Reconstruction of neutrino interactions in SAND with an innovative liquid Argon imaging detector

The Deep Underground Neutrino Experiment will be a next-generation neutrino oscillation long-baseline accelerator experiment with the aim of determining the still unknown neutrino oscillation parameters, observing proton decay and detecting supernova neutrinos exploiting a Liquid Argon Time Projection Chambers (LArTPC) of unprecedented size. However, despite their successful application in neutrino and DM experiments, the performances of LArTPCs are limited in high intensity environments, such as in near-site detectors on neutrino beams, due to the long drift time needed to collect the ionisation charge. The design of SAND at the DUNE Near Detector complex includes a 1-ton LAr target -GRAIN (Granular Argon for Interaction of Neutrinos)- designed to overcome such limitation by imaging the scintillation light produced in neutrino interactions. By capturing “pictures” of the LAr (or LXe), GRAIN will allow to reconstruct the event topologies and energy deposition. Using this information, and that provided by the SAND electromagnetic calorimeter and target tracker system, SAND will allow on-axis beam monitoring, the control of systematics uncertainties for the oscillation analysis, precision measurements of neutrino cross-sections, and beyond Standard Model searches.


Introduction
DUNE, a next generation long-baseline neutrino oscillation experiment under construction in the United States, comprises two key sites: a Near Detector complex in Fermilab, Illinois, and a Far Detector site 1.5 km underground at the Sanford Underground Research Facility (SURF) in South Dakota, 1300 km from Fermilab.The project aims to address various aspects of neutrino physics, proton decay, core-collapse supernovas, solar neutrinos, and other Beyond Standard Model (BSM) searches.To achieve its primary goals of determining neutrino mass ordering and the Pontecorvo-Maki-Nakagawa-Sakata CP-violation phase, DUNE will utilize the world's most intense wide-band (anti)neutrino beam, together with a multi-kiloton far detector based on liquid argon time projection chambers and a near detector designed to minimize systematic uncertainties.During its initial phase (Phase I), DUNE will employ a 1.2 MW proton beam [1], two far detector modules with a 20 kt liquid argon fiducial mass, and a temporary configuration of the near detector complex to achieve early physics objectives.However, to fully realize its scientific program in Phase II, DUNE will necessitate an upgraded 2.4 MW neutrino beam and a complete experimental apparatus, including four far detector modules (with at least 40 kt fiducial mass) and a near detector in its final configuration.The main features of Phase I and Phase II are reported in table 1.The Far Detector design consists of four Liquid Argon Time Projection Chamber (LArTPC) modules, each with a mass of 17.5 kton.In the initial phase (Phase I) of DUNE, two modules, FD1 and FD2, are scheduled for operation, while the remaining modules, FD3 and FD4, will be addded in Phase II.FD1 and FD2 employ distinct technologies, both being LArTPCs.FD1 utilizes a single-phase horizontal-drift design [2], which was successfully tested and validated at CERN through the ProtoDUNE-SP detector -a prototype approximately 20 times smaller than FD1.FD2 is instead planned to be a single-phase LArTPC with a vertical drift [3].The design specifics for the third and fourth modules, FD3 and FD4, are yet to be determined.

Near Detector
The Near Detector complex [4], located 600 m from the neutrino beam source, consists of three detectors: ND-LAr, TMS (Temporary Muon Spectrometer) in DUNE Phase I (to be replaced by ND-GAr, a gaseous Argon Time Projection Chamber, in Phase II), and SAND (System of on-Axis Neutrino Detection).ND-LAr and TMS/ND-GAr can move off-axis with respect to the direction of the beam, while SAND will stay fixed on-axis position [4].
The Near Detector will measure the neutrino beam near its production point, providing data before oscillations take place.This is crucial for constraining systematic uncertainties and contributes to the neutrino interaction model.Figure 1 shows the ND detectors in on-and off-axis positions.

ND-LAr
The ND-LAr is a LArTPC implementing an original design to cope with the large event pileup from the intense neutrino flux at the near site [4].It will consist of multiple small size TPC modules, optically isolated from each other and with individual pixelated readouts able to provide precise timing information.Current design features a 5 × 7 matrix of modules.Reconstructed information from each TPC is then combined to provide the complete event reconstruction.

