Measurements of branching fractions and CP-violating charge asymmetries in charmless $B$ decays reconstructed in 2019–2020 Belle II data

The study of charmless $B$ decays is a keystone of the worldwide flavor program. Processes mediated by $b\to u\bar{u}d$ transitions offer direct access to the unitarity angle $\upphi_{2}/\upalpha$ and probe contributions of non-standard-model dynamics in loops. However, reliable extraction of weak phases and unambiguous interpretation of measurements involving loop amplitudes is spoiled by large hadronic uncertainties, which are rarely tractable in perturbative calculations. Appropriately chosen combinations of measurements from decay modes related by flavor symmetries are used to reduce the impact of such unknowns. An especially fruitful approach consists in combining measurements of decays related by isospin symmetries. For instance, the combined analysis of branching fractions and CP-violating asymmetries of the whole set of $B\to\pi\pi$ isospin partners (with $B$ and $\pi$ charged or neutral) enables a determination of $\upphi_{2}/\upalpha$ [1]. Similarly, isospin constraints between $B\to K\pi$ decays result in simple additive relationships between branching fractions and CP-violating asymmetries, which may offer a stringent null test of the standard model sensible to the presence of non-SM dynamics [2].

The Belle II physics program, featuring the unique capability of studying jointly, and within a consistent experimental environment, all relevant two-, three-, and multi-body final states is therefore particularly promising. This ability can enable significant advances, including an improved determination of the quark-mixing-matrix angle $\upphi_{2}/\upalpha$, a conclusive understanding of long-standing anomalies such as the so-called $K\pi$ CP-puzzle, and a thorough investigation of charge-parity-violating asymmetries localized in the phase space of three-body $B$ decays.

The Belle II detector, complete with its vertex detector, started its collision operations on March 11 2019 and continued until July 1, 2020. The sample of electron-positron collisions used in this work corresponds to an integrated luminosity of $34.6\,$\mathrm{f}\mathrm{b}^{-1}$$ [3] and was collected at the $\Upsilon(4{\rm S})$ resonance as of May 14, 2020. This document reports on the first measurement of branching fractions and CP-violating charge asymmetries in charmless decays at Belle II, which follows the first reconstruction of charmless $B$ decays in Belle II data [4, 5].

We focus on two- and three-body charmless decays with branching fractions of $10^{-6}$, or larger, into final states sufficiently simple to obtain visible signals in the current data set with a relatively straightforward reconstruction. The target decay modes are $B^{0}\to K^{+}\pi^{-}$, $B^{+}\to K^{+}\pi^{0}(\to\gamma\gamma)$, $B^{+}\to\mathit{{\mathit{{K}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}^{0}_{\rm S}(\to\pi^{+}\pi^{-})\pi^{+}$, $B^{0}\to\mathit{{\mathit{{K}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}^{0}_{\rm S}(\to\pi^{+}\pi^{-})\pi^{0}(\to\gamma\gamma)$, $B^{0}\to\pi^{+}\pi^{-}$, $B^{+}\to\pi^{+}\pi^{0}(\to\gamma\gamma)$, $B^{+}\to K^{+}K^{-}K^{+}$, and $B^{+}\to K^{+}\pi^{-}\pi^{+}$. Charge-conjugate processes are implied in what follows except when otherwise stated.

The reconstruction strategy and procedures are developed and finalized in simulated data. They are then applied and refined on a data subset corresponding to 1/4 of the sample prior to applying it to the full sample. Most of the analysis uses the following variables, which are known to be strongly discriminating between $B$ signal and background from $e^{+}e^{-}\to q\bar{q}$ continuum events, where $q$ indicates any quark of the first or second family (i.e., $u$, $d$, $s$, and $c$), and (in the case of $\Delta E$) background from non-signal $B$ decays:

• •

  the energy difference $\Delta E\equiv E^{*}_{B}-\sqrt{s}/2$ between the total energy of the reconstructed $B$ candidate and half of the collision energy, both in the $\Upsilon(4S)$ frame;

• •

  the beam-energy-constrained mass $M_{\rm bc}\equiv\sqrt{s/(4c^{4})-(p^{*}_{B}/c)^{2}}$, which is the invariant mass of the $B$ candidate where the $B$ energy is replaced by the (more precisely known) half of the center-of-mass collision energy.

