BABAR-PUB-23/01

SLAC-PUB-17720

††thanks: Deceased††thanks: Deceased††thanks: Deceased††thanks:
Deceased††thanks: Deceased††thanks: Deceased

The BABAR Collaboration

# Search for $B$ Mesogenesis at BABAR

J. P. Lees  V. Poireau  V. Tisserand  E. Grauges  A. Palano  G. Eigen  D. N.
Brown  Yu. G. Kolomensky  M. Fritsch  H. Koch  R. Cheaib  C. Hearty  T. S.
Mattison  J. A. McKenna  R. Y. So  V. E. Blinov  A. R. Buzykaev  V. P.
Druzhinin  V. B. Golubev  E. A. Kozyrev  E. A. Kravchenko  A. P. Onuchin  S.
I. Serednyakov  Yu. I. Skovpen  E. P. Solodov  K. Yu. Todyshev  A. J. Lankford
B. Dey  J. W. Gary  O. Long  A. M. Eisner  W. S. Lockman  W. Panduro Vazquez
D. S. Chao  C. H. Cheng  B. Echenard  K. T. Flood  D. G. Hitlin  J. Kim  Y. Li
D. X. Lin  S. Middleton  T. S. Miyashita  P. Ongmongkolkul  J. Oyang  F. C.
Porter  M. Röhrken  Z. Huard  B. T. Meadows  B. G. Pushpawela  M. D. Sokoloff
L. Sun  J. G. Smith  S. R. Wagner  D. Bernard  M. Verderi  D. Bettoni  C.
Bozzi  R. Calabrese  G. Cibinetto  E. Fioravanti  I. Garzia  E. Luppi  V.
Santoro  A. Calcaterra  R. de Sangro  G. Finocchiaro  S. Martellotti  P.
Patteri  I. M. Peruzzi  M. Piccolo  M. Rotondo  A. Zallo  S. Passaggio  C.
Patrignani  B. J. Shuve  H. M. Lacker  B. Bhuyan  U. Mallik  C. Chen  J.
Cochran  S. Prell  A. V. Gritsan  N. Arnaud  M. Davier  F. Le Diberder  A. M.
Lutz  G. Wormser  D. J. Lange  D. M. Wright  J. P. Coleman  E. Gabathuler  D.
E. Hutchcroft  D. J. Payne  C. Touramanis  A. J. Bevan  F. Di Lodovico  R.
Sacco  G. Cowan  Sw. Banerjee  D. N. Brown  C. L. Davis  A. G. Denig  W. Gradl
K. Griessinger  A. Hafner  K. R. Schubert  R. J. Barlow  G. D. Lafferty  R.
Cenci  A. Jawahery  D. A. Roberts  R. Cowan  S. H. Robertson  R. M. Seddon  N.
Neri  F. Palombo  L. Cremaldi  R. Godang  D. J. Summers  P. Taras  G. De Nardo
C. Sciacca  G. Raven  C. P. Jessop  J. M. LoSecco  K. Honscheid  R. Kass  A.
Gaz  M. Margoni  M. Posocco  G. Simi  F. Simonetto  R. Stroili  S. Akar  E.
Ben-Haim  M. Bomben  G. R. Bonneaud  G. Calderini  J. Chauveau  G. Marchiori
J. Ocariz  M. Biasini  E. Manoni  A. Rossi  G. Batignani  S. Bettarini  M.
Carpinelli  G. Casarosa  M. Chrzaszcz  F. Forti  M. A. Giorgi  A. Lusiani  B.
Oberhof  E. Paoloni  M. Rama  G. Rizzo  J. J. Walsh  L. Zani  A. J. S. Smith
F. Anulli  R. Faccini  F. Ferrarotto  F. Ferroni  A. Pilloni  G. Piredda  C.
Bünger  S. Dittrich  O. Grünberg  M. Heß  T. Leddig  C. Voß  R. Waldi  T. Adye
F. F. Wilson  S. Emery  G. Vasseur  D. Aston  C. Cartaro  M. R. Convery  J.
Dorfan  W. Dunwoodie  M. Ebert  R. C. Field  B. G. Fulsom  M. T. Graham  C.
Hast  W. R. Innes  P. Kim  D. W. G. S. Leith  S. Luitz  D. B. MacFarlane  D.
R. Muller  H. Neal  B. N. Ratcliff  A. Roodman  M. K. Sullivan  J. Va’vra  W.
J. Wisniewski  M. V. Purohit  J. R. Wilson  A. Randle-Conde  S. J. Sekula  H.
Ahmed  N. Tasneem  M. Bellis  P. R. Burchat  E. M. T. Puccio  M. S. Alam  J.
A. Ernst  R. Gorodeisky  N. Guttman  D. R. Peimer  A. Soffer  S. M. Spanier
J. L. Ritchie  R. F. Schwitters  J. M. Izen  X. C. Lou  F. Bianchi  F. De Mori
A. Filippi  D. Gamba  L. Lanceri  L. Vitale  F. Martinez-Vidal  A. Oyanguren
J. Albert  A. Beaulieu  F. U. Bernlochner  G. J. King  R. Kowalewski  T. Lueck
C. Miller  I. M. Nugent  J. M. Roney  R. J. Sobie  T. J. Gershon  P. F.
Harrison  T. E. Latham  R. Prepost  S. L. Wu

