Some years ago, a method was proposed for measuring the CP-violating phase gamma using pairs of two-body decays that are related by U-spin reflection (d <-> s). In this paper we adapt this method to charmless B -> PPP decays. Time-dependent Dalitz-plot analyses of these three-body decays are required for the measurement of the mixing-induced CP asymmetries. However, isobar analyses of the decay amplitudes are not necessary. A potential advantage of using three-body decays is that the effects of U-spin breaking may be reduced by averaging over the Dalitz plot. This can be tested independently using the measurements of direct CP asymmetries and branching ratios in three-body charged B decays.
In charmless B -> PPP decays, where P is a pseudoscalar meson, there are six possibilities for the symmetry of the final state. In this paper, for P=pi,K, we examine the properties of the fully-symmetric final state. We present expressions for all 32 B -> PPP decay amplitudes as a function of both SU(3) reduced matrix elements and diagrams, demonstrating the equivalence of diagrams and SU(3). We also give 25 relations among the amplitudes in the SU(3) limit, as well as those that appear when the diagrams E/A/PA are neglected. In the SU(3) limit, one has the equalities \sqrt{2} A(B+ -> K+ pi+ p…
Branching fractions and CP-violating asymmetries of charmless $B_s\to PPP$ decays with $P=K,π$ are studied using a simple model based on the factorization approach. The penguin-dominated modes $B_s\to \bar K^0 K^+π^-$ and $K^0K^-π^+$ have the largest rates among the three-body $B_s$ decays and they are dominated by the $K_0^*(1430)$ resonances and nonresonant contributions. The branching fraction of $B_s\to K^0K^+K^-$ is predicted to be $1.4\times 10^{-6}$, which is close to the high end of the measured result $(0.2-3.4)\times 10^{-6}$ obtained by LHCb. We find sizable CP violation in $K^0π^+π…
Utilizing all the experimental measured charmless $B \to PP$, $PV$ decay modes, where $P(V)$ denotes a light pseudoscalar (vector) meson, we extract the CKM angle $γ$ by global fit. All the unknown hadronic parameters are fitted with $γ$ together from experimental data, so as to make the approach least model dependent. The different contributions for various decay modes are classified by topological weak Feynman diagram amplitudes, which are to be determined by the global fit. To improve the precision of this approach, we consider flavor SU(3) breaking effects of topological diagram amplitudes…
In the past, it was believed that one cannot obtain clean weak-phase information from the measurement of CP-violating asymmetries in 3-body B decays. Recently it was shown that this is not true -- by expressing the decay amplitudes in terms of diagrams and using Dalitz plots, one can resolve all the difficulties and cleanly extract weak phases. In this talk I describe how this is done, and present preliminary results on the measurement of gamma using the decays B -> K pi pi and B -> K Kbar K.
The weak phase $γ$ is extracted from three-body charmless decays of $B$ mesons following a method proposed by Bhattacharya, Imbeault \& London. The result is obtained by combining the BABAR amplitude analyses for the processes $B^0 \rightarrow K^+ π^0 π^-$, $B^0 \rightarrow K_S^0 π^+ π^-$, $B^0 \rightarrow K_S^0 K_S^0 K_S^0$, $B^0 \rightarrow K^+ K_S^0 K^-$ and $B^+ \rightarrow K^+ π^+ π^-$, under the assumption of $α_{\rm{SU(3)}}$ flavour symmetry. Six possible solutions are found. One solution is compatible with the Standard Model while the others are not. It is also found that, when average…
The following is an overview of the current status of charmless semileptonic B decays and the extraction of the CKM matrix element $|V_{ub}|$ by the Belle and BaBaR collaborations.
We express the amplitudes for charmless three-body B decays in terms of diagrams. In addition, we show how to use Dalitz-plot analyses to obtain decay amplitudes which are symmetric or antisymmetric under the exchange of two of the final-state particles. When annihilation-type diagrams are neglected, as in two-body decays, many of the exact, purely isospin-based results are modified, leading to new tests of the standard model (SM). Some of the tests can be performed now, and we find that present data agree with the predictions of the SM. Furthermore, contrary to what was thought previously, it…
We study the charmless two-body decays of $B\to {\bf B}_n \overline{\bf B}_n^\prime$ with $B = ( B^+ , B^0 , B^0_s)$ and ${\bf B}_n^{(\prime)}$ the low-lying octet baryons. The factorizable amplitudes are calculated by the modified bag model, while the nonfactorizable ones are extracted from the experimental data with the $SU(3)_F$ flavor symmetry. We are able to explain all current experimental measurements and provide predictions on the decay branching ratios in $B\to {\bf B}_n \overline{\bf B}_n^\prime$. Particularly, we find that ${\cal B}(B_s^0 \to Ξ^0 \overlineΞ^0) = (19.3\pm 2.7 )\times…
Within the factorization-assisted topological-amplitude approach, we studied the 33 charmless $B_{(s)} \to VV$ decays, where $V$ stands for a light vector meson. According to the flavor flows, the amplitude of each process can be decomposed into 8 different topologies. In contrast to the conventional flavor diagrammatic approach, we further factorize each topological amplitude into decay constant, form factors and unknown universal parameters. By $χ^2$ fitting 46 experimental observables, we extracted 10 theoretical parameters with $χ^2$ per degree of freedom around 2. Using the fitted paramet…
Non-leptonic $B$ decays into charmless final states offer an important laboratory to study CP violation and the dynamics of strong interactions. Particularly interesting are $B^0_s\to K^-K^+$ and $B^0_d\toπ^-π^+$ decays, which are related by the $U$-spin symmetry of strong interactions, and allow for the extraction of CP-violating phases and tests of the Standard Model. The theoretical precision is limited by $U$-spin-breaking corrections and innovative methods are needed in view of the impressive future experimental precision expected in the era of Belle II and the LHCb upgrade. We have recen…
