Design, Calibration, and Performance of the MINERvA Detector

The MINERvA experiment is designed to perform precision studies of neutrino-nucleus scattering using $\nu_\mu$ and ${\bar\nu}_\mu$ neutrinos incident at 1-20 GeV in the NuMI beam at Fermilab. This article presents a detailed description of the \minerva detector and describes the {\em ex situ} and {\em in situ} techniques employed to characterize the detector and monitor its performance. The detector is comprised of a finely-segmented scintillator-based inner tracking region surrounded by electromagnetic and hadronic sampling calorimetry. The upstream portion of the detector includes planes of graphite, iron and lead interleaved between tracking planes to facilitate the study of nuclear effects in neutrino interactions. Observations concerning the detector response over sustained periods of running are reported. The detector design and methods of operation have relevance to future neutrino experiments in which segmented scintillator tracking is utilized.


Experiment Overview
There are many uncertainties in the knowledge of the fundamental interactions of neutrinos with the nucleon and the more complex interactions with nuclei. The properties of the neutrino, such as its purely weak interaction and its unique flavor sensitivity, make it an ideal probe, but its small cross sections, together with the difficulty of producing intense neutrino beams, have impeded detailed investigations of the interaction. The intense neutrino beam produced in the Neutrinos at the Main Injector (NuMI) beamline [1] at Fermilab has opened up new possibilities for the detailed study of neutrino interactions with nuclei. The MINERvA experiment takes advantage of this new opportunity.
MINERvA is studying neutrino interactions on a variety of nuclei, including helium, carbon, oxygen, lead, and iron, which complement the wealth of electron scattering data in helping to understand the weak interaction in the nuclear environment.
The field of neutrino oscillations is rapidly advancing towards our understanding the complete picture of neutrino masses and mixings [2,3,4,5]. In particular, the next generation of accelerator-based long-baseline experiments aims to determine the mass hierarchy of neutrinos and test for CP violation by comparing the oscillation probabilities for neutrinos and antineutrinos. Reaching the level of precision needed in these challenging measurements requires a detailed understanding of neutrino-and antineutrinonucleus scattering processes in the relevant energy range of a few hundred MeV to a few GeV. Currently, however, the specific processes that provide signal and background channels for these experiments are, in many cases, either poorly measured or suffer from discrepant measurements across various experiments. In addition, an important feature of oscillation experiments is the need to measure oscillation probabilities as a function of the neutrino energy. This requires experiments to have robust models of the relationship between the initial neutrino energy and the visible energy deposited in the detectors.
Such models must incorporate the impact of the complex nuclear environment in which the interactions are occurring; studies have shown that neglecting these effects can lead to biases in the neutrino energy determination. Both the impact of the initial state an the interactions of final-state particles traversign the parent nucleus must be understood.
Through measurements of specific interaction cross sections and comparisons among different nuclear targets, MINERvA can provide data to considerably improve the models of neutrino-nucleus scattering and thus to reduce systematic uncertainties in the results from oscillation experiments.

MINERvA Physics Goals and Detector Design
The key design features of the MINERvA detector have been determined by the physics goals of the experiment. An overview of the detector design and its component systems is presented in this section. Detailed technical descriptions of the main components are provided in subsequent sections. 6 The physics goals of MINERvA require a detector that can resolve multi-particle final states, identify the produced particles, track low energy charged particles (for energies greater than about 100 MeV), contain electromagnetic showers, contain high-energy (up to at least 10 GeV) final states, and resolve multiple interactions in a single beam spill. The detector must include targets with a wide range of nucleon number A to enable studies of the nuclear dependence of neutrino interactions. In order to track and resolve multiparticle final states with low thresholds, the core of the detector must be fully active with good spatial resolution and of relatively low mass. Full containment of events requires that the inner region be surrounded with electromagnetic and hadronic calorimetry. Ideally, charge identification would be included by adding a magnetic field. This proved impractical for the main detector, as did containment of high energy muons. However, by placing MINERvA immediately upstream of the Main Injector Oscillation Search (MI-NOS) near detector [6] (henceforth referred to as MINOS), a neutrino detector composed of magnetized iron plates interleaved with scintillator planes, charge and energy measurements of forward-going muons can be made.
A schematic view of the detector is shown in Fig. 1. Neutrino reactions in the rock upstream of the detector hall can produce hadrons and muons. A "veto wall" upstream of the main detector shields against lower energy hadrons from the rock and tags the muons (referred to below as "rock muons"), which can traverse all or part of the downstream detector. The veto wall consists of a 5 cm thick steel plate, a 1.9 cm thick plane of scintillator, a 2.5 cm thick steel plate, and a second plane of 1.9 cm thick scintillator. A cubic meter The z axis is defined to place the front face of MINOS at z = 1, 200 cm. In this system the neutrino beam central axis is in the y − z plane and points downward at 3.34 • .
The core of the MINERvA design is the active tracking region, composed purely of scintillator, which serves as the primary fiducial volume where precise tracking, low density of material, and fine sampling ensure that some of the most difficult measurements can be performed. These measurements include particle identification using energy loss per unit length (dE/dx), and reconstruction of the neutrino interaction vertex in the presence of several final state charged particles. The upstream part of the detector contains solid targets of carbon, iron, and lead interleaved with the scintillator planes. Because these targets are relatively thin, the ability to precisely reconstruct the location of the interaction vertex is crucial for studies of the A dependence.
Electromagnetic calorimetry is accomplished using a 0.2 cm thick by 15 cm wide lead "collar" (orange ring in Fig. 1 The MINERvA experiment uses several different simulation codes to model the detector and its performance. The neutrino interactions are modeled by the GENIE v2.6.2 event generator [8]. The final-state particle interactions in the detector itself are modeled by a GEANT4 version 9.4.p02 [9] simulation. The different detector components such as the electronics and scintillator and absorbers are also modeled using GEANT4. Both the GENIE and GEANT4 parts of the detector simulation include a detailed model of the nuclear makeup of the detector, described in Sec. 2.1 and Sec. 2.3. The simulation also takes into account the variations over time and position of the detector components, and includes accidental detector activity.

The MINOS Near Detector
The MINERvA detector is situated 2.1 meters upstream of the MINOS near detector in the NuMI beamline. The MINOS magnetic spectrometer is used to momentum analyze muons which exit the MINERvA detector volume in the forward direction. The detector technology and readout are described in detail in Ref. [6]. The segmentation and layout of the MINOS near detector are described in this section. Performance aspects relevant to its use for MINERvA are discussed in Sec. 7.2.
MINOS, shown in Fig. 2, is a tracking calorimeter composed of planes of magnetized iron and plastic scintillator with a total mass of 1 kTon. It has a toroidal magnetic field of average strength of 1.3 T, which is produced by a current-carrying coil passing through the entire length of the detector. The direction of curvature of a charged particle in the field allows the sign of the sign of the track charge to be determined. In the normal operational mode, the field is set to focus the same charge as that selected in the NuMI secondary beam focusing system.

The NuMI Neutrino Beam at Fermilab
MINERvA uses the Fermilab NuMI beamline to produce a high intensity beam of muon neutrinos and anti-neutrinos [1]. A beam of 120 GeV protons from the Main Injector strikes a graphite target over an 8.1 or 9.72 µs spill every 2.2 seconds. The two different spill durations correspond to different modes of operation for the accelerator complex.
The secondary pions and kaons produced by the incident protons are then focused by a system of two magnetic horns which direct the mesons into a 675 m long decay pipe where most of them decay. A total of 240 m of rock downstream of the decay pipe range out the tertiary muons that are created in the beamline concurrently with the neutrinos.
The focusing horns can be pulsed in either polarity. When the horns are focusing positively charged mesons (forward horn current or FHC) the resulting beam is primarily neutrinos, and when the horn is in the reverse horn current (RHC) the peak of the beam is The NuMI beamline has considerable flexibility and can run with the target in different positions relative to the focusing horns. For most of the run the graphite target was located as close to the horns as possible to create a beam whose energy of the peak in neutrino flux was approximately 3 GeV, a configuration known as the low energy (LE) beam.
Of the total exposure roughly 10% of the protons on target were collected in configurations with the target moved farther upstream of the first horn, which results in a higher peak-neutrino-energy flux. These special runs were taken to better understand the neutrino flux, but the detector calibration and reconstruction procedures remained the same as those described in the remainder of this article. Future runs will use a horn separation that gives a higher peak neutrino energy.
As discussed in Sec. 6.5, an important calibration source produced by this beam comes from muons resulting from neutrino charged-current interactions that occur in the rock located upstream of the MINERvA detector. On average once every two beam pulses a rock muon traverses the entire central tracking region of the MINERvA detector.

