I. INTRODUCTION Particle identication, especially the ability to distinguish from K, plays a key role in the study of CP violation in B meson decays.

Calibration and Performance of the Belle TOF system M. Jones, M. Peters, S. L. Olsen, T. Browder, B. Casey, H. Guler, J. Rodriguez, G. Varner, Y. Zheng, 1 H. Kichimi, N. Gabyshev, S. Uehara, 2 Y. Choi, D. Kim, J. Nam, 3 T. Kim, 4 and J. Zhang 5 1 University of Hawaii, Honolulu, Hawaii, USA 2 IPNS, KEK, Tsukuba, Japan 3 Sungkyunkwan University, Seoul, Korea 4 Yonsei University, Seoul, Korea 5 Tsukuba University. Japan (Dated: January 31, 2003) Abstract The Belle TOF system provides /K separation for particle momentum below 1.2 GeV/c. The TOF resolution is found to be about 100 ps for high-momentum muons in dimuon events and about 115 ps for pions and kaons in hadron events. This note describes the calibration scheme for the TOF system in detail and its performance for the past three years. PACS numbers: Typeset by REVTEX 1

I. INTRODUCTION Particle identication, especially the ability to distinguish from K, plays a key role in the study of CP violation in B meson decays. The /K separation system for the Belle detector [1] consists of: de/dx measurement in the central drift chamber (CDC), eective for particle momenta below 0.7 GeV/c time-of-ight (TOF) detector for momenta below 1.2 GeV/c and an array of silica aerogel threshold Cerenkov counters (ACC) for momenta above 1.2 GeV/c. The TOF using plastic scintillation counters is a powerful method for particle identication, which has been used successfully in the analysis of current Belle data. Details of the geometry, PMTs, and electronics of the TOF system are given in ref. [1, 2]. There are 64 TOF modules covering a cylinder of radius 120 cm and length 255 cm. Each module has one TSC counter of width 12 cm and thickness 0.5 cm and two TOF counters each with width 6 cm and thickness 4 cm. Each TOF counter has a PMT at each end TSC counters have a PMT only at the backward end. This report discusses calibration of the Belle TOF system, the resulting time resolutions achieved for high-momentum muons, the corrections needed for lower-momentum hadrons and the time resolutions achieved for them. We summarize the performance of the Belle TOF in the past three years. II. TIME RESOLUTION FOR MUONS A. Time Walk Calibration using dimuon events Calibrations of the TOF and TSC counters are done using muons in dimuon events after removing run-dependent timing variations (see subsection B). These muons have momenta between 3 and 8 GeV/c. Typically, a calibration uses 50-100 runs and 2000 muons per TOF counter. The TOF forward and backward PMTs and the TSC PMTs are t independently. The rst step in the calibration is a two-dimensional t to the time dierence t dened by t = T raw ; T pred ; z=v(i) ; S(i)= p q ; t(i) (1) where T raw is the raw measured time from the PMT, q is the pulse height value from this PMT, T pred is the ight time predicted for the muon hitting the TOF, z is the displacement along the TOF/TSC scintillator (-72.5 cm to 182.5 cm for TOF counters), v(i) is the eective velocity corresponding to PMT i (v(i) is negative for forward PMTs), S(i) is the coecient of the time-walk correction term corresponding to PMT i, and t(i) is the time oset corresponding to PMT i. The term z/v(i) approximates the eective lighttravel time from the position of the muon in the scintillator to the PMT. The time-walk term S(i)= p q corrects for the pulse height dependence of the raw measured time assuming that the rising edge of the pulse has a quadratic shape and that the measured pulse height q is proportional to light produced by the muon traversing the scintillator. The oset term t(i) allows each PMT to have a dierent time oset the observed spread of t(i) values is about 0.5 ns. The predicted ight time T pred from the interaction point to the scintillator is calculated from the code that does tracking in the CDC plus the ext module [4] which extrapolates the track trajectory from the outer radius of the CDC. This calculation is fairly simple for high-momentum muons because their trajectories are nearly straight lines and the energy loss is small. The calculation is much more complicated for low-momentum hadrons and may result in systematic time shifts that are not present for high momentum particles. 2

