By a judicious choice of the normalisation mode,Λ0b→Λ+c(Λ π+)π−, with a similar
topology and final state to the charmless signal modes, most systematic uncertainties can be assumed to cancel, at least to first order, in the branching fraction ratio. The systematics that are explicitly considered and documented in this section are those related to the selection efficiency and its variation over the phase-space, the PID calibration, the fit model and fit biases, and the normalisation channel branching fraction. These are combined with the statistical uncertainty on the normalisation mode yield and the statistical uncertainties on the signal and normalisation mode efficiencies to form the total systematic uncertainty. In the following, the values are obtained as the individual systematic components on the ratio of the efficiency- corrected yields for the signal and normalisation modes for each data category.
A summary of the various contributions to the absolute total systematic uncer- tainty for each mode, can be found in Table 5.8.
5.5.1 Selection efficiency
The same selection (excluding vetoes) is applied to the Λ0b→ Λ+c(Λ π+)π− mode,
and therefore most contributions in this area are expected to cancel in the ratio. Those that do not are those uncertainties related to the vetoes and the phase-space variation of the selection efficiency.
Vetoes
The absolute systematic uncertainty due to the choice of the veto window is evaluated
by varying the window sizes by±10% and repeating the analysis. The systematic
uncertainties associated with the veto window choice are generally much less than 1% per data category.
Table 5.7: Signal yields for theΛ0b andΞ
0
b decay modes under investigation. The totals are
simple sums and are not used in the analysis. Uncertainties are statistical only.
Mode Run period Λ0b Yield Ξ
0
b Yield
Downstream Long Downstream Long
2011 10.2±5.5 8.7±4.7 −0.6±2.4 4.9±3.2 Λπ+π− 2012a 9.1±5.2 13.6±5.7 5.3±3.6 1.0±2.6 2012b 17.2±7.1 6.2±4.6 3.9±4.0 4.1±2.7 Total 65±14 19±8 2011 20.9±6.4 8.2±3.5 3.5±3.7 −0.7±2.4 ΛK±π∓ 2012a 9.3±3.7 1.7±3.6 −0.1±1.7 0.3±1.5 2012b 39.7±8.9 16.9±5.1 2.9±4.5 −1.8±1.5 Total 97±14 4±7 2011 32.3±6.4 20.1±4.6 0.6±2.3 0.0±0.6 ΛK+K− 2012a 22.2±5.3 15.9±4.2 0.5±2.4 0.0±0.5 2012b 60.5±8.5 34.4±6.1 3.0±2.7 0.0±0.6 Total 185±15 4±4 2011 78.1±9.1 78.9±9.2 Λ+c(Λπ + )π− 2012a 45.0±7.0 63.0±8.3 2012b 115.3±11.1 90.7±9.8 Total 471±22
Table 5.8: Summary of the absolute systematic uncertainties on the branching fraction ratios assigned in this section. ‘PhSp’ corresponds to the uncertainty due to the phase-space distribution of the signal decay (if no significant signal is seen); ‘Fit’ corresponds to the combined uncertainties due to the choice of fit model and the fixed parameters in the fit model; ‘Vetoes’ corresponds to the systematic uncertainty due to the veto width; ‘PID’ corresponds to the systematic due to the particle identification criteria imposed on the data; ‘Norm. yield’ corresponds to the statistical
uncertainty on the normalisation channel yield; ‘’ corresponds to the uncertainty on the efficiency, including the L0 HCAL correction, and where
appropriate the uncertainty due to the phase-space efficiency correction. ‘Total’ corresponds the sum in quadrature of all other entries.
PhSp (10−3) Fit (10−3) Vetoes (10−3) PID (10−3) Norm. yield (10−3) (10−3) Total (10−3)
Λ0b→Λ π+π− 19.7 8.4 2.2 0.4 3.5 2.0 21.9 Λ0b→Λ K+π − — 1.7 1.3 2.9 4.6 11.7 13.1 Λ0b→Λ K+K − — 6.7 2.2 4.2 15.9 5.4 18.7 Ξb0→Λ π+π − 7.0 4.1 — 0.1 1.2 0.7 8.2 Ξb0→Λ π+K− 3.5 1.5 — 0.1 0.7 0.4 4.0 Ξb0→Λ K+K − 0.8 0.1 — 0.0 0.2 0.1 0.8 82
Phase-space variation
As mentioned in Section 5.3.6, for channels where a significant signal is observed, the average efficiency is determined using the information on where the events lie in the phase-space. If no signal is observed however, a value for the average efficiency must be assumed and a corresponding systematic uncertainty needs to be assigned based on the scale of the variation of the efficiency across the phase-space. Specifically, the standard-deviation of the variation of the efficiency across the binned histogram for each phase-space variable is used. The absolute systematic uncertainty on the
efficiency from this is on the order of 1×10−4 for each data category.