Module Assemblies and Nuclear Targets
The MINERvA detector is comprised of 120 modules suspended vertically and stacked A plane can have one of three different orientations, referred to as X-planes, U-planes or V-planes according to the coordinate in the MINERvA system in which each plane measures particle hit positions. X-planes have scintillator strips aligned vertically, hence hits in this view give position information in the horizontal or x-direction. The U-and V-planes are rotated 60 degrees clockwise and counterclockwise from the X-planes in the x-y plane, respectively. Three different views are used in order to avoid ambiguities with reconstructed hit associations that can occur when multiple tracks traverse two orthogonal planes. Each tracking and electromagnetic calorimeter module has one X-plane, and either a U-or V-plane, with modules alternating between a UX or VX structure with the X-planes always located downstream of the U-or V-planes. The nuclear target region contains 22 tracking modules, and the central tracking region contains 62 tracking modules.
The tracking modules are designed to perform electromagnetic calorimetry using a 0.2 cm thick lead collar that starts at roughly 90 cm from the module center and extends to the outer frame. The collar forms a hexagonal ring whose purpose is to reduce the leakage of electromagnetic showers that originate in the central detector.
The chemical composition and areal density (mass per unit surface area) of the planes is determined by combining measured densities (pure scintillator and coated strips), assayed compositions (coated strips and epoxies), and data sheet values (tape and Lexan).  The estimated areal densities of the epoxy and tape are based on their usage in plane construction. The densities and composition of the components are listed in Table 1. The elemental compositions of the strips and assembled tracker scintillator plane are given in Table 2. The chemical composition of the components is well known. There is some uncertainty in the composition of the coated strips due to the uncertainty in the coating thickness, which is estimated to have a relative uncertainty of about 10%. This affects most strongly the fraction of the strips which is scintillator. The estimated areal density for the scintillator plane is 1.65 ± 0.03 g/cm 2 . The estimated areal density of an assembled plane is 2.02 ± 0.03 g/cm 2 , as described in Sec. 3.1.

Electromagnetic and Hadronic Calorimeter Modules
An ECAL module is very similar to a central tracking module. It differs in that it has a 0.2 cm thick sheet of lead covering that the entire scintillator plane instead of a 0.2 cm thick lead collar covering only the outer edge of the scintillator region. A transition module is placed between the last central tracking module and first ECAL module. This module contains a 0.2 cm thick lead sheet on the downstream end of the last plane in the module so that each plane of the ECAL has a lead absorber upstream of it. The fine granularity of the ECAL ensures excellent photon and electron energy resolution and provides directional measurement for these particles. There are 10 modules in the ECAL region of the detector (Fig. 1).
The lead sheets used for the side electromagnetic calorimetry were measured using an ultrasonic device to determine the variation in thickness along the length of the sheet. The thickness along each piece vary at the 5% level, and the average thickness of the different pieces vary at the 3.5% level. The thicknesses of the lead sheets used in the downstream electromagnetic calorimetry also vary at this level.
The HCAL consists of 20 modules that are similar to the tracking modules; however, instead of two planes of scintillator in each module, there is only one plane of scintillator and one 2.54 cm thick hexagonal steel plane in the inner detector region. The scintillator planes located in the HCAL have a repeating pattern of XVXU.

Solid Nuclear Target Modules
In order to study neutrino interactions on different nuclei, the most upstream part of the detector includes five layers of passive targets, the "nuclear targets", separated by four tracking modules each. The four modules (eight planes of scintillator) between one target and the next ensure good vertex position resolution for events originating in the nuclear targets. Each solid nuclear target is mounted in the same instrumented hexagonal steel frame as the scintillator planes for ease of detector construction and for event  aids in upstream electromagnetic calorimetry and serves as the thinnest lead target. Targets 1, 2, and 5 are mixed steel and lead. The steel plate section is larger than the lead plate section, with the dividing line 20.5 cm from the plane center. Target 3 is composed of graphite, iron and steel. The graphite covers half the area of the hexagon, the steel one-third, and the lead one-sixth. The orientation of the planes, as viewed looking downstream, is shown in Fig. 3. The orientation of the planes along the axis of the beamline is shown in Fig. 4. The composition by element of the targets is given in Table 3. with an 85 cm apothem, and a 2.5 cm cut on each side of the boundary between materials.
The z-location of the center of each target and the fiducial mass of each material for each target is given in Table 4. The estimated uncertainty on the fiducial masses due to density and thickness variations is less than 1%.

Water Target
A water target is positioned between solid targets 3 and 4, with a mean position of 530.8 cm. It consists of a circular steel frame with a diameter slightly larger than the MIN-ERvA inner detector size, and Kevlar® (polymerized C 14 H 10 N 2 O 2 ) sheets stretched across the frame as shown in Fig. 5. The shape of the water target is not as well known as that of the solid targets. When the target is filled the lower part expands more than the upper  part, and it is not possible to access the entire target in order to make precise measurements. The shape of the target is estimated via a finite element analysis and compared with the actual volume, which is determined by measuring the volume of water when the target is emptied. The thickness varies from about 17 cm at the edge of the fiducial region to 24 cm at the thickest part. The estimated mass within an 85 cm apothem hexagon is 452 kg with an uncertainty of about 3%. The Kevlar walls add 0.1 g/cm 2 , for a total mass of 2.5 kg. The water target chemical composition by mass is 88.5% O and 11.1% H with negligible amounts of C and N.

Liquid Helium Target
The MINERvA cryogenic helium target is located immediately upstream of the active detector and was filled with liquid helium during the latter parts of the run. Its design reflects the following considerations: the largest volume possible for increased statistics; a minimum of material to be traversed in reaching the tracking detectors by particles originating from interactions in the helium; the largest acceptance possible for neutrino events scattering off helium; and an acceptable level of backgrounds produced from the con- The target is instrumented with the following: a set of four load cells (one on each support leg) for measuring the total weight of the cryostat; a cryogen depth gauge in the inner vessel fill tube for determining the volume of cryogen; a cryogen temperature sensor; and a pressure sensor for measuring the pressure of the vapor in thermodynamic equilibrium with the cryogen. Since the equation of state for helium is known, the temperature and pressure sensors allow an accurate determination of cryogen density. Combining the density and depth gauge measurements provides a determination of the cryogen total mass, which is complementary to the measurement from the load cells. In addition, the temperature is regulated to within 25 mK via a feedback loop which controls a heater. The regulation of the helium density is thus estimated to better than 0.5%.