TABLE I: Typical calibration parameter values PMT v(i) S(i) t(i) cm/ns ns TOF backward 15.5 37. -5.0 TOF forward -15.4 38. 2.2 TSC 16.5 55. 48. TABLE II: Time resolution for muons exp. time resolution runs period luminosity ps fb ;1 7 96.4 12865 Jan.13Jul.23 (2000) 6.6 9 97.4 11220 Oct.13Dec.28 (2000) 4.4 11 98.4 11367 Jan.20Apr.16 (2001) 9.3 13 97.9 11640 Apr.21Jul.16 (2001) 12.0 15 99.7 11437 Oct.6Dec.25 (2001) 14.1 17 100.3 1 937 Jan.18Mar.13 (2002) 12.0 19 101.7 11709 Mar.15Jul.1 (2002) 28.6 The calibration two-dimensional t adjusts the parameters v(i), S(i), and t(i) to make t near zero for all values of z and q. Typical values for the calibration parameters are given in Table I. After this t, there is still a sizable variation of t with z so an additional t to a 5th order polynomial F(z) is done. F (z) = n=5 X n=0 A n z n (2) This t is able to reduce the amplitude of the variations with z to 40 ps for individual TOF PMTs. One could reduce these variations by tting with a higher-order polynomial, but this would require changing the databases of the calibration parameters. In addition, for most tracks the weighted average of the PMT times is used, and the variations in the weighted average time are typically less than 10 ps. Figure 1 shows plots of t versus z after the F(z) correction. The calibration also determines attenuation lengths for each TOF and TSC counter, a gain value for each PMT, and the parameters of a quadratic function that describes the time resolution as a function of z. Figures 2 (a) to (d) show typical time distributions for recent data in exp. 19 the resolutions are 150 ps for backward TOF PMTs, 162 ps for forward TOF PMTs, 103 ps for the weighted average of the backward and forward times, and 688 ps for TSC PMTs. The resolutions for the weighted average time are given in Table II for each experiment. Results from individual calibrations for exps 7-23 are given in the Appendix. 3

FIG. 1: t (ns) as a function of z (cm) for muons after calibration for the fth order polynomial function. The t is dened as a time dierence t corr -t, where t is the predicted time of ight of the track calculated from CDC track parameters and t corr is the corrected measured time after the calibration. The upper plots are for the TOF backward (left) and forward (right) PMTs the lower left plot is for the TOF weighted average time. The lower right plot is for the TSC PMTs. The plots are for the data in exp. 19. 4

FIG. 2: t (ns) distributions for muons after the calibration. The upper plots are for the TOF backward (left) and forward (right) PMTs the lower left plot is for the TOF weighted average time. The lower right plot is for the TSC PMTs. All plots are for data in exp. 19. 5

B. T0 (event time oset) calibration Before running the calibration previously described, we need to determine the run-by-run T0 values and eliminate variations from them. After run-by-run T0 values are determined and installed into the T0 database, the time walk calibration is carried out. The T0 is a common oset time over all PMTs and is run dependent. Here, we describe the run-by-run T0 variation. The T0 value for a run is determined from the mean t value (backward and forward TOF PMTs combined) for all TOF counters with data for that run. Each t value is the corrected measured time minus the muon predicted ight time. The z-dependent, timewalk, and counter-dependent oset parameters used to correct the measured time are those determined by a previous calibration. These parameters generally change slowly for nearly all counters and thus are a reasonable approximation to use to determine thet0values for runs taken just after those from which the parameters were determined. With this procedure variations in the T0 values represent counter-independent variations that could be due to changes in KEKB timing, changes in the beam orbits, or changes in the timing signals used for the time stretcher modules. Figures 3 (a) to (d) show variations of T0 for experiments 13, 15, 17 and 19 respectively. They show slowvariations (e.g. 40 ps in 400 runs) in T0 values as well as occasional sudden shifts of as much as 200 ps. The sudden time shifts do not occur for TSC counters and thus seem to indicate changes in KEKB timing or timing changes associated with the time stretcher modules. 6

FIG. 3: T0 ( event time oset in ns ) as a function of run number for (a) exp. 13, (b) exp. 15, (c) exp. 17 and (d) exp. 19, which correspond to the run periods of April 22 to July 16, Oct.3 to Dec.25 in 2001, Jan.18 to Mar.13 and Mar.15 to July 1 in 2002, respectively. 7

TABLE III: Time resolution for muons during a run. The rst data group is from exp. 19 runs 1-666 the second is from runs 667-1709. The third and fourth groups are from runs 2-189 and 190-324 respectively of exp. 21. The last group is from exp. 23 runs 1-447. exp. event range mean (ps) sigma (ps) 19 all 1.60.09 100.19.07 19 <300000.89.18 100.35.15 19 300000-600000 1.36.17 100.31.14 19 600000-900000 1.94.17 100.11.14 19 >900000 2.47.21 99.80.17 19 all 1.88.11 102.09.09 19 <300000 1.07.20 102.27.16 19 300000-600000 2.06.20 102.07.16 19 600000-900000 2.41.21 101.88.17 19 >900000 2.37.35 101.81.29 21 all 2.52.08 101.22.06 21 <300000 1.27.16 101.98.13 21 300000-600000 2.32.15 101.48.12 21 600000-900000 3.01.15 100.97.12 21 >900000 3.37.16 100.43.13 21 all 1.67.09 102.50.07 21 <300000 -.57.16 103.33.13 21 300000-600000 1.45.16 102.73.13 21 600000-900000 3.56.16 101.89.13 21 >900000 2.96.23 101.26.18 23 all 2.41.11 100.36.09 23 <300000 1.46.18 100.77.15 23 300000-600000 2.63.19 100.27.15 23 >600000 3.61.23 99.76.19 C. Time resolution for mu-pairs in one run Data taken in Fall 2002 show a small variation in the TOF resolution within a run. Table III contains a summary of the results for two groups of data in exp. 19, two groups in exp. 21, and one group in exp. 23. The exp. 19 data exclude TOF counters 1-4 (for which preamps were being tested) and counters 87, 103, and 122. The exp. 21-23 data exclude the four TOF counters with the poorest resolution (counters 66, 87, 103, and 122). (The backward PMT on counter 66 has had very poor resolution since the beginning of exp. 21.) One can see that the resolution changes very little during a run in exp. 19 but improves by 1-2 ps from the beginning to the end of a run in exps. 21-23. 8