Belle II is a $4\pi$ particle-physics spectrometer [6, 7], designed to reconstruct the products of electron-positron collisions produced by the SuperKEKB asymmetric-energy collider [8], located at the KEK laboratory in Tsukuba, Japan. Belle II comprises several subdetectors arranged around the interaction space-point in a cylindrical geometry. The innermost subdetector is the vertex detector, which uses position-sensitive silicon layers to sample the trajectories of charged particles (tracks) in the vicinity of the interaction region to extrapolate the decay positions of their long-lived parent particles. The vertex detector includes two inner layers of silicon pixel sensors and four outer layers of silicon microstrip sensors. The second pixel layer is currently incomplete and covers only a small portion of azimuthal angle. Charged-particle momenta and charges are measured by a large-radius, helium-ethane, small-cell central drift chamber, which also offers charged-particle-identification information through a measurement of particles’ energy-loss by specific ionization. A Cherenkov-light angle and time-of-propagation detector surrounding the chamber provides charged-particle identification in the central detector volume, supplemented by proximity-focusing, aerogel, ring-imaging Cherenkov detectors in the forward regions. A CsI(Tl)-crystal electromagnetic calorimeter allows for energy measurements of electrons and photons. A solenoid surrounding the calorimeter generates a uniform axial 1.5 T magnetic field filling its inner volume. Layers of plastic scintillator and resistive-plate chambers, interspersed between the magnetic flux-return iron plates, allow for identification of $K^{0}_{\rm L}$ and muons. The subdetectors most relevant for this work are the silicon vertex detector, the tracking drift chamber, the particle-identification detectors, and the electromagnetic calorimeter.

We reconstruct the two-body decays

• •

  $B^{0}\to K^{+}\,\pi^{-}$,

• •

  $B^{+}\to K^{+}\,\pi^{0}(\to\gamma\gamma)$,

• •

  $B^{+}\to K_{\rm S}^{0}(\to\pi^{+}\pi^{-})\,\pi^{+}$,

• •

  $B^{0}\to\mathit{{\mathit{{K}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}^{0}_{\rm S}(\to\pi^{+}\pi^{-})\pi^{0}(\to\gamma\gamma)$

• •

  $B^{0}\to\pi^{+}\,\pi^{-}$,

• •

  $B^{+}\to\pi^{+}\,\pi^{0}(\to\gamma\gamma)$,

and three-body decays

• •

  $B^{+}\to K^{+}\,K^{-}\,K^{+}$,

• •

  $B^{+}\to K^{+}\,\pi^{+}\,\pi^{-}$.

In addition, we use the control channels

• •

  $B^{+}\to\overline{D}^{0}(\to K^{+}\pi^{-}\pi^{0})\,\pi^{+}$,

• •

  $B^{+}\to\overline{D}^{0}(\to K^{+}\pi^{-})\,\pi^{+}$,

• •

  $B^{0}\to D^{*-}(\to\overline{D}^{0}(\to K^{+}\pi^{-}\pi^{0})\,\pi^{-})\,\pi^{+}$,

• •

  $B^{0}\to D^{*-}(\to\overline{D}^{0}(\to K^{+}\pi^{-})\,\pi^{-})\,\pi^{+}$,

• •

  $D^{+}\to\mathit{{\mathit{{K}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}^{0}_{\rm S}\pi^{+}$,

• •

  $\mathit{{\mathit{{D}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}^{0}\to K^{-}\pi^{+}$,

for validation of continuum-suppression discriminating variables; optimization of the $\pi^{0}$ selection; determination of $\pi^{0}$ selection efficiency; assessment of data-simulation discrepancies in the distributions of drift-chamber hits, particle-identification likelihoods, and continuum-background suppression variables; and determination of instrumental asymmetries.