The Optical System
Light signals from the over 32,000 scintillator strips in MINERvA must be converted  The ID scintillator strips are triangular in cross-section with a height of 17 ± 0.5 mm and width of 33 ± 0.5 mm (Fig. 6). Each ID strip has a 2.6 ± 0.2 mm diameter hole centered at 8.5 ± 0.25 mm above the widest part of the triangle. Both ends of the scintillator strips are painted with white EJ-510 TiO 2 Eljen paint [11]. The OD scintillator strips have

Wavelength Shifting Fibers
The scintillator strips are read out by 1.2 mm diameter, 175 ppm Y-11 doped, S-35, multiclad wavelength shifting (WLS) fibers produced by the Kuraray corporation. MIN-ERvA reads out only one end of its WLS fibers. To maximize light collection, the unread end of each fiber is mirrored. This mirroring procedure consists of 3 steps: polishing the end to be mirrored using a technique called "ice-polishing" [12], then depositing a 2500 A thick reflective coating of 99.999% pure aluminum by sputtering, and finally applying a protective layer of Red Spot UV Epoxy to the mirrors. the same fiber being scanned when the terminated end has been mirrored versus when it has been blackened. The data are fit to a double exponential and extrapolated to 320 cm.
The quality control is based on the measured attenuation length and the amount of light at 320 cm from the readout end since the longest WLS fibers in MINERvA are 320 cm.
The measured attenuation varied over different batches from 0.31 to 0.37, with standard deviations varying from 0.015 to 0.033.

Optical Connectors and Clear Fiber Cables
The WLS fibers are terminated with optical connectors from Fujikura-DDK [13], referred to as DDK connectors. Each connector groups eight fibers. The DDK connectors are used to connect to cables containing eight clear optical fibers which transmit light from the WLS fibers to the PMT boxes above the detector. These connectors were originally developed by DDK for the plug upgrade for the CDF experiment at Fermilab [14], in consultation with Tsukuba University. and are tested for light tightness and for correct fiber ordering at the end of the assembly.

Photomultiplier Tubes and Optical Boxes
The light output for a minimum ionizing particle (MIP) traversing a scintillator strip in the detector is sufficient to enable the use of a low quantum efficiency photosensor. However, a timing resolution of better than ∼5 ns is important for distinguishing overlapping events within a single spill of the NuMI beamline and for measuring time-of-flight and decay times of charged mesons created in neutrino interactions. With these considerations in mind, the multi-anode photomultiplier tube (PMT) model number H8804MOD-2 manufactured by Hamamatsu Photonics was chosen to serve as the experiment's signal readout photosensor. It is essentially the same PMT as was used by MINOS [16].
The H8804MOD-2 PMT has an 8 × 8 array of pixels laid out on a 2 cm × 2 cm grid, i.e. 64 pixels per PMT with each pixel having an effective size of 2 × 2 mm 2 . The general properties of the H8804MOD-2 PMT are listed in Table 5 and the operating characteristics provided by the manufacturer are given in Table 6. The PMTs for the detector are required to have a minimum quantum efficiency of 12% at 520 nm and a maximum-to-minimum pixel gain ratio less than three. A total of 507 PMTs are used in the fully instrumented detector.  Pulse Linearity ±2% -30 -mA Table 6: Hamamatsu H8804MOD-2 multi-anode photomultiplier tube operating characteristics at 25 o C. board (FEB) that services the PMT is mounted directly to the outside of one of the endplates to reduce input capacitance and allow easy access for connections, testing, and replacement. Within the optical box, the PMT is mounted to a base circuit board that includes a Cockcroft-Walton high voltage generator and provides signal routing to the FEB. On the other endplate is a set of eight connectors to receive clear fiber cables, which connect to the ODU inside the box. Precise alignment of individual fibers to PMT pixels is assured by routing the fibers onto a mounting "cookie." The fiber mounting cookie together with the PMT are firmly held within a mounting holder which guarantees their relative alignment. Each box supports two additional optical fiber ports terminated by diffusers which allow all pixels of the PMT to be "flashed" in a controlled way by an external light injection system (Sec. 6.2.1). An optical box with its component parts before assembly is shown in Fig. 11.
One requirement in designing these assemblies is that light signals from physically adjacent scintillator strips in the detector do not go into physically adjacent pixels on a phototube. This is because nearest neighbor pixels are the most likely to experience signal cross-talk. The ODU uses a special weave of the optical fibers to ensure this separation, as shown in Fig. 12.
MINERvA optical boxes are deployed in the vicinity of the energizing coils and magnetized steel of the MINOS near detector. In some regions occupied by the box array, the ambient magnetic fields are typically 5-10 gauss and can be has high as 30 gauss. Because the efficiency of a PMT begins to degrade when subjected to an ambient field exceeding 5 gauss, some shielding must be provided. Several steps have been taken to reduce the field strength at the PMTs: the 2.36 mm steel provides some shielding; the boxes are oriented perpendicular to the residual magnetic field; a steel "mirror plane" has been placed between MINOS and MINERvA in the region of the return coil; and 40 of the MINERvA PMT boxes closest to MINOS have been augmented with an interior shielding of high permeability metal cylinders. The end of each fiber of the weave is epoxied into a machined fiber cookie; the cookie is precisely aligned, via its mounting to the PMT holder, to witness marks located on the PMT pixel grid.

Readout Electronics and Data Acquisition
Fast analog signals from the PMTs are fed to the FEBs attached to the optical box.
The FEBs digitize timing and pulse-height signals, provide high voltage for the PMTs and communicate with VME-resident readout controller modules over a MINERvA data acquisition (DAQ) system is given in Ref. [18].

Event Formation and Hit Calibration Chain
The neutrino beam is sufficiently intense to produce multiple neutrino interactions in the MINERvA detector within one 10 µsec beam spill. The use of a non-triggered integration-style readout system requires that individual interactions be separated offline using timing information. Figure 13 shows the hit time profile of a typical readout gate.
Several isolated groupings of activity are clearly visible. consideration of any spatial relationships between the scintillator channels by an offline peak-finding algorithm to create "time slices". Time slices are initiated when hits firing the discriminator within an 80 ns time window exceed a total charge threshold of 10 photoelectrons (corresponding to 2/3 of the signal over a plane for an normally-incident minimum ionizing particle). The window then slides forward until the threshold requirement is no longer met. Hits which do not fire the discriminator are then added if they share a TriP-t with a hit already in the collection. The colored peaks in Fig. 13 indicate groupings of hits made with this algorithm in one readout gate. Figure  Raw analog-to-digital converter (ADC) data must be calibrated to provide an estimate of the energy deposited in each scintillator strip. Differences between channels as well as Additional channel-to-channel response variations can exist due to a variety of small effects that are difficult to characterize individually. These include construction differences, the varying quality of connections between components, temperature or humidity dependence, and other effects. The relative differences between channels can be precisely monitored in real time using the high statistics sample of through-going rock muons produced upstream of the detector, as described in Sec. 6.4. The rock muon sample also provides a means for determining the absolute energy scale, as discussed in Sec. 6.5.
Each of the above effects is accounted for in the event reconstruction through multiplicative correction factors applied to the raw ADC data. The energy deposited in scintillator strip i is estimated according to where C(t) is the time dependent overall energy scale constant for the entire detector and S i (t) is the relative correction factor for channel i. The correction factor for attenuation within the scintillator strip, η att i , comes from the point-by-point source map data described in Section 5.1. The factor e i /λ clear is a correction for the attenuation in the clear optical fiber of length i and attenuation constant λ clear = 7.83 m. The function G i (t) is the measured PMT pixel gain, and Q i (ADC) is the ADC-to-charge conversion factor for the FEB channel used to read out strip i.

Ex situ Calibrations of Optical System Components
The previous section introduced the factors that need to be applied to translate be- This section describes the ex situ measurements that are made before the detector is assembled. These measurements ensure that the components met the experimental requirements and provide several of the constants needed to reconstruct energy depositions in the detector.

