The full data PDFs are created by combining the individual signal and background fits detailed in section 5.6, and are then used to extract the yields for each signal channel.
5.7.1 Bs0 →Ds(∗)+D( ∗)− s
The full PDFs for theB0s →Ds(∗)+D( ∗)−
s data distribution, and the twoD±s distributions, are shown in figures 5.24 and 5.25, where the final fit is a simultaneous unbinned max- imum likelihood fit to all three particles. Fitting to all three particles simultaneously gives the fit more information to separate the signal and background events, by consid- ering where the event lies in terms of Bs0 mass, and also both D±s masses. Therefore every event is represented by a single point in the B0s distribution, and a single point in both of the Ds± distributions. A number of parameters in the full data fits are fixed to values taken from the individual simulation fits; these are detailed in the relevant sections. Some of the parameters are found by performing the fit to only the B0
s mass distribution, or only the Ds± distributions; the parameters taken from these partial fits are then fixed in the full simultaneous fit to the three distributions, to aid the stability of the fit. The yields, and a number of other parameters, are allowed to float. A detailed
break down of the parameters in the final data fit and whether they are fixed (and if so, how) or floated can be seen in appendix E. The yields for all three signal channels and the two backgrounds, along with the total signal yield, are shown in table 5.10. The errors on the total signal yield are determined by considering the covariances of the signal yields and are therefore lower than simply combining the errors in quadrature; in regions of the mass distribution where peaks overlap, the fit can determine that an event is part of a signal decay with a small error, but determining the exact identity of that decay is more difficult.
Figure 5.24: Mass fit for the full Bs0 → D (∗)+
s D(s∗)−data set, showing the full B0s
Figure 5.25: Mass fits for the fullBs0 →D (∗)+
s D(s∗)−data set, showing the twoDs±
fits along with their pull plots. Ds1 and Ds2 are arbitrarily assigned labels for the two
Ds± candidates in each event. The cyan line in each case represents the combinatorial
background component of the distribution.
Decay Mode Yield
B0s →D+sDs− 412±23 Bs0 →Ds∗±Ds∓ 1032±39 B0 s →Ds∗±Ds∗∓ 786±48 Combinatorial Background 1342±47 B0 s →Ds(2460)±D∓s 432±42 Bs0 →Ds(∗)+Ds(∗)− 2230±63
Table 5.10: Yields in theBs0→D (∗)+
s D
(∗)−
s data fit.
Due to the relative complexity of the fit, and the large number of parameters involved it was decided to investigate the stability of the fit and look for potential biases, by producing toy Monte Carlo samples from the data fit. The samples were produced with the same fixed parameters and same floated parameters as in the final data fit, with
the yields allowed to vary around their central values. The results of the toy studies are shown in detail in appendix B. All signal yields and their associated uncertainties were reproduced by the toy samples, and the −log(L) of the fit to data was also well reproduced. No evidence of underlying bias was seen in the pull plots for each yield, where all mean and sigma values were consistent with 0 and 1 respectively.
5.7.2 B0 → D± sD
∓
The full fit to theB0 →Ds±(∗)D∓(∗) data distribution is shown in figures 5.26 and 5.27. The parameters of this fit are again found by performing partial fits to either theB0dis- tribution, or theD±(s) distributions. The parameters are then set in the full simultaneous fits, with the yields and a few other parameters allowed to vary. The final data yields are presented in table 5.11. The relatively very small yield from theB0→D±∗s D∓∗ channel is because the vast majority of these decays are reconstructed with a mass lower than the 5050 MeV mass cut imposed on the B0 candidates, and only a small contribution from the tail of this distribution remains, as seen in (a) in figure 5.26. Only the main
Figure 5.26: Mass fits for the fullB0→Ds±(∗)D∓(∗)data set, showing the fullB0 fit with the pull plot beneath.
Decay Mode Yield B0 →Ds±D∓ 3615±64 B0 →D±∗ s D∓/B0 →D±sD∓∗ 3555±110 B0 →Ds±∗D∓∗ 195±86 Combinatorial Background 1643±56
Table 5.11: Yields in theB0→Ds±(∗)D∓(∗)data fit.
(b)
(c)
Figure 5.27: Mass fits for the fullB0 →Ds±(∗)D∓(∗)data set, showing the D±s and
D± fits along with their pull plots.