D. Attenuation length aging eect The attenuation length is found to decrease since data taking started, as shown in Figure 4. Here, the attenuation length can be calculated by assuming that the pulse height q observed in apmtis given by for backward PMTs and q b = Q(z) exp(;(z +72:5)=) (3) q f = Q(z) exp(;(182:5 ; z)=) (4) for forward PMTs. The quantity Q(z) is related to the amount of light produced by the muon in traversing the scintillator, which is propotional to the track length in the scintillator as a function of z. q Q(z) =Q 0 =sin() =Q 0 1+(z=r) 2 (5) where r is the TOF radius, Q 0 is the light produced at normal incidence, and is the polar angle of the muon with respect to the z axis. One can remove this z dependence and determine by doing a linear t to ln(q f =q b )versus z. The slope determined by such a linear t is 2/. This technique is used to determine the values in Figure 4. FIG. 4: TOF attenuation lengths in cm versus time. The circle symbols are for all TOF counters. The "1", "2", diamond, and asterisk symbols are for counters 1, 2, 8, and 65 respectively. The average attenuation length in Dec. 1996 was measured in Hawaii before the counters were shipped to KEK. The TOF calibration code also determines attenuation lengths using the backward and forward PMTs separately. The values determined using backward PMTs for each TOF counter for exp. 13 and exp. 19 are shown in Figs. 5 (a) and (b), respectively. Determining values using a single PMT requires an approximate correction for the variation in the amount 9

of light produced as a function of z. The correction used is to scale the observed pulse height (q f or q b ) by sin(). An exponential t is then done to the scaled pulse height versus zand the attenuation length is the inverse of the slope of the linear term in the argument of the exponential function. The attenuation lengths determined by this method are consistent with those determined using the ratio q f =q b but the ts are much better using the ratio. One can see that the exp. 19 attenuation lengths are generally smaller than those for exp. 13, that counters 8 and 65 have unusually small lengths and counters 1 and 2 have unusually large lengths. FIG. 5: TOF attenuation lengths in cm versus counter for (a) Exp. 13 runs 763-847 taken in May 2001, and (b) Exp. 19 runs 542-666 taken in April 2002. Figure 6 shows that there is a correlation between the time resolution and attenuation length. Excluding the three counters (87, 103, and 122) with the largest resolution values, a least-squares t gives the following: =120:2ps ; (:082ps=cm) (6) This correlation implies a time resolution of 107 ps for an attenuation length of 160 cm this is somewhat less than the currently observed value of 113 ps for counter 65. A linear extrapolation of the average attenuation lengths in Fig. 4 would predict an average attenuation length of 160 cm in 2006 so it is reasonable to expect that the time resolution will have degraded to the 107-113 ps range in 2006. III. TIME RESOLUTION FOR HADRONS A. Sources of Systematics for Hadrons The z-dependent, time-walk, and counter-dependent oset corrections are determined from muons in dimuon events because the muons are well-identied and do not have hadronic 10

FIG. 6: TOF time resolution versus attenuation length for individual TOF counters. The data used is from exp. 19. The points with the smallest attenuation lengths are for counters 65 and 8. The points indicated with diamond symbols are for counters 87, 122, and 103. The line is the result of a least-squares t to all points except those with diamond symbols. interactions or large electromagnetic showers. One would expect these corrections to apply to non-interacting hadrons with near one, but perhaps not to hadrons with lower velocities. One of the complications for low-momentum hadrons is the calculation of the predicted time. The tracking code calculates predicted times in the CDC for dierent particle masses but assumes a pion mass for the tted trajectory. The ext module also assumes a pion mass when extrapolating this trajectory beyond the outermost CDC layer (86.3 cm radius) through the CDC outer cylinder, ACC counters, and TSC counter to the TOF counter (120 cm radius). Hadron decays or interactions in the material between the CDC and the TOF can cause deviations from this extrapolated trajectory and also from the time predicted using it. Such deviations in measured and predicted times are unavoidable for hadrons and are partly responsible for poorer time resolutions for hadrons than for muons. For highmomentum tracks, the extrapolation using a pion mass is a reasonable approximation for kaons or protons and the ight time for a kaon or a proton can be obtained by scaling the pion ight time by / K or by / p respectively. For low-momentum tracks, the extrapolation from the CDC to the TOF needs to be done separately assuming kaon and proton masses. These separate extrapolations are done in the rectof module for kaons when K < 0.81 and for protons when p < 0.82. B. Empirical Correction for Hadron TOF Systematics Systematic time deviations are seen for pions, kaons, and protons with momenta less than 1.3 GeV/c. Plots of the time dierence t (corrected measured time minus the predicted 11