Module Mapper
In order to translate the light output from each channel in the detector into energy deposits for further analysis, it is necessary to determine the attenuation of optical pulses as a function of position along the scintillator strip. A custom "module mapper" makes this measurement on all channels in the detector, one module at a time. The mapper also serves as the final quality check for each module before it is deployed in the detector, identifying dead channels and those having anomalous response distributions.
Corrections need to be made for optical attenuation of scintillation light in order to determine the amount of energy deposited in the scintillator by through-going charged particles. In addition, local anomalies in the optical path (compromised WLS fiber or imperfect coupling between WLS fiber and scintillator, for example) can affect light collection. These anomalies are identified and characterized allowing appropriate corrections to be applied to physics data.
The module mapper is shown in Fig. 16. The scanner provides independent motion to two Cs-137 radioactive sources. As the sources are moved through a pre-defined scan pattern over a detector module, the scintillator response is recorded by a series of Hamamatsu M-64 PMTs interfaced to a computer running custom data-acquisition software. the pedestal value for a given electronics channel shifts to lower ADC counts when the corresponding optical channel is illuminated. This pedestal shift has been determined to be directly proportional to the current from the PMT pixel. In order to measure the pedestal shift due to the response to the source illumination of a fiber, two reference pedestals are recorded: one prior to the illumination and one after the illumination. The mean of these two source-absent pedestal locations is used as the reference point. Then the ADC distribution for this channel is recorded as the source is brought in proximity to the corresponding scintillator strip.
After the strip response is measured at a number of transverse distances from the strip at a given longitudinal position, the pedestal shift is plotted as a function of the transverse position. This distribution is then fit to a Lorentzian profile to locate the center of the fiber position and the maximum response amplitude. Based on the source mapping program there were 15 dead channels identified (out of over 32,000) prior to installation.
After fitting many such transverse scans to obtain the maximum response as a function of longitudinal position along the strip, an attenuation response curve is determined.
The response curve is used to correct for the attenuation once the position of a hit along a strip is determined by later tracking algorithms. The response curves made with the radioactive source technique are in agreement with what is measured in the data using minimum ionizing particles, but are measured to a higher precision using the radioactive source.

PMT Testing
Before installation in its steel enclosure, each of the 507 deployed PMTs is tested for efficiency, linearity, pixel-to-pixel gain variation, dark noise, and cross-talk prior to installation in the steel enclosure of its optical box. Figure 17 shows Once the PMTs are installed in optical boxes, they are subjected to additional tests to better understand the operational properties of the entire unit. Specifically, any misalignment between the PMT and the cookie that holds the clear fibers from the ODUs could introduce additional cross-talk that would not be measured on the test setup described above. The optical box testing uses the same light source as is used for testing the optical cables, but without the PIN diode readout. The test setup additionally uses special optical cables where only one pixel in a row of pixels is illuminated. In this way, four pixels that are far from each other can be tested simultaneously for cross-talk, and PMT boxes which exhibit high cross-talk can be repaired before installation on the detector. The cross-talk used in the detector simulation is that measured using muons in an in situ technique (see Sec. 6.7). DA

FEB Response Measurements
Each PMT is read out by a 64-channel FEB which contains six (32-channel) TriP-t ASIC chips. The signal from each PMT anode segment is divided capacitively in the ratio of 1 : 4 : 12 and routed into separate TriP-t channels to provide a low, a medium, and a high gain response to the same input charge, thereby increasing the dynamic range of the electronic circuits.
Theh 507 deployed FEBs were tested prior to installation in the detector. The tests included burn-in, HV control, basic input/output functionality, discriminator, digital con-trol, charge calibration, and cross-talk measurements.
The charge calibration measurements are performed using a custom built test stand that injects a series of external charges into four selected input channels. The external charge is provided by 10 pF capacitors charged to 4 V by a pulse generator and discharged to the FEB input. The pulse from the generator is divided equally using a passive voltage divider and routed to four charge injection capacitors at the same time using remote controlled relay switches. Injecting charge to four well-separated FEB input channels is a compromise to minimize the impact of cross talk on the measurement and to maximize the number of channels tested one time.
The DAQ of the charge-calibration test stand is a replica of the MINERvA detector DAQ, consisting of a VME crate containing a CRIM and a CROC that read out the FEB being tested via Ethernet cable using the LVDS protocol. The data is passed to the DAQ via optical fiber by a PC/VME controller. The CRIM also provides the external trigger to the pulse generator for synchronous charge injection. The relay switches and the pulse generator voltage levels are controlled via a general purpose interface bus (GPIB) interface and their operation has been integrated into the DAQ software for automatic testing.
A typical response of one FEB channel as a function of the input charge is shown in Fig. 18.
The response of the electronics cannot be characterized by a simple linear function of the input charge. In order to characterize the non-linearity, the high, medium, and low gain response of each channel is fitted to a tri-linear function that consists of three distinct linear segments. This simple parameterization of the response is accurate within approximately 1% over the full dynamic range. As a result, each electronics channel has three sets of six parameters (the slope and the starting point of the three linear segments) describing its high, medium, and low gain response. These parameters are stored in an offline database and used to convert the raw ADC response to linearized charge. The charge is calculated from the high, medium, or low gain response (in that order) if the corresponding digitized output is below the saturation of the electronics (approximately 2500 ADC counts).

In situ Calibrations and Monitoring
Several factors needed to convert ADC counts to an energy deposition are best mea- The following subsections describe the suite of calibration constants that are measured in situ, either using rock muons that occur during the beam spill, or using special calibration triggers taken between beam spills. and captures the noise from cosmic rays, radioactivity, electronic sources, and the PMTs dark current.
Background activity event displays have been hand-scanned for a sample of about 40,000 pedestal gates. A major contributor to this background is cosmic ray muons (at 18 Hz over the entire detector) penetrating the detector after passing through the 100 m rock overburden. Each cosmic ray muon event produces a single high signal during a pedestal gate for the illuminated channels. An example of a signal which is well above the normal pedestal distribution for a representative channel is shown in Fig. 19.
It is necessary to eliminate the high-side readings that occur from background particle entry into the detector and from spurious electronic signals. An outlier removal method known as Peirce's Criterion [21] is utilized to identify such pedestal readings in the raw data stream. After identification and removal of such outlying pedestal measurements, the mean and RMS pedestal is computed for each channel over the course of the subrun.
Pedestal mean values vary by about 7% across all channels, and each channel's pedestal is observed to be stable to within 2% during a pedestal subrun. A summary of the pedestal variation for the entire detector during a single pedestal subrun is given in Table   7. The number of gates per channel varies due to the removal of spurious pedestal val-

PMT Gain Monitoring
MINERvA uses in situ calibration data to monitor fluctuations in the single PE PMT gain for each channel in the detector. The calibration source is LED light from a light injection (LI) system that is similar to that used by the MINOS experiment [22].  The core of the system is a blue AlGaInP (472 nm) LED which has a current limit of 20 mA. It is driven with a pulse generated by a custom circuit [22]. Because the pulse has a width of about 30 ns, the current can be much larger (∼200 mA). The system has 23 LEDs.
Each LED provides light to 50 clear fibers through an optical fanout, and two fibers are

Gain Calculation
The PMT gain (i.e.electrons/PE count) is determined using LI data together with modeling of the photostatistics in the PMT dynode chain.
The gain g of a pixel is defined as where Q is the mean of the pixel's pedestal-subtracted anode charge distribution, λ is the mean number of PEs arriving at the first dynode, and e is the magnitude of the electron charge. Note that the quantum efficiency of the photocathode and the collection efficiency of the first dynode are not included in this definition of the gain. Channel-to-channel differences in the latter quantities are accounted for in the relative strip-to-strip calibration (see Sec. 6.4).
For a PMT with n dynodes, the probability distribution P n (q) of the charge q measured at the PMT anode is equal to the probability distribution of the number of PEs observed at the anode [23] convolved with a Gaussian to account for electronic noise. To good approximation each dynode amplifies according to a Poisson distribution, and the amplification is linear with the number of incoming PEs, the variance σ 2 of P n (q) is Here σ p is the electronic noise (pedestal) width and the gain g is identified as the product of the individual dynode gains g i . The parameter w 2 is defined as Typically w 2 has values between 0.2 and 0.3. Equation (3) states that the variance of the PMT anode charge distribution is the sum of the variance of the pedestal, the variance of the incoming PE distribution, and the variance due to the statistical broadening of the dynode chain.
By solving Eqs. (2) and (3) simultaneously, the gain g can be written as a function of w and the mean and standard deviation of the anode charge distribution: Equation (5) is not sufficient to calculate the pixel gains because the inclusion of w introduces n unmeasured parameters g i . The parameter w can be expressed solely as a function of the total gain by noting that each g i is proportional to a power of V i , the potential difference that accelerates each PE arriving at the ith dynode The exponent α typically has values between 0.7 and 0.8 [24]. MINERvA uses α = 0.75, which introduces less than a 1% systematic uncertainty into the gain measurement.
The measured distribution of PMT gains in MINERvA is shown in Fig. 21. Figure   22 shows the statistical significance of gain fluctuations in consecutive measurements, demonstrating that daily fluctuations in the measured gains are mostly accounted for by the measurement's statistical uncertainty of 3% to 5%. Additionally, this gain measurement procedure is used to set the operating HV for each PMT box at the start of the data taking. The HVs are tuned such that the lowest-gain pixels have uniform gains across the detector. This is done by measuring the gain of the eight lowest-gain pixels on each tube, then adjusting the HV to give an average gain of 4.38×10 5 . The results of the HV tuning procedure can be seen in Fig. 21, as this data was collected shortly after the tuned target HVs were applied. The gains vary over the two years of data collection as shown in Fig. 23.