ND-GAr
The ND-GAr will be a high-pressure gaseous argon TPC (HPgTPC) surrounded by an electromagnetic calorimeter within a 0.5 T magnetic field [4].It will provide muon momentum and charge reconstruction for events not contained within the ND-LAr volume.ND-GAr is foreseen to operate during DUNE Phase II.In Phase I it will be replaced by the Temporary Muon Spectrometer (TMS).The design of TMS is based on magnetized steel planes interleaved with scintillator strips to provide muon momentum resolution up to 5%.

SAND
SAND will be the only detector at the DUNE ND complex to be permanently in an on-axis position.It will be based on the refurbishment of the existing electromagnetic calorimeter and superconducting magnet from the KLOE experiment, with the inner magnetic volume filled with a straw tube target tracker (STT), and a 1-ton LAr detector (GRAIN).SAND will perform beam monitoring, measurements to control systematic uncertainties for the oscillation analysis as well as a broader physics program, including precision measurements of neutrino cross-sections.It will be able to study neutrino interactions on different target materials, as in the liquid Argon of the GRAIN subdetector and in the targets of the STT.
Magnet and electromagnetic calorimeter.The SAND magnet will be refurbished from the KLOE experiment.The KLOE magnet [5] was designed to produce a 0.6 T magnet field over a 4.3 m long, 4.8 m diameter cylindrical volume.The coil's cooling is performed using Helium gas at 5.2 K injected at 3 bar from the cryogenic plant and liquefied into a reservoir in thermal contact with the coil.
The SAND calorimeter, also refurbished from the KLOE experiment [5], is a lead-scintillating fiber sampling calorimeter.It is composed of 24 modules arranged in a nearly cylindrical configuration and two endcaps, each consisting of 32 vertical modules.The horizontal modules are trapezoidal, with bases of 52 and 59 cm, a length of 4.3 m, and a thickness of 23 cm.Endcaps' modules, ranging from 0.7 to 3.9 m in length, feature a rectangular cross-section with both ends bent in a C-like shape for insertion into the calorimeter barrel (see figure 2).Each module is constructed with 200 lead foils, each 0.5 mm thick, alternated with 200 layers of cladded scintillating fibers of 1 mm diameter glued together with compatible epoxy.The end faces of each module are divided into a 5 × 4 grid by light guides, with each cell read by a phototube, for a total of 4880 phototubes.The performances of the calorimeter evaluated during the KLOE commissioning and running periods, are [5]: / = 5%/ √︁  (GeV) and   = 54/ √︁  (GeV) ps.

Straw tube tracker.
The inner region of the ECAL will be equipped with a straw-tube-based tracker.Such tracker will provide high momentum, angular, and space resolutions thanks to the low density and high granularity, will minimize secondary interactions by limiting the total thickness to about one radiation length while also providing the possibility to change the target material during the run to study neutrino interactions on different elements.The target will be arranged in thin solid layers of different materials and will account for more than 97% of the total detector mass [6].The STT will be organized in modules; each module can be operated and configured independently.A default configuration consists of a 5 mm thick solid polypropylene (CH 2 ) target slab, a polypropylene radiator composed of 105 foils 18 μm thick, alternating with air gaps 117 μm thick, four layers of straws (each made of 5 mm diameter, 12 μm mylar walls coated with Al, and a 20 μm tungsten wire coated with gold) arranged in an XXYY pattern.Alternative module configurations are possible, -3 - allowing to offer great control on the chemical composition and mass of the neutrino target.Possible alternative materials for the target are C, Ca, Fe, and Pb.

GRAIN.
The upstream section of the SAND inner volume will be occupied by a liquid Argon detector called GRAIN (GRanular Argon for Interaction of Neutrinos), with a mass of approximately 1 ton.A novel approach, based on detecting exclusively scintillation light in Argon, is under development.
Leveraging the large light yield and fast emission time, the photon collection can be limited to a few nanoseconds to achieve high spatial resolution.To do so, an optical system must be coupled to a fast, segmented photon detector.GRAIN will be composed of two cryostats: an inner vessel (Aluminium, measuring 147 cm in height, 150 cm in width, and a maximum depth of 47 cm) and an outer vessel (composed of layers of Aluminum alloy, honeycomb, and Carbon fiber, measuring 190 cm in height, 200 cm in width, and with a maximum depth of 83 cm).A 2D depiction of GRAIN is presented in figure 3. The light collection in GRAIN is done by instrumenting the inner vessel with Vacuum UltraViolet cameras operating at LAr temperatures (78 K).Two optical systems are currently being developed, one based on lenses, and one based on Coded Aperture Masks.An example of the geometry of both cameras is shown in figure 4. Both optical systems offer their own set of advantages and drawbacks.Cameras based on lenses are better known, and provide a direct reconstructions of the source image.However, constructing them is challenging in cryogenic environments and the high refractive index of Liquid Argon (LAr) makes them having a limited Field of View (FoV) while also occupy a large volumes.On the other hand, mask-based cameras are easier to build, have a larger Depth of Field, and boast a more compact design.Nevertheless, they require complex reconstruction algorithms for imaging.Details on the reconstruction algorithms used to perform track and energy reconstruction exploiting both systems will be given in the next section.Both optical systems are coupled to a light sensor comprised of a Silicon Photomultiplier (SiPM) matrix.Currently, the available options are the S14160 and S13615 Hamamatsu arrays [7], featuring 8 × 8 and 16 × 16 SiPM matrices, respectively.A notable drawback of these SiPMs is their limited sensitivity to the 127 nm wavelength of Argon scintillation light.To address this, a wavelength-shifter (WLS) will be needed to convert UV light into visible light, where SiPMs have optimal photon detection efficiency (PDE).

