Study of $\overline{B}{}^{0}\rightarrow D^{+}h^{-}(h=K/\pi)$ decays at Belle

Two-body decays of $B$ mesons serve as an important test bed for phenomenological studies of the quark flavor sector of the Standard Model of particle physics. The Cabibbo-favored mode $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ is an especially clean and abundant hadronic decay that provides a good opportunity to test models of hadronic $B$ meson decays. Due to the large mass of the $b$ quark, the influence of the strong interaction in these decays can be calculated more reliably than those in light-meson decays. It has been suggested that improved measurements of color-favored hadronic two-body decays of $B$ mesons will lead to a better understanding of poorly known quantum chromodynamics (QCD) effects cite-qcdeffetcs . The decays of $B$ mesons to two-body hadronic final states can be analyzed by decomposing their amplitudes in terms of different decay topologies and then applying SU(3) flavor symmetry of QCD to derive relations between them. The Cabibbo-suppressed mode $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ only receives contributions from color-allowed tree amplitudes while $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ receives contributions from both color-allowed tree and exchange amplitudes cite-arXiv:1012.2784 . These two decay modes can be related by a ratio cite-belleold ,

where $\theta_{\rm C}$ is the Cabibbo angle, and $f_{K}$ and $f_{\pi}$ are meson decay constants. The theoretical description for these hadronic decays has considerably improved over the years cite-theory1 ; cite-theory2 and has been followed by several recent developments cite-arXix1606.02888 ; cite-arXiv:2007.10338 . This description relies on factorization and SU(3)-symmetry assumptions, so measurements of these modes can be used to test these hypotheses in heavy-quark hadronic decays. The above two modes are also important because they constitute high-statistics control samples for the hadronic $B$-decay measurements related to time-dependent $CP$ violation and the extraction of the Cabibbo-Kobayashi-Maskawa unitarity-triangle angle $\phi_{3}$ cite-theory3 . Experimentally, calculating the ratio of the branching fractions of $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ and $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ modes has the advantage that many systematic uncertainties cancel, enabling tests of theoretical predictions, particularly those of factorization and SU(3) symmetry breaking in QCD.

The theoretical predictions made in Refs. cite-arXix1606.02888 ; cite-arXiv:2007.10338 are based on the framework of QCD factorization, at next-to-next-to-leading order. However, these predictions significantly differ from the experimental values. Several attempts cite-arXiv:2103.04138 ; cite-arXiv:2109.04950 ; cite-arXiv:2008.01086 have been made to explain the discrepancy in both $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ and $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ decays within the context of new physics. Final-state rescattering effects on $\overline{B}{}^{0}\rightarrow D^{+}h^{-}(h={K/\pi})$ have also been proposed to explain the discrepancy cite-arXiv:2109.10811 . The results in Ref. cite-arXiv:2109.10811 rule out rescattering effects as a cause for the discrepancies and hence hint at a possible beyond-the-SM explanation.

Earlier, Belle reported a study of the Cabibbo-suppressed $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ decay using a small data datasetset cite-belleold by measuring the ratio of branching fraction of Cabibbo-suppressed $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ to that of the Cabibbo-favored $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ decay. The branching fraction for $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ decay was previously measured by BABAR cite-BaBar1 ; cite-BaBar2 , CLEO cite-cleo1 ; cite-cleo2 and ARGUS cite-argus . LHCb measured the branching fraction of $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ as well as the ratio of hadronization fractions $f_{s}/f_{d}$ cite-DKlhcb . A clear understanding of $\overline{B}{}^{0}\rightarrow D^{+}h^{-}(h={K/\pi})$ decays constitutes an important ingredient for the measurement $f_{s}/f_{d}$, which in turn will aid the measurement of rare decay $B_{s}^{0}\rightarrow\mu^{+}\mu^{-}$. Currently, the world averages cite-PDG for the branching fractions of $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ and $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ decays are $\mathcal{B}(\overline{B}{}^{0}\rightarrow D^{+}K^{-})=(1.86\pm 0.20)\times 10^{-4}$ and $\mathcal{B}(\overline{B}{}^{0}\rightarrow D^{+}\pi^{-})=(2.52\pm 0.13)\times 10^{-3}$, respectively, where the uncertainty is the sum in quadrature of the statistical and systematic errors. LHCb cite-ratiolhcb measured the ratio of the branching fractions for $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ and $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ to be $0.0822\pm 0.0011(\rm stat)\pm 0.0025(\rm syst)$, which dominates the current world-average value.

In this paper, we present measurements of the branching fractions of $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ and $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ decays using the full $\Upsilon(4S)$ dataset collected with the Belle detector.