Scintillator Plane Alignment
The active MINERvA detector is built of 120 mechanically-independent modules, hung in series upon a rack. Small variations in the relative module positions are inevitable.
The tracking and electromagnetic calorimeter modules have two active scintillator planes while the hadronic calorimeter modules have only one. Co-modular planes, although sharing support from one steel frame, can be perturbed independently by stresses and strain within the frame and manufacturing tolerances. Typical offsets are comparable to or less than the strip widths of 33 mm. These offsets are determined by an alignment procedure and corrected for in event reconstruction.
The plane-based alignment procedure treats the 127 individual strips in a plane as a rigid unit. The first-order effect is an offset in the coordinate that corresponds to the direction of measurement in that plane. This can be expressed as a translation in the direction of the measurement. In addition to the translational parameter, a parameter for rotation about the z-axis is also introduced. Rotations are found to be on the order of a few The energy is corrected for normal incidence such that the maximum occurs at the strip center where the muon path length is greatest. The average energy in bins of triangle base position is fitted to the shape of the strip as shown in Fig. 24; the shift parameter is the peak of the fit. This procedure is performed in 6 bins along the strip. The shift is then plotted as a function of longitudinal position and the rotation parameter is extracted from the slope. One iteration of this procedure is sufficient to align all the planes. The residual alignment parameter uncertainties are < 1 mm and < 1 mrad. No further reduction in residuals is obtained if a second iteration of alignment is performed.

Relative Strip-to-Strip Response Variations
Variations in light level between ID strips can be caused, for example, by differences in the composition of batches of scintillator, by air bubbles in the epoxy used to fill the fiber hole, or by couplings between the optical fibers and photomultiplier tube. These variations are corrected by applying a multiplicative constant to strip energy deposits so that the response is uniform throughout the detector. The constants are determined from the path length-normalized peak energy deposited by through-going rock muons. The calibration consists of three stages. Initially, an iteration of strip-by-strip corrections is generated using the truncated mean energy [25]. Secondly, dead channels are identified and a second iteration of strip-by-strip corrections is produced. Finally, the peak energy is equalized plane by plane. The constant for each strip is the product of the output of each iteration, normalized so that the average constant is 1.0 over the entire inner detector.
The calibration is performed in time intervals such that every strip is intersected by at least several hundred rock muon tracks in a given period. This imposes a requirement of hundreds of thousands of rock muons for adequate statistics. The boundaries of the intervals are defined by hardware changes in the detector, such as when a front end board or PMT is replaced. The energy spectrum of the incident rock muons is not measured.
However, the peak energy loss per unit path length for a minimum ionizing particle is known to be a slowly varying function of the energy of the particle. Fitting for the peak requires higher statistics than can be obtained for each strip in a single interval, so this is done only on a plane-by-plane basis. For the strip-to-strip correction, the truncated mean is used as a proxy for the peak.
Differences in the relationship between the truncated mean and the peak could arise due to differences in the shape of the energy distributions between channels. Scintillator aging and absorber effects are expected to be among the leading causes of such shape differences. Scintillator within a plane was manufactured and installed at the same time, so aging effects might exist between planes but are uniform across strips within a plane.
Absorber effects are uniform across a plane in the downstream calorimeters.
Non-uniform absorbers exist in the upstream nuclear target region and in the side ECAL. This could introduce differences in the shape of the response within a plane. The size of this difference is estimated by comparing the size of the fitted peak correction of Eq. (8) between the central tracking region and downstream ECAL region. This correction is essentially the amount by which the truncated mean overestimates the peak; it is 1.6% higher on average in the ECAL than in the tracking region. A similar difference might exist in the side ECAL but is not taken into account. The truncated mean is computed iteratively. The mean for the first iteration is the full mean of events from 0 to 20 MeV per centimeter path length. In each successive iteration, the mean is calculated using events that fall between 50% and 150% of the mean from the previous iteration. Eight iterations are used; however the procedure typically converges within four iterations.
Events for which there is reconstructed path length but with null energy are counted separately. A channel is considered dead when zero-energy tracks represent more than 30% of all events. In addition to removing dead channels in which the zero-energy percentage is near 100%, this cut also eliminates extremely low-light channels where the ex- The constant C i for strip i is where x i is the truncated mean energy in strip i, and N is the number of good channels in the inner detector. The sum in the denominator is over all good channels, indexed by j. This definition guarantees that the average constant is 1.0, so that application of the constants will correct for strip-to-strip energy differences without affecting the overall energy scale.
The fitted peak correction is performed only after data is processed with the first iteration of strip-to-strip constants based on the truncated mean. This ensures that the energy distribution in a plane is not due to large variations between constituent strips.
The correction factor C j for plane j is where E j is the truncated mean energy averaged over a plane, p j is the fitted peak energy for a plane, n is the number of planes, and the sum in the denominator is over planes. The applied strip-to-strip constant is the product of the constant from Eq. (7) for two iterations and the plane-to-plane constant from Eq. (8).
After applying the calibrations, the plane-to-plane peak energy is roughly uniform over the modules, as shown in Fig. 25. Non-statistical fluctuations, such as in the ECAL region from module 85 to 95, could be reduced by further iterations of fitting but are already approximately the size of the fit uncertainty after one iteration.

Absolute Energy Scale Determination Using Minimum Ionizing Particles
The absolute energy scale of MINERvA is calibrated using the well understood muon The trial MEU factor is corrected by the ratio of simulated to data reconstructed energy and by the slope of the simulated reconstructed to simulated true energy to give the final MEU factor. The tuning uses the peak reconstructed cluster energy to minimize absorber effects and muon energy loss. Absorber effects, particularly delta ray propagation and absorption, vary by subdetector due to the passive materials. Delta rays contribute primarily to the high-side tail of the cluster energy distribution, and sampling the peak minimizes this contribution.
Reconstructed cluster energy in the simulation includes simulated detector effects that smear true cluster energy. Detector smearing shifts the peak of the true cluster energy distribution while preserving the mean. It gives the correct absolute energy scale by correcting the reconstructed cluster energy mean from the simulation to the true cluster energy mean using the slope of reconstructed versus true cluster energy in the simulation.
The light output of the scintillator is found to vary with time due to scintillator aging and environmental conditions of the detector hall. Figure 28 shows the peak cluster PE

Cross-talk Measurements
A number of processes can cause light incident on one PMT channel to produce a signal in another channel. These are collectively known as "cross-talk." While these can, in principle, be differentiated by tests on the bench, once the detector components are assembled and installed it is virtually impossible to separate them from one another with any significant confidence, particularly at large pulse-heights. As discussed in Sects. 5.2 and 5.3 the dominant types of cross-talk in MINERvA are optical (fiber-to-PMT coupling) and PMT internal (dynode chain). Effects other than the readout electronics cross-talk discussed in Sect. 5.3 will be discussed here.
The ideal probe for a measurement of either type of cross-talk in the detector would be one in which individual pixels were illuminated with a well-defined light pulse. Unfortunately, once a PMT is mounted on the detector there is no system available to MINERvA that can accomplish this goal. The LI system discussed in Section 6.2.1 cannot be used because it illuminates all pixels at once. The next best option is to use data generated by neutrino interactions. For this measurement, we use the data-set from rock muons described in Section 6.5.
Hits within a rock muon's time slice are classified as signal or noise based on whether or not they have been associated with the track by the track reconstruction software. The fiber weave described in Section 3.4 moves cross-talk hits far enough away from the track that they are not associated with it. Cross-talk hits can be further distinguished from other noise by assuming that the hit occurs in the same PMT as on-track activity, and associating each cross-talk hit to the on-track hit that is nearest to it on the PMT pixel grid. A sketch of how this process would work for a typical muon event is shown in Fig.

