Nuclear Effects and CP Sensitivity at DUNE

The precise measurement of neutrino oscillation parameters is one of the highest priorities in neutrino oscillation physics. To achieve the desired precision, it is necessary to reduce the systematic uncertainties related to neutrino energy reconstruction. An error in energy reconstruction is propagated to all the oscillation parameters, hence a careful estimation of neutrino energy is required. To increase the statistics, neutrino oscillation experiments use heavy nuclear targets like Argon(Z=18). The use of these nuclear targets introduces nuclear effects that severely impact the neutrino energy reconstruction which in turn poses influence in the determination of neutrino oscillation parameters. In this work, we have tried to quantify nuclear effects on the determination of CP phase at DUNE using final state interactions.


I. INTRODUCTION
Neutrino oscillation physics has entered into the era of precision measurement from the past two decades. Significant achievements have been made in the determination of the known neutrino oscillation parameters and continuous attempts are being made to estimate the unknown neutrino oscillation parameters precisely. The neutrino oscillation parameters governing the three flavor neutrino oscillation physics are three mixing angles θ 12 , θ 13 , θ 23 , a leptonic CP phase δ CP and two mass-squared differences, ∆m 2 21 (solar mass splitting) and ∆m 2 31 (atmospheric mass splitting). Many experiments working in collaboration [1][2][3][4] worldwide have led to the precise determination of the above mentioned neutrino oscillation parameters leaving some ambiguities yet to be resolved. The unknown oscillation parameters in the picture are: (1) the octant of θ 23 whether it lies in the lower octant (θ 23 < π/4) or in the higher octant (θ 23 > π/4) (2) the sign of |∆m 2 31 | i.e. neutrino mass eigenstates m i (i=1,2,3) are arranged in normal order (m 1 m 2 m 3 ) or inverted order (m 2 ≈ m 1 m 3 ) (3) the leptonic δ CP phase which can lie in the entire range −π < 0 < +π. Accurate measurement of the leptonic CP phase can lead to further studies on the origin of leptogenesis [5] and baryon asymmetry of the universe [6]. Determination of precise δ CP value is also required for explaining the phenomenon of sterile neutrinos [7]. The global analysis results as indicated in [8] report current bounds on oscillation parameters which have been performed by several experimental groups.
A defining challenge for neutrino experiments is to determine the incoming neutrino energy since the configuration of the outgoing particles and kinematics of the interaction within the nucleus are completely unknown. In collider experiments, the neutrino beams are generated via secondary decay products which assign a broad range of energies to the neutrinos thus causing their energy reconstruction to be difficult. Hence neutrino energy is reconstructed from final state particles. The present-day neutrino oscillation experiments use heavy nuclear targets like argon(Z=18), in ii order to collect large event statistics. With a nuclear target, where neutrinos interact with fermi moving nucleons, uncertainties in the initial state particles produced at the primary neutrino-nucleon interaction vertex arise. These nuclear effects are capable enough to change the identities, kinematics and topologies of the outgoing particles via final state interactions (FSI) and thus hiding the information of the particles produced at the initial neutrino-nucleon interaction vertex which gives rise to fake events. Detailed discussion regarding the impact on atmospheric oscillation parameters due to the presence of FSI in the QE interaction process can be found in [9] and due to fake events stemming from QE and RES processes can be found in [10]. The impact of cross-sectional uncertainties on the CP violation sensitivity can be found in [11]. For futher studies on the impact on neutrino oscillation parameters due the presence of FSI, one can refer to [12][13][14].
In this work, we attempt to study the impact of nuclear effects imposed by FSI in the QE(Quasi Elastic), resonance (RES) and deep inelastic scattering (DIS) interaction processes. Understanding nuclear effects will give us a handle to filter out true events from the fake events in a given neutrino-nucleon interaction which will lead to an accurate measurement of neutrino oscillation parameters.

II. NEUTRINO OSCILLATION STUDIES WITH THE LONG-BASELINE EXPERIMENT-DUNE:
The Deep Underground Neutrino Experiment, DUNE [15,16], an upcoming long baseline neutrino oscillation experiment, to be set up in the US is aiming for discovering the unknown oscillation parameters and explore new physics.
The 1300km baseline, stretching from LBNE facility at Fermilab to Sanford Underground Research Facility (SURF) at South Dakota, is ideal for achieving the desired sensitivity for CP violation and mass hierarchy. The far detector will be composed of 40 ktons of liquid argon (nuclear target with Z=18) as detector material which will provide large event statistics. The DUNE-LBNF flux spreads in the energy range 0.5 to 10 GeV, with an average energy peaking at 2.5 GeV. It is composed of QE, Resonance, DIS and Coherent neutrino-nucleon interaction processes with resonance being the dominant interaction process in this energy regime. The energy dependent cross-section is different for each interaction process.
To evaluate the sensitivity of LBNE and to optimize the experimental design, it is important to accurately predict the neutrino flux presented in Figure 1(left panel) produced by the neutrino beam. The corresponding neutrino oscillation probability is presented in Figure 1(right panel) for ν µ disappearance and ν e appearance channels.

