First let me describe the process I analyze. It's an exclusive diffractive production of central, light and neutral state X:
p + p -> p + X + p,
X -> pi^+pi^-  or  K^+K^-  or  (...)

The trigger for this process (RP_CPT2) required the signal in Roman Pot detectors on both sides of STAR (to be sure that protons survived an interaction), TOF multiplicity to be >=2 (we expect at least two particles in central rapidity), and no signal in small BBC tiles on both sides of STAR (no particles are produced in forward rapidity except scattered protons). In the analysis of exclusive pair production I require:
- reconstructed tracks in Roman Pot detectors on both sides of STAR (scattered protons),
- exactly 2 TPC tracks matched with reconstructed TOF hits originating from the same vertex (in addition vertex has to be the only one that has tracks matched with TOF).

The problem arises when I want to make use of TOF to improve the PID. With dE/dx I can poorly identify kaons and protons of higher momenta, TOF could probably help. But because of the nature of analyzed process (in principle there should be no signal in VPD coming from the interaction vertex) it's extremely hard (impossible?) to calculate t_0. BTW, I understand that t_0 = time of interaction, correct me if I'm wrong.
I tried to work it around by using method presented in https://drupal.star.bnl.gov/STAR/system/files/TOF_PID.pdf. In short, if I know the lengths, momenta, and times of discrimination in TOF of two tracks coming from the same interaction, I can calculate m^2 of particle #2 under assumption that particle #1 has some particular mass (e.g. is a pion). It's effectively calculation of t_0 from parameters of track #1 and using it to calculate m^2 of track #2. The result of described procedure is shown in https://drupal.star.bnl.gov/STAR/system/files/mSq_vs_nSigmaPion.pdf Histogram was filled with events for which at least one track (out of two) had |nSigmaPion|<3. The track with lower |nSigmaPion| (more probable to be pion) was assumed to be pion, and m^2 of the second track was calculated (vertical axis).  On horizontal axis there's nSigmaPion of 2nd track. I took length of tracks from StMuTrack::length() and times of discrimination in TOF from StMuBTofPidTraits::timeOfFlight(). As one can see, resolution is not sufficient to determine PID (though the m^2 peaks at ~0 which is consistent with squared mass of pion ~0 GeV^2 - majority of particles are indeed pions).

I was curious what is the resolution of t_0 reconstruction with the method I used. For this purpose I used set of equations (3) in the first file (TOF_PID.pdf). I selected events with both particles in TPC having |nSigmaPion|<3 and all the other variables |nSigma_X_|>3 (to be sure that both tracks are pions). The distribution of the difference and correlation of t_0s extrapolated from hits in TOF from those pion tracks can be found at
https://drupal.star.bnl.gov/STAR/system/files/delta_t0_2.pdf and  https://drupal.star.bnl.gov/STAR/system/files/t0A_vs_t0B_2.pdf . To me it is very surprising that the width of the difference of t0s is so large (1.5 ns). I thought that TOF resolution is of the order of 200 ps (what would resulted in width of delta t_0 distribution equal ~0.3 ns). This fact encouraged me to try to use timing in Roman Pots to calculate t_0. So far we've used timing to determine the z_vertex, the resolution of this method is ~11 cm. This translates to ~350 ps resolution in the reconstruction of the time of interaction.
I plotted averaged t_0 calculated from two TPC tracks (vertical axis) versus t_0 calculated from the time of protons detection in weast in east detectors, t_0 = 0.5*(t_west + t_east) + offset. Such plot can be found at https://drupal.star.bnl.gov/STAR/system/files/t0TPC_vs_t0RP_2.pdf . I don't understand why there's no correlation (at all!) between those two t_0s.
I thought that maybe I'm using the wrong "time in TOF", so instead of StMuBTofPidTraits::timeOfFlight() I started using StMuBTofPidTraits::leadingEdgeTime() (the latter seems to be in [ps], whereas the former in [ns], it's my guess). The same types of plots as before, but with different time variable used are here: