Reconstruction Algorithms in the Super-Kamiokande Large Water Cherenkov Detector on Behalf of Super-Kamiokande Collaboration M

Nuclear Instruments and Methods in Physics Research A 433 (1999) 240}246

Reconstruction algorithms in the Super-Kamiokande large water Cherenkov detector On behalf of Super-Kamiokande collaboration M. Shiozawa! "

!Institute for Cosmic Ray Research, University of Tokyo, Tanashi, Tokyo 188-8502, Japan "Kamioka Observatory, Higashi-Mozumi, Kamioka-cho, Yoshiki-gun, Gifu-ken, 506-1205 Japan

Abstract

The Super-Kamiokande experiment, using a large underground water Cherenkov detector, has started its operation since "rst April, 1996. One of the main physics goals of this experiment is to measure the atmospheric neutrinos. Proton decay search is also an important topic. For these analyses, all measurement of physical quantities of an event such as vertex position, the number of Cherenkov rings, momentum, particle type and the number of decay electrons, is automatically performed by reconstruction algorithms. We attain enough quality of the analyses using these algorithms and several impressive results have been addressed. ( 1999 Elsevier Science B.V. All rights reserved.

PACS: 29.40.K

Keywords: Atmospheric neutrinos; Proton decays; Super-Kamiokande

1. Introduction lation in the atmospheric neutrino observation The Super-Kamiokande experiment, which util- [1}4]. These exciting results were also reported in izes a large water Cherenkov detector, has rich this workshop [5]. Moreover, baryon number viol- physics topics such as atmospheric neutrinos, solar ated proton decays, which are predicted by Grand neutrinos, proton decays, and so on. Thanks to the Uni"ed Theories, have been searched for and we set huge target volume of 22.5 kton and the large the most stringent limit on the partial lifetime of the photo coverage area, this detector has a capability proton [6]. to collect neutrino events with high statistics and In the atmospheric neutrino and proton decay to perform the precise measurement of physical analyses, we measure the physical quantities of an quantities. Recently, the Super-Kamiokande col- event such as vertex position, the number of laboration reported the evidence of neutrino oscil- Cherenkov rings, momentum, particle type and the number of decay electrons. We start from the vertex "tter program to obtain the vertex position of * Tel.:#81-578-5-9611; fax:#81-578-5-2121. events. With the knowledge of the vertex position, E-mail address: [email protected] (M. Shiozawa) the ring "tter positively identi"es each ring. After

0168-9002/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 9 ) 0 0 3 5 9 - 9 M. Shiozawa / Nuclear Instruments and Methods in Physics Research A 433 (1999) 240}246 241 that, the particle identi"cation program identi"es the particle type for each ring. For single ring events, this particle-type information is used to improve the reconstructed vertex position. Finally, the momentum for each ring is determined and decay electrons are identi"ed. The vertex "tter, ring "tter, particle identi"cation, and momentum reconstruction are described here. Moreover, ring separation, which separates the observed photoelectrons (p.e.'s) in each photomultiplier tube (PMT) and assigns the fractional p.e.'s to each Cherenkov ring, is explained for the reconstruction of multi-ring events. Fig. 1. The residual time distributions after TOF subtraction. The time of #ight is calculated with (a) true vertex position and (b) 4 m o! from the true vertex position. With the true vertex, the 2. Super-Kamiokande detector residual time distribution has a sharp peak.