The paper is organized as follows. Sec. II describes the Belle detector, as well as the data and simulation samples used in this analysis. The event selection requirements are outlined in Sec. III. Sec. IV describes how the values of $R^{D}$ and the $\overline{B}{}^{0}\rightarrow D^{+}h^{-}(h=K/\pi)$ branching fraction are determined from the data. The results and the evaluation of systematic uncertainties are described in Sec. V, and the conclusion is given in Sec. VI.

We use the full $\Upsilon(4S)$ data sample containing $772\times 10^{6}~{}B\overline{B}$ events recorded with the Belle detector cite-Belle at the KEKB asymmetric-beam-energy $e^{+}e^{-}$ collider  cite-KEKB . Belle is a large-solid-angle magnetic spectrometer that consists of a silicon vertex detector, a 50-layer central drift chamber (CDC), an array of aerogel threshold Cherenkov counters (ACC), a barrel-like arrangement of time-of-flight scintillation counters (TOF), and an electromagnetic calorimeter comprised of CsI(Tl) crystals. All these detector components are located inside a superconducting solenoid coil that provides a 1.5 T magnetic field cite-Belle .

A Monte Carlo (MC) simulated event sample is used to optimize the event selection, study background and compare the distributions observed in collision data with expectations. A signal-only simulated event sample is utilized to model the features of the signal for fits and determine selection efficiencies. One million signal events are generated for both decay channels. The so-called generic MC sample consists of simulated events that include $e^{+}e^{-}\to$ $B\overline{B}{}$, $u\overline{u}$, $d\overline{d}$, $s\overline{s}$, and $c\overline{c}$ processes in realistic proportions, and corresponds in size to more than five times the $\Upsilon(4S)$ data. The generic MC sample is used to study background and make comparisons with the data. The $B$- and $D$-meson decays are simulated with the EvtGen generator cite-EvtGen where the D_DALITZ model is used for the $D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$ final state. The effect of final-state radiation is simulated by the PHOTOS package cite-PHOTOS . The interactions of particles with the detector are simulated using GEANT3 cite-GEANT .

We use the Belle II Analysis Software Framework (basf2) cite-basf2 for the decay-chain reconstruction and convert the Belle data to basf2 format using the B2BII software package cite-b2bii . The decays $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ and $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ have nearly the same kinematic properties. The former is used to establish selection criteria on kinematic variables and determine the experimental resolution due to its larger data size compared to the latter. Charged particle tracks originating from $e^{+}e^{-}$ collisions are selected by requiring $dr<0.2~{}\rm cm$ and $|dz|<1.5~{}\rm cm$, where $dr$ and $|dz|$ represent the distance of closest approach to the interaction point (IP) in the plane transverse to and along the $z$ axis, respectively. The $z$ axis is the direction opposite the $e^{+}$ beam.

Information from the CDC, ACC, and TOF is used to determine a $K/\pi$ likelihood ratio $\mathcal{L}(K/\pi)=\frac{\mathcal{L}_{K}}{\mathcal{L}_{K}+\mathcal{L}_{\pi}}$ for charged particle identification (PID), where $\mathcal{L}_{K}$ and $\mathcal{L}_{\pi}$ are the likelihoods that a particular track is either a kaon or a pion, respectively. The likelihood value ranges from 0 to 1 where 0 (1) means the track is likely to be a $\pi$ ($K$). To ensure high efficiency and purity, we require $\mathcal{L}(K/\pi)>0.6$ for kaon candidates and $\mathcal{L}(K/\pi)<0.6$ for pion candidates. The charged $D^{+}$ candidate is formed using $K^{-}\pi^{+}\pi^{+}$ combinations, which is then combined with a prompt hadron $(h=K/\pi)$ to form a $\overline{B}{}^{0}$ candidate. (The inclusion of charge conjugate states is implied throughout this paper.) $D^{+}$ meson candidates are required to have a mass within $\pm 2.5\sigma$ of the known $D^{+}$ mass value cite-PDG , where the Gaussian resolution $\sigma$ is approximately $5~{}\rm MeV$. The effective $\sigma$ value is obtained by fitting the invariant mass distribution of $D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$ decays with a double Gaussian function for signal and a first-order polynomial for background as shown in Fig. 1.

