First, Kaon TOF from T0 2nd layer upstream surface to its stop is simulated by GEANT 3.21, with realistic object locations detected by vertex analysis for E570 setup, taking the target modification into account. Cycle-by-cycle shift of target position, and the replacement of radiation shield is clearly seen. The modification is properly taken into account to obtain z-vs-Kaon TOF distribution.
Kaon TOF from T0 2nd layer (nsec) VS vertex z (mm). Red points are stopped component, while black ones are the in-flight. Note that incident K^- is produced considering the incident angle/position distribution.
As the result of the target modification, the correlation is substantially different between E549 and E570.
Time residual defined as the difference between expected stopping time duration from vertex z and the obtained correlation above and simulated stopping time. time resolution, ~20 psec, is expected.
Now, we tune the T0 offsets with (&pi+, X) at run 223(cycle1)/405(cycle2), with respect to PA Rarm ID4 as the initial guess. After the adjastment, the time residual is studied with (K-stopped, X+/-) data. The tentative results are shown below. T0offset(i) of i-th row is now defined as
-T0offset(i) = Tpa(R,ID=4)-Tt0(ID=i)-TOF&pi - TOFsec,
whereTOFsec = (c&beta)-1 * LTOF:verteex->PA .
This 1/&beta is just calculated from the PAPB slewing parameters as obtained by K+stopped analysis.
A correlation between T0-PA time residual (Tpa - Tt0 - TOF(t0->ksop:simulated) - TOFsec(PA-PB determined)) and vertex z, and its projection onto horizontal axis are shown below. The time deviation up to ~150 psec is seen at the upstream region(-60~-50mm), to which TOF ambiguity is fairly large as expected from the Monte-Carlo. On the bottom, The "stop K" comonent by T0 energy-vertex z correlation are overlayed with red solid line, while .NOT."stop K" component with the correlation is shown with green solid line. Note that T0 offsets are kept at the value obtained by (pi^-,X) analysis. Since ~250 psec deviation is seen for both cycle results on both arms, it is very likely that the T0 z position have a certain offset by 2~3 cm. This may produce the residual bending of the vertex(z)-VS-T0PA time residual correlation. Since T0 offsets are re-adjasted by stopped K- data systematically, this does not cause any serious problem, although tiny residual correlation may affect the resulting resolution moderately.
Here, we study the run-by-run time walk of T0/PA with Kstop-charged-triggered event set, by
&delta T(T0->PA) = Tpa - Tt0 - TOFkstop - TOFsec,
where TOFsec is caluculated from the 1/&beta determined PA-PB TOF, TOFkstop is simulated value. In order to achieve better resolution of the distribution center, we fully impose KstopID > -1. (MeVee) condition. Note that we cannot determine the offset for all of the existing counters - we do need to select a counter to give a absolute reference. The PA R segment 4 is selected as the reference, and absolutely fixed. Then, segment-by-segment tune is performed for T0 row 2,3,4 with PA R-4, the PA L/R arms with T0 2-4 segment-by-segment. Finally, T0 1/5 is tuned with respect to PA R arm. Note that TOFsec is dependent on Tpa - but the dependence of TOFsec on Tpa is smaller than that of DeltaT, by factor 0.2. Thus, at the initial stage of the tunning, the possible error on TOFsec due to PA/PB time walk is consciously neglected. That would be minimized after all T0->PA->PB iterative process has been teriminated. The results of the run-by-run offset study are shown below.
From now, we define new time residual, deltaT'(T0->PA), by
&delta T'(T0->PA) = Tpa' - Tt0' -TOFkstop -TOFsec ,
after first stage PA/T0 time walk correction on Tpa/Tt0, i.e.Tpa' = Tpa - PAOFFSET1(idrun)
andTt0' = Tt0 + T0OFFSET1(idrun).
As already intensively studied in E549 data analysis, we expect PB time walk as well. In order to eliminate the effect, we set the delayed-condition,
&delta T'(T0->PA) > 0.8 (nsec) ,
for 1st stage PB arm-by-arm offset tune.Now, we examine the run-by-run behavior of the Kmu2 peak taking the PA time walk determined by T0-PA TOF analysis into account, namely,
&delta T (PA->PB) = Tpb - Tpa -TOFkmu2
->&delta T' (PA->PB) = Tpb - Tpa'-TOFkmu2
.
We activate the PB run-by-run, but arm-by-arm offset obtained here, and calculate the 1/&beta' by
1/&beta'(PA->PB) = (Tpb'-Tpa')*c/L_TOF
, where
Tpb' = Tpb - PBOFFSET1(idrun).
PBOFFSET1(idrun) is defined as the Gaussian center of the distribution of &delta T'(PA->PB).
With this 1/&beta definition, go back to T0->PA TOF analysis again.Here, we study the 2nd stage T0-PA time walk by studying the Gaussian center of
&delta T''(T0->PA) = Tpa' - Tt0' - TOFkstop - TOFsec',
where TOFsec' is calculated from the 1/&beta'.
From now, we define new time residual, &delta T'''(T0->PA), by
&delta T'''(T0->PA) = Tpa'' - Tt0'' -TOFkstop -TOFsec' ,
after the 2nd stage PA/T0 time walk correction on Tpa/Tt0, i.e.Tpa'' = Tpa' - PAOFFSET2(idrun)
andTt0'' = Tt0' + T0OFFSET2(idrun).