The Super-Kamiokande detector is a large water Cherenkov detector which is located deep under- with (a) true vertex position and (b) wrong position ground to reduce cosmic ray muon backgrounds. 4mo! from the true vertex position. With the true The detector is a cylindrical stainless-steel tank vertex, the residual time distribution has a sharp holding 50 kton of ultra-pure water. The detector is peak as shown in Fig. 1(a). The "nite width of the optically separated into two concentric cylindrical distribution comes from the time resolution of the regions, the inner detector and outer detector. PMTs. The long tail is made by scattered light and The inner detector measuring 36.2 m height and re#ected light from the detector wall. On the other 33.8 m in diameter is viewed by 11146, inward- hand, with the wrong vertex position, the residual facing, 50 cm diameter PMTs. These PMTs uni- time becomes a wide distribution as shown in formly surround the inner detector region giving Fig. 1(b). 40% photocathode coverage. The data acquisition To "nd the vertex position where the timing system records the number and arrival times of the residual distribution becomes most peaked, the "t- photons collected in each PMT. From these values, ting estimator G is de"ned as along with the positions of the PMTs, the events 1 (t !t ) G"+ exp ! G (1) are reconstructed. p A 2(1p2;1.5)B The outer detector completely surrounds the in- G G p ner detector region with 2.0}2.2 m thickness. 1885 where i is a PMT number, G is timing resolution of outward pointing 20 cm PMTs view this region the ith PMT as a function of detected p.e.'s, 1p2 is and entering cosmic ray muons are rejected by the the timing resolution for the detected p.e.'s aver- outer detector information. aged over "red PMTs and tG is the TOF subtracted timing information of the ith PMT. In the TOF subtraction, the track length of the charged particle 3. Vertex 5tter is taken into account. The vertex "tter searches for a vertex position where the estimator G takes max- The reconstruction procedure starts from the imum value. vertex "tting. The principle of the "tting is that the The performance of the vertex "tter is investi- timing residual ((photon arrival time)-(time of gated for the proton decay mode of pPe>p. Us- #ight)) distribution should be most peaked with the ing Monte Carlo events, the vertex resolution is correct vertex position. In Fig. 1, the time-of-#ight estimated to be 18 cm. The vertex resolution for (TOF) subtracted TDC distributions are shown single ring events are 34 and 25 cm for electrons

SECTION V 242 M. Shiozawa / Nuclear Instruments and Methods in Physics Research A 433 (1999) 240}246 and muons, respectively, for the momentum region of p(1.33 GeV/c. These performances are ob- tained after vertex position correction using determined particle types.

4. Ring 5tter

After reconstruction of the vertex position, possible rings are looked for and probable rings are reconstructed in this ring "tter. Using the recon- Fig. 2. The Hough transformation. Suppose there are four "red structed ring(s), we can reconstruct the total mo- PMTs on the unknown ring (radius r) and we want to "nd the mentum and total invariant mass of pPe>p center of the ring (left "gure). By Hough transformation, the events and those of atmospheric neutrino events. detected p.e.'s are mapped to a circle with radius r centered on the PMT (right "gure). By accumulating the mapped circles, we We use a known technique for a pattern recogni- can "nd the peak in the Hough space, giving the center of the tion, Hough transformation [7], to search for pos- unknown ring. sible ring candidates. The essence of the Hough transformation is shown in Fig. 2. Suppose there are four "red PMTs on the unknown ring (radius r) and we want to "nd the center of the ring (left "gure). By Hough transformation, the detected p.e.'s are mapped to a circle with radius r centered on the PMT. All mapped circles cross at the center of the unknown ring. By accumulating the mapped circles, we can "nd the peak in the Hough space, giving the center of the unknown ring. Before the mapping, the p.e. contribution from the rings which already have been regarded as true rings are subtracted in order to enhance the possible ring candidates. In the ring "tter, the Hough space is made up of two-dimensional arrays divided Fig. 3. The e$ciency of single-ring identi"cation for quasi- by polar angle H (36 bins) and azimuthal angle elastic scattering events. Using the atmospheric neutrino Monte U (72 bins), resulting in 36;72 pixels. These angles Carlo, the fraction of (single-ring quasi-elastic events)/(quasi- are measured from the reconstructed vertex. Detec- elastic events) is plotted as a function of momentum. The e$- & ted p.e.'s in each "red PMT, which are corrected for ciency is 96% for the momentum region shown. acceptance and attenuation length, are mapped to H U pixels ( G, G) for which the opening angle toward Peaks found in the Hough space are identi"ed as the PMT is 423. In the actual case, a Cherenkov centers of possible ring candidates. However, any ring in the Super-Kamiokande detector has ring candidate for which the direction is very close a broad p.e. distribution rather than an ideal thin to one of the true ring directions (opening angle circle. In order to take into account the actual p.e. (153) is discarded as a fake candidate made by distribution, the expected p.e. distribution for the true ring. For the pPe>p events, 98% of the a 500 MeV/c electron as a function of opening events are reconstructed as two or three rings. angle h is used as a weight in the p.e.'s mapping. The two-ring classi"cation is primarily for events Namely, the corrected p.e.'sofa"red PMT are with one of the two c rings taking only a small H U p mapped to pixels ( G, G), for which the opening fraction of the 's energy or overlapping too much angles toward the PMT are h, with weight of ex- with other rings. The performance of the ring "tter h pected p.e.'s Q%( ). for single-ring events is also studied. Fig. 3 shows M. Shiozawa / Nuclear Instruments and Methods in Physics Research A 433 (1999) 240}246 243

