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Particle Identification by Correlating Time-of-flight and Momentum Measurement 11/4/2011 T.Chujo, H.Ohnishi BNL R.Averbeck, J.Burward-Hoy, A.Drees, F.Messer, F.Muehlbacher, J.Velkovska SUNY Stony Brook A. Kiyomichi Univ. of Tsukuba Abstract In this note we discuss technical details of time and momentum analysis as well as the particle identification used for presentations at the QM2001 meeting. All results shown are obtained from V03 DSTs, of which 30-50% were available at the time of this analysis. In the first section we discuss the corrections applied to the flight time and the resulting time resolution of 125 ps. The second section summarizes the momentum analysis. The momentum scale is known within 2% systematic errors. The momentum resolution is limited at low momenta by multiple scattering to p/p ~ 0.6 0.1% and at high momenta by the drift-chamber resolution to p/p2 ~ 2.5 0.5% and p/p2 ~ 6 2% for tracks reconstructed fully (X1+X2) or partially (X1 or X2), respectively. The final section discusses the cuts developed to identify p, and p on the basis of time and tracking . In an Appendix we give a brief description of the software available in the CVS repository. 1 1 Flight-Time Calculation TOF time scale After the DST production started, it was discovered that the initial TOF calibration was based on the assumption of a 10 MHz beam clock. The true RHIC beam clock, however, is 9.43 MHz. Closer investigation showed that the actual scale factor to equalize the BBC and TOF time scales is 1.046. This factor was measured as the slope of the time tTOF versus expected time T0-L/c. Here T0 is the start time derived from the BBC, L the path length, and p/E. Figure 1 shows the measured correlation for pions selected in m2 vs p. Figure 1 Correlation of measured flight time and expected flight time for pions Time Zero Calibration The T0 derived from the BBC for the DST production needs to be corrected for run-by-run variations and centrality dependence. The centrality dependence is shown in Figure 2. As a measure of the centrality we use the number of PC1 hits. The exact origin of this effect is unknown. We suspect it is due to the limited dynamic range of the BBC ADCs. For saturated ADC pulse-heights the BBC slewing correction becomes inaccurate, which will result in a multiplicity depended time zero calculation. 2 Figure 2 Measured BBC T0 as a function of number of hits detected in PC1 In addition, to this correction a run-by-run adjustment of the BBC T0 is required. As seen from Figure 3 the offset varies by about 100 ps. Figure 3 Run by run variation to BBC time zero offset Time resolution For the analysis presented at QM2001 the time read from the DST is recalibrated according to: T flight 1.046 tTOF T0 0.691 0.815 * N pad / 1000 Here tTOF is the time read for the TOF, T 0 from the BBC, and Npad the clusters detected in PC1. After applying the correction we measure the time resolution from the difference of measured and expected time: T T flight L / c At high momenta the uncertainty in does not contribute to the variance of t and thus for high momenta t is a direct measure of the time resolution. From Figure 4 we measure t = 120-130 ps for pions between 1.5 and 2.0 GeV. 3 Figure 4 Measured time difference t for pions with momenta between 1.5 and 2.0 GeV At lower momenta error on the expected flight time contributes the measured t due to the increasing uncertainty in the momentum determination. The observed dependence of t can be fully described by the measured momentum resolution: L p 1 2 2 2 2 T 2 t c p2 c L 2 The uncertainty of the path length L can be estimated from the angular uncertainty of the trajectory, it only contributes to T below 200 MeV momentum. The momentum resolution is also directly related to The determination of is discussed in the next section. Figure 5 Momentum dependence of T. The solid line describes the expected resolution due to the measured momentum resolution as discussed in the next section. 4 2 Momentum measurement The momentum used for the PID analysis was calculated by the PHTrack track-model developed by S.Johnson and B.Burward-Hoy. No further corrections are applied to the momentum measurement. Momentum scale We know the momentum scale to better than 2%. The analysis has been described in detail in PHENIX analysis note # (http://www.phenix.bnl.gov/phenix/WWW/p/draft/janebh/pt/systematicsII/systII.htm). Here we summarize the results. To determine the momentum scale we use the well-known method of correlating particle mass and momentum. The correlation is shown in Figure 6. Figure 6 correlation of m2 and momentum after final T flight calibration We calculate m2 according to: 1 m 2 2 1 p 2 2 T flight b c 2 L2 2 2 p L2 Again, L is the path length and T flight is the calibrated flight time. In the equation we have introduced a momentum scale factor and an additional time offset b. By fixing the particle mass we can fit and b. The parameters have been fitted individually to all particles. A 2 analysis was performed to determine 1 5 regions for the two parameters, the result is shown in Figure 7. The bands overlap and are consistent with and