&delta T'''(T0->PA) = Tpa'' - Tt0'' -TOFkstop -TOFsec' > 0.8 (nsec) ,
to study run-by-run behavior of the Kmu2 peak taking the PA time walk determined by T0-PA TOF analysis into account, namely,
&delta T'' (PA->PB) = Tpb' - Tpa' -TOFkmu2 (centered at 0 by definition)
->&delta T''' (PA->PB) = Tpb' - Tpa''-TOFkmu2
We activate the PB run-by-run, but arm-by-arm offset obtained here, and calculate the 1/&beta'' by
1/&beta''(PA->PB) = (Tpb''-Tpa'')*c/L_TOF
, where
Tpb'' = Tpb' - PBOFFSET2(idrun).
PBOFFSET2(idrun) is defined as the Gaussian center of the distribution of &delta T'''(PA->PB).
With this 1/&beta definition, go back to T0->PA TOF analysis again.Here, we study the 3rd stage T0-PA time walk by studying the Gaussian center of
&delta T''''(T0->PA) = Tpa'' - Tt0'' - TOFkstop - TOFsec'',
where TOFsec'' is calculated from the 1/&beta''.
From now, we define new time residual, &delta T'''''(T0->PA), by
&delta T'''''(T0->PA) = Tpa''' - Tt0''' -TOFkstop -TOFsec'' ,
after the 3rd stage PA/T0 time walk correction on Tpa/Tt0, i.e.Tpa''' = Tpa'' - PAOFFSET3(idrun)
andTt0''' = Tt0'' + T0OFFSET3(idrun).
&delta T'''''(T0->PA) = Tpa''' - Tt0''' -TOFkstop -TOFsec'' > 0.8 (nsec) ,
to study run-by-run behavior of the Kmu2 peak taking the PA time walk determined by T0-PA TOF analysis into account, namely,
&delta T'''' (PA->PB) = Tpb'' - Tpa'' -TOFkmu2 (centered at 0 by definition)
->&delta T''''' (PA->PB) = Tpb'' - Tpa'''-TOFkmu2
We activate the PB run-by-run, but arm-by-arm offset obtained here, and calculate the 1/&beta''' by
1/&beta'''(PA->PB) = (Tpb'''-Tpa''')*c/L_TOF
, where
Tpb''' = Tpb'' - PBOFFSET3(idrun).
PBOFFSET3(idrun) is defined as the Gaussian center of the distribution of &delta T'''''(PA->PB).
With this 1/&beta definition,&delta T(6)(T0->PA) = Tpa''' - Tt0''' -TOFkstop -TOFsec''' ,
can be defined.Even after arm-by-arm time walk has been solved, we expect substantial segment-dependent time walk which broaden the peaks, and the resolution can be improved more if that effect could be eliminated. For the purpose, whole production runs are divided into 35 parts (roughly saying, each part covers 1-day-equivalent production term), and segment-by-segment tune is performed for each of parts. The definition of the part is tabulatted below.
| Part | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Run | 31~43 | 45~65 | 66~87 | 88~98 | 99~110 | 111~122 | 123~135 | 136~148 | 155~168 | 169~181 | 182~194 | 196~210 | 212~221 | 228~240 | 241~254 |
| Part | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| Run | 255~267 | 268~281 | 282~294 | 300~313 | 314~325 | 326~337 | 338~354 | 355~368 | 417~428 | 429~442 | 443~454 | 455~462 | 466~481 | 482~493 | 494~509 |
| Part | 31 | 32 | 33 | 34 | 35 | ||||||||||
| Run | 510-525 | 526-539 | 540-552 | 553-564 | 565~583 |
Under the condition, &delta T(6)(T0->PA) = Tpa''' - Tt0''' -TOFkstop -TOFsec'''>0.8 nsec , we study the time residual,
&delta T(6) (PA->PB) = Tpb''' - Tpa'''-TOFkmu2
. By definition, &delta T(6) (PA->PB) is centered arm-by-arm, but not segment-by-segment. Therefore, we study PB segment i by the time residual,&delta T(6) (PA->PBi) = Tpbi''' - Tpa'''-TOFkmu2
. The part-by-part Gaussian center of &delta T(6) (PA->PBi) is defined as the segment-by-segment factor. Then we define &delta T(7)(PA->PB) as&delta T(7) (PA->PB) = Tpb'''' - Tpa'''-TOFkmu2
, whereTpb'''' = Tpb''' - PBOFFSET_SEG(i,idpart)
. The resulting run-by-run behaviour of &delta T(7)(PA->PB) is shown below.
By using Tpb'''' defined here, 1/&beta'''' can be defined as
1/&beta''''(PA->PB) = (Tpb''''-Tpa''')*c/L_TOF
The comparison of the 1/&beta spectra before/after time-walk tune is given below.
The final version of &delta T(T0->PA) can be defined as
&delta T(7)(T0->PA) = Tpa''' - Tt0''' -TOFkstop -TOFsec''''
.
The comparison of the &delta T(T0->PA) spectra before/after time-walk tune is given below.
We have no S/N gain with the delayed gate value larger than 1.2 nsec. Hereafter, 1/&beta performance for K- runs are studied by &delta T(T0->PA) > 1.2 nsec, by fitting it with 3 Gaussian + 3rd order polynomial.
Since PA->PB offset tune has been finalized here, T0->PA TOF resolution is checked again with the finalized PA-PB TOF analysis. The run-by-run variation of arm-by-arm T0->PA TOF resolution is shown below.
Segment-by-segment results with E570 100% statistics are exhibitted below.
