWro includes muon only and pion and neutron production. There is no cluster production in NuWro.

Proton momentum before (left) and after (right) FSI in CCQE events with T2K neutrino energy flux. Top: INCL, middle: INCL + ABLA, bottom: NuWro SF. The shape of proton momentum before FSI is by definition identical for INCL and NuWro cascades. The 0 proton channel in NuWro includes muon only and pion and neutron production. There is no cluster production in NuWro.

Average number of particles produced per event for INCL, INCL coupled with ABLA and NuWro. NuWro produces only protons and neutrons.

$\dalphat$ (left) and $\dpt$ (right) simulated with INCL (top), INCL+ABLA (middle), and NuWro (bottom) models for CCQE events and T2K neutrino flux.

$\dalphat$ (left) and $\dpt$ (right) simulated with INCL (top), INCL+ABLA (middle), and NuWro (bottom) models for CCQE events and T2K neutrino flux.

$\dalphat$ (left) and $\dpt$ (right) simulated with INCL (top), INCL+ABLA (middle), and NuWro (bottom) models for CCQE events and T2K neutrino flux.

$\dalphat$ (left) and $\dpt$ (right) simulated with INCL (top), INCL+ABLA (middle), and NuWro (bottom) models for CCQE events and T2K neutrino flux.

$\dalphat$ (left) and $\dpt$ (right) simulated with INCL (top), INCL+ABLA (middle), and NuWro (bottom) models for CCQE events and T2K neutrino flux.

$\dalphat$ (left) and $\dpt$ (right) simulated with INCL (top), INCL+ABLA (middle), and NuWro (bottom) models for CCQE events and T2K neutrino flux.

$\dalphat$ simulated with INCL, INCL+ABLA and NuWro comparison to the T2K (top) and MINER$\nu$A (bottom) data.

$\dalphat$ simulated with INCL, INCL+ABLA and NuWro comparison to the T2K (top) and MINER$\nu$A (bottom) data.

$\dalphat$ simulated with INCL+ABLA (solid lines) and NuWro (dashed lines) with no cuts on muon angle ($\Theta_\mu$) and different options of detector acceptance for the leading proton momentum threshold ($p_p$). The bottom panel presents the ratios of NuWro and INCL+ABLA models for different cuts applied.

Momentum distribution of some particles produced during cascade and de-excitation.

Shape comparison of the neutrino energy reconstruction. Top: all events simulated with NuWro, INCL, and INCL+ABLA, neutrino energy reconstruction using all outgoing particles; middle: INCL+ABLA simulation of the FSI events with proton and muon only and with all outgoing particles; bottom: INCL+ABLA simulation of the no FSI events with proton and muon only and with all outgoing particles.

Shape comparison of the neutrino energy reconstruction. Top: all events simulated with NuWro, INCL, and INCL+ABLA, neutrino energy reconstruction using all outgoing particles; middle: INCL+ABLA simulation of the FSI events with proton and muon only and with all outgoing particles; bottom: INCL+ABLA simulation of the no FSI events with proton and muon only and with all outgoing particles.

Shape comparison of the neutrino energy reconstruction. Top: all events simulated with NuWro, INCL, and INCL+ABLA, neutrino energy reconstruction using all outgoing particles; middle: INCL+ABLA simulation of the FSI events with proton and muon only and with all outgoing particles; bottom: INCL+ABLA simulation of the no FSI events with proton and muon only and with all outgoing particles.

Total visible energy deposited by all particles in the event obtained with the Geant4 simulation of the CH cube in the 1(3)~cm sphere around the neutrino vertex.

Average vertex activity as a fraction of the initial neutrino energy depending on the neutrino energy, simulated with NuWro (top) and INCL+ABLA (bottom). The leading proton and muon are not considered. The bands correspond to the standard deviation uncertainty.

Average vertex activity as a fraction of the initial neutrino energy depending on the neutrino energy, simulated with NuWro (top) and INCL+ABLA (bottom). The leading proton and muon are not considered. The bands correspond to the standard deviation uncertainty.

Average sum of the kinetic energy of all clusters, neutrons, and non-leading protons in the event as a fraction of the initial neutrino energy depending on the neutrino energy simulated with INCL+ABLA and NuWro. The bands correspond to the standard deviation uncertainty.