b=0. Figure 7 One regions for momentum scale factor and time offset b. The best estimate of the momentum scale factor is determined by simultaneously fitting Kaons and protonsThere is some indication that the magnetic field in the 2D map currently used in the analysis is lower by about 2% compared to the actual measured field map, compatible with our analysis of the momentum scale. Since we could not clarify which field map gives the best approximation for the actual field of the magnet during data taking we did not apply a momentum scale correction and conclude the momentum scale is known within 2% systematic accuracy. Momentum resolution The momentum resolution is given by the angular resolution of the drift chamber measurement. In principle, the angular resolution is determined by the single hit resolution, i.e. the precision with which the drift distance to a single anode wire is measured. This resolution has been measured to be hit ~ 150 m. With this intrinsic resolution and a fully functioning drift chamber we expect a momentum resolution of p/p2 ~0.4%. In practice, the resolution is also determined by the accuracy of the wire positions, which has not been taken into account in the analysis up to now. Systematic shifts of groups of wires by a few hundred m result in a resolution of about p/p2 ~2.5% and p/p2 ~6% depending on how the track was reconstructed. In Figure 8 the angles measured by the drift chamber, DC and , referred to a reference radius RDC of about 2.2 m. The depth in radial direction of the X1 and X2 sections is d = 6 cm and they are separated by R ~ 27 cm. To first order the momentum (in GeV) is measured by the angle according to: 84 mrad p The 84 mrad/GeV correspond to the field integral K1= 0.3 RDC lBdl . 6 Figure 8 Definition of the angles measured in the drift chamber. The precision with whichis reconstructed is different depending on whether the trajectory was fully reconstructed in X1 and X2 or only partially in either X1 or X2. We introduce net and net as the resolution of a track reconstructed in X1 or X2 only. Ideally we expect: 2 hit X1 or X2: net 3.5 mrad d X1 and X2: ~ 2 net RDC 2 hit 0.35 mrad R N hit R The resolution net and net can be measured directly from tracks reconstructed in X1 and X2. For these tracks we determine 1,2 and independently for X1 and X2. The resolutions can be derived from the variance of the =1-2 and = distributions. We analyze no-filed data (run 10629) to avoid residual magnetic field effects; note that the multiple scattering in the 27 cm of Ar/C 2H6 is negligible. The data is shown in Figure 9. We measure the following resolutions, the errors are systematic errors resulting from repeating the analysis in different phase space regions and fit ranges: Data: 7.2 0.7 mrad 5.1 0.5 mrad net 0.4 0.04 mrad net 0.28 0.03 mrad The same analysis was repeated with simulated events. From Figure 10 we determine smaller resolutions, close to the expected values. MC: 4.8 mrad 3.4 mrad net 0.25 mrad net 0.17 mrad 7 Figure 9 Measured =1-2 and = distributions for no field data. Only tracks with angles less than 5 mrad were used. Figure 10 Determination of =1-2 and = from MC generated tracks. In the following we consider two systematic uncertainties of the wire positions: A random rotation of a X1 or X2 wire net * around its center and a rotation of the wire net around the beam axis *. We extract their values by subtracting from the measured and the expected values determined from the MC simulation: 3.8 0.5 mrad * 0.22 0.03 mrad * A powerful cross check of the above results is obtained from tracking particles to PC3 and matching the trajectory to reconstructed clusters in PC3. For this analysis multiple scattering can not be neglected. For 8 data taken with magnetic field the match between predicted and measured point can be measured as a function of momentum, and thus the multiple scattering contribution and detector resolution can be separated. Figure 11 shows the match in azimuthal angle for all tracks reconstructed and, separately, for those reconstructed in X1 or X2, as well as X1 and X2. In addition, also the result from the MC simulation is shown. Note that the azimuthal angle is measured relative to the beam axis. All data sets have been fitted above 0.5 GeV with two parameters. We denote them as c ms and track , the contribution due to multiple- scattering and the detector resolution, respectively. match cms / p 2 track 2 Figure 11 Match of tracks to PC3. For the MC simulation track is reproduced by the known PC3 resolution, in good agreement with the naïve expectation of 1.7cm / 12 / RPC3 ~ 1 mrad. However, the data show much larger uncertainties in the track match. For each case track can be determined from the PC3 resolution PC3 and the drift chamber resolutions net and net: 2 X1 or X2: RPC 3 RDC track PC 3 net 3.5 6 0.25 mrad 2 2 2 net 2 RPC 3 2 2 X1 and X2: RDC RPC 3 RDC track PC 3 0.5 net 2 net 2.2 0.15 mrad 2 2 2 2 R RPC 3 Assuming that the MC simulation givesPC3 , net and net can be calculated from the above equations. The result is: 5.8 0.5 mrad net net 0.28 0.03 mrad 9 The results are in excellent agreement with the values previously derived from the DC measurement. Yet