# A study of electron recombination using highly ionizing particles in the ArgoNeuT Liquid Argon TPC

^{1}, Yale University

^{2}, Syracuse University

^{3}, Kansas State University

^{4}, Michigan State University

^{5}, University of L'Aquila

^{6}, University of Bern

^{7}, University of Texas at Austin

^{8}, Lodz University of Technology

^{9}

## Summary (3 min read)

### 1. Introduction

- Liquid Argon Time Projection Chambers (LAr TPCs) offer excellent calorimetry and mm-scale position resolution in a large volume and are increasingly favored for the next generation of neutrino detectors.
- Particles in the MeV - few GeV energy range of interest for neutrino detectors are usually contained within the TPC and can be well characterized by range, calorimetry and decay topology.
- Calorimetric reconstruction requires calibration to correct for detector specific effects such as liquid argon impurities and electronics response and calibration for charge loss due to electron-ion recombination.
- The data were taken during an exposure of 1.35x1020 protons on target in the Fermilab NuMI neutrino beam[1].

### 2. Recombination Models

- Electrons emitted by ionization are thermalized by interactions with the surrounding medium after which time they may recombine with nearby ions.
- In the columnar model of Jaffe[3], published in 1913, recombination depends on the collective electron and ion charge density from multiple ionization interactions in a cylindrical volume surrounding the particle trajectory.
- The relative importance of these two theories for liquid argon can be estimated by comparing the average electron-ion distance with the average ion-ion distance.
- These studies favor a columnar theory approach and imply that collective effects are important.
- (2.2) In this equation, s is a dimensionless variable that characterizes the time dependent overlap of the electron and ion distributions.

### 2.1 Theoretical application

- The Birks and Box model equations do not provide a consistent global description of all data, which is not remarkable considering the assumptions made in their development.
- They do however provide good agreement with data in some regimes, for example radioactive source data where dE/dx is fixed and the electric field is varied.
- A technical difficulty arises when applying a Birks model correction to highly ionizing particles.
- The recombination factor using the Birks model with ICARUS parameters is shown by the blue curve with an electric field of 0.5 kV/cm and liquid argon density of 1.383 g/cm3.
- One can adjust the canonical Box model β value to 0.30 cm/MeV to match the blue curve at dE/dx = 7 MeV/cm and achieve good qualitative agreement to very high values of stopping power (solid red curve).

### 3. Calorimetric Reconstruction in the ArgoNeuT Detector

- The ArgoNeuT detector is described in reference [10].
- All data were taken with an electric field of 0.481 kV/cm.
- Clusters in each wire plane, or view, are matched to form three-dimensional (3D) tracks comprised of a set of space points.
- A calorimetric measurement of the stopping power, (dE/dx)calo, is then found for each space point by applying a recombination correction using equation 2.9.
- The rms difference between (dE/dx)calo and (dE/dx)hyp is found for each value of ∆.

### 4. Stopping Particle Identification

- Unlike the situation in a test beam where the incident particle type and energy is known, a wide variety of particles are produced by the neutrino beam in a wide range of energies.
- The authors introduce a particle identification technique using this feature that is intended to minimize potential sources of selection bias.
- The energy lost by ionization in the first step is found by multiplying the stopping power as calculated from the BetheBloch equation[11] by the step length.
- Table 1 shows the power law parameterization for particles of interest in this analysis.
- If, for example, there is an overall scale error in the detector calibration, the mean values of the Gaussian peaks will be shifted from the expected values of A. Likewise, use of an incorrect recombination correction will shift the peaks and possibly broaden the PIDA distributions.

### 5. Data Selection

- There are several sources of protons that will stop in the detector.
- Fully contained protons produced by neutrino interactions in the detector are an obvious source.
- Tracks entering the detector are not rejected.
- The shaded histograms in figure 4 show the PIDA distributions of these samples.
- The pion and deuteron Gaussian distributions are extrapolated into the proton selection region to estimate the proton selection purity (≈95%) and efficiency (≈95%).

### 6. Detector Simulation

- The LArSoft simulation is based on GEANT4.
- One track travels parallel to the wire plane (φ = 90◦) and the other is inclined relative to the wire plane.
- Ionization electrons arrive at the collection plane with a larger spread in time for the inclined track case than for the parallel track case.
- Hits and tracks are then reconstructed using the same calorimetry code that is used to analyze the data.
- The authors next confirm that this calibration correction does not introduce an artificial angular dependence in the recombination analysis.

### 7. Recombination Simulation

- Jaskolski and Wojcik provided a theoretical-computational approach to the columnar model in [16] to test the validity of the theoretical premises.
- Positive ions are uniformly distributed along a line representing the track trajectory.
- The simulation results are insensitive to the assumptions used for the initial electron distributions because the magnitude of the initial state conditions is small compared to conditions after thermalization.
- The poorer agreement at low dE/dx can be rectified by introducing a factor that accounts for energy loss due to δ -rays which are not included in the model.
- Studies show that the recombination factor becomes independent of ymax for tracks at φ = 40◦ when ymax ≥ 7000 nm.