ight time) also show a momentum dependence. Initially, these eects were roughly corrected but shifting the global T0 by 30 ps. This shift made the mean t for kaons nearly zero. As larger data samples became available in exp. 7, it became clear that the systematic dierences between hadron types were larger than 30 ps and that a particle-dependent correction was needed. The rst particle-dependent correction was to add dierent constant osets to the pion, kaon, and proton predicted times. In July 2000 Jorge L. Rodriguez found that the deviations for the dierent hadron types were approximately linear in the particle's. This dependence could be removed by adding a correction time (linear function of ) to the particle's predicted ight time in the rectof module. The coecients of the linear function were dierent for dierent run ranges, however. 1. correction version 1 The original corrections determined in July 2000 were for exp. 5, for exp. 7runs1-535, for exp. 7runs536-1439, and :273 ; :259 (7) :220 ; :198 (8) :325 ; :316 (9) :425 ; :415 (10) for exp. 7 runs > 1440. The linear function derived from data at the end of exp. 7 worked reasonably well for exps. 9-13. 2. correction version 2 Checks using the large D* event sample for exp. 7-13 revealed a systematic t shift of about 20 ps for pions and kaons with >.95. This shift could be removed by using a modied correction (default starting with exp. 15) :425 ; :415 min( :95) (11) This is the same as the correction we had been using for <.95 but has a value of 30.8 ps for >.95. This change mostly aects pions because no protons and only kaons with momenta above 1.5GeV/c have >.95. Another systematic deviation was seen for pions and kaons with momenta below 0.5 GeV/c. The deviation increased from near zero at a momentum of 0.5 GeV/c to about 90 ps at a momentum near the threshold (0.27 GeV/c) for a particle to hit the TOF system. It is approximated by the following low-momentum correction (default starting with exp. 15) :12 exp(;(p ; :168) 2 =:0366) (12) This low-momentum correction time is added to the predicted ight time along with the -dependent correction for data. For Monte Carlo events the low-momentum correction is added to a constant oset of 15 ps. The low-momentum correction has a small eect on K- separation because the kaon-pion predicted time dierences are much larger than the size of this correction, whose maximum value is 90 ps at a momentum of 0.27 GeV/c. 12

TABLE IV: Time resolution for positive hadrons exp. kaons kaons pions pions P<1.3 P>1.3 P<1.3 P>1.3 ps ps ps ps 7 105 110 114 115 9 103 110 117 117 11 109 111 115 119 13 108 111 116 116 13 MC 112 105 111 104 15 111 113 117 120 17 108 114 122 120 17 MC 107 105 106 105 19 111 117 122 122 TABLE V: Time resolution for negative hadrons exp. kaons kaons pions pions P<1.3 P>1.3 P<1.3 P>1.3 ps ps ps ps 7 109 116 115 112 9 115 116 118 116 11 112 115 115 120 13 112 114 112 115 13 MC 108 109 106 108 15 114 118 120 119 17 114 118 116 121 17 MC 109 108 103 105 19 119 122 122 122 3. check of systematics The modied -dependent correction and the low-momentum correction reduce systematics but are not expected to improve the TOF time resolutions or K- separation dramatically compared to the previous -dependent correction alone. The time resolutions in Tables IV and V conrm this expectation. These resolutions are obtained using pions and kaons from D o decays in D* event samples. The resolution values are the 's from Gaussian ts to the t distributions. The following cuts were made to select a clean sample of D o decays to K in the D* sample: :144 <m D ;m D <:147 GeV (13) 13

TABLE VI: Time resolution in ps for pions and kaons with momenta > 1.3 GeV/c. The resolutions in the rst three columns are 's from Gaussian ts with jtj < 0.3 ns. The resolutions in columns labeled "tight" are from ts with jtj < 0.15 ns. Resolutions for muons used for exp. 19 calibrations are given for comparison. particle exp. 7-13 15-17 19 7-13 15-17 19 tight tight tight K ; 115.7 118.4 121.8 101.2 108.1 109.4 K + 111.7 113.9 117.1 99.0 101.7 104.4 ; 116.6 120.0 121.8 101.2 107.4 112.1 + 117.2 120.6 121.6 103.6 108.9 108.8 100.5 95.3 1:835 <m D < 1:895 GeV (14) jt K j <:3 ns ;:511 <cos( K ) <:827 (15) jt j <:3 ns ;:511 <cos( ) <:827 (16) where K and are the polar angles of the kaon and pion respectively. Plots of the resolutions as a function of time are in Figs. 7and8. FIG. 7: TOF time resolution in ps versus time. The circle symbols are for muons in dimuon events. The diamond and square symbols are for + and ; respectively. The asterisk symbol is for K + and the X with square at the center is for K ;. The pions and kaons in this plot have momenta above 1.3 GeV/c. 14