5.5.2 PID calibration
A possible bias is introduced in the calculation of the PID efficiencies, as thePIDCalib
calibration data differs from the real signal data. The assumptions are that the
RICH response can be completely parameterised by p,pT, and nTracks, and that
the efficiency is slowly varying within the chosen bins in these variables. In addition, the kinematics of the signal MC samples are assumed to match those of the data.
To evaluate the uncertainty introduced by any deviations from these assumptions,
different binning schemes are considered for the PIDCalib calibration data and
the calculation of the efficiencies repeated. Specifically, the number of bins in
each dimension is reduced by 1/3. Only the relative differences in the phase-space
integrated efficiencies are considered, rather than those that depend on the phase- space location via the extracted sWeights. This is in an attempt to isolate only those
effects due to to the PIDCalibprocedure rather than statistical fluctuations from
the relatively low signal yields. The absolute systematic uncertainty estimated from this procedure is on the order of 1% per data category.
In addition, an absolute systematic uncertainty of 0.1% is assigned due the
uncertainty on the sWeights in PIDCalib. This accounts for small correlations in
the control mode between the distributions of the variables used to parameterise the efficiency and those used to obtain the sWeights, which violates one of the assumptions of the sWeight procedure.
5.5.3 Trigger
In the case of a significant signal yield, theL0Hadronefficiency is calibrated using a
high statistics calibration sample (see Section 5.3), rather than assigning a systematic uncertainty related to this mis-match. If no significant signal is observed, a systematic is assigned equal to the standard deviation of this correction across the MC phase- space (along with a correction corresponding to the average of this value). This
5.5.4 Fit
The fitting procedure introduces three major systematic uncertainties. The first is the choice of fit model, which is estimated by repeating the fit with alternative fit models for each component. The second is introduced by fixing certain model shape parameters to MC data to stabilise the final simultaneous fit, and the uncertainty introduced by this is evaluated by toy pseudoexperiments where the parameters in question are varied within their uncertainties when generating the various datasets. The third source is from bias in the fitting procedure, and likewise is estimated by using toy pseudo-experiments, where the systematic deviation from the true signal yield is evaluated.
Fit model choice
The nominal fit consists of double Crystal-Ball PDFs for the signal and cross-feed distributions, an ARGUS function convoluted with a Gaussian resolution function to model the partially-reconstructed background, and an exponential function to account for the combinatorial background. To estimate the systematic uncertainty introduced by the choice of these models they are replaced with equivalent alternative models, the fit repeated, and the systematic uncertainty taken to be the deviation of the result with respect to that of the nominal fit.
In particular, the signal and cross-feed models are replaced with double Gaussian functions with a common mean, the partially reconstructed background PDFs are
replaced withRooKeysPdfkernel density estimates, and the combinatorial background
model is replaced with a second order Chebychev polynomial.
The absolute systematic uncertainty on the ratio of the signal and normalisation yields, when averaging over all data categories, is less than 1% when the signal models are substituted, less than 1% when the partially-reconstructed background models are substituted, and around 2% when the combinatorial background model is substituted.
Fixed parameters
To increase the simultaneous fit stability certain shape parameters are determined by fits to MC and then fixed in the final fit. To estimate the systematic uncertainty introduced by these fixed parameters, an ensemble of toy pseudoexperiments is generated based on the nominal fit results. Using the covariance matrix from the fits to simulation, new sets of values for the fixed PDF parameters are also generated. Every toy experiment is fitted using each of these new sets of values as well as the nominal values. The difference between the yield returned by the fit using the nominal parameter values and the yields from each of the fits using the modified parameter values is determined, and the systematic uncertainty is assigned to be the average value of the standard deviation over the ensemble of toy experiments. To
reduce statistical fluctuations due to the small yields extracted in the fit to data, these toys are generated with yields that are several times those observed in data.
The absolute systematic uncertainty on the ratio of signal and normalisation yields estimated from this procedure is, when averaging over all data categories, less
than 1% for all modes exceptΛ0b→Λ K+K−, where it is around 2%.
5.5.5 Normalisation channel branching fraction
The product branching fraction of the Λ0b → Λ+c(Λ π+)π
−
normalisation mode is
(6.29±0.78)×10−5 [120, 142, 143]. This uncertainty is included as a systematic on
the absolute branching fraction. Also included in the systematic uncertainties is the statistical uncertainty on the normalisation yield extracted from the fit.