I Estimating decay yields from fits to these distributions

[Floyd_13]

I'm currently reading various papers on the violation of Lepton Flavour Universality in rare B-decays and I would appreciate some help in understanding the methodology for measuring the ratios in these decays.

Here is a quote from a recent paper from the LHCb collaboration (p.5):

An unbinned extended maximum-likelihood fit to the m(K⁺e⁺e⁻) and m(K⁺µ⁺µ⁻) distributions of nonresonant candidates is used to determine R_K [the ratio]. In order to take into account the correlation between the selection efficiencies, the different trigger categories and data-taking periods are fitted simultaneously. The resonant decay mode yields are incorporated as constraints in this fit, such that the B⁺→K⁺µ⁺µ^- yield and R_K are fit parameters.

My question is how exactly are the yields extracted from the fits performed on the mass data points using maximum likelihood estimations? Does this mean that the fitted function has to be a function of the yield N? If yes, how is this achieved?

 

[mfb]

For details you would have to ask the people doing the analysis, but the non-resonant yield and the ratio are free parameters in the fit function. The fit then determines the optimal values and their uncertainties.

 

[Dedu]

Plotting the invariant mass of the final state particles gives a mass distribution of the B meson. In this distribution, the events are not only real B meson decays but they could come from different sources of background. Almost always you will have combinatorial background and, as it is the case in the analysis you are referring to, partially reconstructed background (see Fig 2, top-left). Some functions/shapes are then used to model these several contributions that add up to the observed mass distribution. For example, combinatorial background is usually fitted only with an exponential function, while the (non-resonant, i.e. non-Jpsi mode) signal is fitted probably with a Gaussian with exponential tails (DSCB).

What they mean by (signal) yield is actually the number of events in the initial mass distribution that fall under the signal shape in their fit model. The yield along with its uncertainty are determined by the fit.