% % l the e$ciency of single-ring identi"cation for quasi- opening angle. Optimizations of qG (e) and qG ( ) elastic scattering events of atmospheric neutrinos. are performed by changing the direction and the The e$ciency is &96% for the momentum region Cherenkov opening angle of the ring in order to get of p(1.33 GeV/c. maximum-likelihood values of ¸(e) and ¸(l). In order to combine the likelihood with another estimator which uses the Cherenkov opening angle, 5. Particle identi5cation the likelihood is transformed into the s distribution as The particle identi"cation (PID) classi"es a par- 1 ticle as a showering particle (e!,c) or a nonshower- s l " ;! ¸ l (e or ) ( log (e or )) ing particle (l!, p!), using the photon distribution log e of its Cherenkov ring. Showering (nonshowering) ! particles are sometimes called e-like (l-like). At constant. (4) "rst, the expected p.e. distributions are calculated Using the s(e) and s(l), probabilities from the with an assumption of the particle type. Using the Cherenkov ring pattern are calculated as expected p.e. distributions, the following likelihood is calculated for the electron and muon assump- 1 s(e or l)!s P!% l " ! * tions. (e or ) expA A p B B (5) 2 Q ¸ l " % % l (e or ) prob(qG, qG (e) or qG ( )). (2) s " s s l p A where min[ (e), ( )] and is calculated FG( "F ) * Q from the degree of freedom as p "(2N where Here ¸(e) is calculated using the electron expecta- Q " N is the number of PMTs used in Eq. (2). tion q%(e) and ¸(l) is calculated using the muon " G Moreover, another probability is de"ned using expectation q%(l) . prob(q , q%) is the statistical G G G only the Cherenkov opening angle. Given the re- probability of observing q with the expectation of G constructed opening angle as h#$dh, the probabil- q% and de"ned as G ity is calculated as prob(q", q%)" P!' %(e or l)"constant 1 (q"!q%) exp ! for q"'20 p.e. 1 h#!h%(e or l) ( pp A 2p B ;exp ! 2 A 2A dh B B convolution of one p.e. for q"(20 p.e. (6) G distribution and Poisson % % distribution where h (e) and h (l) is the expected Cherenkov opening angle for an electron and muon, respec- (3) tively, calculated from estimated ring momentum using the detected p.e.'s. Using the probability from where the p is de"ned as p"(1.2;(q%) the pattern and the probability from the angle, total #(0.1;q%) in which the factor 1.2 takes into probability is de"ned as account the di!erence of the actual PMT resolution from the ideal one and the factor 0.1 corresponds to P(e or l)"P!%(e or l)#P!' %(e or l). (7) the uncertainty of the gain calibration. The probability function for q"(20 p.e. is calculated by For a single ring event, when P(e)'P(l) convolution of the measured one p.e. distribution (P(e)(P(l)), the ring is identi"ed as showering and a Poisson distribution. The production of the (nonshowering) type. However, for a multi-ring probability in Eq. (2) is performed for all of the ith event like a pPe>p, we do not use the angle PMTs for which the opening angles toward the ring probability P!' % in the particle-type determina- h c direction G are within 1.5 times the Cherenkov tion. That is because a from the decay of the