FIG. 8: TOF time resolution in ps versus time. The diamond and square symbols are for + and ; respectively. The asterisk symbol is for K + and the X with square at the center is for K ;. The pions and kaons in this plot have momenta below 1.3 GeV/c. The resolutions for pions and kaons in Fig. 7 are clearly larger than those for muons. Much of the dierence is due to non-gaussian tails of the t distributions, which are more prominent for hadrons than for muons. Table VI contains resolutions for the t cut used for Tables IV and V and also for a tight cut, jtj < 150 ps. The tight cut reduces the resolution for muons by about5ps,but the reduction for pions and kaons is usually more than 10 ps. Figures 9(a) and (b) contain plots of the means from Gaussian ts to the t distributions versus momentum. These results are obtained for hadrons in the general hadron event (HadronB) sample for exp. 17 runs 78-103. One can see from the mean values for pions and kaons that any remaining systematic eects are typically less than 20 ps. However clear systematic dierences between positive and negative kaons and between protons and anti-protons are seen. The mean t values for negative kaons are typically 10 ps larger than those for positive kaons. The mean t values for protons and anti-protons have a rapid variation at low momentum and those for anti-protons are typically 20 ps larger than those for protons for momenta above 1 GeV/c. These systematic dierences are related to the observed dierences in the ADC distributions. (For example, the mean ADC value is about 840 for protons and 1130 for anti-protons.) Corrections for these remaining systematics were incorporated into a module that corrects mdst les. (See Appendix.) Figures 9 (c) and (d) show the results for exp. 17 runs 78-103 after the mdst corrections. 4. correction version 3 Systematic eects for kaons and protons can also be seen by examining t versus plots removing the linear correction (eq. 11) and the low-momentum correction (eq. 12). 15

FIG. 9: t systematics as a function of momentum (GeV/c). (a) negative charged tracks and (b) positive charged tracks before the x-mdst-tof correction. (c) negative charged tracks and (d) positive charged tracks after the x-mdst-tof correction. The plots are shown for the data in exp. 17. Figures 10 (a) to (c) show these plots for pions, kaons, and protons respectively using data from the general hadron sample for exp. 17 runs 78-103. For these plots, the dierent 16

particle types are selected using the best i d function, which is part of the atc p id class. [5] This function assigns a bestid value equal to the particle index (2 for pions, 3 for kaons, 4 for protons) for the particle type with the largest PID likelihood. One can see in Fig. 10 (a) that the current corrections (dashed curves) describe the pion data rather well. Similarly, Fig. 10 (b) shows that these corrections (dashed curves) describe the K + data well, but there are some small systematic deviations for the K ; data. Fig. 10 (c) shows clear deviations from the current corrections (dashed curves) for both protons and anti-protons. These deviations are mostly removed by the module that corrects mdst les. Any attempts to further reduce systematics in the initial dst production would need to address the dierent responses of the TOF for K + and K ; and for protons and anti-protons. The systematic deviations for protons and anti-protons could be mostly removed by replacing the current rectof corrections with the following: for protons and :365 ; :338 ; :046 exp(;( ; :429) 2 =:00856) (17) :533 ; :528 ; :167 exp(;( ; :418) 2 =:00573) (18) for anti-protons. These functions are represented by the dash-dot curves in Fig. 10 (c). C. Current Hadron Corrections In summary, the corrections implemented in the rectof module to the predicted hadron times since exp. 15 are given by equations 11 and 12 for pions and kaons. Both of these correction terms are added to the time calculated by the ext module's trajectory extrapolation. These same corrections were also used for protons and anti-protons for exps. 15-19. Starting with exp. 21, the correction in eq. 17 has been used for protons and that in eq. 18 for anti-protons. Checks of the exp. 21 and exp. 23 data conrm that the current corrections generally limit remaining systematic deviations to less than 20 ps. 17

FIG. 10: (a) pion uncorrected t values in ns versus for + on the left and ; on the right ( Exp.17 data ). The momentum range is 0.3 to 0.8 GeV/c. Pions are selected by requiring the pion corrected t < 0.5 ns and the particle ID quantity bestid=2. The dashed curve is the current rectof correction the dotted curve is the linear correction only. (b) kaon uncorrected t values in ns versus for K + on the left and K ; on the right. The momentum range is 0.3 to 0.8 GeV/c. Kaons are selected by requiring the kaon corrected t < 0.5 ns and the particle ID quantity bestid=3. The dashed curve is the current rectof correction the dotted curve is the linear correction only. (c) proton uncorrected t values in ns versus for protons on the left and anti-protons on the right. The momentum range is 0.4 to 1.3 GeV/c. Protons are selected by requiring the proton corrected t < 0.5 ns and the particle ID quantity bestid=4. The dashed curve is the current rectof correction the dotted curve isthelinear correction only. The dash-dot curves are proposed new corrections given in eqs. 17 and 18 in the text. 18

