First usage of Intra-Nuclear Cascade of Liège (INCL) model for nuclear transport of protons from neutrino-nucleus scattering

Neutrino oscillation physics enters the precision era, and the modeling of neutrino-nucleus interactions constitutes a challenging source of systematic uncertainty for such measurements. A new generation of detectors is being developed to measure the complete (exclusive) final state of particles resulting from neutrino interactions. To fully benefit from the improved detector capabilities, precise simulations of the nuclear effects on the final-state nucleons are needed. We have employed the Intra-Nuclear Cascade of Liège model to simulate the propagation of hadrons through the nuclear medium after the neutrino interaction to address this problem. We present a characterization of the hadronic final state after Final State Interactions (FSI) and comparisons to available measurements of transverse kinematic imbalance. The study presented here [1] is a crucial milestone towards the precise simulation of final state interactions in neutrino-nucleus interactions and a complete estimation of related uncertainties.


Introduction
Modern accelerator technology can produce a neutrino beam with a known direction, but the crucially important beam energy is not known event-by-event but only on average through the flux distribution.The neutrino-nucleus interactions are one of the most important biases on neutrino energy reconstruction and event classification.A new generation of near detectors is being developed for an accurate and comprehensive reconstruction of the final-state particles.We need reliable Monte-Carlo models that describe the exclusive final states of the neutrino-nucleus interaction to use the new near detectors upgrades' capabilities fully.In this study, we want to employ the INCL model that is not initially designed for neutrino-nucleus interaction simulations but is a nuclear-physics model that is mainly used for the prediction of the total nuclear reaction cross sections and is successfully compared against the extensive list of experimental data [2,3].
INCL is primarily a nuclear model dedicated to the simulation of the reactions induced by baryons (nucleons, Λ, Σ), mesons (pions and Kaons) or light nuclei (A ≤ 18) on a target nucleus.Currently, the neutrino is not among the available projectiles in INCL so we will use the neutrino vertex simulated by another Monte Carlo event generator, NuWro [4].NuWro is a neutrino generator widely used in the neutrino community.More details about NuWro can be found in [5].
INCL nuclear model is mainly classical, with the inclusion of some additional ingredients to mimic quantum effects.Unlike the NuWro cascade model, where particles are propagated in the continuous medium (space-like cascade model), each INCL nucleon is attributed with its position and momentum and moves freely in the potential well.In INCL, position and momentum are correlated, but this correlation is made less strict using HFB (Hartree-Fock-Bogoliubov) formalism, also to consider the quantum properties of the wave functions [6].
There are two main options for the Pauli blocking modelling available in INCL: the strict model that forbids any interaction below the Fermi momentum and the statistical one that takes into account only nearby nucleons and acts only in the given phase-space.The default option applies strict Pauli blocking to the first interaction and statistical Pauli blocking to the consecutive interactions.Since in the presented study the first interaction is a neutrino interaction taken from NuWro, we use only a statistical Pauli blocking model in INCL.
Inside the cascade, there are a few possible scenarios of events.The participant can interact with nucleons of the target nucleus and, for some particles, can decay.If trying to leave the nuclear medium, the particle can be either deflected back inside the nuclear medium or emitted from the nucleus.If the nucleon is about to be ejected from the nucleus, with some probability, it can clusterize with nearby nucleons and leave the nucleus as a nuclear cluster.Nuclear cluster production is a remarkable feature of INCL that is known and benchmarked for the need of nuclear physics but is absent in any current neutrino generator.
INCL can be coupled to de-excitation models such as ABLA, but in the present study, we are interested in comparing cascade models between each other, so we do not enable any deexcitation model after the cascade.
Here we discuss some differences between INCL and NuWro cascade models in Charged-Current Quasi-Elastic (CCQE) muon neutrino interactions on carbon using the T2K neutrino energy flux at the near detector.We focus on modelling the Single Transverse Variables (STV) that are sensitive to nuclear effects.

Results
We will focus on Single Transverse Variables that can be measured experimentally and are extensively described in [7].STV are defined in the transverse plane with respect to the neutrino direction.The first variable of interest is the δp T : where p p T is the transverse component of the leading proton (a proton with the highest momentum).The unique feature of δp T is its sensitivity to the Fermi Motion: if the neutrino interacted on the nucleon at rest, we would expect δp T to be equal to zero.Final State Interactions might smear this distribution by shifting the position of the peak and contribution to the long tail in the high δp T region.Fig. 1 supports these conclusions: the bulk of the distribution corresponds to the channel with no FSI, and FSI channels give a significant contribution to the high energetic tail.The overall δp T distribution is very similar for both INCL and NuWro, which is expected since the vertex simulation and, therefore, Fermi motion modelling comes from NuWro.
The second variable we will focus on is the transverse boosting angle δα T : where p µ T is the transverse component of the muon momentum and δ p T is the vector sum of the transverse components of the final nucleon momentum and muon momentum and is discussed below.
Typically, FSI tends to decelerate the outgoing particles, which corresponds to δα T being more than 90 degrees, so we expect the enhancement of the distribution in the high δα for the FSI events.This behaviour is also shown in Fig. 2. The "no FSI" part that contains the events with no change of energy of the proton and no production of additional particles is uniform.At the same time, channels with FSI (one proton, multiple nucleons, and multiple nucleons with pions production) feature the excess of events for the δα T higher than 90 degrees.This behaviour is similar for both INCL and NuWro models, but the shape of the FSI part in the region of interest diverges between the two simulations: INCL tends to suppress the high δα T values that are populated by low momentum protons.We associate this divergence with the difference in the Pauli Blocking models used in INCL and NuWro.Especially in fig.2, the differences between the two models are noticeably pronounced.Nevertheless, while compared to the T2K [8] or MINERvA [9] data, the applied cuts of the current detector acceptance minimize the discrepancies between the two models.We await future measurements with the lower detector threshold to be able to constrain the nuclear effects better.

Conclusions
We have compared the simulation of the final state interactions for the muon neutrino CCQE reaction, modelled with INCL and NuWro.We have described the modification of the leading proton kinematics caused by FSI and illustrated its impact on experimental observables such as STV.Regarding δα T , the low energy protons correspond to the high δα T region that is sensitive to FSI.The proton momentum threshold of current detectors seriously limits the sensitivity of the available data to the difference between the two FSI models.The studies are ongoing to provide more precise measurements of the low-momentum particles.
The results of this study are an essential step towards accurately simulating FSI in neutrinonucleus interactions and comprehensively evaluating associated uncertainties.