31.
Once hits have been identified as signal or cross-talk and the rest discarded, an average cross-talk fraction f xt for the PMT is defined as the ratio of the energy of cross-talk hits to the energy of the on-track hits. Various permutations of this metric are also used, most notably the "nearest neighbor" pixel cross-talk f xt,NN average for each PMT, because the strongest cross-talk is generally generally between nearest-neighbor pixels.
The measured values of f xt,NN for PMTs currently in use in MINERvA are shown as the black points in Fig. 32. The vast majority of PMTs have total nearest-neighbor crosstalk fractions below 4%. Comparisons with the detector simulation can also be made using this method. The red curve in Fig. 32 depicts the simulation's prediction for the optical cross-talk component only (the dominant mechanism and the sample used to tune Though the simulation's per-PMT averages do not identically match the data, the individual pulse height spectra for simulated cross-talk hits do agree. Figure 33 illustrates this: within the 1-3.5 photoelectron range (where cross-talk is most important), the difference between simulation and data is typically less than 10%. Below this range, agreement is less important in practice because the electronic discriminator threshold for nearly all FEBs is roughly 0.8 PE. Above this range, agreement is again less essential because the Poisson probability for a resultant cross-talk hit of this pulse height is extremely low. For example, the probability of a 4 PE cross-talk hit resulting from a 100 PE hit from neutrinoinduced activity, assuming the nominal 1% nearest-neighbor cross-talk leakage quoted above, is roughly 1.5%; for a 25 PE hit, the probability drops to about 0.01%. Moreover, ≥ 100 PE hits (corresponding to roughly 25 MeV of energy deposited in a single strip) are rare; they comprise less than 1% of usable (i.e., discriminated) hits in typical LE data. in the two detectors. The momentum is measured using range or curvature in MINOS and the sign of the track charge is determined using the direction of track curvature as described below.

Cluster Formation
Due to the overlapping triangular profiles of the scintillating strips in the central detector, particles traversing a plane will normally pass through at least two strips in the plane, and can induce activity in more than two strips, giving a "cluster" of activity. The first step in reconstruction of events is identification of clusters. Clusters are formed from groups of hits directly adjacent to each other in a single plane, within the same time slice.
Any strip which does not register hits between strips with valid hits leads to a new clus-ter being formed. An isolated strip without neighbors that has registered a hit is also identified as a cluster.
A position is calculated for each cluster based on the energy deposition in the strips.
The energy-weighted position is calculated using all hits contained within a cluster. A time is also found for a cluster, where the time from the hit with the most energy within the cluster is assigned as the cluster time. The resulting clusters are classified by their composition. The types of clusters are: low activity, trackable, heavily ionizing, superclusters, or cross-talk.
(i) Low activity clusters are those with a total energy deposit of less than 1 MeV.
(ii) Trackable clusters meet the following requirements: total cluster energy between 1 and 12 MeV, four hits or fewer, and at least one hit with more than 0.5 MeV. If more than two hits have a hit energy greater than 0.5 MeV, they must be adjacent to each other.
(iii) Heavily ionizing clusters must meet similar criteria to trackable clusters: total cluster energy greater than 1 MeV and one to three hits with energy greater than 0.5 MeV.
If two or three hits are greater than 0.5 MeV, they must be adjacent to each other. In addition, it must not be a trackable cluster. Heavily ionizing clusters are important in forming high angle tracks.
(iv) Superclusters are those with more than 1 MeV in energy that do not meet the criteria for either trackable or heavily ionizing clusters. Any cluster with five or more hits is automatically considered a supercluster.
(v) Cross-talk clusters are identified by inspecting the PMT pixels associated with hits within that cluster. The PMT pixels associated with that cluster are compared to PMT pixels associated with a particle interaction. If these cluster PMT pixels are found to be directly adjacent to the pixels related to the particle interaction, the cluster is considered to be a cross-talk cluster.

Track Reconstruction in MINERvA
A "track" is a reconstructed object that approximates a charged particle's trajectory through the detector. Typically, only one track is needed to reconstruct a particle trajectory, but multiple tracks may be necessary if the particle undergoes a large-angle scatter or else decays. A single track pattern recognition scheme is used multiple times to find all tracks in an event.
The track pattern recognition uses all "seeds" within a single time-slice, where a seed is a collection of three trackable or heavy-ionizing clusters that meet the following requirements: no two clusters in the same plane; each cluster's plane is in the same orientation (X, U, or V); clusters must be in consecutive planes, when the planes are sorted by orientation and longitudinal position; and clusters must satisfy a fit to a two-dimensional line.
A single cluster may be used to make multiple seeds. These requirements limit seeds to an angle of less than 70 • with respect to the longitudinal axis, which in turn imposes a similar limit upon reconstructed tracks.
Seeds within the same plane orientation are merged to form track "candidates". The merger of two seeds requires that: the slope of the seeds' linear fits are consistent; the seeds share at least one cluster; and the seeds do not contain different clusters in the same scintillator plane. If the algorithm merges two seeds into a candidate, it will attempt to merge additional seeds to the candidate using the same criteria. A seed may only be used by one candidate, therefore this stage of the algorithm is sensitive to the order of merging attempts. After all candidates are built, they may be merged using criteria similar to those for seeds; they must have consistent fitted slopes and intercepts and may not contain different clusters in the same scintillator plane. Track candidates are not required to share clusters and therefore may contain gaps, i.e. tracks that cross a scintillator plane without containing a cluster in that plane. This allows a track candidate to accurately follow particle trajectories that intersect dead regions in the detector.
Two algorithms are used in succession to attempt to form 3D-track objects from track candidates. The first algorithm examines all possible combinations of three candidates in which no two candidates share the same plane orientation. Such a combination of candidates are formed into a 3D-track if they overlap longitudinally and are mutually consistent with the same three-dimensional line. By requiring a track candidate in each view, this algorithm is unable to form tracks that intersect fewer than 11 planes. The algorithm also searches for a particular topology in which a particle trajectory bends in only two views. In this instance, the combination of candidates will fail the overlap requirement because the candidate in the view without a visible bend will be longer. If this topology is detected, the longer candidate is broken into two shorter candidates and kinked tracks are found.
The second algorithm considers all remaining candidates that have not been used to make a track. It forms all possible combinations of two candidates which do not share the same plane orientation. If the candidates have a similar longitudinal overlap, they are used to construct a three-dimensional line. A search for unused clusters that have a position consistent with the candidate pair is then performed in the remaining view and a 3D-track is formed if a sufficient number of clusters is found. This algorithm is more successful in tracking particle trajectories that are obscured by detector activity in one of the three orientations and is able to make tracks that intersect as few as 9 planes.
Both algorithms reject candidates that contain only one seed with an angle greater than 60 • with respect to the neutrino beam direction; such candidates typically correspond to random energy deposits that happen to fit a straight line.
All 3D-tracks that are found are fit by a Kalman filter fit routine that includes multiple scattering [19]. The fit is required to converge, but there is no requirement placed on the fit χ 2 . Figure 34 shows the tracking position resolution after the Kalman filter fit. The fit is then used to add additional clusters to the track by searching nearby planes for which the track does not contain a cluster. Superclusters are made available here, allowing the track to project into a region of shower-like activity (as in the case of a muon track that is partially obscured by a hadronic shower in all three views). Multiple tracks are allowed to claim the same cluster, each taking a fraction of its energy, to handle situations where two tracks intersect the same supercluster. The track pattern recognition scheme described above is used by a master reconstruction algorithm designed to reconstruct high-multiplicity final states while imposing restrictions to reduce the number of tracks formed from unrelated detector activity. If at least one track of 25 clusters or more is found, the longest track is designated the "anchor track" and its clusters are marked as used. The starting point of the anchor track is used to define the neutrino interaction location, called the primary vertex. The track pattern recognition is then re-run on the remaining un-used clusters. Tracks consistent with emerging from the primary vertex are identified and the primary vertex location is re-estimated with the Kalman filter technique [20] using all tracks. Tracks that are inconsistent with emerging from the primary vertex are deleted. The procedure is repeated, searching for tracks consistent with the endpoint of each track emerging from the primary vertex, in order to find particle trajectories that abruptly change direction due to secondary interactions. Figure 36 illustrates this procedure using event displays.
Each found track is submitted to a procedure, called "cleaning," that removes extra energy, which varies according to the type of track found. The purpose of cleaning is twofold: to remove the energy that is likely to be unrelated to the tracked particle so that it may be used by future iterations of the track pattern recognition, and to improve the vertex energy measurement. Anchor tracks are typically found to be muons and are thus expected to deposit energy as a MIP. If the track contains energy near the vertex that is inconsistent with a MIP, or contains a supercluster, the extra energy is removed from the track. Non-anchor tracks are assumed to be hadronic and only their superclusters are cleaned thereby minimizing bias in downstream particle identification algorithms. The non-anchored track will only use energy from the supercluster in strips that intersect the track fit. If the supercluster is near the track's endpoint, the track will incorporate as much energy as possible from the intersected strips in order not to disturb the energy loss profile of the Bragg peak. Otherwise, the track will use an energy equal to its mean cluster energy.

