6.4 Calculation of R
6.4.1 Tagging effects
The two parameters that accounts for the possible tagging errors are: the tag-ging efficiency εT and the mistagging probability αLS.
The first one is the efficiency for measuring the hit in the tagging counters of the proton that produces a KS, in time with the reconstructed arrival time of the event in the detector. An inefficiency can possibly be induced both by an inefficiency in measuring the time of either the proton or the event, as well as by resolution effects in the time reconstruction that could induce a difference larger than the coincidence window. This effect induces a number of KS to be identified as KL, and is expected to be very small.
We call mistagging instead the probability of an accidental coincidence be-tween the time of a KL event and the hit time of an uncorrelated proton in the tagging counters. The mistagging induces KL events to be identified as KS
events. Given the large intensity of the proton beam on the KS target, the mistagging effect is expected, unlike the tagging efficiency, to be quite a large effect.
While the small tagging inefficiency can possibly be different between charged and neutral decays, the mistagging probability, that depends mainly on the rate of protons in the tagging counters is expected to be almost the same for the two decay modes.
To understand the effect of the tagging errors on R, one can easily derive that:
NS,m+− = ε+−T · NS,t+− + αLS+−· NL,t+− (6.3) NL,m+− = (1− ε+−T )· NS,t+− + (1− αLS+−)· NL,t+− (6.4) where NS,t+− and NL,t+− indicate the true numbers of KS → π+π− and KL → π+π− decays while NS,m+− and NL,m+− the corresponding measured values. The same equations can be written for neutral decays.
The scenario is actually slightly complicated by the fact that the tagged KS and KL events are treated differently in the analysis. The tagged KS events are selected with no upstream cut on the longitudinal vertex position while the tagged KL are weighted (see section 2.1.1).
Taking into account these differences, we can invert equations 6.3 and 6.4 to obtain:
6.4. CALCULATION OF R 143 where NS,m(L)+− is the measured number of events tagged as KS but treated as KL (cut upstream in the vertex distribution and weighted), and NL,m(S)+− is the measured number of events tagged as KL but treated as KS (not cut upstream in the vertex distribution and not weighted). Again an analogous equation holds for the neutral decays.
Measurement of εT and αLS
In the charged decays the vertex tagging allows the very precise measurement of both quantities. Figure 6.3 shows the separation of the KS and KLcomponents of figure 6.1.
Selecting the vertex tagged KS decays one can measure the fraction of KS charged events not in coincidence with a proton hit in the tagging counter.
From 1997 data I measure:
ε(ch)T = (99.985± 0.001)%.
The mistagging probability for the charged events is instead measured se-lecting vertex tagged KL and counting what fraction of them is accidentally in coincidence with a proton hit in the tagging counters. I thus measure:
α(ch)LS = (11.20± 0.03)%.
The analogous measurements for neutral decays are of course more compli-cated as we don’t have any independent tagging mechanism.
A direct measurement of tagging efficiency in neutral decays is obtained from the analysis of neutral events with either a π0 → e+e− Dalitz decay or the conversion of one of the photons in the Kevlar window at the end of the vacuum tube. Those events can be tagged at the same time by the vertex of the electron-positron pair, and with the usual coincidence between the proton hits and the event time reconstructed from the remaining 3 photons. The precision of such a direct measurement is limited by the amount of useful events. The result obtained from 1997 data [65, 66] is: ε00T = (2.3+3.0−1.0)× 10−4.
A better estimate can be obtained if one just tries to measure the difference ε00T − ε+−T . Detailed studies have shown in effect that the tagging inefficiency is dominated by the inefficiency of the tagging counters more than by problems in the event time reconstruction. This means that the difference in efficiency between charged and neutral events is expected to be very small. Using the same Dalitz decays one can compare, for the same event, the time reconstructed by the charged hodoscope with the one reconstructed by the electro-magnetic
Figure 6.3: Time difference between the “best” proton time and the event time for charged events, separate in the KL component (continuous line) and KL component (dashed line).
calorimeter. This comparison shows [67] that the neutral tagging inefficiency is equal to the charged one, with an accuracy of ±1 × 10−4.
The same differential approach is used to investigate the mistagging proba-bility for neutral events. The difference α00LS − α+−LS is measured looking at the accidental coincidences between the events and protons passing in the tagging counter at times shifted relatively to the true coincidence time. This means
6.4. CALCULATION OF R 145 that one looks, for both charged and neutral decays, for coincidences in a time window that is artificially shifted from its proper centre value.
The actual measurement is carried out with 3 different windows. To per-form such a measurement one has to consider the effects linked to the beam temporal structure and to the fact that the offset intervals could have a differ-ent contamination of acciddiffer-ental activity than the cdiffer-entral one. A detailed study of this latter effect has been carried on [68] and a correction has been applied to the measurement. From 1997 data I measure: α00LS − α+−LS = (9± 5) × 10−4.
From this measurements I find out a global correction on R due to the tagging of:
ΔR = (+75± 9) × 10−4. (6.7)