The inclusive reconstruction of Charmed Mesons on B-factory

. We present the study of the inclusive branching ratios of the double charmed decays with strangeness B → ¯ D ( ∗ ) D ( ∗ ) s ( J ) . The study based on the missing mass distributions in inclusive transitions B → ¯ D ( ∗ ) X , and thus in a way free from the assumptions about resonance decays D ( ∗ ) s ( J ) . There are also presented the perspective of such studies on the next generation Belle II experiment.


Introduction
The main subject of this study are double-charmed (quasi)two-body decays of beautiful mesons B →D ( * ) D ( * ) s(J) . At the quark level this is a process dominated by the transition b → W − c → ccs, and its diagrams are shown in fig. 1. In the context of the standard model such transitions occur as a result of the weak interaction through the exchange of charged intermediate bosons W ± . The coupling constants in the vertices, and thus the amplitudes of the processes, are modified by the appropriate factor resulting from the CKM matrix. In the CKM mechanism, the most favored are the transitions between quarks of the same generation, despite this transition b → c ( fig. 1a) will be dominating in the B decays, since the b → t process is not allowed kinematically because of the very large mass of the t quark. The transition c → s is preferred as a transition within the same family of quarks. It follows from the above considerations that the B →D ( * ) D ( * ) s(J) decays will be relatively frequent [1]. The branching ratios of these decays depend, however, on the properties of the D s(J) mesons produced in the final state, which is discussed in the following chapters. In addition to the dominant tree-type diagram ( fig. 1a), the tested decays may also take place via a higher order penguin diagram ( fig. 1b), where in the loop, in addition to the W ± boson there is also an exchange of quarks u, c, t. However, the contribution of these amplitudes to SM is negligible.

General scheme of the analysis
One of the biggest advantages of B factories compared to hadronic accelerators (Tevatron or LHC) is the thorough knowledge of the initial state and production process of B mesons. This property can be used to reconstruct one of the B mesons, so-called B tagging, denoted as B tag . Full or partial B tag reconstruction provides information about the momentum and quantum numbers of the second B meson produced in a given event, so-called signal B that will be denoted as B sig . As part of this work a full reconstruction of B tag in purely hadron final states was used. In the next step the charmed meson D ( * ) sig coming from the B sig decay is exclusively reconstructed. The above procedure contributes simultaneously to the combinatorial background from other BB decays and continuum events suppression.
The mass M X of the remaining unreconstructed meson decay products B sig , denoted as X, is calculated as the missing mass: where p is a four-momentum of the particle. The D ( * ) s(J) mesons from two-body decays B → D ( * ) D ( * ) s(J) will appear as reinforcements in the M X distribution at values corresponding to their mass. Multi-body decays of the B →D ( * ) nπmK type (n and/or m > 1) will be in M X visible as broad structures and in this analysis will be treated as a background.

2.1D
( * ) sig meson reconstruction sig mesons are reconstructed in decay channels given below:

Reference channels
The analysis is covering the missing mass range 1.7 < M X < 2.7 GeV, which contains the majority of resonances in the cs system. The upper M X mass area has been excluded from the analysis due to the lowD ( * ) sig reconstruction efficiency. Missing mass range 1.7 < M X < 2.2 GeV was treated as a control. Signal quantities and branching ratios for individual channels are determined from the fit of the missing mass distributions in the tested M X range, simultaneously for all decay channels. All fits are made using the maximum likelihood method event after event. The analysis is carried out in a mode called "user blind", i.e. all signal measurement elements are determined from the Monte Carlo samples and control areas in the data.

Signal measurement
s(J) decays signals has been extracted by the fitting of the missing mass distribution. To determine the number of signal events and its shape parameters, the unbinned extended maximum likelihood fit for the M X variable including crossfeeds between individual decay channels was used. Probability density functions (PDF) for PDF S i signals were parameterized using the Gauss function: (index i numbers signal channels), while for background PDF i bkg are represented by normalized Chebychev polynomials, 1st, 2nd or 3rd order: Probability density functions for crossfeeds PDF i→k x− f eed are described using normalized histograms: PDF i→k received from the GMC samples. The probability function has the following form: where N is the total number of fitted events, N sig and N bkg are the corresponding total numbers of signal and background events, M j X l denotes missing mass of j-th event calculated for l channel, N i→k sig (B i ) and N i→i sig (B i ) are defined by the formulas: and depend on the measured branching ratios B i , which are the free fit parameters. In addition, the free parameters are the numbers of background events N i bkg . The adjustment was carried out at fixed ε i and µ i values determined from the dedicated SMC samples.

Results for GMC in the entire M X range
The results of PDF fitting (eq. 5) to the missing mass distribution in the entire test range obtained for GMC are shown in fig. 4. In addition to the signals from reference channels    Table 1. Comparison of the measured branching ratios with the PDG values [2], inclusive measurements of the BaBar experiment [3] and theoretical predictions [4]. The uncertainties quoted are due to statistics (first), experimental systematic (second) errors and uncertainties of branching fractions for the decays of intermediate resonances for a given channel (third).

Summary
On Belle data we can improve the BF measurements by reducing statistical and systematic uncertainties by factor 3 in respect to the current measurements. On Belle II data (50 times more) we can study the properties of higher excited states of D ( * ) s(J) mesons. Further improvement can come from the including in the simultaneous fit D * * mesons.
With the similar method we can study recoil mass in respect to D s hence reconstruct inclusively D ( * * ) mesons.