###### Abstract

A new mechanism has been proposed to simultaneously explain the presence of
dark matter and the matter-antimatter asymmetry in the universe. This scenario
predicts exotic $B$ meson decays into a baryon and a dark sector anti-baryon
($\psi_{D}$) with branching fractions accessible at $B$ factories. We present
a search for $B\rightarrow\mathchar 28931\relax\psi_{D}$ decays using data
collected by the BABAR experiment at SLAC. This reaction is identified by
fully reconstructing the accompanying $B$ meson and requiring the presence of
a single $\mathchar 28931\relax$ baryon in the remaining particles. No
significant signal is observed, and bounds on the $B\rightarrow\mathchar
28931\relax\psi_{D}$ branching fraction are derived in the range
$0.13-5.2\times 10^{-5}$ for
$1.0<m_{\psi_{D}}<4.2{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$. These results
set strong constraints on the parameter space allowed by the theory.

###### pacs:

95.35.+d, 11.30.Fs, 14.40.Nd

The nature of dark matter (DM) and the baryon asymmetry of the Universe (BAU)
are perhaps two of the deepest mysteries of modern particle physics. The
latest cosmological observations reveal that visible matter only accounts for
about 15% of the matter in the universe, while the remaining 85% is
constituted by DM [1, 2]. Beyond its coupling to gravity, the particle
properties of DM remain to be elucidated, and many models have been proposed
to explain the observed abundance. The visible matter density is equally
mysterious, as cosmology predicts a universe born with equal amount of matter
and antimatter. A dynamical mechanism, baryogenesis, is required to produce an
initial excess of baryons over anti-baryons consistent with cosmic microwave
background and big-bang-nucleosynthesis measurements [3, 4].

The $B$-Mesogenesis scenario has been recently proposed [5, 6] to
simultaneously explain the DM abundance and the BAU. This model introduces
several new fields, including a light dark-sector anti-baryon and a new TeV-
scale color-triplet bosonic mediator. The baryogenesis mechanism relies on the
out-of-thermal-equilibrium production of $b$ and $\bar{b}$ quarks in the early
universe through the decay of a massive, long-lived scalar field $\Phi$, as
illustrated in Fig. 1. A fraction of these quarks hadronizes into $B^{0}$ and
$\bar{B}^{0}$ mesons, which undergo $C\\!P$-violating oscillations before
decaying into a baryon $\cal{B}$, a dark-sector anti-baryon $\psi_{D}$, and
any number of additional light mesons $\cal{M}$. As a result, matter-
antimatter asymmetries are generated in the visible and dark sectors with
equal but opposite magnitudes, keeping the total baryon number conserved.

We note that our search is strongly related in its experimental signature to a
recently proposed [7] search for supersymmetry in $B$ meson decay to a baryon
and undetected light neutralino.

