Particle Identification by Correlating Time-of-flight and Momentum Measurement
2/6/2016
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:
2
 L  p  1  2
  L
 T   t2   2  2  
 c
 c  p
2
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:


2
T flight  b c 2  L2 2 2
 1

m   2  1 p 2 
 p
L2


2
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 protonsThere 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:
p
84 mrad

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 whichis 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:
X1 or X2:
2 hit
 3.5 mrad
d
 net 
X1 and X2:  ~ 2 net RDC 


R
2 hit
N hit R
 0.35 mrad
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
   0.4  0.04 mrad
  net  5.1  0.5 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
   0.25 mrad
  net  3.4 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 multiplescattering and the detector resolution, respectively.
2
cms / p 2   track
 match 
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:
X1 or X2:
X1 and X2:
 RPC 3  RDC
RPC 3

2
2
net
 track
  PC
  net 
3 
2
2
 RDC
 R
2
2
net
 track
  PC
 2 net 
3  0.5 
2
2



2
2

  3.5 6  0.25 mrad

 RPC 3  RDC

RPC 3

2

  2.2  0.15 mrad

Assuming that the MC simulation givesPC3 , net and net can be calculated from the above equations.
The result is:
 net  5.8  0.5 mrad
 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
=3.20.2 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:
    rms 
R
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
Be beam pipe
MVD silicon detector
MVD shell
Thickness (mm)
Air
DC mylar window
Total
2000
0.2
-
0.3
X/X0 (%)
0.3
0.3
0.4
R (m)
0.04
0.04
0.4
rms(mrad)
0.58
0.58
0.69
mrad)
0.01
0.01
0.13
0.7
0.07
1.77
1.1
2.0
-
0.92
0.26
-
0.46
0.24
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 0.60.1mrad, 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  0.0012  0.061  0.0052 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:
 m2 
2
 2
2
1
K
4m p   K
4
2
2
ms
2
1
 4  m 2    t2c 2
 4 m 1  2    2 4 p 2 m 2  p 2


p  
L


 

11
From the previous sections we take t = 1255 ps, =3.00.2 mrad, and ms=0.60.1 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.
P
p
+
K+
K-
m2
0.8300.056
0.8220.056
0.01570.001
0.01680.001
0.2290.016
0.2270.018
expected m2
0.874
0.874
0.0193
0.0193
0.244
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