The kinematic variables used to discriminate $B$ decays from background are the beam-energy-constrained mass

and the energy difference

Here $E_{B}$ and $p_{B}$ are the $B$ candidate’s energy and momentum, respectively, and $E_{\rm beam}$ is the beam energy; these quantities are calculated in the $e^{+}e^{-}$ center-of-mass frame. Natural units $\hbar$ = c = 1 are used throughout the paper. For correctly reconstructed signal events, $M_{\rm bc}$ peaks at the known mass of the $\overline{B}{}^{0}$ meson and $\Delta E$ peaks at zero. We retain the $\overline{B}{}^{0}$ candidates satisfying $M_{\rm bc}>~{}5.27~{}\rm GeV$ and $|\Delta E|<0.13~{}\text{GeV}$.

The background from $e^{+}e^{-}\rightarrow q\overline{q}$ $(q=u,d,s,c)$ continuum processes are suppressed by requiring the ratio of the second-to-zeroth order Fox-Wolfram moments cite-r2 to be less than 0.3. This selection removes $\sim$$70\%$ of the continuum while rejecting $\sim$$30\%$ of the signal in both $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ and $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ decays. After applying the aforementioned selection criteria, only $0.7\%$ of events are found to have more than one candidate. In such events, we choose the best candidate as the one having the smallest value of $|M_{\rm bc}-m_{B}|$ where $m_{B}$ is the known $\overline{B}{}^{0}$ mass. The kaon identification efficiency $\epsilon_{K}$ is determined from a kinematically selected sample of high momentum $D^{*+}$ mesons, which is used to calibrate the PID performance. With the application of the requirements $\mathcal{L}(K/\pi)<0.6$ for pions and $\mathcal{L}(K/\pi)>0.6$ for kaons, the kaon efficiency ($\epsilon_{K}$) value is found to be $(84.48\pm 0.35)\%$ and the rate of pions misidentified as kaons is $(7.62\pm 0.44)\%$.

As the $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ branching fraction is an order of magnitude larger than that of $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$, the former can serve as an excellent calibration sample for the signal determination procedure. Furthermore, there is a significant contamination from $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ decays in the $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ sample in which the fast charged pion is misidentified as a kaon. A simultaneous fit to samples enriched in prompt tracks that are identified as either pions $[\mathcal{L}(K/\pi)<0.6]$ or kaons [$\mathcal{L}(K/\pi)>0.6$], allows us to directly determine this cross feed contribution from data. An unbinned maximum-likelihood fit is performed to extract the signal yield by fitting the $\Delta E$ distribution simultaneously in pion and kaon enriched samples. The yields of the $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ and $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ signals, as well as their cross feed contributions, in the pion and kaon enriched samples can be expressed by the following relations:

Here the values of $N^{D^{+}h^{-}}_{\text{pion enhanced}}(h=K/\pi)$ are the kaon and the pion yields in pion enriched sample with [$\mathcal{L}(K/\pi)<0.6$], and the $N^{D^{+}h^{-}}_{\text{kaon enhanced}}(h=K/\pi)$ are the kaon and pion yields in the kaon enriched sample with [$\mathcal{L}(K/\pi)>0.6$]. The pion misidentification rate $\kappa$ is a free parameter, as well as $R^{D}$ and $N^{D^{+}\pi^{-}}_{\rm total}$, where the latter is the total signal yield for the $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ decay. Due to a small contribution from $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ cross feed in the pion-enriched sample, the kaon identification efficiency $\epsilon_{K}$ is fixed to the value given in Sec. III. The yields are obtained from fitting the $\Delta E$ distribution. The background components are divided into the following categories in the fit:

1. 1.

   continuum $q\overline{q}$ background and combinatorial $B\overline{B}$ background, in which the final state particles could be from either the $B$ or $\overline{B}$ meson in an event; and

2. 2.

   cross feed background from $\overline{B}{}^{0}\rightarrow D^{+}h^{-}$, where $h=\pi,K$, in which the charged kaon is misidentified as a pion or vice versa.

The $\overline{B}{}^{0}\rightarrow D^{+}h^{-}(h=K/\pi)$ signal distributions are represented by the sum of a double Gaussian function and an asymmetric Gaussian with a common mean. These signal probability density functions (PDFs) are common to both kaon- and pion-enhanced samples. The means of the signal PDFs for $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ and $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ are directly extracted from the data, along with a single scaling factor to the narrowest signal Gaussian to account for any difference in $\Delta E$ resolution between simulated and data samples. Other parameters are fixed to those obtained from a fit to a large simulated sample of signal events.

A combined PDF is used to model combinatorial background consisting of continuum background and $B\overline{B}$ background for $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ ($\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$) decay, where the continuum is modeled with a first-order polynomial and the combinatorial $B\overline{B}$ background with an exponential function. The slope of the linear background and the exponential function’s exponent are determined from the fit to data; other parameters are fixed to those obtained from a fit to the corresponding simulated sample.