For each channel, we optimize the selection to isolate abundant, low-background signals using simulated and control-sample data. We vary the selection criteria on continuum-suppression output, charged-particle identification information, and choice of $\pi^{0}$ (when appropriate) to maximize ${\rm S}/\sqrt{{\rm S}+{\rm B}}$, where ${\rm S}$ and ${\rm B}$ are signal and background yields, respectively, estimated in the same signal-rich region used in the analysis. Continuum-suppression and particle-identification requirements are optimized simultaneously using simulated data. The $\pi^{0}$ selection is optimized independently by using control $B^{+}\to\overline{D}^{0}(\to K^{+}\pi^{-}\pi^{0})\pi^{+}$ decays in which S is the $B^{+}\to\overline{D}^{0}(\to K^{+}\pi^{-}\pi^{0})\pi^{+}$ signal yield, scaled to the expected $B^{+}\to K^{+}\pi^{0}$ yield, and B is the background observed in an $M_{\rm bc}$ sideband of $B^{+}\to K^{+}\pi^{0}$.

More than one candidate per event populates the resulting $\Delta E$ distributions, with average multiplicities ranging from 1.0 to 1.2. We restrict to one candidate per event as follows. For channels with $\pi^{0}$, we first select the $\pi^{0}$ candidate with the highest $p$-value of the mass-constrained diphoton fit. If more than one candidate remains, and for all other channels, we select a single $B$ candidate randomly.

Signal yields are determined with maximum likelihood fits of the unbinned $\Delta E$ distributions of candidates restricted to the signal region $M_{\rm bc}>5.27$ GeV/$c^{2}$ and $-0.15<\Delta E<0.15$ GeV. Fit models are determined empirically from simulation, with the only additional flexibility of a global shift of peak positions determined in data when suggested by likelihood-ratio tests. Because of the small sample size, in fits of $B^{0}\to\mathit{{\mathit{{K}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}^{0}_{\rm S}\pi^{0}$ candidates the global shift is Gaussian-constrained to the value observed in $B^{+}\to K^{+}\pi^{0}$ candidates. Similarly, the $B^{+}\to K^{+}\pi^{0}$ and $B^{+}\to\pi^{+}\pi^{0}$ yields are determined through a simultaneous fit of two independent data sets.

We use the sum of a single or double Gaussian and a Crystal Ball model [13] for all signals and exponential or straight-line functions, with parameters determined in data, for continuum backgrounds. We model subleading charmless signals arising from misidentification of final-state particles, or $B\to DX$ signals escaping our vetoes with simplifications of the shapes used for signal (Gaussian, or a Gaussian plus Crystal Ball). The normalizations of such components are determined by the fit for misidentified final states or Gaussian-constrained from simulation otherwise. We use sums of Gaussian functions or kernel-density estimated models constrained from simulation for inclusive $B\bar{B}$ backgrounds. The $\Delta E$ distributions with fit projections overlaid are shown in Figs. 2–9. Prominent narrow signals are visible overlapping smooth backgrounds dominated by continuum. Final states including a $\pi^{0}$ show a low-$\Delta E$ tail, due to resolution effects in $\pi^{0}$ reconstruction. Subleading signals from kinematically similar misreconstructed decays are visible in the $B^{0}\to K^{+}\pi^{-}$, $B^{0}\to\pi^{+}\pi^{-}$, and $B^{+}\to K^{+}\pi^{-}\pi^{-}$ decays.

In addition, we use a nonextended likelihood to fit simultaneously the unbinned $\Delta E$ distributions of bottom and antibottom candidates decaying in flavor-specific final states for measurements of direct CP violation. We use the same signal and background models as used for branching-fraction measurements and use the raw partial-decay-rate asymmetry as a fit parameter,

where $N$ are signal yields and $b$ ($\bar{b}$) indicates the meson containing a bottom (antibottom) quark. Charge-specific $\Delta E$ distributions are shown in Figs. 10–15 with fit projections overlaid.