We discuss the determination of the CKM angle $α$ using the non-leptonic two-body decays $B\to ππ$, $B\to ρρ$ and $B\to ρπ$ using the latest data available. We illustrate the methods used in each case and extract the corresponding value of $α$. Combining all these elements, we obtain the following determination of $α_{\rm dir}=( 86.2^{+4.4}_{-4.0}~~ \cup~~ 178.4^{+3.9}_{-5.1})^\circ$. We assess the uncertainties associated to the breakdown of the isospin hypothesis and the choice of statistical framework in detail. We also determine the hadronic amplitudes (tree and penguin) describing the QCD…
With the experimental evidences of $\overline B {}^0\to p \overline{p}$ and $B^-\toΛ\overline p$ decays, it is now possible to extract both tree and penguin amplitudes of the charmless two-body baryonic $B$ decays for the first time. The extracted penguin-tree ratio agrees with the expectation. Using the topological amplitude approach with the experimental results on $\overline B {}^0\to p \overline{p}$ and $B^-\toΛ\bar p$ decay rates as input, predictions on all other $\overline B_q\to {\cal B} \overline {\cal B}$, ${\cal B} \overline {\cal D}$, ${\cal D} \overline {\cal B}$ and ${\cal D} \ov…
We analyze charmless two-body non-leptonic $B$ decays under the framework of factorization assisted topological amplitude approach. Unlike the conventional flavor diagram approach, we consider flavor $SU(3)$ breaking effect assisted by factorization hypothesis for topological diagram amplitudes of different decay modes, by factorizing out the corresponding decay constants and form factors. The non-perturbative parameters of topology diagram magnitudes $χ$ and strong phase $ϕ$ are universal that can be extracted by $χ^2$ fit from current abundant experimental data of charmless $B$ decays. The n…
We analyze charmless two-body non-leptonic B decays $B \to PP, PV$ under the framework of factorization assisted topological amplitude approach, where $P(V)$ denotes a light pseudoscalar (vector) meson. Compared with the conventional flavor diagram approach, we consider flavor $SU(3)$ breaking effect assisted by factorization hypothesis for topological diagram amplitudes of different decay modes, factorizing out the corresponding decay constants and form factors. The non-perturbative parameters of topology diagram magnitudes $χ$ and strong phase $ϕ$ are universal that can be extracted by $χ^2$…
Three-body $B$ decays not only significantly broaden the study of $B$ meson decay mechanisms, but also provide information of resonant particles. Because of complicate dynamics, it is very hard for us to study the whole phase space in a specific approach. In this review, we take $B\to K({\cal R}\to) K^+K^-$ decays as examples and show the application of the perturbative QCD (PQCD) approach in studying the quasi-two-body $B$ decays, where two particles move collinearly with large energy and the bachelor one recoils back. To describe the dynamics of two collinear particles, the ($S$, $P$ and $D$…
We study charmless two-body baryonic $B$ decays using the topological amplitude approach. We extend a previous work to include all ground state octet and decuplet final states with full topological amplitudes. Relations on rates and CP asymmetries are obtained. The number of independent topological amplitudes is significantly reduced in the large $m_B$ asymptotic limit. With the long awaited $\overline B{}^0\to p\bar p$ data, we can finally extract information on the topological amplitudes and predict rates of all other modes. The predicted rates are in general with uncertainties of a factor o…
To date, the weak-phase $γ$ has been measured using two-body $B$-meson decays such as $B\to D K$ and $B\to Dπ$, whose amplitudes contain only tree-level diagrams. But $γ$ can also be extracted from three-body charmless hadronic $B$ decays. Since the amplitudes for such decays contain both tree- and loop-level diagrams, $γ$ obtained in this way is sensitive to new physics that can enter into these loops. The comparison of the values of $γ$ extracted using tree-level and loop-level methods is therefore an excellent test for new physics. In this talk, we will show how U-spin and flavor-SU(3) symm…
We propose to study the multiparticle configurations of isovector scalar mesons, saying $a_0(980)$ and $a_0(1450)$, in the charmless three-body $B$ decays by considering the width effects. Two scenarios of $a_0$ configurations are assumed, in which the first one take $a_0(980)$ as the lowest-lying $q{\bar q}$ state and $a_0(1450)$ as the first radial excited state, the second one take $a_0(1450)$ as the lowest-lying $q{\bar q}$ state and $a_0(1950)$ as the first radial excited state while $a_0(980)$ is not a $q{\bar q}$ state. Within these two scenarios, we do the PQCD calculation for the quas…
We present $O(α_s^2)$ QCD corrections to the fully-differential decay rate of a $b$-quark into inclusive semileptonic charmless final states. Our calculation provides genuine two-loop QCD corrections, beyond the Brodsky-Lepage-Mackenzie (BLM) approximation, to any infra-red safe partonic observable that can be probed in $b \to X_u e \bar ν$ decays. Kinematic cuts that closely match those used in experiments can be fully accounted for. To illustrate these points, we compute the non-BLM corrections to moments of the hadronic invariant mass and the hadronic energy with cuts on the lepton energy a…
We present in this work a study of tree-dominated charmless three-body decays of $B$ mesons, $B^-\to K^+K^-π^-$ and $B^-\toπ^+π^-π^-$, within the factorization approach. The main results are: (i) There are two distinct sources of nonresonant contributions: one arises from the $b\to u$ tree transition and the other from the nonresonant matrix element of scalar densities $\langle M_1M_2|\bar q_1 q_2|0\rangle^{\rm NR}$. It turns out that even for tree-dominated three-body decays, dominant nonresonant contributions originate from the penguin diagram rather than from the $b\to u$ tree process, as i…