Charge Determination and Energy Reconstruction
The Charged particles traversing MINOS are deflected due to the magnetic field. From this deflection, information about the charge and momentum of the particle can be extracted using the same procedures used by the MINOS collaboration. [27]. In neutrino mode, if the deflection is towards the coil, the muon is negatively charged; and if the muon is deflected away from the coil, the charge is positive. The coil polarity is normally The µ ± momentum in MINOS is determined by two different methods: range and curvature. The range method is based on total energy loss through interactions in the MINOS detector and is applied only to muons that are contained inside the calorimeter region. The curvature method reconstructs the momentum by means a track fitting algorithm developed by MINOS [29]. The algorithm relates the curvature of the track (K), the magnetic field (B) and the momentum component perpendicular to the field (P ), according to where R is the radius of curvature.
The two methods differ in their ability to reconstruct momentum, as illustrated in Figs. 37 and 38. The P range method is more precise; its estimated systematic uncertainty is 2% [27] derived from uncertainties on the simulation of the MINOS geometry, detector mass, and dE/dx parameterization, and track vertex reconstruction. The momentum resolution for muons in MINOS is 10% (5%) for muons measured by curvature (range) [28].
For muons initiated in MINERvA which are sufficiently energetic to escape from the calorimeter region of MINOS, the momentum is reconstructed via the P curv method. This is done because the coarser sampling in the MINOS spectrometer region and the fact that the signals in that region are summed together. Both facts together result in a potential bias in momentum determinations based on range due to the high accidental activity.
MINERvA has developed an approach to calculate the systematic uncertainty of the P curv method that is similar to that used by the MINOS collaboration [27].
This study does differ from that of MINOS because it uses a high-statistics rock muon sample illuminating the entire face of the MINOS detector and it uses a well-defined track vertex at the front face of the MINOS detector. For this study, only muon tracks that are contained in the fully instrumented part of MINOS are used, so that information is available from both the P range and P curv methods.
In order to determine the systematic error on P curv , the (1/P curv −1/P range ) distributions of the data and the simulation were divided into six P range bins to determine the error as a function of the momentum. The arithmetic means for the data,μ data , and simulation, µ M C , distributions are found. Then the curvature difference, defined as ∆K = |μ data −μ M C |, or the deviation of the 1/P curv measurement from the 1/P range measurement is obtained.
For small curvature uncertainty, ∆K, ∆P curv = −P 2 curv ∆K. The additional systematic uncertainties on muon momenta measured by curvature are 0.6% for muons with momenta greater than 1 GeV/c and 2.5% for those less than 1 GeV/c. The range and curvature uncertainties for muons measured by curvature are added in quadrature to obtain the total muon momentum uncertainty for muons measured by curvature of 2.1% (3.1%) for muons with momenta above (below) 1 GeV.

Muon Reconstruction Efficiency and Acceptance
The muon reconstruction efficiencies are evaluated using simulated inclusive charged current muon neutrino interactions inside the MINERvA detector tracker region. All muons are counted in the efficiency denominator, and the efficiency numerator is determined by matching reconstructed tracks to the true particle trajectory that deposited the most energy into the clusters on the track. A true muon is "tracked" if a track is matched to it in this manner.

Recoil Energy Reconstruction
MINERvA is a finely grained detector, capable of identifying individual particles in the recoil system (event energy not associated with the primary lepton) for moderate multiplicity events. As of early 2013, the energy of the recoil system is reconstructed MINERvA currently employs a simple calorimetric sum in which energy in the subdetectors not associated with the muon track is weighted to account for the active fraction of the scintillator planes and additional passive absorber. The calorimetric constants are determined by the dE/dx of a minimum ionizing particle at normal incidence. For a given sub-detector, the calorimetric constant is given by: where E abs is the energy loss in one absorber plane, E sc is the energy loss in one scintillator plane, and f is the active fraction of the scintillator plane in that sub-detector. For the central tracking region, E abs = 0, yielding C sd = 1/f = 1.222 from the 81.85% active fraction. The corresponding fractions for the ECAL and HCAL are 2.013 and 10.314.
The constant for the OD is likewise calculated assuming normal incidence into the OD (orthogonal to the beam axis).
An overall calorimetric scale is derived by fitting calorimetric reconstructed recoil energy to true recoil energy for simulated events. True recoil energy is defined as the energy of the neutrino minus the energy of the outgoing lepton Calorimetric reconstructed recoil energy is defined as: where α is the overall scale, i = {central tracking region, ECAL, HCAL, OD}, C sd i is the calorimetric constant for sub-detector i and E i is the total visible recoil energy in subdetector i, calculated from all clusters of hits within a −20 to 35 ns window around the event time (defined by the muon) and not identified as cross-talk. This time window is narrower than a typical time slice to remove pile-up from neutrino and background interactions that are adjacent in time. The cross-talk rejection prevents energy from the muon track being included in the calorimetric sum.
The parameter α is determined by minimizing the quality factor Q where the summation is over events of true recoil energy between 1.0 and 10.0 GeV, and N is the total number of such events. This metric is less susceptible to the asymmetric tails of the E cal recoil /E true recoil distribution, which is bounded below by zero, and bounded from above by energetic hits in the active portion of the calorimeters (which are weighted up by the calorimetric constants) and overlapping events.
After fitting α, ∆E/E true recoil = (E cal recoil − E true recoil )/E true recoil is plotted in bins of true recoil energy. A per-bin energy correction is derived in the form of a polyline mapping E cal recoil to E cal recoil . Each node on the polyline corresponds to one true recoil energy bin, with where E true recoil is the average true recoil energy in the bin, and η is the mean of a Gaussian fit to the distribution. For example, if a bin with E true recoil = 1.0 GeV is 3% low (η = -0.03), the polyline maps 0.97 GeV to 1.0 GeV. The lower limit of the polyline is fixed at (0.0, 0.0) GeV; the upper limit is fixed at (50.0, 50.0) GeV.
For simulated charged-current events with MINOS-matched muons and with vertices within the fiducial tracking region, the value α = 1.568 is obtained, with a calorimetric energy resolution of σ/E = 0.134⊕0.290/ √ E (see Fig. 40). The observed calorimetric energy resolution is a convolution of many effects: final-state interactions, shower fluctuations to electromagnetic, hadronic and neutral components, passive absorber deposition, scintillator, PMT and electronics response, attenuation along scintillator strips, containment in the detector, and overlapping events. For the lowest recoil energies (below 1 GeV) the systematic uncertinty is considerably lower than suggested by the parameterization. This is due to the fact that for those events the recoil system is dominated by a single proton that is not subject to many of the sources of shower fluctuations, and the particle is usually contained in the fully active region. In these cases the resolution is better if the ionization profile is fit to a proton hypothesis, as described in Sec. 10.2.

