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Electron attenuation measurement using cosmic ray muons at the MicroBooNE LArTPC

The MicroBooNE experiment at Fermilab uses liquid argon time projection chamber (LArTPC) technology to study neutrino interactions in argon. A fundamental requirement for LArTPCs is to achieve and maintain a low level of electronegative contaminants in the liquid to minimize the capture of drifting ionization electrons. The attenuation time for the drifting electrons should be long compared to the maximum drift time, so that the signals from particle tracks that generate ionization electrons with long drift paths can be detected efficiently. In this talk we present MicroBooNE measurement of electron attenuation using cosmic ray muons. The result yields a minimum electron 1/e lifetime of 18 ms under typical operating conditions, which is long compared to the maximum drift time of 2.3 ms.


Introduction
Liquid Argon Time Projection Chamber (LArTPC) detectors provide exceptional calorimetric and track reconstruction capabilities compared to various other detector technologies. This technology has already shown great promise to be one of the ideal detector technologies to study neutrino interactions with matter. In a LArTPC, neutrinos interact with argon atoms and produce secondary charged particles (e.g protons, muons etc). These secondary charged particles ionize argon atoms and produce ionization electrons and scintillation light. The ionization electrons drift to the anode wire planes under an external electric field whereas scintillation light is collected by photo multiplier tubes (PMTs) located behind the anode wire planes. Ultimately, one can retrieve the information registered in the PMT system and anode wire planes to reconstruct 3D images of particle tracks and their energies.
One of the critical operational requirements of a LArTPC is ultra pure liquid argon. Electronegative contaminants like H 2 O and O 2 can degrade the liquid argon purity. These contaminants can capture some of the drifting ionization electrons and thus directly impact the reconstruction of particle energies. This capture process is electric field dependent where at higher electric fields ionization electrons have more chance of drifting all the way to the anode wire planes.
Here n e (t 0 ) stands for the initial number of electrons whereas n e (t drift ) is the number of electrons after a time t drift . An important parameter in this equation is τ , which stands for the electron lifetime. The electron lifetime contains information about the amount of electronegative contaminants present in the detector where a higher electron lifetime is indicative of low levels of contamination [1,2]. If liquid argon is 100% pure then τ should ideally be infinite. Figure 1 shows the fractional loss of ionization electrons as a function of their drift distance for different electron lifetimes. It is obvious that having a higher electron lifetime in the system guarantees that more ionization electrons survive. where each plane has a wire pitch (separation between two of the neighboring wires, which make up the plane) of 3 mm. The two induction planes (U and V) are inclined +60 o and -60 o with respect to the vertical collection plane (Y). The maximum drift distance of the experiment is 2.56 m where it takes ∼2.3 ms for ionization electrons to drift from cathode to anode across the detector. The light collection system of the experiment consists of 32 8-inch PMTs located behind the anode wire planes.
The state of the art purification system in the experiment maintains the electronegative contaminants at extremely low levels which is vital for the performance of the detector. The purification system consists of two pairs of filters [9,10]

Measuring electron lifetime(τ ) in MicroBooNE
There are several methods one can use to measure the electron lifetime in Micro-BooNE. They are: • Gas analyzers • Purity monitors [3] • Laser tracks [5,19] • Long minimum ionizing cosmic ray muon tracks [4] Since MicroBooNE is located close to the surface, it sees abundant cosmic muons. Quantitatively, in the 4.8 ms wide readout window of MicroBooNE there are approximately 25 comic muons crossing the detector ( Figure 3). Because of this cosmic muons provide good statistics to perform the measurement. In addition cosmic muons are uniformly distributed throughout making the measurement to be sensitive to any local variations of external electric field and electronegative contaminant levels inside the detector. But knowing the correct arrival time (or, t 0 ) of these cosmic muons is critical for this measurement as one needs to know how long the charge drifted in the TPC. There are two types of cosmic muon datasets for which t 0 information is known.
• Cosmic muons tagged by a small external cosmic ray counter [20] • TPC anode-cathode crossing tracks (Crossing tracks) Since crossing tracks have wide angular coverage compared to tracks tagged by the small external cosmic-ray counter and cover the full drift distance, these tracks are preferred. The measurement shown in this document uses the TPC anode-cathode crossing tracks.