The baryon asymmetry is determined by the charge asymmetry in semi-leptonic
$B$ decays, which specifies the level of $C\\!P$ violation in mixing in the
$B^{0}-\bar{B}^{0}$ system, and the branching fraction of the inclusive
$B\rightarrow\psi_{D}\cal{BM}$ decays. The $B$-Mesogenesis mechanism would
imply a robust lower bound on the total branching fraction
$\text{BR}(B\rightarrow\psi_{D}{\cal BM})>10^{-4}$ [6]. Constraints on
exclusive $B^{0}\rightarrow\psi_{D}{\cal B}$ decays are calculated using
phase-space considerations for different baryons [6]. The results depend on
the effective operators ${\cal O}_{i,j}=\psi_{D}bij$ mediating the decay,
where $i=u,c$ and $j=d,s$ specify the quark content. The ratio of exclusive to
inclusive branching fractions ranges from about 1 to $100\%$, depending on the
$\psi_{D}$ mass. Furthermore, bounds on inclusive $b$ decays with missing
energy [8], searches for TeV-scale color-triplet scalars at the LHC [9, 10],
and dark matter stability require
$0.94<m_{\psi_{D}}<3.5{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ [6]. At
present, the best constraints on this scenario arise from a measurement of the
exclusive $B\rightarrow\psi_{D}\mathchar 28931\relax$ decay by the Belle
Collaboration [11] excluding branching fractions larger than $\sim(2-3)\times
10^{-5}$ for $m_{\psi_{D}}>1.0{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$.

Figure 1: Illustration of the $B$ Mesogenesis mechanism. Figure taken from
Ref. [6].

We report herein a search for the decay $B^{0}\rightarrow\psi_{D}\mathchar
28931\relax$ in the mass range
$1.0<m_{\psi_{D}}<4.2{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$. The analysis
is based on 398.5 $\rm fb^{-1}$ of data collected at the $\mathchar
28935\relax{(4S)}$ resonance with the BABAR detector at the PEP-II
$e^{+}e^{-}$ storage ring at SLAC, corresponding to $4.35\times 10^{8}$
$B\bar{B}$ pairs [12]. The BABAR detector is described in detail elsewhere
[13, 14]. An additional 32.5 $\rm fb^{-1}$ of data are used to optimize the
analysis strategy and are subsequently discarded. The remaining data are not
examined until the analysis procedure is finalized.

Simulated signal events are created using the EVTGEN [15] Monte Carlo (MC)
event generator. Eight different samples, each with a different $\psi_{D}$
mass, are generated. The mass values range from 1 to
$4.2~{}{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$. The background is studied
with samples of inclusive $e^{+}e^{-}\rightarrow B\bar{B}$ decays (EVTGEN) and
continuum $e^{+}e^{-}\rightarrow q\bar{q}$ events with $q=u,d,s,c$ (JETSET
[16]). The detector response is simulated with Geant4 [17, 18].

Since dark-sector particles escape undetected, we identify the signal by fully
reconstructing the second $B$ meson ($B_{\rm tag}$) from hadronic decay modes,
and require the presence of a single $\mathchar 28931\relax$ baryon among the
remaining particles. The $\psi_{D}$ is identified as the system recoiling
against the $B_{\rm tag}$ and $\mathchar 28931\relax$ candidates. Hadronic $B$
meson decays proceed mostly through charmed mesons, and the $B_{\rm tag}$
candidate is reconstructed via the decays $B\rightarrow SX$ by a hierarchical
algorithm that combines a “seed” meson $S$, such as $D^{(*)0}$, $D^{(*)\pm}$,
$D_{s}^{*\pm}$, or $J/\psi$, with a hadronic system $X$ containing up to five
kaons and/or pions with total charge 0 or $\pm 1$ [19]. The selection of
$B_{\rm tag}$ candidates is based on two kinematic variables: the energy
difference $\Delta E=E_{\rm beam}-E_{\rm tag}$ and the beam-energy-substituted
mass $m_{\rm ES}=\sqrt{E_{\rm beam}^{2}-p_{B_{\rm tag}}^{2}}$, where $E_{\rm
tag}$ and $p_{B_{\rm tag}}$ are the energy and momentum of the $B_{\rm tag}$
candidate in the $e^{+}e^{-}$ center-of-mass frame, and $E_{\rm beam}$ is the
beam energy in the same frame.

