Today's Progress 23. May. 2007

T0->TC TOF analysis: E570

Method

Since we have now the KstopCharged triggered event set, &gamma-ray events are available even on TC_B/C/D with TC_A as VETO. Adopting that, we examine a TOF analysis with B/C layer, and A layer time offset is tuned with respect to B layer. The analysis procedure is as follows. Let we define the time residual, &delta T(T0->TC_B), as

&delta T(T0->TC_B) = Ttc_b - Tt0 - TOFkstop(z) - TOF&gamma,

where Ttc_b is LR meantime of the fired B segment, Tt0 is T0 time established by T0-PA-PB analysis, TOFkstop(z) is the simulated kaon TOF from T0 to its stop. TOF&gamma, TOF of &gamma from its production to TC_B, is defined as

TOF&gamma = LTOF/c,

LTOF = sqrt((TC_x-Vx)**2+(TC_y-Vy)**2+(TC_z-Vz)**2,

where (TC_x,TC_y,TC_z) is &gamma detection point on TC, (Vx,Vy,Vz) is reaction vertex determined by BLC-PDC. TC_x is determined by the L-R time difference, and TC_y and TC_z are represented by x/y-center of the fired segment. Then, we examine a slewing correction procedure to the quantity &delta T(T0->TC_B). Note that we adopt Compton-like &gamma-ray events.

Process of Analysis

The analysis procedure is as follows:

1. Construct the conversion function from L-R time difference VS x on TC with charged particle track. Applying the conversion function, calculate distance-of-flight for neutral particle.

2. Apply the slewing correction to the &delta T(T0->TC_B), namely, study f(sqrt(phL*phR))

3. Perform part-by-part(or run-by-run) tune of TC time walk.

4. Study g(&xi) with 100% &gamma-ray statistics.

L-R time difference VS x on TC conversion

First, L-R time difference is compared to the VDC-detected x position on B/C layers for run 231-245(1st cycle)/418-434(2nd cycle). By using that, time difference->x conversion function is constructed, to be applied to neutral particle analysis. The conversion function, X(T) is defined as a linear function of the L-R difference, T(L-R):

X(T) = a * T(L-R) + b,

where a and b is determined to fulfill the relationship,

X(VDC) = a * T(L-R) + b,

where X(VDC) is the VDC-detected x position of the TC segment. Note that the slope, a, is the half of the effective light velocity inside the segment.
Performance of TC B/C segments studied by charged particle events. Light velocity, resolution values are compared with E549/E570-1/E570-2.
Layer UD ID Light Velocity (cm/nsec)x Resolution &sigma (cm)
B UP 1 15.4/15.5/15.7
B UP 2 15.4/15.5/15.5
B UP 3 15.4/15.6/15.1
B UP 4 15.5/15.5/15.6
B UP 5 16.0/15.4/15.5
B DOWN1 15.0/15.2/15.3
B DOWN2 14.9/15.0/15.1
B DOWN3 15.2/15.3/15.3
B DOWN4 15.1/15.2/15.2
B DOWN5 15.0/15.2/15.3
C UP 1 14.7/15.0/15.0
C UP 2 14.9/15.0/15.0
C UP 3 14.8/14.9/14.9
C UP 4 14.7/14.8/15.0
C UP 5 14.8/14.9/15.0
C DOWN1 14.5/14.6/14.9
C DOWN2 14.7/14.9/14.9
C DOWN3 14.6/14.7/14.7
C DOWN4 14.7/14.9/14.9
C DOWN5 14.5/14.8/14.8

Since the time walk is naturally expected, we do need to check the stability of the function.

Run-by-run segment-by-segment variation of the center of residual of x by VDC - x by LR time difference on TC B_layer. Generally, conversion functions work well. On top ID2, occasional jumps are seen especially on 2nd cycle.
Run-by-run segment-by-segment variation of the center of residual of x by VDC - x by LR time difference on TC C_layer. Conversion functions work well for all of them.

We correct observed run-by-run deviation of the position as run-dependent constant term, assuming that the slope of the linear function is quite stable, i.e.

X(T) = a * T(L-R) + b + c(idrun).

Slewing Correction

As the initial guess, ph-dependent term is studied cycle-by-cycle.

Part-by-part tune of TC time walk

After 1st stage slewing correction, TC time walk is checked. As shown below, a large jump and continuous variation are found. Activating seg-by-seg part-by-part offset parameter, we remove the time walk.
&delta T(T0->TCB/C) before seg-by-seg offset elimination.
part-by-part time walk of B-layer segments determined by &gamma-ray events.
part-by-part time walk of C-layer segments determined by &gamma-ray events.
&delta T(T0->TCB/C) after seg-by-seg offset elimination.