Event Selection
Several selection cuts are applied in the analysis to select the best quality cosmic tracks.
• The track projected length in the drift direction (X) must be between 250 cm to 270 cm.
Ideally the X projected track length of a crossing track should be 256 cm (drift distance of MicroBooNE). But due to track reconstruction and space charge effects a spread of this quantity is observed ( Figure 4). • Exclude tracks with the angular orientation 75 0 <θ XZ < 105 0 or 85 0 <θ Y Z < 95 0 .
θ XZ is the angle defined in X-Z plane with respect to the Z direction whereas θ Y Z is the angle defined in the Y-Z plane with respect to the Z direction. The θ XZ (θ Y Z ) cut eliminates tracks that are nearly perpendicular (parallel) to the collection plane wires. These tracks tend to be mis-reconstructed with low quality calorimetric information.
• The track must have a minimum of 100 hits registered in the collection wire plane.
This ensures a uniform density of hits along the drift direction and better reconstructed tracks.
• Exclude hits from tracks which correspond to shorted channel TPC regions.
We require that hit Y and Z coordinates are not in the regions, (-100 cm<Y< 20 cm) and (250 cm<Z<675 cm), respectively. In the shorted channel regions of the TPC, the collection wire plane response is altered and properly reconstructed calorimetric information was not available for hits [13].

Analysis Method
The following method is used to calculate the electron attenuation (electron lifetime) from a set of crossing tracks which satisfy all the selection criterion described in the previous section.
• The start time (t 0 ) of the track is calculated : For TPC crossing tracks either light information or hit information can be used to extract t 0 . At the time of this analysis, light reconstruction wasn't reliable. So hit information is used to get t 0 . Minimum drift coordinate of the crossing track provides the t 0 . Once t 0 is known, each drift coordinate of the track is corrected using Equation 2.
• The full drift time window (2.2 ms) is split into smaller 100 µs wide time windows ( Figure 5(a)).
• For each drift time bin, the charge deposited per unit length (dQ/dx) distribution is produced and fit with a Landau convoluted with a Gaussian function [15] to get the Most Probable Value (MPV) of dQ/dx representing that time bin ( Figure 6).
• All 22 most probable dQ/dx values are plotted against drift time and this final distribution is fit with a function f(t) to get the final Q A /Q C charge ratio ( Figure  5(b)).
The final Q A /Q C charge ratio is calculated using Equation 3 which gives the fractional change in charge due to capture by electronegative contaminants when a cloud of ionization electrons drift from cathode to anode. Ideally f(t) should be exponential. But the presence of space charge and other effects can skew the dQ/dx distribution resulting in non-exponential shapes. Second-order polynomial and exponential plus constant functions are also used to fit to the final distribution. Once the Q A /Q C charge ratio is calculated, assuming an exponential behavior, one can translate it into an electron lifetime using Equation 4. It was observed that for most of the runs, the final Q A /Q C value is greater than 1 due to space charge effects.
In Equation 3, the numerator and denominator stand for the amount of charge arriving at the anode after 2.2 ms and charge leaving the cathode at 0 ms, respectively.
Here t drift should be replaced by 2200 µs to get τ .

Space Charge Effects
Since MicroBooNE is surface-based, a lot of cosmic activity is present in the detector. As a result of slow moving positive argon ions get accumulated leading to distortions in the applied electric field both in its magnitude (Figure 7(a)) and direction. Once the directionality of the electric field is impacted, it can affect reconstructed position of ionization electron clusters (Figure 7(b)) and calorimetric information (dQ/dx). The magnitude change of the electric field directly affects electron-ion recombination. The lower the applied electric field the stronger the recombination gets. From MicroBooNE simulations, it is estimated that the electric field close to the cathode increases by ∼12% whereas at the anode it decreases by ∼5%. The modified box model is used to describe the electron-ion recombination [14] in MicroBooNE where it shows dQ/dx values increasing by ∼3.55% close to the cathode and decreasing by ∼1.2% close the to anode. (See section 9.3 for more details on recombination).
In order to see the impact of space charge effects on the final measurement, a 3D space charge model is implemented in simulation and isotropic single muon monte carlo samples are created with a very high electron lifetime switching off all other effects such as diffusion which can affect the attenuation mesurement. The positive slope of Figure 8(b) shows final Q A /Q A charge ratio can be greater than 1 due to space charge effects.

