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Measurements were made for the proper lifetime of the Lambdas and Ks that were identified using DDC and TOF information. The proper lifetime c*tau is obtained by fitting, to a plot of the acceptance-corrected distribution of d/(gamma*beta), the exponential function A*exp(-(d/(gamma*beta))*(1/(c*tau))). For a reconstructed particle, d is the distance from the target to the decay vertex. The fitted values of c*tau are expected to agree with the known lifetimes of the Lambda (c*tau = 7.89 cm) and Ks (c*tau = 2.68 cm).
For both Lambdas and Ks mesons, the acceptance correction factors were determined for each bin in d/(gamma*beta) space. Several million Monte Carlo Lambdas (or Ks mesons) were generated and propagated through the E896 experiment using Geant. The DDC and TOF Geant ntuple information was converted into simulated DDC and TOF data. This data was embedded within actual Au98 raw data; the embedded event was then propagated through the same neutral vertex reconstruction code, and subjected to the same cuts to neutral vertex quantities, as were the experimental data. Two d/(gamma*beta) distributions were compiled: (1) a d/(gamma*beta) distribution for all Monte Carlo particles generated, and (2) a distribution for all Monte Carlo particles reconstructed. The bin-by-bin ratio of distribution (2) to distribution (1) provides the acceptance correction factor for each bin. The number of Lambdas (or Ks mesons) reconstructed from the Pass II data set was divided by the correction factor, bin by bin, to obtain the acceptance-corrected d/(gamma*beta) distributions shown in Figures 1, 2, and 5 below.
Figure 1 shows the acceptance-corrected decay length distribution for Ks mesons measured using DDC and TOF information. The value of c*tau obtained from the fit, 2.68 +/- 0.82 cm, agrees very well with the lifetime 2.6762 +/- 0.0027 cm reported by the Particle Data Group.
A similar measurement was attempted for Lambdas as well. Figure 2 shows the acceptance-corrected d/(gamma*beta) distributions for Lambdas without TOF cuts (left frame) and with TOF cuts included (right frame). The TOF cuts remove additional counts that had been located at higher values of d/(gamma*beta), between 40 cm and 60 cm. Fitting an exponential to the TOF-cut plot over the range d/(gamma*beta) > 20 cm (dashed line in the right frame) yields a c*tau measurement consistent with the Particle Data Group value for Lambda lifetime. However, for d/(gamma*beta) < 15 cm, there exist extra counts that are inconsistent with the trend observed from the fit to the higher d/(gamma*beta) values.
An attempt was made to search for variables with which these extra counts might correlate. Figure 3 shows distributions, without acceptance corrections, of gamma*beta (left frame) and decay distance d (right frame) for Lambdas. Solid lines represent all d/(gamma*beta) values, dashed lines represent Lambdas with d/(gamma*beta) > 15 cm, and dotted lines represent Lambdas with d/(gamma*beta) < 15 cm. The right frame shows no significant correlation between decay distance and the d/(gamma*beta) cut. This suggests that the problem is not due to a geometric effect. The left frame, however, indicates that d/(gamma*beta) greater than (less than) 15 cm correspond to gamma*beta values less than (greater than) about 9.
Also investigated was dependence of rapidity and transverse momentum upon d/(gamma*beta). Figure 4 shows the distributions, without acceptance corrections, of rapidity (left frame) and transverse momentum (right frame) for Lambdas. The line styles in Figure 4 have the same meanings as in Figure 3. The right frame shows a modest dependence of d/(gamma*beta) upon transverse momentum. The left frame indicates a much stronger dependence upon rapidity. Values of d/(gamma*beta) greater than (less than) 15 cm correspond to rapidities less than (greater than) about 3.0.
Figure 5 shows the acceptance-corrected Lambda d/(gamma*beta) distributions for rapidity < 3.0 (left frame) and rapidity > 3.0 (right frame). Solid lines indicate exponential fits. For the distribution with rapidity < 3.0, the fitted c*tau of 7.68 +/- 1.22 cm is consistent with the Particle Data Group's value to the 0.2*sigma level. The fitted c*tau for the rapidity > 3.0 distribution is 1.37 +/- 0.05 cm.
To summarize, the observed c*tau distributions are consistent with the Particle Data Group values for all Ks mesons in the DDC+TOF analysis. Also consistent with the PDG values are the lifetimes observed for Lambdas with rapidity less than 3.0. Lambdas with rapidity in excess of about 3.0 have an apparent lifetime that is significantly shorter than expected (about 1.4 cm versus 7.9 cm).