The remaining particles are associated with the signal $B\rightarrow\mathchar
28931\relax\psi_{D}$ candidate ($B_{\rm sig}$). The $\mathchar 28931\relax$
candidates are reconstructed as pair of oppositely charged tracks identified
as a proton and a pion. A kinematic fit is performed on the $\mathchar
28931\relax$ candidate, constraining the two tracks to originate from the same
point in space and requiring the momentum vector to point back to the beam
interaction region. The $\mathchar 28931\relax$ flight length is calculated as
the distance between the primary interaction point and the secondary decay
vertex. The flight length significance, defined as the flight length divided
by its uncertainty, must be greater than 1.0. If more than one combination of
$B_{\rm tag}$ and $\mathchar 28931\relax$ candidates is found, the one with
the smallest $\chi^{2}$ is selected. After reconstructing the $B_{\rm tag}$
and $\mathchar 28931\relax$ candidates, no additional track must be present in
the event. The distributions of $m_{\rm ES}$ and the reconstructed $\mathchar
28931\relax$ mass ($m_{\mathchar 28931\relax}$) are shown in Fig. 2. We
require events to satisfy $5.27<m_{\rm
ES}<5.29{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ and $1.110<m_{\mathchar
28931\relax}<1.121{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$.

Figure 2: Distribution of (top) the energy-substituted mass, $m_{\rm ES}$, and
(bottom) the reconstructed $\mathchar 28931\relax$ mass, $m_{\mathchar
28931\relax}$, for data (points), signal MC for
$m_{\psi_{D}}=2.0{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ (red histogram) and
inclusive background MC predictions (stacked histograms). The normalization of
the signal events is arbitrary.

A multivariate selection using boosted decision trees (BDT) [20] is used to
further increase the signal purity. The BDT includes the following variables:
$m_{\rm ES}$ and $\Delta E$ of the $B_{\rm tag}$ candidate; information about
the $B_{\rm tag}$ hadronic decay channel and its purity, defined as the
fraction of correctly reconstructed $B_{\rm tag}$ candidates for a given decay
mode [21]; the magnitude of the $B_{\rm tag}$ thrust vector, defined as the
sum of the magnitudes of the momenta of all tracks and calorimeter clusters
projected onto the thrust axis [21]; the $B_{\rm sig}$ momentum vector in the
laboratory frame, inferred from the initial beam electrons and the recoiling
$B_{\rm tag}$; the number of calorimeter clusters associated with $B_{\rm
sig}$; the total neutral energy associated with $B_{\rm sig}$; the number of
$\pi^{0}$ candidates associated with $B_{\rm sig}$; the $\mathchar
28931\relax$ flight length significance; the $\chi^{2}$ of the kinematic fit
performed on the $\mathchar 28931\relax$ candidate; and the energy and
momentum of the $\mathchar 28931\relax$ candidate in the laboratory frame. The
$\psi_{D}$ mass is specifically excluded from the BDT in order to limit
potential bias in the classifier, and the BDT is trained on a signal sample
spanning a wide range of $\psi_{D}$ masses. The distribution of the BDT score,
$\nu_{\rm{BDT}}$, is shown in Fig. 3. We select events with a BDT score
greater than 0.75, selecting 41 events in the data. The resulting $\psi_{D}$
mass distribution is shown in Fig. 4. Approximately half of the expected
background consists of $e^{+}e^{-}\rightarrow q\bar{q}$ events, and the
remainder arises from $B\bar{B}$ events.

Figure 3: The distribution of the BDT score after applying all other selection
criteria for data (points), signal MC for
$m_{\psi_{D}}=2.0{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ (red histogram) and
inclusive background MC predictions (stacked histograms). The normalization of
the signal events is arbitrary. Figure 4: The distribution of the $\psi_{D}$
mass ($m_{\psi_{D}}$) after applying all selection criteria for data (points),
signal MC for $m_{\psi_{D}}=2.0{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ (red
histogram) and inclusive background MC predictions (stacked histograms). The
normalization of the signal events is arbitrary.

