Time imaging reconstruction for the PANDA Barrel DIRC
R. Dzhygadlo, A. Ali, A. Belias, A. Gerhardt, M. Krebs, D. Lehmann, K. Peters, G. Schepers, C. Schwarz, J. Schwiening, M. Traxler, L. Schmitt, M. Böhm, A. Lehmann, M. Pfaffinger, S. Stelter, F. Uhlig, M. Düren, E. Etzelmüller, K. Föhl, A. Hayrapetyan, I. Köseoglu, K. Kreutzfeld, J. Rieke, M. Schmidt, T. Wasem, C. Sfienti
PPrepared for submission to JINST
Time imaging reconstruction for the PANDA Barrel DIRC
R. Dzhygadlo, a , A. Ali, a , b A. Belias, a A. Gerhardt, a M. Krebs, a D. Lehmann, a K. Peters, a , b G. Schepers, a C. Schwarz, a J. Schwiening, a M. Traxler, a L. Schmitt, c M. Böhm, d A. Lehmann, d M. Pfaffinger, d S. Stelter, d F. Uhlig, d M. Düren, e E. Etzelmüller, e K. Föhl, e A. Hayrapetyan, e I. Köseoglu, a , e K. Kreutzfeld, e J. Rieke, e M. Schmidt, e T. Wasem, e C. Sfienti f a GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany b Goethe University, Frankfurt a.M., Germany c FAIR, Facility for Antiproton and Ion Research in Europe, Darmstadt, Germany d Friedrich Alexander-University of Erlangen-Nuremberg, Erlangen, Germany e II. Physikalisches Institut, Justus Liebig-University of Giessen, Giessen, Germany f Institut für Kernphysik, Johannes Gutenberg-University of Mainz, Mainz, Germany
E-mail: [email protected]
Abstract: The innovative Barrel DIRC (Detection of Internally Reflected Cherenkov light) counterwill provide hadronic particle identification (PID) in the central region of the PANDA experimentat the new Facility for Antiproton and Ion Research (FAIR), Darmstadt, Germany. This detectoris designed to separate charged pions and kaons with at least 3 standard deviations for momentaup to 3.5 GeV/c, covering the polar angle range of 22 ◦ − ◦ . An array of microchannel platephotomultiplier tubes is used to detect the location and arrival time of the Cherenkov photons witha position resolution of 2 mm and time precision of about 100 ps. The time imaging reconstructionhas been developed to make optimum use of the observables and to determine the performance ofthe detector. This reconstruction algorithm performs particle identification by directly calculatingthe maximum likelihoods using probability density functions based on detected photon propagationtime in each pixel, determined directly from the data, or analytically, or from detailed simulations.Keywords: Cherenkov detectors; Particle identification methods. Corresponding author. a r X i v : . [ phy s i c s . i n s - d e t ] S e p ontents The PANDA Barrel DIRC [1, 2] is a key component of the particle identification (PID) system forthe PANDA detector [3], which will be installed at the Facility for Antiproton and Ion Research(FAIR) in Germany. The PID goal for the Barrel DIRC is to reach 3 standard deviations (s.d.) π / K separation for momenta up to 3.5 GeV/c, covering the polar angle range of 22 ◦ − ◦ . Figure 1 . Rendered CAD drawing of the PANDA Barrel DIRC (left) and the simplified cross section of oneBarrel DIRC sector (right, not to scale).
The Barrel DIRC is constructed in the shape of a barrel using 16 optically isolated sectors,each comprising a radiator box and a compact, prism-shaped expansion volume (EV) (see figure 1).The radiator box contains three synthetic fused silica bars of 17 × × size, positionedside-by-side with a small air gap between them. A flat mirror at the forward end of each bar is usedto reflect Cherenkov photons to the read-out end, where a 3-layer spherical lens images them on anarray of 8 Microchannel Plate Photomultiplier Tubes (MCP-PMTs). The MCP-PMT has 64 pixels– 1 – propagation time [ns] en t r i e s [ ]
10 15 20 25 30 35 40 propagation time [ns] en t r i e s [ ] Figure 2 . Hit patterns (top) and time spectra (bottom) for a single pion (left) and kaon (right) at 22 ◦ polarangle and 3.5 GeV/c momentum. of 6.5 × size and, in combination with the FPGA-based readout electronics, will be ableto detect single photons with a precision of about 100 ps.Depending on the polar angle and momentum of the charged particle, the system detects 20-100photons. Figure 2 shows a typical hit pattern and time spectra for a single pion (left) and kaon(right) at 22 ◦ polar angle and 3.5 GeV/c momentum. Using this information in combination withknowledge of the charged particle momentum and direction, the reconstruction algorithms performparticle identification (PID). Two algorithms have been developed to make optimum use of theobservables and to determine the performance of the detector. The "geometrical reconstruction"[4], initially developed for the BaBar DIRC [5], performs PID by reconstructing the value ofthe Cherenkov angle and using it in a track-by-track maximum likelihood fit, relying mostly onthe position of the detected photons in the reconstruction, using the time information primarilyto suppress backgrounds. The "time imaging" utilizes both, position and time information, anddirectly performs the maximum likelihood fit. The time imaging method is based on the approach used by the Belle II time-of-propagation (TOP)counter [7]. The basic concept is that the measured arrival time of Cherenkov photons in eachsingle event is compared to the expected photon arrival time for every pixel and for every particlehypothesis, yielding the PID likelihoods. Figure 3 shows an example of the accumulated hit patternand the propagation time spectra for 30k simulated pions and kaons for one specific pixel. Thearrival time of the Cherenkov photons produced by e , µ , π , K, and p is normalized for every pixelto produce probability density functions (PDFs). The total PID likelihood is then calculated as:log L h = N (cid:213) i = log (cid:0) S h ( p i , t i ) + B ( p i ) (cid:1) + log P h ( N ) , (2.1)– 2 –here N is the number of detected photons in a given event, S h ( p i , t i ) is the PDF for a pixel p i andparticle type h , and B ( p i ) is the expected background contribution, which includes MCP-PMT darknoise and accelerator background.
