and $B_{s}^{*}$ and their transition to $B_{(s)}\gamma$ and $D_{(s)}^{*}+V$,
$V\in\\{\rho,K^{*},D^{*},D_{s}^{*}\\}$. The radiative deexitation processes
use the formalism presented in Sec. 2.4 to describe the decay: a photon can be
radiated from one of the valence quarks or from the non-local quark-hadron
vertex. In the latter case, however, it can be shown that the contribution
vanishes due to the anomalous nature of the $V\to P\gamma$ process and so the
calculation is simplified. The results on decay widths of $B^{+}$, $B^{0}$ and
$B_{s}^{*0}$, presented in Tab. V of the work, depend on radiative decay
constants of the particles given in Tab. IV. For what concerns the decays to
two vector particles, the computation proceeds in a usual way, where the CCQM
invariant form factors are combined to helicity amplitudes to give branching
fractions. Due to small cross sections of the studied processes the
experimental numbers are not available and so the CCQM results are compared to
other theoretical approaches (Tab. XII of [458]).

##  6 Summary and outlook

We provided in this text a review of the results of the covariant confined
quark model for $B$ decays presented together with a survey of selected
experimental and theoretical results. Unlike for other physics models and
their achievements mentioned here, we explained in depth the principles of the
CCQM (Sec. 2) and presented computational details for chosen processes, namely
$B_{s}\to\ell^{+}\ell^{-}\gamma$ (Sec. 3.2),
$B_{s}\to\phi\ell^{+}\ell^{-}\gamma$ (Sec. 4.2), $B\to D_{(s)}^{(*)}h$,
$(h=\pi,\rho)$ and $B_{s}\to J/\psi\eta^{(^{\prime})}$ (Sec. 5.2). For the
sake of the review the decays were divided into three groups: leptonic,
semileptonic and non-leptonic. Although somewhat arbitrary, this division
allowed us to demonstrate the application of the CCQM in various situations.
Generally speaking, despite some studies on NP contributions, the CCQM results
do not provide strong indications for NP and suggest that further efforts
within the SM may be needed.

One should also recall that we presented only a small section of what the CCQM
can provide: it was, in many papers, successfully applied to describe baryon,
tetraquark and other (than $B$) mesonic states. The quality of the CCQM is
also confirmed by the interest of other authors. Narrowing the large number of
citations to those related to $B$ decays and referring to the recent version
of the model (2010 and later, without conference papers) one sees that the
model was noticed by large collaborations (LHCb [58, 459], ATLAS [460]).

The ongoing physics program on existing and future high-luminosity machines
implies that the CCQM may also in the future be an appropriate theoretical
tool which will contribute to unraveling the questions brought by experiments
about the presence of NP or the nature of various (exotic) states. Together
with other approaches, it may help to understand model-related uncertainties
beyond which new physics observations can be claimed.

## Acknowledgement

S. D., A. Z. D. and A. L. acknowledge the support of the Slovak Grant Agency
for Sciences VEGA, grant no. 2/0105/21.

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