The cross feed background is described by a double Gaussian function in the $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ ($\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$) sample. The mean and scale factor for the $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ cross feed component PDF in the kaon-enhanced $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ sample are determined from the fit to data.

There is a background that can peak in the same manner as the $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ signal mode, which we call the “peaking background”. The most prominent decay that peaks in the $\Delta E$ distribution is $B^{0}\rightarrow K^{*}J/\psi,K^{*}\rightarrow K^{+}\pi^{-},J/\psi\rightarrow\mu^{+}\mu^{-}$ or $e^{+}e^{-}$. This source accounts for $\sim$2$\%$ of the total background. To reject this contamination arising due to leptons misidentified as pions, we veto candidates with an invariant mass $M(\pi^{+}\pi^{-})$ value falling within $\pm 3\sigma$ of the known $J/\psi$ mass cite-PDG . This essentially removes this peaking background with $\sim$3$\%$ signal loss. The remaining peaking background contributions include semileptonic $D$ decays for which the normalization is fixed from MC simulation. All yields are determined from a fit to data except for the peaking background yield. The uncertainty associated with the fixed peaking component is included in the systematic uncertainties. All other shape parameters are fixed to their MC values. The yields obtained from the fit are listed in Table 1, and the signal-enhanced fit projections for the data are shown in Fig. 2.

The branching fraction of $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ decay is calculated as,

where $N^{\rm total}_{D^{+}\pi^{-}}$ is the yield of $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ obtained from the fit, $N_{B\overline{B}}$ is the total number of $B\overline{B}$ pairs, $\epsilon_{D^{+}\pi^{-}}=(24.09\pm 0.04)\%$ is the detection efficiency for $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ determined from signal MC events where the error is the associated statistical error from MC sample. The factor $f_{00}$ represents the neutral $B$ meson production ratio at the $\Upsilon(4S)$, which is $0.486\pm 0.006$ cite-PDG , and $\mathcal{B}(D^{+}\rightarrow K^{-}\pi^{+}\pi^{+})$ is the subdecay branching fraction of $D^{+}$, which is $(9.38\pm 0.16)\%$ cite-PDG . The branching fraction for $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ decay is calculated by multiplying the $R^{D}$ value from the fit by the calculated $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ branching fraction.

The systematic uncertainties in the measurements from various sources are listed in Table 2. Since the kinematics of $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ and $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ processes are similar, most of the systematic effects cancel in the ratio of their branching fractions. The main source of systematic uncertainty that does not cancel is the uncertainty in $K/\pi$ identification efficiency. All the sources of systematic uncertainty are assumed to be independent, such that the total uncertainty is the quadratic sum of their contributions. The uncertainty associated with the $D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$ subdecay branching fraction is taken from its world average cite-PDG . The uncertainty due to prompt tracking efficiency is based on a previous study of high momentum $(p>200~{}\rm MeV)$ tracks. Tracking efficiency is calculated as the ratio between partially and fully reconstructed $D^{+}$ decays in data and MC events. The entry for $N_{B\overline{B}}$ represents the uncertainty in the total number of $B\overline{B}$ events in data. Here $f_{00}$ refers to the uncertainty due to $\mathcal{B}(\Upsilon(4S)\rightarrow B^{0}\overline{B}{}^{0})$ branching fraction calculated from PDG 2020 cite-PDG along with the uncertainty due to isospin asymmetry calculated in cite-isospin . The efficiency variation due to the $D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$ model is evaluated by varying the model and adding a phase space component. The resulting difference with respect to the measured central value of the branching fraction is treated as a systematic uncertainty. The systematic uncertainty due to PDFs for the $D^{+}h^{-}(h=K/\pi)$ components and the $D^{+}h^{-}(h=K/\pi)$ cross feed components are evaluated by varying the fixed shape parameters by $\pm 1\sigma$. The uncertainty due to the kaon identification efficiency is calculated by varying the measured value by its uncertainty obtained in data from the $D^{*}$ calibration sample as described in Sec. III. The $D$ mass window and $M(\pi^{+}\pi^{-})$ for veto position have been varied and the resulting difference with respect to the measured branching fraction is taken as a systematic. The uncertainty due to the peaking background is obtained by varying its yield by the statistical uncertainty in its estimation. The uncertainty associated with the reconstruction efficiency is measured using signal MC data samples. We perform tests to validate the fit procedure and determine any possible bias in the fit procedure. The bias is not corrected and is used as a systematic uncertainty. The uncertainty due to the continuum suppression requirement is found to be negligible.