10 12 14 16 18 20 22 24 26 28 30 propagation time [ns] en t r i e s [ ] pionskaons Figure 3 . Accumulated hit pattern (left) and the propagation time spectra for one example pixel, number238 (right), for 30k pions and kaons simulated at 22 ◦ polar angle and 3.5 GeV/c momentum. The second term in Eq. 2.1 is the Poisson distribution, which accounts for a difference in photonyields of different particle types. This contribution can be quite significant at low momenta but isnegligible at higher momenta, where the photon yield is almost independent of the particle type.
The PDFs are created from the photon arrival time, which can be obtained in several ways. The bestPID performance is expected from the PDFs created using propagation times from the experimentaldata. In this case, the propagation time is a direct measurement which already includes all detectorimperfections and, therefore, provides the most realistic PDFs. In this method a large amount ofdata for the whole angular and momentum acceptance is required. If the amount of experimentaldata is not sufficient, a full detector simulation can be used to pre-generate a large number of tracks.Both methods require a large amount of memory to store all possible PDFs and, therefore, are notpractical for application in PANDA. The full simulation can also be performed during reconstructionfor each event with a given track direction but excessive simulation time makes it, again, impracticalto use. Finally, the PDFs can be calculated analytically, as shown by the Belle II TOP group [7]. In time [ns] - · en t r i e s / N [ ] t ki t t ki t Figure 4 . Simplified detector configuration without expansion volume and focusing system (left). Exampleof a PDF as a superposition of Gaussians with mean values t ki (right). – 3 –his case, the PDF S h is represented as a sum of m i weighted Gaussians: S h ( p i , t i ) = m i (cid:213) k = n ki g ( t ki , σ ki ) , (3.1)where n ki is the number of photons in the k -th peak of the pixel i , t ki and σ ki are position and widthof the peak, respectively.Considering a simplified configuration without expansion volume and without focusing system(see figure 4, left), the positions of the Gaussian peaks can be expressed through the direction of thecharged track ( θ, ϕ ), the Cherenkov angle θ c of the assumed particle hypothesis, and the positionsof the emission ( x , y , z ) and detection ( x d , y d , z d ) of the Cherenkov photons: t ki = z d − z (cid:0) cos θ cos θ c − sin θ sin θ c cos φ kic (cid:1) n g c , (3.2)where n g is the group refractive index of the radiator, c is the speed of light in vacuum, and φ kic isthe azimuthal angle of the Cherenkov photon in the charged particle’s coordinate system, which isdefined as: cos φ kic = a ki b ki ± d (cid:113) d + b ki − a ki b ki + d , (3.3)where a ki = x kid − x z d − z cos θ cos θ c − cos ϕ sin θ cos θ c , b ki = x kid − x z d − z sin θ sin θ c + cos ϕ cos θ sin θ c , d = sin ϕ sin θ c . (3.4)Here the value of x kid represents the exit position of the Cherenkov photon in the unfolded radiatorplane at z d : x kid = (cid:40) ka + x id , k = , ± , ± , ... ka − x id , k = ± , ± , ..., (3.5)where k is the number of reflections inside the radiator and is a running parameter.The width σ ki includes contributions from the photon emission spread ∆ λ , multiple scattering ∆ θ , chromatic error ∆ σ e , pixel size ∆ x id and the propagation time measurement error σ m : σ ki = (cid:118)(cid:117)(cid:116)(cid:18) ∂ t ki ∂λ (cid:19) ∆ λ + (cid:18) ∂ t ki ∂θ (cid:19) ∆ θ + (cid:18) ∂ t ki ∂σ e (cid:19) ∆ σ e + (cid:32) ∂ t ki ∂ x id (cid:33) ∆ x i d + σ . (3.6)Finally, the number of photons in each peak is defined as: n ki = N l sin θ c ∆ φ kic π , (3.7)– 4 –here N is the Cherenkov photon production constant, l is the length of the charged particletrajectory in the radiator, and ∆ φ kic is the range of the Cherenkov azhimuthal angle coverage of the i -th pixel.By adding the expansion volume and focusing system, the positions of the photons exiting theradiator ( x d , y d , z d ) i become ambiguous. An additional running parameter can be used to mitigatethis but it will significantly slow down the reconstruction speed. Instead, a look up table (LUT)is used to determine the exit direction of the Cherenkov photon from the radiator. The LUT isconstructed using Geant4 [8] simulations and comprises all possible directions from the end ofradiator which can lead to a hit in a given pixel. The Gaussian mean t ki then can be determined as(see also figure 5, left): t ki = z cos β ki n g c + t Lki , (3.8)where z is the distance from the photon emission point to the readout end of the radiator and t Lki isthe propagation time of the photon inside the expansion volume, which is also stored in the LUT. [rad] c q en t r i e s [ ] c p q cK q Figure 5 . Detector configuration with an expansion volume and focusing (left). Example of the LUTsolutions with a selection based on the reconstructed Cherenkov angle (right). Vertical black lines show thevalues of the reconstructed Cherenkov angle for one detected photon. Shaded red and blue areas show theselection around the expected Cherenkov angle for kaons and pions, respectively.