Space Charge Correction
As space charge effects (SCE) significantly impact the final measurement, a correction is derived using the following procedure.
• The correction "C" is derived for dQ/dx values.
The correction for dQ/dx values is defined for all 22 drift bins using Equation 5 based on the two dQ/dx distributions in Figure 8.
• A third order polynomial fit is used to extract corrections.
To make the derived corrections uniform, the correction "C" is plotted as a function of drift time and the resultant distribution is fit with a third order polynomial ( Figure  9). The final corrections "C" for each bin are extracted using the polynomial fit. This space charge correction can be applied to data using Equation 6. Here, dQ/dx stands for the uncorrected value from data including space charge effects.

Data Sample
Cosmic muon data ranging from 02/16/2016 to 04/21/2016 is used in this analysis. Each dataset has approximately 5000 events processed to study the variation of electron attenuation on a daily basis. The time difference between two consecutive data sets is ∼24 hours and the detector spans a range of low purity conditions to high purity conditions during the selected time period. Some of the datasets are missing in this time period due to data processing problems.

Variation of Q A /Q C
The plot in the Figure 10 shows the variation of the Q A /Q C charge ratio over time by analyzing 56 datasets described in section 7 using the procedure explained in section 5 with and without the space charge corrections derived in section 6.1.

Systematic Uncertainties
A number of possible sources of systematic uncertainty are considered in this analysis. Among them, the dominant systematic uncertainty comes from the space charge correction used in the analysis. The other systematics that effect this measurement in a minor way are recombination and diffusion. Both data-drive and monte-carlobased techniques are used in addressing systematics.

Space charge correction uncertainty
Space charge corrections described in section 6.1 are derived from the 3D space charge model implemented in the simulations which is only valid for the central Z region. So to account for space charge model dependency, a large uncertainty is associated to the final Q A /Q C charge ratio values corresponding to 50% of the difference of the two Q A /Q C charge ratios before and after the space charge correction. This is done separately for all 56 data sets where the systematic varies between 1.4% to 7.5% with an average uncertainty of 4.6%. The systematic is assigned to be 5.0% of the final Q A /Q C charge ratio for all data sets.

Diffusion
Diffusion can smear the ionization electron cloud as they drift from cathode to anode by affecting the charge collected by the anode plane wires. In particular, the transverse component of the diffusion which is perpendicular to the drift direction can leak the charge to neighboring wires from the target wire inducing modifications to the The systematic is assigned to be the difference between Q A /Q C charge ratios with and without diffusion, which is 2.0% of the final value.

Recombination
As explained before, in the current MicroBooNE simulation the electron-ion recombination is described by modified box model. Equation 7 shows the relationship between the recombination factor "R box " and the electric field.
To account for the model dependency of recombination in the electron attenuation measurement, two single isotropic muon monte carlo samples are generated, one having the default values for β p and α in the recombination model whereas in the other these two values are maximally changed ( by 0.01 (kV/cm)(g/cm 2 )/MeV and 0.1 respectively). In both of these samples all the other effects are turned off such as diffusion with the exception the change in the magnitude of the electric field due to space charge effects. The percentage difference of the Q A /Q C charge ratios between samples with modified parameter and default parameter settings is found to be 1.0% with respect to the Q A /Q C charge ratio extracted for default parameter setting. This is assigned to be the systematic value coming from recombination model dependency. Table 1 summarizes all the systematics considered in the analysis.  Table 1: Systematic uncertainties in the final Q A /Q C charge ratio. The total is calculated by adding individual systematics in quadrature.