The ratio of branching fractions is found to be,

The total $D^{+}\pi^{-}$ yield from the simultaneous fit is used to determine the branching fraction of the $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ decay,

where the first uncertainty is statistical, the second is systematic, and the third is associated with $D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$ branching fraction. The branching fraction of $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ is calculated by multiplying Eq. (9) by Eq. (10),

The $\kappa$ value obtained from the fit is $(7.79\pm 0.21)\%$, which agrees within one standard deviations with the expected pion misidentification rate as given in Sec. III. In both measurements listed in Eqs. (10) and (11), one of the dominant sources of systematic uncertainty arises from the fixed PDF parametrization.

In summary, we have reported measurements of the branching fraction ratio between Cabibbo suppressed $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ and Cabibbo favored $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ using the full $\Upsilon(4S)$ data sample collected by the Belle experiment, which supersedes the previous Belle measurement cite-belleold . We also present a measurement of the branching fractions for $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ and $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ decays.The $\overline{B}{}^{0}\rightarrow D^{+}h^{-}(h=K/\pi)$ branching fraction and $R^{D}$ values are compatible with the corresponding world averages cite-PDG within their uncertainties. Individual branching fractions of $\overline{B}{}^{0}\rightarrow D^{+}\pi^{-}$ and $\overline{B}{}^{0}\rightarrow D^{+}K^{-}$ deviate from the theory predictions in Refs. cite-arXix1606.02888 ; cite-arXiv:2007.10338 , however, the ratio agrees within uncertainties.

We thank the KEKB group for the excellent operation of the accelerator; the KEK cryogenics group for the efficient operation of the solenoid; and the KEK computer group, and the Pacific Northwest National Laboratory (PNNL) Environmental Molecular Sciences Laboratory (EMSL) computing group for strong computing support; and the National Institute of Informatics, and Science Information NETwork 5 (SINET5) for valuable network support. We acknowledge support from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan, the Japan Society for the Promotion of Science (JSPS), and the Tau-Lepton Physics Research Center of Nagoya University; the Australian Research Council including Grants No. DP180102629, No. DP170102389, No. DP170102204, No. DP150103061, and No. FT130100303; Austrian Federal Ministry of Education, Science and Research (FWF) and FWF Austrian Science Fund No. P 31361-N36; the National Natural Science Foundation of China under Contracts No. 11435013, No. 11475187, No. 11521505, No. 11575017, No. 11675166, and No. 11705209; Key Research Program of Frontier Sciences, Chinese Academy of Sciences (CAS), Grant No. QYZDJ-SSW-SLH011; the CAS Center for Excellence in Particle Physics (CCEPP); the Shanghai Science and Technology Committee (STCSM) under Grant No. 19ZR1403000; the Ministry of Education, Youth and Sports of the Czech Republic under Contract No. LTT17020; Horizon 2020 ERC Advanced Grant No. 884719 and ERC Starting Grant No. 947006 “InterLeptons” (European Union); the Carl Zeiss Foundation, the Deutsche Forschungsgemeinschaft, the Excellence Cluster Universe, and the VolkswagenStiftung; the Department of Atomic Energy (Project Identification No. RTI 4002) and the Department of Science and Technology of India; the Istituto Nazionale di Fisica Nucleare of Italy; National Research Foundation (NRF) of Korea Grants No. 2016R1D1A1B01010135, No. 2016R1D1A1B02012900, No. 2018R1A2B3003643, No. 2018R1A6A1A06024970, No. 2019K1A3A7A09033840, No. 2019R1I1A3A01058933, No. 2021R1A6A1A03043957, No. 2021R1F1A1060423, No. 2021R1F1A1064008; Radiation Science Research Institute, Foreign Large-size Research Facility Application Supporting project, the Global Science Experimental Data Hub Center of the Korea Institute of Science and Technology Information and KREONET/GLORIAD; the Polish Ministry of Science and Higher Education and the National Science Center; the Ministry of Science and Higher Education of the Russian Federation, Agreement 14.W03.31.0026, and the HSE University Basic Research Program, Moscow; University of Tabuk research Grants No. S-1440-0321, No. S-0256-1438, and No. S-0280-1439 (Saudi Arabia); the Slovenian Research Agency Grants No. J1-9124 and No. P1-0135; Ikerbasque, Basque Foundation for Science, Spain; the Swiss National Science Foundation; the Ministry of Education and the Ministry of Science and Technology of Taiwan; and the United States Department of Energy and the National Science Foundation.