FIG. 11: Clocked Time Stretcher for the Belle TOF system. 19

V. PMT GAIN AGING EFFECT DUE TO INTEGRATED ANODE CURRENT Figure 12 shows an accelerated test result for PMT gain aging, which was carried at the Hamamatsu Photonics company at a higher anode current of 200A. The plot shows the average gain of 8 test PMTs as a function of operation year, scaled to 1A, which corresponds to the nominal current of Belle TOF operation. Thus, the HPK result predicts a lifetime of 40 years for PMTs under present operation conditions. Figure 13 shows a history of PMT gain averaged over 256 PMTs from exp. 5toexp. 21 for the last three years. The time scale of the HPK test results is scaled by a factor of 38 (determined empirically by HPK). As the data and the HPK test results seem to be consistent, we conclude the PMT gain aging will be no problem for another ten years. 120 R6680 PMT gain vs years at 1uA (scaled by 38.) 100 80 60 40 20 0 0 10 20 30 40 50 120 100 80 60 40 20 0 0 0.5 1 1.5 2 2.5 3 3.5 4 FIG. 12: Accelerated test results of PMT gain aging eects, carried out at the Hamamatsu Photonics Company (HPK) with an anode current of 200A in 0 Tesla (open circles) and in 1 Tesla (dark circles). 8PMTswere tested in 0 Tesla at a nominal HV of 2000V, and 2 PMTs were tested in 1 Tesla at a nominal HV of 2750V. The gain is normalized with 100% for the initial value. The actual test time of one year is scaled by a factor of 38 to predict performance for an estimated anode current of1a for Belle TOF PMTs. The bottom gure is expanded for the rst four years. 20

PMT gain vs operation years for exp5 to exp21 600 exp7 500 exp5 exp9 exp13 exp15 exp19 400 exp11 exp17 exp21 300 200 100 Gain(1/2) preamp(x4.5) 5uA 2.5uA 0.5uA 0.7uA 0 1999.5 2000 2000.5 2001 2001.5 2002 2002.5 2003 120 calendar years 100 80 60 1uA 1T(HPK) 1uA 0T(HPK) 40 20 0 0 0.5 1 1.5 2 2.5 3 operation years FIG. 13: PMT gain aging eect of Belle TOF PMTs. The top gure shows the average ADC values for 256 PMTs as a function of calendar years and experimental numbers. We recognized an aging eect during Exp. 5 and lowered the gain by a factor of 2 in Exp. 7 to reduce this eect. Then, we decided to install preampliers to amplify signals by a factor of 4.5 from Exp. 9 for further reduction of the aging eect. The bottom gure shows the PMT gain as a function of Belle operation year. The gain is normalized to the initial gain as of June 1999, and renormalized at the two gain changes. The x-axis indicates actual operation time of the Belle detector. The open circles indicate the expectation from Hamamatsu test results for 0 Tesla and the dark circles indicate those for 1 Tesla. The time scale is normalized for the Belle operation condition of 1A (see previous gures). VI. AGING EFFECT OF TIME RESOLUTION AND SOURCES In this section, we summarize the aging of the Belle TOF system. Figure 14 shows the attenuation length as a function of years. The top gure is for 2000 to 2003, and the bottom gure is for 1996 to 2010. The line indicates a t result of 281:5 e ;0:0704year cm. The point in1996 indicates the measurement at the Univ. of Hawaii. The attenuation length is found to be decreasing at a rate of 7% per year. Figure 15 shows time resolutions for -pair, and K tracks as a function of calendar 21

Ave. atten. length vs calendar years since Jan.2000 500 400 300 cm ~ 7% / year 200 Att.L =281.5 exp(-0.0704*year) 0 0.5 1 1.5 2 2.5 3 2000 2001 2002 2003 500 450 cm 400 350 300 250 200 150 100 50 0-4 -2 0 2 4 6 8 10 1996 1998 2000 2002 2004 2006 2008 2010 FIG. 14: Average attenuation length of 128 TOF scintillators as a function of calendar year. The data is tted to a function 281:5e ;0:0704year cm, where the point in 1996 indicates an attenuation length measured at Hawaii right after delivery from the Bicron company. The top gure is for the years 2000 to 2003 on a logarithmic scale, and the bottom one is for 1996 to 2010 on a linear scale. year. The top gure shows the data in the years 2000 to 2003 and the bottom one shows its extrapolation up to 2010. The lines are t results to the data with a function TOF = 95 + 2:5 year ps for -pair tracks. The dark squares indicate the time resolution of - pair tracks. The others indicate time resolutions for (dark symbols) and K (open symbols) tracks, which are larger by 1520ps than those of -pair tracks. The dierence is due to our calibration procedure to determine time walk correction parameters using -pair tracks and then to apply this correction to hadron tracks with additional corrections as described in this note. The time resolutions of and K tracks are aected by the particle identication scheme used in this analysis, which is dependent on the t function and and K contamination. The open crosses indicate an expectation assuming a N pe decrease due to the attenuation length aging. It explains two-thirds of the time resolution aging eect. The remainder may be due to an aging of light yield of scintillators, while it is not conrmed in the data. We predict a linear increase of time resolution for the -pairs it would exceed 110 ps in 2006. As the Belle PID is made in combination of CDC, ACC and TOF, and ACC covers momentum over 1.2 GeV/c, the eect of this time resolution degradation is not serious. The momentum cuto at a xed sigma separation is proportional to the square 22