SECTION V 244 M. Shiozawa / Nuclear Instruments and Methods in Physics Research A 433 (1999) 240}246 p sometimes penetrates in water (mean free path of where qG L is the fractional p.e.'s of the ith PMT &55 cm) before causing the electromagnetic assigned to the nth ring. With the assumption of the % shower and this gives a small reconstructed open- symmetry, the qG L can be calculated from % h ing angle of the Cherenkov ring. The small opening QL ( G L) which is the expected p.e. distribution as angle makes P!' %(e) small, resulting in small P(e). a function of opening angle h. Therefore, calcu- % h Therefore, for the multi-ring event, we use only lation of the QL ( ) is essential in the ring separ- the pattern probability P!%(e) and P!%(l)to ation. % determine the particle type. Namely, when At "rst step, all qG L are set assuming that all P!%(e)'P!%(l)(P!%(e)(P!%(l)), the particles are electrons. Then, initial expected p.e. ring is identi"ed as showering (nonshowering) type. distributions are determined by minimizing the fol- The performance of the PID is important for the lowing s: pPe>p search to detect signal but reject back- ground events. This is also essential for the atmo- q !+ q% s" + GY LY GY LY . (9) spheric neutrino observation. For single ring L A ( B FGY L3 qGY events, the particle misidenti"cation probability is estimated to be less than 1.0% using the atmo- The summation is performed for all of ith PMT for spheric neutrino Monte Carlo. This is con"rmed which the opening angle toward the nth ring direc- h s with stopping cosmic ray muons and their asso- tion GY L is within 703. By minimizing the 's, we ciated decay electrons. The PID performance was obtain the initial separated p.e.'s qG L using the con- % also checked using a 1 kton water Cherenkov de- verged qG L and Eq. (8). l tector with e and beams from the 12 GeV proton Using the initial separated p.e.'s qG L, we make the % h synchrotron at KEK [8]. However, the misidenti"- expected p.e. distribution QL ( ) as a function of cation probability di!ers between single and the opening angle h toward the nth ring direction. % h multi-ring events due to overlapping rings. Using The QL ( ) is the expected p.e.'s projected on a hy- the pPe>p Monte Carlo sample the multi-ring pothetical spherical surface centered at the recon- % h misidenti"cation is estimated to be 2%. structed vertex. For making the QL ( ) from the qG L, we need to correct the number of p.e.'s for the distance from the vertex, the attenuation length, 6. Ring separation and acceptance. By summing up the corrected p.e.'s within each opening angle bin, we obtain the % h The `ring separationa program determines the QL ( ). Here, optimization is done so that main % h fraction of p.e.'s in each PMT due to each ring. contribution to the QL ( ) comes from non-over- As a result, this separation gives the observed p.e. lapping region of the ring. Proper normalization % h distributions for individual rings. We need this sep- and smoothing are also done in making the QL ( ). aration for the ring "tting and the particle identi- In the next step, we iteratively optimize the % h "cation of each ring as well as the momentum QL ( ) using the likelihood function. The expected % reconstruction. The strategy of the separation is as p.e.'s for ith PMT qG L is recalculated from the % h % follows. Given a vertex position and each ring di- QL ( G L). Using the new qG L , separation of the rection, the expected p.e. distribution for each ring observed p.e.'s is performed again by maximizing ¸ as a function of opening angle h is calculated ac- the following likelihood function L: cording to the observed p.e. distribution assuming the #at distribution in azimuthal angle . Using the ¸ " + log prob(q , + a ) q% ) expected p.e. distribution q%, where i refers to L A GY LY GY LY B G L FGY L3 LY a PMT number and n refers to a ring number, the ;( % h ; (h# h observed p.e.'s of the ith PMT (qG) are separated as QL ( GY L) min[1, L/ GY L] (10) q% a q "q ; G L where LY is a parameter used for the optimization, G L G + % (8) h# LYqG LY L is the reconstructed Cherenkov opening angle of M. Shiozawa / Nuclear Instruments and Methods in Physics Research A 433 (1999) 240}246 245

+ a ) % the nth ring, and the prob(qGY LY, LY LY qGY LY) is the probability of observing qGY with expected p.e.'sof + a ) % LY LY qGY LY and de"ned in Eq. (3). The factor ( % h (h# h QL ( GY L) and min[1, L/ GY L] in the Eq. (10) enhance the contributions from PMTs around the Cherenkov edge and inside of the Cherenkov edge, a respectively. By optimizing the factor L, the pro- a gram looks for the best L which maximizes the ¸ a likelihood function L.At"rst, is optimized so ¸ that is maximized. The same optimization is iteratively performed for the second ring, third ring, a and so on until all L's converge. a Given the best L's, the observed p.e.'s of the ith PMT are separated again as a ) q% q "q ; L G L G L G + a ) %. (11) LY LY qG LY % Finally, the procedure from making QL to Eq. (11) is repeated two more times (three times in total), to improve the separated p.e.'s qG L. An example of the result of the ring separation is shown in Fig. 4. In the "gures, observed p.e.'s in a three ring event of pPe>p are separated and assigned to one of the rings. We can see the clearly separated ring.