Simulation and reconstruction in GRAIN
A dedicated software, utilizing the Monte Carlo simulation toolkit Geant4 [8], has been developed to fully simulate the generation and propagation of scintillation light in GRAIN, as well as the response of the cameras.Additionally, a preliminary reconstruction code has been developed based on the output of the optical simulation.The optical simulation module was developed to withstand the heavy computation of the photon propagation resulting from multi-GeV neutrino events.It features a full parametrization of the scintillation process and includes all optical properties of liquid argon, such as Rayleigh scattering and absorption.It also contains a detailed geometrical description of the cameras and their materials in order to properly take into account all physical effects.While the simulation is shared between both lens and coded mask readout technologies, each option requires a distinct reconstruction flow to properly interpret the results.
-5 - The algorithm for the lens-based solution is divided in two different steps: a 2D pattern recognition step on raw images and a subsequent 3D matching and extrapolation step.In the initial 2D step, the images captured by the cameras are independently analyzed to identify tracks, fit them, and compute their intersection points.The primary objective of this step is to determine the 2D features recorded in each image, particularly identifying visible tracks and their best fit.Such 2D information are then matched across multiple views from different cameras, enabling the production of 3D reconstructed tracks and the localization of the interaction vertex.The second part of the reconstruction algorithm aims to recover the three-dimensional layout of the event, determining the position of the interaction vertex and the position and direction of the tracks in liquid argon.Figure 5 provides an example of 2D images obtained with lens-based cameras, while figure 6 shows the distribution of residuals of the 3D position of the neutrino interaction vertex obtained from the 3D reconstruction.A comprehensive description of the design of lens-based cameras, their placement within GRAIN, and the reconstruction algorithms (both 2D and 3D) is available at [9].-6 -

Masks
The Coded Aperture technique, already known in X-and gamma-ray astronomy, is being explored for the first time in particle physics applications [10].This technique utilizes a matrix of holes on an opaque target (a mask) to expand the concept of a single pinhole camera.The objective is to achieve a significantly larger Field of View (FOV) and Depth of Field (DOF) compared to traditional optical systems while maintaining high throughput.Exploiting an optical-sensor system based on this technique and combining multiple cameras arranged in a stereo view, it should be possible to perform a complete 3D reconstruction of the events.In contrast to lens-based cameras, the 2D image detected by mask-based cameras is a convolution of multiple images, one projected from each hole of the mask.To retrieve the source image, deconvolution of the detected signal is required.Various methods, developed over the past decades, are available for this purpose, with the choice depending on specific goals, available computational power, and instrument configuration.The Maximum Likelihood Expectation Maximization (ML-EM) algorithm [11] is the primary technique under development for reconstructing tracks in GRAIN with mask-based cameras.This algorithm exploits a combinatorial approach to directly perform a 3D reconstruction of images.The volume where particles propagate is segmented into voxels, and for each voxel, an emission probability is computed by projecting backward each photon detected by a camera through all possible mask holes.Combining projections from all cameras, the position of the light source is related to the voxels with the highest probability.While this technique is versatile and can work with various mask models and a low number of detected photons, it is computationally intensive, requiring a large number of operations for the reconstruction of a single event.Ongoing development and optimization efforts are actively addressing these computational challenges.The results of this method are promising as visible in figure 7, where the reconstruction of proton and muon tracks from a muon neutrino interaction in a GRAIN-like geometry is shown.The direction of the reconstructed tracks can be compared with the MC-truth, and the residuals between the true and reconstructed track directions are presented in figure 8 for both the XY and YZ planes.Further details on this technique can be found in [12].-7 -