root of the time resolution, P cutoff p TOF, thus the separation in the momentum region of 1.12 to 1.2 GeV/c is decreased and the fake rate is increased. The total eect is expected not to be signicant. Time resolution vs calendar years since Jan.2000 140 130 120 ps 130 ps 110 100 90 80 0 0.5 1 1.5 2 2.5 3 2000 2001 2002 2003 140 130 ps 130 ps 120 110 2.5ps /year 100 90 Att. length aging(npe) 80 0 1 2 3 4 5 6 7 8 9 10 2000 2002 2004 2006 2008 2010 FIG. 15: Time resolutions for -pair, and K tracks as a function of calendar year. The top gure shows the data in the years 2000 to 2003 and the bottom one shows an extrapolation up to 2010. The lines are t results to the data with a linear function. The function is TOF = 95 + 2:5 year ps for -pair tracks. The dark squares indicate the time resolution of -pair tracks ( see text for details ). VII. MQT300A DEAD TIME AND PMT PREAMPS We also checked the dead time of Q and T measurements. The dead time in the Q- measurement with MQT300A is expressed as T deadtime = 0:025 rate(khz)%, where the rate is the TOF single rate [3]. It amounts to about 5% at a rate of 200 KHz, and recently the TOF single rate is above 200KHzatthebeginningofeachrun. We now need to adjust MQT300A gain and oset time to minimize the dead time, where the oset is about 1200 channels (600 ns) and the range of Q is up to 1000 ch. We expect a reduction of the MQT dead time by a factor of 50% by reducing the oset to 500 ch. On the other hand, the time stretcher has a smaller dead time of 600 ns, which is due to its time expansion factor of 20 and using the second edge of the TS clock to latch and digitize the input timing. We need 23

to check and adjust MQT300A to reduce the dead time for higher luminosity runs. For KEKB continuous injection runs, wehavechecked the original preampliers in several test runs and found that the current mirror circuit causes a latchup problem of the output level at 50mV. We have modied all the preampliers to AC coupling to avoid the problem. We have also prepared a new set of 350 preampliers by removing the current mirror circuit from the original design. VIII. SUMMARY We summarize the performance of the Belle TOF system over the last three years. The time resolution for -pair tracks is found to increase with a linear function TOF =95+2:5 year ps since Jan. 2000. The attenuation length shows an aging eect as a function of year att = 281:5cm exp(;0:0704 year), which explains two thirds of the time degradation. The remainder may be due to a light yield reduction of the scintillator itself or to higher TOF background rates. The Belle TOF system will continue to provide a time resolution of about 100 ps with a 2.5 ps degradation per year. The dead time in the Q-measurement isexpected to be about 5.0% at a TOF single rate of 200 KHz, when we get a luminosity 8 10 +33 =cm 2 s ;1. We can easily accomodate a luminosity as high as 1 10 +34 by optimizing the present MQT300A parameters, where we expect an ineciency less than 5% for an expected TOF rate of 300 400 KHz. Finally, we have to make a comment on calibration systematics. As described, we nd systematic dierences between measured TOF times and those expected from CDC tracking, for, K and proton tracks the dierences are mass- and momentum-dependent. Empirical corrections have been done to minimize the systematics down to a 20 ps level. We also see a worse time resolution for hadron tracks (115120 ps) than -pair tracks (100 ps). We need to understand the causes, which may be due to interaction eects and/or systematics of track extrapolation in the ACC detector region at a radial depth of about 30 cm between the CDC and TOF counters. There are also systematic eects in event selections and ttings to get the hadron time resolution itself. [1] K. Abe et al. (Belle Collaboration) Nucl. Inst. and Meth. A479. (2002) 117. [2] H. Kichimi et al. The Belle TOF System. Nucl. Instr. and Meth. A453 (2000) 315. [3] J.W.Nam et al. A detailed Monte-Carlo Simulation for the Belle TOF System. NIM A491(2002)54 (belle-prep-2002-9). [4] Y. Teramoto, Belle note 259. [5] KID group, Belle note 321, page 23. 24

