Muon tracking with the fastest light in the JUNO central detector
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Abstract
Background:
The Jiangmen Underground Neutrino Observatory (JUNO) is a multipurpose neutrino experiment designed to measure the neutrino mass hierarchy using a central detector (CD), which contains 20 kton liquid scintillator (LS) surrounded by about 18,000 photomultiplier tubes (PMTs), located 700 m underground.
Purpose:
The rate of cosmic muons reaching the JUNO detector is about 3 Hz, and the muoninduced neutrons and isotopes are major backgrounds for the neutrino detection. Reconstruction of the muon trajectory in the detector is crucial for the study and rejection of those backgrounds.
Methods:
This paper will introduce the muontracking algorithm in the JUNO CD, with a leastsquares method of PMTs’ firsthit time (FHT). Correction of the FHT for each PMT was found to be important to reduce the reconstruction bias.
Results:
The spatial resolution and angular resolution are better than 3 cm and 0.4 degree, respectively, and the tracking efficiency is greater than 90% up to 16 m far from the detector center.
Keywords
JUNO Central detector Muon tracking First hit time Least squares methodIntroduction
The Jiangmen Underground Neutrino Observatory [1, 2] is a multiple purpose neutrino experiment to determine neutrino mass hierarchy and precisely measure oscillation parameters, using reactor antineutrinos from Yangjiang and Taishan nuclear power plants. Figure 1 shows the schematic view of the JUNO detector. Twenty kiloton LS is contained in a spherical vessel with the radius of 17.7 m as the central detector (CD). The light emitted by the LS is watched by about 18,000 20inch PMTs installed in the water pool, with the photocathode at a radius of 19.5 m, with more than 75% optical coverage. There is a top tracker made of plastic scintillator bars, on top of the water pool.
In the JUNO detector, cosmogenic radioactive isotopes—especially \(^9\)Li and \(^8\)He—and fast neutrons are serious correlated background sources to reactor antineutrinos, which can be efficiently rejected by sufficient time veto after the tagged muons. For example, the time window to veto \(^9\)Li and \(^8\)He is required to be no less than 1.2 s, according to their lifetimes. However, according to the Monte Calor simulation, the rate of muon reaching CD is about 3 Hz with the mean energy of about 215 GeV. If the full LS volume is vetoed, there is almost no live time in the detector. Since the vertex of the cosmogenic isotopic is correlated with the primary muon in both time and space, the most effective way is to only veto a cylindrical volume along the muon trajectory instead of the full detector. This approach requests precise tracking of the muon. The top tracker above CD can also track muons, but it has small coverage and can only measure 25% of the total cosmic muons; therefore, muon reconstruction in the CD is necessary for the entire 4\(\pi \) solid angle.
Algorithm
Least square method
The straight track of a muon in the detector can be described by seven independent parameters: \(x_\mathrm{inj}\), \(y_\mathrm{inj}\), \(z_\mathrm{inj}\), \(t_\mathrm{inj}\), \(\theta _\mathrm{p}\), \(\phi _\mathrm{p}\), and \(l_\mathrm{trk}\). \(x_\mathrm{inj}\), \(y_\mathrm{inj}\), \(z_\mathrm{inj}\) and \(t_\mathrm{inj}\) are the position and time of the muon injecting into the LS with the center of the LS ball as the origin of coordinates. \(\theta _\mathrm{p}\) and \(\phi _\mathrm{p}\) are the direction of the muon track in spherical coordinates, and \(l_\mathrm{trk}\) is the length of muon trajectory in LS. Muons that are generated outside the detector and stopped inside are very rare in JUNO and are not considered in this paper. For muons going through the detector, the injection and outgoing points can be fixed at the surface of the LS sphere; thus, \(x_\mathrm{inj}\), \(y_\mathrm{inj}\), \(z_\mathrm{inj}\) and \(l_\mathrm{trk}\) can be replaced with another two parameters \(\theta _\mathrm{inj}\) and \(\phi _\mathrm{inj}\).
Fastest light model
As shown in Fig. 2, when a muon travels through the central detector, energy is deposited in the LS and scintillation lights are emitted isotropically along the muon track. There are also Cherenkov lights; however, most of them are absorbed by the LS and reemitted as scintillation lights. As a result, only less than 1% of lights detected by PMTs carries the directional information, which is extremely difficult to separate from scintillation lights. Therefore, all lights are treated as isotropic in our reconstruction.
Residual of the first hit time
Monte Calor simulation was done based on Geant4 with the JUNO detector geometry. A muon with 200 GeV kinetic energy was simulated going through the detector. The simulation software is a part of the JUNO offline software, and all the geometry parameters and optical properties used in the detector simulation are from JUNO Yellow Book [2].
The first hit time of each PMT obtained from MC truth was subtracted by the predicted time of the fastest light under the optical model in “Fastest light model” section (using the track parameters in MC truth), and the distribution \(\Delta \)FHT is shown in Fig. 3.

The scintillating light is not emitted instantaneously. Instead, the decay time follows a doubleexponential distribution, with the time constants of 4.93 and 20.6 ns for the fast and slow components, respectively.

Because of different refractive index between LS and water, there should be reflection and refraction at the boundary of the LS ball, which are ignored in the optical model. In particular, when the light emission point is at the edge of the LS sphere, there is a region in which all PMTs cannot see the light because of the total reflection. This effect is not included in the optical model either.

