12th Workshop on the CKM Unitarity Triangle
Santiago de Compostela, 18-22 September 2023
CP violation measurements in three-body charmless B decays

The decays of heavy mesons into three-body can be comprehended by considering a combination of intermediate states featuring resonances. Within this framework, the CP-integrated asymmetries ($A_{CP}$) observed in charmless three-body decays of B mesons are the sum of asymmetries associated with each intermediate state, weighted by their respective fractions. This study investigates CP violation in four charmless B meson decays involving three charged pseudoscalar particles: $B^{\pm}\rightarrow K^{\pm}\pi^{+}\pi^{-}$, $B^{\pm}\rightarrow K^{\pm}K^{+}K^{-}$, $B^{\pm}\rightarrow\pi^{\pm}K^{+}K^{-}$, and $B^{\pm}\rightarrow\pi^{\pm}\pi^{+}\pi^{-}$. The analysis focuses on measuring phase-space integrated CP asymmetries and asymmetries within specific regions of the Dalitz plots. To take into account the production asymmetries of the B mesons, the decay $B^{\pm}\rightarrow J/\psi(\rightarrow\mu^{+}\mu^{-})K^{\pm}$ is employed as a control channel.

The yield and raw asymmetry of each decay are derived through simultaneous unbinned extended maximum likelihood fits to the $B^{\pm}$ invariant mass distributions, as shown in Fig. 1. Signal components within each of the four channels are modeled by a combination of a Gaussian and two Crystal Ball functions, sharing a common mean. Combinatorial backgrounds are parametrized by an exponential function. Backgrounds arising from partially reconstructed four-body B decays are represented by the ARGUS function [3] convolved with a Gaussian resolution function. Simulated event samples are used to model detector efficiency effects. The resultant signal yields and raw asymmetries ($A_{raw}$) are outlined in Table 1.

This study investigates quasi-two-body B meson decays into PV (pseudoescalar and vector) final states, leading to three-body configurations arising from the subsequent decays of the vector meson.

A novel approach, independent of a full amplitude analysis, is employed. The method is based on three key features of three-body B decays [2]: the large phase space; the dominance of scalar and vector resonances with masses below or around 1 GeV/$c^{2}$; and the signatures of the resonant amplitudes in the Dalitz plot.

Usually, the decay amplitudes of $B^{\pm}$ are represented as a coherent sum of intermediate amplitudes, where the magnitude and phase of each amplitude are adjustable parameters. When a single vector resonance interferes with a scalar component, the decay amplitudes can be expressed as $\mathcal{M}_{\pm}=a_{\pm}^{V}e^{i\delta^{V}_{\pm}}F_{V}^{BW}cos\theta(s_{\perp},s_{\parallel})+a_{\pm}^{S}e^{i\delta^{S}_{\pm}}F_{S}^{BW}$. The Matrix element squared is:

Given that the decay rates are proportional to $|\mathcal{M}_{\pm}|^{2}$, the CP asymmetry $A_{CP}^{V}$ in $B\rightarrow PV$ is given as function of $p_{2}^{\pm}$:

Given the approximation $cos\theta(s_{\parallel},s_{\perp})\approx cos\theta(m^{2}_{V},s_{\perp})$, $cos\theta$ becomes a linear function of $s_{\perp}$ [5], with this approximation the CP asymmetry can be obtained from the distribution of $s_{\perp}$. The function on Eq. 2.3 is used to fit the histograms of data projected onto $s_{\perp}$ axes in order to determine the $p_{0,1,2}^{\pm}$ and then calculate the $A_{CP}^{V}$.

The efficiency-corrected yields of $B^{\pm}$ as a function of $s_{\perp}$ can be seen in Fig. 3, with the results of the polynomial function from Eq. 2.3. The impact of a CP conservation is evident in almost all of the plots, where the vector parabolas of $B^{+}$ and $B^{-}$ are very close. The $B^{\pm}\rightarrow\rho(770)^{0}K^{\pm}$ channel stands out from the others as the only one which shows a significant CP asymmetry, measured to be $A_{CP}=+0.150\pm 0.019$ with a statistical-only significance of 7.9 standard deviations. For the other channels, the results are: $A_{CP}(\rho(770)^{0}\pi^{\pm})=-0.004\pm 0.017$, $A_{CP}(K^{*}(892)^{0}\pi^{\pm})=-0.015\pm 0.021$, $A_{CP}(K^{*}(892)^{0}K^{\pm})=0.007\pm 0.054$, $A_{CP}(\phi(1020)K^{\pm})=0.004\pm 0.014$.

Two interesting analyses are presented in this document. The first one showed the inclusive CP asymmetries of the $B^{\pm}\rightarrow K^{\pm}\pi^{+}\pi^{-}$, $B^{\pm}\rightarrow\pi^{\pm}K^{+}K^{-}$, $B^{\pm}\rightarrow K^{\pm}K^{+}K^{-}$, and $B^{\pm}\rightarrow\pi^{\pm}\pi^{+}\pi^{-}$ charmless three-body decays. Significant CP asymmetries were found for the latter three B decay channels, the last two being observed for the first time. The localized CP asymmetry observed in specific regions of the phase space indicates that CP asymmetries are unevenly distributed within it, with both positive and negative $A_{CP}$ values present in the same charged B decay channel.

The second analysis employs a novel method to measure CP asymmetries in charmless $B\rightarrow PV$ decays, without the need for amplitude analyses, considering two-body interaction with one spectator meson. It assumes constant magnitudes and phases of amplitudes across the entire phase space, a common assumption in amplitude analyses, supported by the quality of the fits. Five decays are studied and for the $B^{\pm}\rightarrow\rho(770)^{0}K^{\pm}$ the CP asymmetry obtained is $A_{CP}=+0.150\pm 0.019\pm 0.011$. For the remaining channels, the observed CP asymmetries are compatible with zero.