First, Kaon TOF from T0 2nd layer upstream surface to its stop is simulated by means of GEANT 3.21, with realistic object locations detected by vertex analysis for E549 setup. Note that it must be done separately for E570 setup - maybe, non-negligible difference will be detected, then.
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 just produced without considering the incident angle/position distribution, namely, just from the center (x=0, y=0) with direction cos (0,0,1).
Time residual defined as the difference between expected stopping time duration from vertex z and the obtained correlation above and simulated stopping time. 13.1 psec time resolution is expected, if we assume infinite z resolution and ideal Kaon beam condition.
Very narrow band and good time resolution are obtained, hence the z-correction seems to work perfectly. However, this clear correlation between TOF and z-vertex can be broken if we consider the broad (by both means of position and angle) incident beam distribution and/or finite resolution of z-vertex. Therefore, more realistic simulation is indispensable.
In order to obtain the realistic beam distributon, x/y/a/b distributions are studied below, for E549 281-290, assuming trigger bias effect being negligible (i.e. They are not sampled from Kbeam-triggered events, but from Kst-charged-triggered events). Note that any additional selections, say, fiducial volume/stop K selections are not applied to plot them.
As the result, weak correlations between x-a and y-b are found, as expected. The realistic simulation must be performed taking both of this weak correlation and Gaussian-like broad x/y/a/b distributions into account.
Time residual, T_siml - T_exp, defined as the difference between expected stopping time duration from vertex z and the obtained correlation above (T_exp) and simulated stopping time (T_siml). For the top, the incident beam distribution is properly taken into account, and 15.9 psec time resolution is expected. For the bottom, the vertex is replaced by detected one (i.e. BLC-PDC the closest approach) from realistic one, placing the BLC/PDC planes at realistic position. Hence, multiple-scattering effect on incident kaon is taken into account here. It shouldbe noted that the final state(stopped K^- reaction on 4He) is not reliable at all even with GEANT, and no hyperon is in the final state (p/n/d and/or triton appear in the final state, instead) - hence, this result is considered to still underestimate the broadenning of the residual.
Simulated TOF from T0 second layer upstream surface to K^- stop on 4He, considering the incident beam distribution. Blue, black, and red are corresponding to the case with no / 75 micron mylar /150 micron mylar entrance windows, respectively, and the bottom is the enlarged figure at the upstream region. At downstream side, the effect of material thickness uncertainty is negligible, while it is visible at upstream region of the target. The uncertainty of the thickness of the radiation shield and last degrader are also considered to give non-negligible deviation of the function from the realistic one.
Since we have tuned the T0 offsets with respect to PA R arm row 1~4 at run 292, let we check the consistency between (K^-, X) and (pi^-,X), firstly. Then, tune the T0 offsets again with (K^-, X) at around run 135, for which all PA segments offsets are complately tuned with (stopK^+,X). Then, T0-PA-PB would be available around run 135, consistemtly, hence we can proceed to PA-NC analysis with run 136-141. We must keep the tunning of all existing offsets in systematic way after the study of all TOF-related run-wise-local analysis in mind. Otherwise, (K^-,X) and (pi^-,X) cannot be directly connected.
A correlation between T0-PA time residual (Tpa - Tt0 - TOF(t0->ksop:simulated) - TOFsec(PA-PB determined)) and vertex z (top), and its projection onto horizontal axis (bottom). 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. Since T0 offsets are kept at the value obtained by (pi^-,X) analysis, this plot means i) consistent TOF of pi/stop K, hence ii) Monte-Carlo simulation and obtained geometry by chamber analysis are fairly accurate, and iii) larger pulse height on T0 does not produce any visible deviation of time residual, with present correction function. Now, (pi^-, X) and (stop K^-, X) analysis are consistent each other.
Hereafter, correlations presented for (pi^-, X) are exhibitted for (K^-,X) by similar way. Applied event selections are i) Fuducial volume cut by vertex, ii) PA Rarm row 1~4 (except for pay vs time residual plot) and iii) beta inverse 1.0~1.30 .
As the result, substantial dependence of time residual on T0 meantime is found. It is found to be attributed to the time-walk (of T0, maybe.), as depicted below. Therefore, this can be resolved if term-by-term T0 offsxet tune has been performed.
At run 135, T0 offset is shiftted from that detetrmined at run 292, with respect to PA. All PA/PB have been relatively adjusted at run 136-141, hence we once fix all the offsets here, so as to
Now, PA relative shift observed at around run 290 does not exist, while T0 offset tuned at run 292 does not work. We tune the T0 offset with run 129-135, nextly.
Result of offset tuning. T0 offset has been tuned with respect to PA R arm 1~8 (red). Then, arm-by-arm offset factor has been introduced (it is defined as 0. for R arm), and L arm has been adjusted to give the center 0 (black).