Energy reconstruction
Mask-based cameras have the potential to contribute to the neutrino event reconstruction in SAND by providing calorimetric information on the total energy loss in argon by secondary particles.As GRAIN uses only an optical readout, this information must be obtained from the scintillation light collected for each event, which depends, among different things, on the position of the interaction points.This is clearly visible in figure 9 (left), showing the total number of detected scintillation photons as a function of the energy deposited by secondary particles in neutrino interactions.While a linear relationship between the two quantities is observable, there is a considerable spread for a specific energy deposition value.This is expected as events with similar energy deposition but occurring at different positions inside GRAIN may be observed by a different number of optical cameras, directly influencing the total collected photons.To calibrate the GRAIN detector accurately, multiple calibration coefficients should then be computed, each for a small region of the detector, mitigating the impact of this spatial dependence.This is shown in figure 9 (right), where the total number of detected scintillation photons is shown as a function of the energy deposited by secondary particles in neutrino interactions within a small region near the center of the detector, for which a dedicated calibration coefficient was computed.It is clear how the distribution narrows, allowing a better reconstruction of the energy deposited in GRAIN.To verify the correct calibration of the detector, neutrino interactions in the   + Ar →  − +  +  channel were selected from the MC-truth, and their energy deposition was reconstructed starting from the total collected scintillation light.Results of such reconstruction are presented in figure 10, where the ( reco −  true )/ true values are shown.A detailed description of the method used to obtain the calibration coefficient and to reconstruct the energy deposition in GRAIN can be found in [13].

Conclusions
The GRAIN liquid argon target is an important component of SAND and a unique asset for DUNE.It also represents a technologically interesting innovation in the field of liquid argon detectors due to its optical readout.Two optical systems are currently being studied to be used in GRAIN, one based on lenses and one based on Coded Aperture masks.Results obtained with both systems were -8 -Figure 9. Number of detected photons as a function of the true deposited energy in GRAIN for events with interaction points uniformly distributed in GRAIN (left) and for events with interaction points distributed in a small region near the center of the detector (right) [13].presented and show how it is possible to perform track reconstruction and calorimetric measurements exploiting only the scintillation light.The GRAIN final design will be decided by looking at the reconstruction performance of both systems in an upcoming prototype and could foresee a combination of lenses and masks to exploit the advantages each system provides.The GRAIN measurements, together with the information provided by the other SAND components, will be used to characterize the DUNE neutrino beam, improve the knowledge of the systematics uncertainties as well as perform a broad complementary physics program.

Figure 1 .
Figure 1.3D view of the DUNE Near Detector hall: (left) all detectors are in on-axis position; (right) ND-LAr and ND-GAr are in an off-axis position, and SAND remaining on axis [4].

Figure 2 .
Figure 2. Picture of the electromagnetic calorimeter of the KLOE experiment, with both the barrel and endcaps modules visible.

Figure 3 .
Figure 3. 2D rendering of GRAIN in the YX (left) and YZ (right) view.

Figure 4 .
Figure 4. 3D models of lens-and mask-based cameras.Both models exploit a SiPM matrix as sensor beyond the optical system.The lenses are represented by blue and grey circles in the left image, while the mask is represented by the yellow squares in the right image.

CHAPTER 6 .
ν-AR EVENT SAMPLES IN SAND

Figure 6 . 4 :Figure 5 .
Figure 6.4: Complete set of all the 38 images collected by cameras in GRAIN for the ν µ interaction of Fig. 6.3.Three tracks are clearly visible, as well as the interaction vertex.The dierent scaling eect between left and right cameras can also be noticed.

Figure 6 .
Figure 6.Vertex residuals from an initial sample of 15k   CC interactions in GRAIN.The 3D plot is normalized so that each bin represents the same volume in space[9].

Figure 7 .
Figure 7. 3D reconstruction of a muon and proton track in a GRAIN-like geometry obtained with the ML-EM algorithm.More information can be found in[12].

Figure 8 .
Figure 8. Angle distribution between the reconstructed direction of the particle and the true track direction, on the XZ (left) and YZ (right) plane respectively.More information can be found in[12].

Figure 10 .
Figure 10.( true −  reco )/ true values for neutrino events in the   + Ar →  − +  +  channel.The reconstructed energy is computed by exploiting the proper calibration coefficient related to the position of the interaction point [13].

Table 1 .
Detail on the two-phased approach to DUNE.