IX. APPENDIX A. Time resolution for mu-pairs during Jan. 2000- Oct. 2002 (exps. 7-23) The resolutions for the weighted average time for mu-pair events are given in Tables VII to IX for exps. 7-23. For comparison, the resolutions obtained applying the same calibration program to Bhabha events are about 113 ps in exp. 9 and exp. 13 and 114 ps at the end of exp. 19. The time resolution has slowly degraded in the three years since Jan. 2000. B. correction formulae for hadron systematics Hadron events reprocessed in Spring 2002 were observed to have some systematic shifts. The following corrections for these shifts were implemented in the x-mdst-tof module that can be used on mdst les. The functional forms used for pions are for exp. 7runs1-535, for exp. 7runs536-1439, for exp. 7runs> 1440, for exps. 9-13, and no correction (21) :5054 ; :5216 min( :955) (22) :8321 ; :8648 min( :96) (23) 1:089 ; 1:131 min( :955) (24) ;:0183 exp(;( ; :911) 2 =:00161) (25) for positive pions in exp. 15. This exp. 15 correction was needed to x a tracking bug in the 20020405 library that aected only low-momentum positive pions. There are no corrections for pions for exps. 17-19. The functional forms used for kaons are for exp. 7runs1-535, for exp. 7runs536-1439, for exp. 7runs> 1440, for exps. 9-13, ;:0414 exp(;( ; :538) 2 =:0569) (26) ;12:3 exp(;( + :288) 2 =:1197) (27) no correction (28) no correction (29) ;6:6 exp(;=:1) (30) for exp. 15. There are no corrections for kaons for exps. 17-19. Dierent corrections are made for protons and anti-protons. The functional forms used for protons are ;:876 exp(;( + :1818) 2 =:1947) (31) 25

TABLE VII: Time resolution for muons for data taken in the year2000tosummer2001 exp. runs resol. (ps) time 7 1283-1379 96.8 Jan.13Jul.23 (2000) 7 1418-1463 95.7 7 2294-2515 96.6 9 17-354 96.5 Oct.13Dec.28 (2000) 9 456-490 97.4 9 566-634 97.2 9 635-735 97.4 9 738-796 96.8 9 797-893 97.8 9 895-1064 97.9 9 1096-1220 98.5 11 1-106 98.8 Jan.20Apr.16 (2001) 11 191-362 98.3 11 381-446 98.3 11 451-555 98.3 11 566-681 98.5 11 774-924 98.8 11 941-1037 97.9 11 1038-1229 98.5 11 1293-1367 98.3 13 1-198 99.0 Apr.21Jul.16 (2001) 13 200-415 98.8 13 416-440 98.6 13 454-570 97.5 13 571-662 97.4 13 664-711 97.5 13 713-738 96.9 13 881-973 98.0 13 973-1024 97.7 13 1031-1059 97.4 13 1060-1171 97.8 13 1176-1292 97.8 13 1298-1376 98.4 13 1385-1464 98.2 13 1468-1606 98.2 15 52-242 100.1 Oct.6Dec.25 (2001) 15 178-242 99.4 15 243-374 99.8 15 383-423 99.4 26

TABLE VIII: Time resolution for muons for data taken starting Fall 2001 exp. runs resol. (ps) time 15 494-568 100.2 15 643-710 99.8 15 714-764 99.9 15 850-950 100.3 15 954-1018 99.4 15 1100-1154 99.6 15 1157-1186 100.0 15 1188-1248 99.6 15 1252-1343 99.5 15 1344-1437 99.3 17 2-75 101.8 Jan.18Mar.13 (2002) 17 78-103 100.1 17 169-220 100.7 17 227-297 101.1 17 308-363 99.9 17 364-422 99.8 17 426-491 99.9 17 493-544 99.9 17 545-608 99.7 17 610-671 100.1 17 674-740 100.7 17 741-804 99.9 17 805-854 100.5 17 855-937 99.4 19 1-59 101.0 Mar.15Jul.1 (2002) 19 64-94 100.1 19 95-150 100.3 19 151-191 100.2 19 192-284 100.4 19 286-335 100.5 19 390-475 100.9 19 476-541 100.7 19 542-666 101.2 19 667-770 103.6 19 771-923 103.8 19 925-1061 103.2 19 1062-1159 102.7 19 1161-1389 102.7 19 1407-1520 102.6 27

TABLE IX: Time resolution for muons for data taken through Fall 2002 exp. runs resol. (ps) time 19 1522-1643 102.4 19 1644-1709 102.9 19 1644-1709 114.1 Bhabha 21 2-49 101.5 Fall in 2002 21 50-80 101.5 21 81-120 102.0 21 121-189 102.4 21 190-245 102.8 21 246-276 102.5 21 277-324 103.4 23 1-65 102.1 23 66-91 101.0 23 92-167 101.0 23 168-250 101.3 23 253-356 100.5 23 357-447 100.7 23 448-527 101.2 23 528-609 101.3 for exps. 7-13, for exp. 15, and ;:736 exp(;( + :04158) 2 =:119) (32) ;:3259 exp(;( ; :1042) 2 =:0817) (33) for exps. 17-19. The functional forms used for anti-protons are for exps. 7 runs 1-1439, for exp. 7runs> 1440, :01 ; :1028 exp(;( ; :4454) 2 =:00272) (34) :01 ; :064 exp(;( ; :4273) 2 =:00317) (35) :01 ; :1028 exp(;( ; :4454) 2 =:00272) (36) for exps. 9-13, and :02 ; :1475 exp(;( ; :4267) 2 =:00249) (37) for exps. 15-19. 28