The signal efficiency varies between $5.9\times 10^{-4}$ at
$m_{\psi_{D}}=1.0{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ and $2.1\times
10^{-4}$ around $m_{\psi_{D}}=4.2{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$,
taking into account the $B_{\rm tag}$ reconstruction efficiency, the selection
criteria, and the $\mathchar 28931\relax\rightarrow p\pi^{-}$ branching
fraction. As shown in Fig. 3, the inclusive background MC samples do not
accurately reproduce the data. This discrepancy arises from a mis-modeling of
several branching fractions used in the simulation, resulting in differences
in $B_{\rm tag}$ reconstruction efficiencies [22], as well as differences in
charged and neutral particle reconstruction efficiencies, PID efficiencies,
and the modeling of variables used in the BDT. We correct the simulation in a
two-step procedure, using sideband data selected with the criteria, described
above, applied before the BDT selection, except with the looser requirement
$5.20<m_{\rm ES}<5.29{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$. The region
$-0.5<\nu_{\rm{BDT}}<0.75$, largely dominated by $e^{+}e^{-}\rightarrow
q\bar{q}$ ($q=u,d,s,c$) events, is used to extract a correction factor for
continuum production, $f_{udsc}$, by rescaling the corresponding MC
predictions to the number of observed events. The correction factor for
$B\bar{B}$ production, $f_{B^{0}\bar{B}^{0}}$, is determined from data in the
complementary region $\nu_{\rm{BDT}}<-0.5$, assuming equal contributions from
$B^{0}\bar{B}^{0}$ and $B^{+}B^{-}$. We obtain $f_{udsc}=1.34\pm 0.10$ and
$f_{B^{0}\bar{B}^{0}}=1.06\pm 0.08$. Under the assumption that the $B\bar{B}$
correction factor is independent of the signal $B$ decay mode, we rescale the
signal efficiency by $f_{B^{0}\bar{B}^{0}}$, and propagate the corresponding
uncertainty as a systematic uncertainty.

We extract the signal yield by scanning the $\psi_{D}$ mass spectrum in steps
of the signal mass resolution, $\sigma_{m}$, probing a total of 193 mass
hypotheses. The resolution is estimated by performing fits of a Bukin function
[23] to the $\psi_{D}$ mass distribution for each signal MC sample, and
interpolating the results to the full mass range. The results vary between
$90{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ at
$m_{\psi_{D}}=1.0{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ and
$6{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ at
$m_{\psi_{D}}=4.2{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$. The signal yield
is determined by counting the number of events in a window of $\pm
3\sigma_{m}$ centered around the $\psi_{D}$ mass hypothesis. The background is
evaluated in two sideband regions of $\pm 3\sigma_{m}$ surrounding the signal
window, except near
$m_{\psi_{D}}=4.2~{}{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$, where a single
region is used. The largest local significance is found to $2.3\sigma$,
observed near $m_{\psi_{D}}=3.7{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$,
corresponding to a global significance of $0.4\sigma$ after including trial
factors [24], consistent with the null hypothesis.

In the absence of a signal, upper limits on the branching fraction
$B^{0}\rightarrow\psi_{D}\mathchar 28931\relax$ are derived at 90% confidence
level (CL) by applying a profile likelihood method [25] for each $\psi_{D}$
mass hypothesis. The number of signal and background events is assumed to
follow Poisson distributions, while the efficiency is modeled with a Gaussian
having a variance equal to the total systematic uncertainty. Systematic
uncertainties arising from track and neutral reconstruction efficiencies,
$B_{\rm tag}$ reconstruction efficiencies, selection criteria, and modeling of
the BDT variables are included in the $B\bar{B}$ correction factor described
above. Other sources of uncertainty include the $\mathchar
28931\relax\rightarrow p\pi^{-}$ branching fraction (0.8%), the integrated
luminosity (0.6%) [12], and the limited statistical precision of the signal MC
samples (0.7-4.6%). The total systematic uncertainty, obtained by summing in
quadrature the different contributions, varies between 7.8 and 9.1%.

The results are displayed in Fig. 5, together with the previous measurement
from the Belle Collaboration and theoretical predictions for different type of
operators generating $B$ Mesogenesis. We probe branching fractions in the
range $0.13-5.2\times 10^{-5}$, improving previous constraints by up to an
order of magnitude. These bounds exclude most of the remaining parameter space
for the $\mathcal{O}^{2}_{us}=(\psi_{D}s)(ub)$ and
$\mathcal{O}^{3}_{us}=(\psi_{D}u)(sb)$ operators, and a significant fraction
of the region allowed for $\mathcal{O}^{1}_{us}=(\psi_{D}b)(us)$ operators
above $m_{\psi_{D}}>2.8{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$.