The raw event yields observed in data are corrected for selection and reconstruction effects to obtain physics quantities. For the measurements of branching fractions, we divide the observed yields by selection and reconstruction efficiencies. The efficiencies are determined from simulation and range between $22\%$ and $41\%$ with typical statistical uncertainties around $0.03\%$. For those factors of the efficiencies where simulation may not accurately model data, we perform dedicated checks on control samples of data and assess systematic uncertainties (see next section).
In measurements of CP-violating asymmetries, the observed charge-specific raw event yield asymmetries $\mathcal{A}$ are in general due to the combination of genuine CP-violating effects in the decay dynamics and instrumental asymmetries due to differences in interaction or reconstruction probabilities between opposite-charge hadrons. Such combination is additive for small asymmetries, $\mathcal{A}=\mathcal{A}_{\rm CP}+\mathcal{A}_{\rm det}$, with

where $X$ corresponds to a given final state and $\overline{X}$ to its charge-conjugate. Hence, observed raw charge-specific decay yields need be corrected for instrumental effects to determine the genuine CP-violating asymmetries. We estimate the instrumental asymmetry associated with the reconstruction of $K^{\pm}\pi^{\mp}$ pairs by measuring the charge-asymmetry in an abundant sample of $D^{0}\to K^{-}\pi^{+}$ decays. For these decays, direct CP violation is expected to be smaller than 0.1%, if any [12]. We therefore attribute any nonzero asymmetry to instrumental charge asymmetries. Figure 16 shows the $K^{\pm}\pi^{\mp}$-mass distributions for $D^{0}\to K^{-}\pi^{+}$ and $\overline{D}^{0}\to K^{+}\pi^{-}$ candidates with fit projections overlaid. The resulting $K^{\pm}\pi^{\mp}$ asymmetry is directly applied to the raw measurements of charge-dependent decay rates in $B^{0}\to K^{+}\pi^{-}$ to extract the physics asymmetry.
We correct the observed raw yield asymmetry of $B^{+}\to\mathit{{\mathit{{K}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}^{0}_{\rm S}\pi^{+}$ decays using the yield asymmetry observed in an abundant sample of $D^{+}\to\mathit{{\mathit{{K}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}^{0}_{\rm S}\pi^{+}$ decays (Fig. 17), in which direct CP violation in $D^{+}\to\mathit{{\mathit{{K}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}^{0}_{\rm S}\pi^{+}$ decays is expected to vanish. We correct the observed raw yield asymmetry of $B^{+}\to\pi^{+}\pi^{0}$ decays for possible $\pi^{+}/\pi^{-}$ reconstruction asymmetries by using the same sample of $D^{+}\to\mathit{{\mathit{{K}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}^{0}_{\rm S}\pi^{+}$ decays and subtracting the component $\mathcal{A}(\mathit{{\mathit{{K}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}^{0}_{\rm S})$ deriving from CP violation in neutral kaons, estimated by using the results obtained by the LHCb collaboration [14]. We finally estimate the instrumental asymmetry related to charged kaon reconstruction alone by combining all inputs in the relationship $\mathcal{A}_{\rm det}(K)=\mathcal{A}_{\rm det}(K\pi)-\mathcal{A}_{\rm det}(\mathit{{\mathit{{K}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}^{0}_{\rm S}\pi)+\mathcal{A}(\mathit{{\mathit{{K}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}}{}_{\mspace{-3mu}\scriptstyle{}}^{\mspace{-1mu}\scriptstyle{}}}^{0}_{\rm S})$. In each case, control channel selections are tuned to reproduce the kinematic conditions of the charmless final states that receive the corrections. Table 2 shows the resulting corrections.