III. FINAL STATE INTERACTIONS AND NUCLEAR EFFECTS
A neutrino when interacts with a fermi moving neutron within the nucleus giving a muon and a proton as final state products, is defined as a true charged current quasi elastic(CC-QE) process and is represented as : νn → µ − p These processes are accompanied by certain other processes in which a pion or a delta resonance is also produced in the initial neutrino-nucleon interaction vertex e.g. νp → µ − pπ + or νp → µ − ∆ ++ , but gets absorbed in the nuclear uncertainties in the QE cross section measurement. Contrary to the above process, another possibility is production of a nucleon in the initial neutrino-nucleon QE interaction, which might get rescattered within the nucleus and produce a pion in the final state. Such an event, though having a true QE origin will be tagged as QE-like event due to presence of a pion in the final state. The appearance of such events give way to uncertainties in the reconstruction of neutrino energy and the error caused in the energy reconstruction of neutrino, is further propagated to the measurement of neutrino oscillation parameters. Figure 2 presents migration matrices constructed between true (t) and reconstructed (r) neutrino energies for QE, RES, 2p2h(multi-nucleon processes) and Non-RES interaction processes, using argon as the nuclear target. Every element n(E t , E r ) in each of the migration matrices represents the probability that an event which had a particular true energy has now a completely different reconstructed neutrino energy, which corresponds to an energy smearing, evident in Figure 2. Should the true and reconstructed neutrino energies be same, we would get a diagonal line without any smearing. The Non-RES and RES events appear to smear maximally while the 2p2h and QE events smear to a lesser extent as compared to the other two processes. From Figure 2, we can see that the

IV. SIMULATION AND RESULT
Event statistics of approximately 2 lakh is generated using DUNE flux for muon disappearance channel with the help of GiBUU (Giessen Boltzmann-Uehling-Uhlenbeck) [17,19]. The GiBUU model, developed as a transport model for various interaction processes induced by nucleus, nucleon, pion and electron is based on a coupled set of semi-classical kinetic equations [18]. GiBUU applies a semi-classical approach and models the FSI by solving the Boltzmann-Uehling-Uhlenbeck equations. Recently, the GiBUU code has also included the DIS interaction process successfully [20]. The migration matrices are obtained using GiBUU and are inserted in the required format into GLoBES [21][22][23][24][25][26]. The systematics considered in our work are as follows-signal efficiency is 85%, normalization error and energy calibration error for the signal and background are-5%, 10% and 2% respectively. The running time considered is 10 years in neutrino mode with 35 kton fiducial mass of the detector. The values of oscillation parameters used in this work are motivated from [27,28].
Here, we consider a parameter α, which help us to incorporate nuclear effects in our analysis. It can be considered as a way of including systematic uncertainties, such approach has been considered previously in [9,10]. We present the position of the best fit corresponding to values of α taken as 0 and 1, by plugging them in equations (1) and (2)- where N is the total number of events. Two cases arise-1. When α = 1, the second term in each of the equations (1) and (2) cancels out which imply that nuclear effects are completely disregarded. v 2. When α = 0, the presence of fake events are registered which imply that nuclear effects are incorporated.
We notice from Figure 3(left panel) that the value of octant of θ 23 shifts from maximal toward lower octant when QE and QE-like events are examined while from Figure 3(right panel) we can see that the θ 23 shifts to the higher octant when we include contribution of nuclear effects from QE+RES+DIS interaction processes.

V. CONCLUSION
We notice a 3σ shift in the best fit point value for charged current QE events shown in the left panel of Figure   3 and a shift of more than 3σ for QE+RES+DIS events as shown in the right panel of Figure 3. In a future work we will report the results by considering different values of the parameter α as defined above, since α can take on any value between 0 and 1. In an outlook of the study, we can conclude that the best strategy for third generation neutrino-oscillation experiments seems to minimize detection thresholds of the employed detectors and to perform an extensive authentication of the accuracy of nuclear models employed in data analysis. Employment of nuclear targets in neutrino oscillation experiments aid in boosting the event statistics which reduce the statistical error but we need to pin down the systematic uncertainties arising from the persistent nuclear effects that will bring us a step closer in achieving our goals.

VI. ACKNOWLEDGEMENT
This work is partially supported by Department of Physics, Lucknow University. Financially it is supported by government of India, DST project no-SR/MF/PS02/2013, Department of Physics, Lucknow.