Today's Progress 17. Sep. 2005

T0 analysis 1 (Slewing correction and T0 time resolution)

In order to obtain T0 slewing correction factors, we have two pissible procedures - the one is to adopt pi beam data, selecting fast pion passage, and extrapolate the correction fanction. The other is to apopt K data, in which pulse height distributes at around the region of interest, hence the correction factor obtained is almost directly applied. However, The time-of-flight between T0 two layers are strongly pulse-height dependent, hence the proper dependence of the meantime difference on the pulse heights is destroyed. The dependence of the TOF between two layers and pulse height detected on T0 is exhibitted for K^- below. Birk saturation effect is already taken into account.

First, we do need event selection, by which the events in which pi or K penetrated the 2 layers without any reaction, are properly discriminated. We introduce row-by-row pion or Kaon selection with correlation between dE/dx on those two layers as below -

Event selection and resulting correlation for K beam. Event set is gradually cleaned up.

Event selection and resulting correlation for pi beam. Maybe, K locus is due to proton, in fact.

After event selection is succsessfully performed, correlation between meantime difference and pulse height is safely studied with pion and kaon data. The results from pion (black) and kaon (red), for which pion or kaon penetration conditions are imposed respectively, are orverlayed below. The result is now understood by the net effect of slewing and dependence of 1 -> 2 TOF on the pulse height for kaon. Therefore, when slewing factors obtained by pion is applied for kaon, then pulse-height dependence of meantime difference naturally appears, and the width of the meantime difference does not represent T0 resolution for Kaon. It should be noted that this clean linear correlation for pion is just obtained only by the pulse-height information, without refering any TDC-related values.

The result of slewing corrrection is shown below. After the slewing correction, it has been confirmed for all rows that T0 2 - 1 time difference does not depend on any of 4 pulse heights.

Gain tune and non-linearity of T0 pulse height

Gain tune can be done with pi beam. The dE/dx peak is set to be 1.70 MeVee for all T0 segments from GEANT 3.21 with 650 MeV/c pi^- beam and realistic setup.

However, strong nonlinearity appears, and kaon peak position is segment-dependent, as below. This counter-dependent nonlinearity cause a certain difficulty on the stop K selection. We may need segment-dependent selection procedure, then.

It may be helpful to show the expected delta E distribution, to which Birk saturation is taken into account (0.013 cm^2/MeV). The expected delte E spectra for T0 1st (top) and 2nd (bottom) layers are shown below, for kaon beam after the passage of our experimental setup, originally centered at 650 MeV/c and distributed unifoamally by plus-minus 2%. According to the simulation result, the first bump appear in the detected energy spectrum must be at arount 4.7 MeVee, but sometimes below 4.0, and segment-dependent non-linearity by ~20 % is found at around the energy region of interest.

Detected energy dependence of TOF resolution for pi beam

Since T0 gain tune has been performed, we can study the dependence of TOF resolution on the detected energy (nearly equal to photo-electron number, but slightly different due to non-linearity between photo-electron number and detected pulse height). The dependence is shown row-by-row below:black:row1,red:row2,green:row3,blue:row4,magenta:row5. The systematic energy dependence is very clearly seen, by which we can expect 75/sqrt(2) ~ 50 psec for MIP(1,7 Mevee). The dependence of peak center on the detected energy is also studied, and stable within several psec, as shown in a table below the figure.

Study of applicability of obtained slewing parameters to kaon

In order to study the applicability of the slewing parameters obtained by pion beam to kaon data, now we apply the obtained parameters to kaon data, and check the energy dependence of meantime 2 - 1. If it is universal (i.e. does not depend on row), then the deviation is considered to be due to the dependence of kaon 1->2 TOF on the energy. It should be noted that we cannot expect complete agreement due to PMT-dependent non-linearity, at least at this moment. The energy dependences of TOF are exhibitted below, row-by-row. Those for pi beam are shown by black, while those fotr K, red. Except for the time origin, all of have very similar functional shape, and pion and kaon components are smoothly connected, which can occur only if slewing correction is successfully done for both components. The universal energy-dependent TOF for kaon component, exhibitted just after global ones being enlarged,is moderately similar to that obtained from a calculation, which verifys the validity of slewing correction for kaon.

Existing small inconsistency or deviation can be attributed to the row-dependent Energy non-linearity, hence we can return back here after its removal, but it is valuable to study the energy dependence of time resolution for kaon after the removal of 1->2 TOF by energy information, at this moment. The energy dependence of the time resolution defined by gaussian sigma fitted to the time difference distribution after eliminating the energy-dependent-TOF between layer 1 and 2, is shown below, together with pion result previously obtained. Here, we can observe an improvement of the resolution along with detected energy for all rows. Since stopped K appeares over 4.5 MeVee, time resolution for them is below 50/sqrt(2) = 35 psec.