The tagging of the determined Gaussian peaks g ( t ki , σ ki ) with a particle hypothesis is done byreconstructing the Cherenkov angle θ LUT c using the geometrical method [4] and comparing it to theexpected value of the given particle hypothesis θ hc (see also figure 5, right): (cid:12)(cid:12) θ hc − θ LUT c (cid:12)(cid:12) < w σ SPR , (3.9)where σ SPR is the single photon resolution of the DIRC counter, and w is the selection constant,which varies in a range of 0.3-1 depending on the polar angle of the charged particle.The construction of the PDF S h for a given particle hypothesis is done using Eq. 3.1 with t ki from Eq. 3.8 which survives the Cherenkov angle selection Eq. 3.9. The performance of the algorithm was evaluated with Geant4 simulation of the prototype config-uration which was tested with a π / p beam at CERN PS in 2018 [9] (see figure 6). The Barrel– 5 –IRC prototype contained all relevant parts of one PANDA Barrel DIRC sector. A narrow fusedsilica bar (17.1 × × ) was used as radiator. It coupled on one end to a flat mirror,on the other end to a 3-layer spherical focusing lens with a fused silica prism as EV. An array of2 × Figure 6 . Geant4 simulation of the DIRC prototype configuration at 20 ◦ polar angle. Yellow lines showthe path of Cherenkov photons inside the bar and the prism. momentum of the mixed hadron beam was set to 7 GeV/c since π / p PID challenge at this momentais equivalent to π / K ’s at 3.5 GeV/c, due to similar Cherenkov angle difference. A time-of-flightsystem was used to cleanly tag pions and protons.Figure 7 shows an example of analytical PDFs (solid lines) compared to simulated distributions(shaded histograms) for 30k pions (blue) and protons (red) at 20 ◦ polar angle. The analytical PDFswere obtained with selection constant w =0.5 and are in a reasonable agreement with simulation.A slight disagreement in the heights and the positions of the peaks is the result of using idealizedgeometry for creation of the analytical PDF.
10 12 14 16 18 20 22 24 time [ns] - · en t r i e s / N [ ] propagation time for pionpropagation time for protonpdf for pionpdf for proton
10 12 14 16 18 20 22 24 time [ns] - · en t r i e s / N [ ] propagation time for pionpropagation time for protonpdf for pionpdf for proton Figure 7 . Examples of PDFs for two pixels, number 245 (left) and 285 (right) for pions (blue) and protons(red) at 20 ◦ polar angle and 7 GeV/c momentum. Shaded histograms correspond to the Geant4 simulationsfor 30k pions and protons while the solid colored lines show analytically determined PDFs. The resulting likelihood difference distributions of 2k protons and pions are shown in figure 8 forthe reconstruction with analytical (left) and simulated (right) PDFs. The time imaging reconstructionwith analytical PDFs delivers 4 . ± . . ± . . ± . - - - ) p ln L(p) - ln L( en t r i e s [ ] pions protons - - - - ) p ln L(p) - ln L( en t r i e s [ ] pions protons Figure 8 . The performance of the time imaging reconstruction for the PANDA Barrel DIRC prototypesimulation. The π / p log-likelihood difference distributions for pions (blue) and protons (red). The π / p separation power from the Gaussian fits is 4 . ± . . ± . The time imaging reconstruction uses both position and time of the detected Cherenkov photons.The photon propagation time distributions are used to construct probability density functions forlikelihood calculations. The fastest and most efficient way to create those PDFs is to use analyticalcalculations. The initial implementation by the Belle II TOP group was extended with look-up-tables to account for the specific focusing system of the PANDA Barrel DIRC. The performancecomparison showed that the analytical approach provides a performance close to the best possibleone, obtained with simulated PDFs.
Acknowledgments
This work was supported by BMBF, HGS-HIRe, HIC for FAIR.
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