Test Beam Detector Response Calibration
The

Pions
The GEANT4 simulation of pions is approximately consistent with the pion data in the ECAL + HCAL configuration as illustrated in Fig. 41. At the low end of the momentum range, differences between the data and simulation are 5% on average, with the simulated response somewhat lower. Consequently a 5% uncertainty is assigned to the calorimetric energy response for pions in that energy regime. The energy resolution is well reproduced in the simulation.

Protons
A proton sample is used to set constraints on the proton calorimetry response. An analysis similar to the pion case for the ECAL + HCAL configuration gives an uncertainty in the calorimetric response of 5% for protons of momenta between 1 and 2 GeV/c.

Stopping protons and Birks' parameter
The proton sample is also used to study the Birks' law behavior of stopping protons in the central tracking region. The central tracking + ECAL configuration has too little material to contain interacting protons of momenta exceeding 1 GeV/c, but does provide constraints on calorimetry for lower momenta. A subset of the latter sample is used to study saturation behavior of the scintillator, which is commonly parameterized using Birks' Law, where the ionization is scaled by a factor of (1 + k B × dE/dx) −1 . Events are selected which terminate in a tracking region plane between 11 and 19 and have a gap of no more than one plane upstream of that point.
For all planes of all selected proton events, the distribution of energy loss per plane is formed as a function of the number of planes from the end of the event and shown in and higher (bottom), corresponding to higher and lower response, respectively. The ratio is taken relative to the default simulation (not shown).
A full description of the test beam program and associated measurements is the subject of a separate manuscript which currently is in preparation.

Detector Performance
Once all calibration procedures are complete, several checks are done to ensure that the detector's energy scales are accurate, well-modeled in the simulation, and constant over time. Charged current events in the detector are used as checks, since their analysis requires all the calibration steps described in this article, and occur at high enough rates to provide precise measurements of the energy scales as a function of time. Another check of the reconstruction is the energy deposition at the end of a track for particles that stop in the active region of the detector. Other calibration cross-checks use the electrons that come from muon decays, for those muons that stopped in the detector (Michel electrons).
This chapter demonstrates the performance of the calibrated detector using these three data samples.

Charged Current Interactions
Muon neutrino and muon antineutrino charged current (CC) interactions occurring within the ID volume provide high statistics checks of both the muon and recoil energy reconstruction, since the CC reactions ν µ (ν µ )N → µ − (µ + ) + X, include both a muon and a hadronic recoil system.
Events are selected as follows: first, the event must contain a reconstructed track which matches a muon reconstructed in the MINOS detector where its momentum and charge are determined; second, the reconstructed muon vertex must lie within a fiducial volume in the scintillator-only section of the MINERvA ID (see Sect. 1.1). The event must not contain any dead channels induced by previous interactions. Channels whose discriminators trip due to detector activity experience a dead-time, where they are insensitive to new energy, during an approximately 100 ns push-and-reset period which follows the ∼150 ns charge integration window. We require that there be no more than one such dead discriminator in a path projected upstream of the muon track. This selection is essential to prevent rock muons with tracks partially lost to dead time from being confused with fiducial events.

Energy Loss for Stopping Particles
The granularity and light yield of the detector make it possible to use dE/dx profiles near the ends of the tracks to identify some of the particles that stop in the detector. In cases where the hadron loses energy via electromagnetic processes, decays in flight, elastically scatters, or undergoes minimum inelastic hadron scattering, the dE/dx distinguishes between minimum and heavily ionizing particles. However, because hadrons traversing the detector can undergo various other processes, such as inelastic scattering, pion charge exchange, and absorption in flight, the particle's dE/dx profile cannot always be used in this fashion.
In practice, for every track that is found, a χ 2 is determined by comparing the energy deposited per scintillator plane to templates derived from the dE/dx profile expected in the detector for different momenta and for two different particle types: pion and proton. When available, the dE/dx information is also used to measure energy for stopping particles more precisely than a calorimetric energy sum. Figure 45 shows the predicted momentum resolution derived from dE/dx information for protons and pions that stop in the inner tracking region of the MINERvA detector.

Michel Electrons
Michel electrons are produced by a stopped (anti-) muon from a neutrino interaction or the decay chain of π ± . The response of the detector to Michel electrons at different locations provides a cross-check of the relative calibration. The overall electromagnetic energy scale can also be checked by comparing the Michel electron spectrum in the data to that predicted by a simulation tuned to muon energy depositions.
In principle, a Michel electron is most cleanly identified by searching for a delayed

Energy loss by Electrons and Photons
The separation of electrons from photons is important for studying electromagnetic final states in MINERvA. The high granularity and low Z nuclei of the central tracking region allows the dE/dx near the beginning of electromagnetic showers to be used to distinguish electrons from photons. Electrons lose energy as a single highly-ionizing particle near the start of a track. Because a photon produces an electron-positron pair when it converts to form a track, the energy loss is then twice that of an electron. This difference in dE/dx is only valid near the start of a shower because an electromagnetic (EM) shower develops stochastically as it propagates. Consequently, the average dE/dx over the first four planes at the start of an EM shower is a good discriminant. A distribution of the average dE/dx over the first 4 planes for Michel electron events is shown in Fig. 47.

Conclusions
The MINERvA detector has been operating since March 2010, and has achieved a total integrated live time exceeding 97% for the "Low Energy" run that extended through the end of April 2012. During that time over 99.5% of the channels were live and calibrated, using in situ neutrino beam-induced calibration samples and ex situ tests.
The detector energy scale for the signal initiated by minimum ionizing particles is understood at the 2% level and the response has been calibrated to be constant to better than 1% across the 200 scintillator planes in the detector. Although the light level decreased by over 15% due to scintillator aging during the course of the initial two-year run, a calibrated energy stability of better than 2.5% and a timing resolution of better than The detector composition is an important part of any cross section measurement. The fiducial masses and chemical makeup of this detector and its various nuclear targets have been measured at the 1.5% level for the scintillator planes and at the 1% level for the solid nuclear targets.
The MINOS near detector plays an integral role in any MINERvA CC cross section measurement. The MINERvA implementation of the MINOS near detector geometry and reconstruction are shown to give an absolute muon energy scale to 2.6% (3.1%) for muons above (below) 1.0 GeV for muon momenta measured by curvature. The momentum uncertainty for muons measured with range is 2%, as determined by MINOS material assay, dE/dx parameterization, and track reconstruction uncertainties.
In summary, detailed neutrino cross section measurements for both exclusive and inclusive channels for a wide range of target nuclei is now underway as the result of implementation by MINERvA of the detector design and calibration approaches reported in this article.

Acknowledgments
This work was supported by the Fermi National Accelerator Laboratory, which is op- ERvA Collaboration wishes to express its thanks to the MINOS Collaboration for the use of its near detector data, reconstruction, calibration and simulation. Finally, the authors are grateful to the staff of Fermilab for their contribution to this effort, during the design, construction, data taking and data analysis phases of the experiment.