another cross-check results from analyzing the width of m2 momentum correlation shown in Figure 6. A simultaneous fit of the width of and p (for details see next section) gives an angular resolution of =3.20.2 mrad for the track reconstruction. This is in good agreement with the mrad determined from Figure 11 for the overall track sample. Note both analyses average over full and partially reconstructed tracks. Finally, to derive the momentum resolution we also need to consider the contribution from multiple scattering to. Obviously, multiple scattering in material close to the beam pipe contributes only to . I contrast, material close to the drift chamber contributes only to Figure 12 illustrates how material at a distance R from the vertex contributes to It can easily be shown that an average multiple scattering angle of rms at a distance R contributes as: R rms RDC drift chamber rms RDC scatterer R Figure 12 Illustration of the contribution of a material at a distance R from the vertex to . Material Thickness (mm) X/X0 (%) R (m) rms(mrad) mrad) Be beam pipe 0.3 0.04 0.58 0.01 MVD silicon detector 0.3 0.3 0.04 0.58 0.01 MVD shell 0.4 0.4 0.69 0.13 Air 2000 0.7 1.1 0.92 0.46 DC mylar window 0.2 0.07 2.0 0.26 0.24 Total - 1.77 - - 0.53 Table 1 materials in front of the drift chamber and their contribution to 10 The overall multiple scattering contribution is ~ 0.53 mrad. A fit to the width of the correlation of m 2 and momentum gives 0.60.1mrad, in perfect agreement with the expectation. Using the angular field kick of 84 mrad/GeV the momentum resolution reached in the V03 DST production is: X1 and X2: p 0.006 0.001 2 0.026 0.003 2 p 2 p X1 or X2: p 0.006 0.0012 0.061 0.0052 p 2 p 3 Particle Identification In this section we discuss the cuts used to identify pions, Kaons and protons. The main idea is to cut on m 2 as function of momentum. Track selection cuts To analyze identified particles several cuts on the event and the track are applied before the particle identification cut: Event vertex within 20 cm Reconstruction of the z coordinate of the track (quality>20, error =0) matching cut on residual of track and TOF hit position Typically a 2.5 or 3 sigma cut on the TOF matching will be required. The width of the match is measured as function of momentum independent in r and z. Additional matching-cuts to PC3 can be applied. At this point in time these cuts are not fully optimized and case significant loss in particle yields below 1 GeV momentum, thus they are not applied. Width of the mass squared distribution The error on m2 can be calculated assuming the error on the path length L can be neglected: 4 m 2 t2c 2 4m p 2 2 m 2 4 2 ms 4 m 1 2 2 4 p 2 m 2 p 2 2 2 2 p K1 K 1 L 11 From the previous sections we take t = 1255 ps, =3.00.2 mrad, and ms=0.60.1 mrad. In Figure 13 one sigma bands are shown around pion, Kaon and proton m2. All particle identification cuts are based on these contours. Figure 13 2.5 sigma cut on m2. The green dotted line corresponds to the contribution of ms , the red dashed line to , and the blue dash-dotted line to t. 12 Figure 14 typical m2 distribution for two different momentum regions. As expected the mass peaks are clearly separated even at 1.5 GeV momentum. Figure 15 width of measured m2 compared to values used in PID-cut, the bands correspond to the upper and lower error limits quoted on the resolution parameters t , , and ms. 13 Imperfections of the geometrical alignment of the detectors, the time calibration, and momentum scale are taken into account by empirically adjusting the center of the m2 bands. We have fitted the centroid in small momentum intervals between 0.5 and 2 GeV. The results are given in Table 2. As a final crosscheck we measure the width of the m2 bands in Figure 6 as a function of momentum and compare them to the width of used in our PID-cuts. Typical fits are shown in Figure 15. m2 expected m2 P 0.8300.056 0.874 p 0.8220.056 0.874 + 0.01570.001 0.0193 - 0.01680.001 0.0193 K+ 0.2290.016 0.244 K- 0.2270.018 0.244 Table 2 mean m2 values between 0.5 and 1.2 GeV momentum Within the errors we reconstruct the same mass for particle and anti-particles. The average mass values are low by about 3%. The centroids of all bands decrease slightly with momentum. At all momenta up to 2 GeV the deviation from the mean m2 is not more than 0.3 m2 at that momentum. 4 Appendix float classMicroTrack::getBbcT0() This method return the BBC T0 after correction of multiplicity dependence of T0. You need to call getBbcT0() in your analysis routine to get correct BBC T0. Extra action or extra file to feed parameters are not necessary. float classMicroTrack::getToF() This method returns the fully corrected Time-of-Flight(ToF) value. "Fully corrected" means, ToF scale factor, multiplicity dependence of Bbc T0 and run by run ToF shift are applied by this method. You need to call getToF() in your analysis routine, if you need ToF value. However, one the extra ASCII file "tof_Run-by-Run-offset.txt" must be located in your working directory to correct "run by run ToF shift". You can find the file in the CVS repository. classMicroTrack::getPid() … 14

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