One remaining item I have not yet considered is the z_vertex calculated from the VPD time bins. By requiring a match between the VPD vertex and the primary TPC vertex, it should be reasonable to assume a robust matching between the TPC vertex and the true vertex. Thus, I can eliminate my systematic uncertainties from matching to the wrong vertex in the VPDMB sample. I do not currently simulate the VPD, thus, I cannot evaulate this procedure in the simulation. However, these seem reasonable assumptions.

Figure 1

In Fig. 1 I show the correlation of TPC vertices (labeled "z_reco") and VPD vertices. There is a strong correlation within ±10 cm. My current reconstructed vertex cut is ±50 cm, and I may revisit that, soon.

Figure 2

In Fig. 2,  show Δz_vertex integrated over z_reco. I have fit the distribution with a two-Gaussian function. The "signal" distribution has a width of around 2 cm. Thus, it seems to me a cut of ±6 cm is reasonable.

Figure 3

For reference, in Fig. 3, I show the distributions of z_reco - z_thrown for the 2011 VPDMB embedding. One can see there is a strong correlation within ±2 cm. I have fit the z_reco-integrated Δz_vertex distribution with a two-Gaussian function. One can see the "signal" distribution has a width of around 0.2 cm; so a cut of ±2 cm is quite generous. To match such a cut in the VPD vertex matching, I would need to loosen my ±6 cm cut considerably, perhaps, to ±10 cm. Perhaps, this is even reasonable, though, it will not gain much in terms of statistics.