7. Momentum determination

The momentum is estimated from the total sum of p.e.'s detected within a 703 half opening angle from the reconstructed ring direction. The number of p.e.'s collected in each PMT is corrected for light attenuation in water, PMT angular acceptance, and PMT coverage. In the momentum reconstruction, we assume that showering particles are electrons and nonshowering particles are muons. For Fig. 4. An example of the result of the ring separation. PMTs single-ring events, the reconstructed momentum which are located in the part of the detector and have more than >p resolution is estimated to be $(2.5/(E(GeV)# one p.e. are shown. The top "gure shows a pPe Monte $ Carlo event in which three Cherenkov rings are seen. The 0.5)% for electrons and 3% for muons. For observed p.e.'s in each PMT are separated by `ring separationa. multi-ring events, the ring separation program The separated p.e.'s for the right ring are shown in the bottom (Section 6) is applied with particle-type assumption "gure. The observed p.e.'s are clearly separated and assigned to to determine the fraction of p.e.'s in each PMT the ring. due to each ring. Then, the momentum for each ring is determined by the same method used for The energy scale stability is checked by the re- single-ring events. The reconstructed momentum constructed mean energy of decay electrons from resolution is $10% for each ring in the pPe>p stopping cosmic ray muons. It varies within $1% events. over the exposure period. The absolute energy scale

SECTION V 246 M. Shiozawa / Nuclear Instruments and Methods in Physics Research A 433 (1999) 240}246

of these sources and Monte Carlo simulation, the absolute calibration error is estimated to be smaller than $3%.

8. Summary

The reconstruction algorithms for the atmospheric neutrino observation and proton decay search by the Super-Kamiokande detector have been described. The vertex resolution is 18 cm for pPe>p events and 34 and 25 cm for single-ring electrons and muons, respectively, for the momentum region of p(1.33 GeV/c. In ring "tting, 98% of the pPe>p events are reconstructed as two or three rings and 96% of quasi-elastic scattering events of atmospheric neutrinos are reconstructed as single ring events. The misidenti"cation probability of particle types is only of order 1%. The energy resolution is estimated as &3% and systematic uncertainty of the energy scale is $3%.

Acknowledgements

We gratefully acknowledge the cooperation of the Kamioka Mining and Smelting Company. The Super-Kamiokande experiment was built from, and has been operated with, funding by the Japanese Ministry of Education, Science, Sports and Culture, Fig. 5. The invariant mass distributions for neutrino-induced and the United States Department of Energy. n events. (a) Data and (b) atmospheric neutrino Monte Carlo. Reconstructed mass distributions are "tted by a combined function of f(x)"P1#P2;x#P3;exp[!(x!P4)/2P5]. The "tted peaks of invariant mass agree well with each other within References 3%. [1] Y. Fukuda et al., Phys. Lett. B 433 (1998) 9. [2] Y. Fukuda et al., Phys. Lett. B 436 (1998) 33. [3] Y. Fukuda et al., Phys. Rev. Lett. 81 (1998) 1562. is checked with many calibration sources such as [4] T. Kajita, talk given at International Conference on Neu- electrons from a linear accelerator [9], decay elec- trino Physics and Astrophysics, Takayama, 1998. trons from stopping cosmic ray muons, stopping [5] M. Shiozawa, talk given at International Workshop on cosmic ray muons themselves, and the reconstruc- Ring Imaging Cherenkov Detectors, Dead-Sea, 1998. ted mass of p events observed in atmospheric [6] M. Shiozawa et al., Phys. Rev. Lett. 81 (1998) 3319. [7] Davies, E. Roy, Machine Vision: Theory, Algorithms, Prac- neutrino interactions. Fig. 5 shows the reconstruc- ticalities, Academic Press, San Diego, 1997. p ted mass of events in (a) data and (b) atmo- [8] S. Kasuga et al., Phys. Lett. B 374 (1996) 238. spheric neutrino Monte Carlo. From comparisons [9] M. Nakahata et al., Nucl. Instr. and Meth. A 421 (1999) 113.