There is an intrinsic transient time spread (TTS) of photoelectrons in the PMT. In this study, \(\sigma _\mathrm{TTS}\) was assumed to be 3 ns, i.e., a 3 ns Gaussian smearing was added to the hit time of each photoelectron in MC.

Scintillating lights are not infinite, and their emitting points are discrete along the track after all, which means that the fastest light for a given PMT does not have to come from the predicted position. Assuming the dE/dx of muon is 0.2 MeV/mm, and the average number of photoelectrons collected by all PMTs correlated with every MeV energy deposit in the CD center is about 1200, considering the total number of PMT (20 in) is about 18,000, along the track about \(1200\times 0.2/18,000\approx 0.013\) p.e./mm (\(\mathrm p.e.\equiv photoelectron\)) can hit on each PMT on average. This means that on average the muon emits a photoelectron hit for one PMT when flying every \(1/0.013\approx \) 77.0 mm long, which can be considered as the mean uncertainty of the position at which the fastest light is emitted, and the corresponding uncertainty of FHT is about 77 mm/\(c_\upmu \approx 0.26\) ns, which is acceptable. From another view, if we want the uncertainty of FHT smaller than 1 ns, we need the muon emitting 1 p.e. when flying every \(c_\upmu \times \) 1 ns for each PMT. And for a trajectory through the CD center, with the track length of about 35,000 mm, this means that 35,000 mm/\((c_\upmu \times \,\)1 ns)\(\,\approx 120 \,\mathrm p.e.\) are needed for each PMT. This is a strict PMT selecting condition when reconstructing and 100 p.e. cut condition is used in the performance study in “Performance study with MC data” section.

For a cosmic muon, there are multiple photoelectrons in each PMT. Assuming all hits are from the same point source and the probability density function (PDF) of the single hit time, after the timeofflight subtract, is f(x), then the PDF of FHT in case of n photoelectrons is: \(F(t,n)=nf(t)\left( \int _{t}^{+\infty }{\mathrm{d}xf(x)}\right) ^{n1}\). However, for a muon, photons may be from any point along the track; thus, the PDF of FHT cannot be analytically expressed.
Correction to the first hit time
In this study, MC muon samples were used to correct the first hit time of each PMT, taking into account the full detector geometry, with all optical parameters taken from Ref. [2]. In reality, there is a top tracker which can detect a small fraction of cosmic muons going through the LS ball with very good tracking resolution, which can be used as a calibration source to tune MC.

\(\varvec{d}\): as shown in the left panel of Fig. 4, the distance between the injecting point to the projection of the PMT falling at the track, which ranges from \(\,19.5\) m (when the track is at the edge of the LS ball, half of PMTs have negative d) to 37.2 m (when the track goes through the center of CD).

\(\varvec{a}\): the azimuth angle of each PMT, in the plane perpendicular to the track, which ranges from 0 to \(\pi \) (the area \(\pi \sim 0\) can be combined into that of \(0\sim \pi \) for the symmetry).

\(\varvec{D(ist)}\): the distance between the track and the CD center.

\(\varvec{q}\): the number of Photoelectrons.
Performance study with MC data
Comparison of different FHT correction methods
The FHT correction mainly aims to solve the reconstruction biases. In this section, we will evaluate the biases by \(\alpha \) which is the angle between the reconstructed track and the MC truth one, and \(\Delta D\) which means the error of reconstructed D(ist).
Figure 6 compares the different performances with different FHT correcting methods. We can see the mean \(\alpha \) and D(ist) without any correction can reach several degrees and dozens of centimeters, respectively. And the only qbased correcting method cannot improve the performance too much.
Correcting methods “corr1d XXX” means correcting the FHT by the parameters XXX one by one with relevant onedimensional correcting curves, while the “corr2d XXX” methods are correction by all the two correctingparameters at the same time with a corresponding twodimensional correcting map.
Reconstruction resolution and efficiency
In this section, the spatial and angular resolution and the tracking efficiency are shown using the correction method ”corr2d a–d.”
Conclusion
We have developed a reconstruction algorithm of muon in JUNO CD based on the least square method and the fastest light model, but which has biases on account of the inaccurate prediction of the FHT. Considering that the top tracker in JUNO above the CD can track some tracks downwards from top, we can use them to obtain the FHT correction data versus related observed correcting factors, and then with which correct the predicted FHT in the reconstruction. With this algorithm, we can effectively reconstruct the muon track in the CD almost without biases and the spatial and angular resolution can be better than 3 cm and 0.5\(^\circ \), respectively. And in most cases the tracking efficiency can be better than 90%. More studies on the fastest light model will be done to get better prediction of the FHT and thus to improve the reconstruction performances.
Notes
Acknowledgements
This work is supported by National Natural Science Foundation of China (Grant Nos. 11575226, 11605222), Joint Large Scale Scientific Facility Funds of NSFC and CAS (Grant No. U1532258) and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDA10010900)
References
 1.Z. Djurcic et al., (JUNO Collaboration), arXiv:1508.07166
 2.F.P. An et al., (JUNO Collaboration), arXiv:1507.05613. J. Phys. G: Nucl. Part. Phys. 43, 030401 (2016)
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