Study of g(&xi)

Now, we determine g(&xi) as a forth order polinomial of &xi cycle-by-cycle basis. In order to determine g(&xi), we study the quantity, (&delta T(T0->TC_B/C) - f(1/ph) - const(idpart))/f(1/ph), according to the approximational equality,

&delta T(T0->TC_B/C) = f(1/ph)*g(&xi) + const(idpart)

= f(1/ph)+f(1/ph)(g(&xi)-1.0) + const(idpart).

g(&xi)-1.0 for E570 1st cycle.
g(&xi)-1.0 for E570 2nd cycle.

Performance study of TOF with B/C layers for &gamma-ray

Here, we study the distribution of the slew-corrected time residual,

&delta T'(T0->TC_B/C) = &delta T(T0->TC_B/C) - f(1/ph)*g(&xi) - const(idpart),

and examine the performance of the T0->TC TOF measurement.
Segment-by-segment plot of the Gaussian center of &delta T'(T0->TC_B)/&delta T'(T0->TC_C) VS light output on TC. All production runs have been accumulated.
Segment-by-segment plot of the Gaussian &sigma of &delta T'(T0->TC_B)/&delta T'(T0->TC_C) VS light output on TC for &gamma-ray. All production runs have been accumulated.

The resulting TOF resolution is about 250 psec equivalent for &gamma with MIP-equivalent light output, and dependence of the time origin on the light output is now moderate for both B and C.

Neutral Particle Spectra by B/C

Firstly, 1/&beta distribution for &gamma-ray are studied layer-by-layer.
Layer-by-layer plots of the variation of 1/&beta Gaussian center (top) and &sigma (bottom). Black/Red/Green/Yellow represent B_top/B_bottom/C_top/C_bottom, respectively. The TOF origin is stable within ~+- 30 psec, and the 1/&beta resolution is stable around 0.08 for Minimum ionization equivalent light outputs.

The performance of top/bottom layers are well-balanced, and B-layers are found to have fairly good resolution. Now, 1/&beta spectra of neutral particles detected on B/C layers are shown.

Global 1/&beta spectra of neutral particles on TC B top(top figure)/bottom(bottom figure) layers for software threshold values 3, 5, 7, and 10 MeVee.
Global 1/&beta spectra of neutral particles on TC C top(top figure)/bottom(bottom figure) layers for software threshold values 3, 5, 7, and 10 MeVee.
Local 1/&beta spectra of neutral particles on TC B(top)/C(bottom) under 3(black)/5(red)/7(green)/10(magenta) MeVee software threshold level. Note that constant BG level is substantially low compared to NT.
The correlation between 1/&beta (ordinate) and light output on B/C layers.

TOF analysis of A-layer

Here, we try to finalize the A-layer TOF analysis for E570 cycles.

Method

We just tune A-layer correction function/part-by-part parameters, by studying

&delta T(TC_A->TC_B) = Ttc_b' - Ttc_a - TOF(TC_A->TC_B),

where

Ttc_b' = Ttc_b - f(1/ph)*g(x) -const(idpart),

Ttc_a = (Ttc_a_L + Ttc_a_R)/2,

and

TOF(TC_A->TC_B) = 1/&beta * L(TC_A->TC_B)/c,

for charged events. 1/&beta is now just determined with T0->TC_B TOF analysis as described previously.

Firstly, we study the run-part-dependence of the DeltaT(TC_A->TC_B).

The segment-by-segment run dependence of the &delta T(TC_A->TC_B).

Secondly, after the subtraction of the observed run-dependence, we study f(1/sqrt(ph)) and g(x) with charged particle (p/&pi^+-). Here,we adopt 5th order polinomial as f(1/sqrt(ph)).

The correlation between 1/sqrt(ph) (horizontal) and DeltaT(TC_A->TC_B) (vertical) together with the fitted 5th order polimomial curve, on top ID 2 on E570 1st cycle.
The Gaussian center and width of all 10 A-B combinations after f(1/sqrt(ph)) correction.

Thirdly, we study g(x). As already done for B/C layers, we study the distribution of the quantity,

&delta T(TC_A->TC_B) - f(1/sqrt(ph)) -const(idpart) = f(1/sqrt(ph))*(g(x)-1.),

with respect to x on TC.

The correlation between time residual after f(1/sqrt(ph)) correction (horizontal) and x on TC (vertical).

Then, g(x) can be obtained. The resulting distribution of &delta T(TC_A->TC_B) - f(1/sqrt(ph))*g(x) -const(idpart) is shown below. The x-dependence has vanished.

The correlation between time residual after f(1/sqrt(ph))*g(x) correction (horizontal) and x on TC (vertical).

Therefore, we define the stop timing on TC_A, as

T(TC_A) = Ttc_a + f(1/sqrt(ph))*g(x) + const(idpart),

by adopting f(1/sqrt(ph)),g(x), and const(idpart) obtained. Then, 1/&beta on TC_A can be defined as

1/&beta(T0->TC_A) = (T(TC_A) - Tt0 - TOFkstop(z))*c/L_TOF,

and now 1/&beta on TC_A is well-defined.