### 8.1 Proton Sample

- The Birks and Box recombination parameters are found by fitting histograms of dQ/dx vs (dE/dx)hyp.
- The error on (dE/dx)hyp is found by propagating the 0.1 cm residual range error (Section 3) using equation 4.1.
- The recombination fits in each angle bin are shown in figure 10.
- Both the Birks and modified Box model equations provide a good representation of the data in the range 2 MeV/cm < dE/dx < 24 MeV/cm.

### 8.2 Deuteron Sample

- Recombination at higher stopping power can in principle be studied with deuterons.
- The small number of tracks in their sample limits its usefulness however.
- The deuteron sample is subjected to the stopping point fitting algorithm described above with (dE/dx)hyp calculated using the deuteron hypothesis.
- The red points and curve are the data and modified Box fit parameterization for protons in the same φ bin.
- The authors conclude that deuterons are indeed present in this sample and that the recombination fits found above are applicable to dE/dx = 35 MeV/cm.

### 9. Discussion

- The significant disagreement between published data and theory belies that statement however.
- A calculation of the Debye length using the measured drift electron lifetimes in the ArgoNeuT detector results in a screening length of 400 - 600 nm.
- This is four times larger than the Onsager length [2] and should therefore not be a significant contribution.
- This result can be understood by noting that the electron thermalization distance in liquid argon is ∼2500 nm[4], so the electrons that are assumed to escape recombination at ymax = 2000 nm have rather high kinetic energies.
- This may be due to the presence of positive and negative charges that are left from different ionization events.

### 10. Conclusions

- The angular dependence is significantly weaker than that predicted by the Jaffe columnar theory and by a recombination simulation.
- As noted above, this is not the sole example of disagreement with recombination models.
- The authors have presented two possibilities to explain this discrepancy.
- Both possibilities have a common theme - that impurities in the argon may affect the micro-physics of electron recombination.

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##### Citations

341 citations

### Cites background from "A study of electron recombination u..."

...ArgoNeuT performed a series of detailed studies on the interaction of medium-energy neutrinos [6] producing the first published neutrino cross section measurements on argon [7–9]....

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### Cites background or methods from "A study of electron recombination u..."

...Finally, to account for charge loss due to recombination, also known as “charge quenching,” a second correction is applied to convert dQfree/dx to dE/dx based on the modified Box’s model [86] or the Birks’s model [87]....

[...]

...External Measurements Tests of detector model, techniques and systems ArgoNeuT [86], ICARUS [87, 116, 117], MicroBooNE Model parameters (e....

[...]

...The second method calculates the quantity PIDA = 〈Ai〉 = 〈(dE/dx)iR i 〉 [86], which is defined to be the average of Ai = (dE/dx)iR i over all track points where the residual range Ri is less than 30 cm....

[...]

...Some electrons are recombined with the positive ions [86, 87] while the rest of the electrons are drifted towards the wire planes....

[...]

...ArgoNeuT [122], MicroBooNE [123, 124, 125, 115, 126, 86], ICARUS [127, 128, 129], ProtoDUNE Test of calibration techniques and detector model (e....

[...]

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165 citations

### Cites methods from "A study of electron recombination u..."

...In particular, the analysis of the data from the ICARUS[7, 73, 17, 74] and ArgoNEUT experiments[63, 75, 76] required the development of a variety of new reconstruction techniques, forming the basis for precision neutrino physics measurements....

[...]

134 citations

##### References

^{1}, University of Manchester

^{2}, KEK

^{3}, CERN

^{4}, Imperial College London

^{5}, Stanford University

^{6}, Tata Institute of Fundamental Research

^{7}, Istituto Nazionale di Fisica Nucleare

^{8}, University of Pittsburgh

^{9}, Lyon College

^{10}, TRIUMF

^{11}, Northeastern University

^{12}, Thomas Jefferson National Accelerator Facility

^{13}, University of Córdoba (Spain)

^{14}, Goethe University Frankfurt

^{15}, University of Southampton

^{16}, University of Udine

^{17}, University of Alberta

^{18}, Tokyo Metropolitan University

^{19}, Helsinki Institute of Physics

^{20}, National Research Nuclear University MEPhI

^{21}, University of Bath

^{22}, Niigata University

^{23}, Naruto University of Education

^{24}, Kobe University

^{25}, University of Calabria

^{26}, University of Trieste

^{27}, European Space Agency

^{28}, University of Birmingham

^{29}, Ritsumeikan University

^{30}, Qinetiq

^{31}, École Polytechnique Fédérale de Lausanne

^{32}, Massachusetts Institute of Technology

^{33}, Brookhaven National Laboratory

^{34}

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###### Q2. What are the future works in this paper?

The authors have presented two possibilities to explain this discrepancy. Both possibilities have a common theme - that impurities in the argon may affect the micro-physics of electron recombination.