Figure 5: Upper limits on the $B^{0}\rightarrow\psi_{D}\mathchar 28931\relax$
branching fraction at 90% CL, together with previous constraints [11]. The
light blue and orange (orange only) region shows the values of the
$B^{0}\rightarrow\psi_{D}\mathchar 28931\relax$ branching fraction allowed to
successfully generate $B$ Mesogenesis for the
$\mathcal{O}^{1}_{us}=(\psi_{D}b)(us)$ ($\mathcal{O}^{2}_{us}=(\psi_{D}s)(ub)$
and $\mathcal{O}^{3}_{us}=(\psi_{D}u)(sb)$) effective operators [6].

In summary, we report a search for baryogenesis and dark matter in the process
$B^{0}\rightarrow\mathchar 28931\relax\psi_{D}$ with a fully reconstructed
$B_{\rm tag}$ meson. No significant signal is observed, and upper limits on
the branching fraction at the level of $10^{-6}-10^{-5}$ are set. These
results exclude a large fraction of the parameter space allowed by $B$
Mesogenesis. Future measurements at Belle-II should be able to fully explore
the remaining region.

###### Acknowledgements.

We thank G. Elor and M. Escudero for useful discussions on the B-Mesogenesis
mechanism. We are grateful for the extraordinary contributions of our PEP-II
colleagues in achieving the excellent luminosity and machine conditions that
have made this work possible. The success of this project also relies
critically on the expertise and dedication of the computing organizations that
support BABAR. The collaborating institutions wish to thank SLAC for its
support and the kind hospitality extended to them.

## References

  * [1] P. A. R. Ade et al. [Planck Collaboration], Astron. Astrophys. 594, A13 (2016).
  * [2] N. Aghanim et al. [Planck Collaboration], Astron. Astrophys. 641, A6 (2020).
  * [3] M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018).
  * [4] R. H. Cyburt, B. D. Fields, K. A. Olive and T.-H. Yeh, Rev. Mod. Phys. 88, 015004 (2016).
  * [5] G. Elor, M. Escudero and A. E. Nelson, Phys. Rev. D 99, 035031 (2019).
  * [6] G. Alonso-Álvarez, G. Elor and M. Escudero, Phys. Rev. D 104, 035028 (2021).
  * [7] C. O. Dib, J. C. Helo, V. E. Lyubovitskij, N. A. Neill, A. Soffer and Z. S. Wang, arXiv:2208.06421 [hep-ph].
  * [8] R. Barate et al. [ALEPH Collaboration], Eur. Phys. J. C 19, 213 (2001).
  * [9] A. M. Sirunyan et al. [CMS Collaboration], JHEP 10, 244 (2019).
  * [10] G. Aad et al. [ATLAS Collaboration], JHEP 02, 143 (2021).
  * [11] C. Hadjivasiliou et al. [Belle Collaboration], Phys. Rev. D 105, L051101 (2022).
  * [12] J.P. Lees et al. [BABAR Collaboration], Nucl. Instrum. Meth. A 726, 203 (2013).
  * [13] B. Aubert et al. [BABAR Collaboration], Nucl. Instrum. Meth. A 479, 1 (2002).
  * [14] B. Aubert et al. [BABAR Collaboration], Nucl. Instrum. Meth. A 729, 615 (2013).
  * [15] D.J. Lange, Nucl. Instrum. Meth. A 462, 152 (2001).
  * [16] T. Sjöstrand, S. Mrenna and P. Skands, JHEP 05, 26 (2006).
  * [17] S. Agostinelli et al. [GEANT4 Collaboration], Nucl. Instrum. Meth. A 506, 250 (2003).
  * [18] J. Allison et al., IEEE Trans. Nucl. Sci. 53, 270 (2006).
  * [19] J.P. Lees et al. [BABAR Collaboration], Phys. Rev. D 100, 111101 (2019).
  * [20] Y. Freund and R.E. Schapire, J. Comput. Syst. Sci. 55, 119 (1997).
  * [21] A.J. Bevan et al., Eur. Phys. J. C 74, 3026 (2014).
  * [22] B. Aubert et al. [BABAR Collaboration], Phys. Rev. D 80, 111105 (2009).
  * [23] A. Bukin, Fitting function for asymmetric peaks, arXiv:0711.4449 (2007).
  * [24] E. Gross and O. Vitells, Eur. Phys. J. C 70, 525 (2010).
  * [25] W. A. Rolke et al., Nucl. Inst. and Meth. A 551, 493 (2005).