Belle II Research Articles

Towards heavy double-gluon hybrid mesons with exotic quantum numbers in QCD sum rules

The double-gluon hybrid meson configuration was recently proposed and investigated within QCD sum rules. In this talk, we discuss the color structures of the double-gluon hybrid meson and construct current operators with exotic quantum numbers JPC=1−+ and 2+− for two of the structures. In the framework of QCD sum rules, we consider the condensates up to dimension-8 at the leading order of αs for both charmonium and the bottomonium systems. The results indicate that the masses of the 1−+ and 2+− charmonium double-gluon hybrid mesons are approximately 6.1−7.2 GeV and 6.3−6.4 GeV, respectively. As for the bottomonium systems, their masses fall within the range of 13.7−14.3 GeV and 12.6−13.3 GeV for the 1−+ and 2+− channels, respectively. Additionally, the charmonium hybrids could be produced in the radiative decays of bottomonium mesons in BelleII experiment.

Purely leptonic decays of heavy-flavored charged mesons

We study the purely leptonic decays of heavy-flavored charged pseudoscalar (P) and vector (V) mesons (D(s)(*)+, B(c)(*)+) in the relativistic independent quark (RIQ) model based on an average flavor-independent confining potential in an equally mixed scalar-vector harmonic form. We first compute the mass spectra of the ground-state-mesons and fix the model parameters necessary for the present analysis. Using the meson wave functions derivable in the RIQ model, and model parameters so fixed from hadron spectroscopy, we predict the decay constants: fP(V), ratios of decay constants: fV/fP, fP1/fP2, fV1/fV2, and the branching fractions (BFs): B(P(V)→l+νl), l=e, μ, τ, which agree with the available experimental data and other Standard Model (SM) predictions. For the unmeasured decay constants, especially in the purely leptonic decays of the charged vector mesons, our predictions could be tested in the upcoming Belle-II, SCTF, CEPC, FCC-ee, and LHCb experiments in the near future. Published by the American Physical Society 2024

Semileptonic and nonleptonic decays of in the covariant light-front approach* *This study was partly supported by the National Natural Science Foundation of China (11347030), the Program for Science and Technology Innovation Talents in Universities of Henan Province (14HASTIT037), and the Natural Science Foundation of Henan Province, China (232300420116)

The semileptonic and nonleptonic decays of the b-flavor vector mesons and are investigated within the covariant light-front quark model (CLFQM). By calculating the form factors of the transitions under the CLFQM, with P denoting a pseudoscalar meson, i.e., , we predict and discuss several physical observables, including the branching ratios, polarization fractions , and forward-backward asymmetries . The total widths of the single-photon radiative decay channels for these b-flavor vector mesons are estimated using their partial widths. In these considered decays, one can find that the semileptonic decays and , with being e or , and the nonleptonic channels have the largest branching ratios, which can reach up to the 10-7 order, and are most likely to be accessible at the future high-luminosity LHCb and Belle-II experiments.

CP-violating observables of four-body B(s)→(ππ)(KK¯)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{(s)} \\rightarrow (\\pi \\pi )(K\\bar{K})$$\\end{document} decays in perturbative QCD

In this work, we investigate six helicity amplitudes of the four-body B(s)→(ππ)(KK¯)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{(s)} \\rightarrow (\\pi \\pi )(K\\bar{K})$$\\end{document} decays via an angular analysis in the perturbative QCD (PQCD) approach. The ππ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi \\pi $$\\end{document} invariant mass spectrum is dominated by the vector resonance ρ(770)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho (770)$$\\end{document} together with scalar resonance f0(980)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_0(980)$$\\end{document}, while the vector resonance ϕ(1020)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi (1020)$$\\end{document} and scalar resonance f0(980)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_0(980)$$\\end{document} are expected to contribute in the KK¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K\\bar{K}$$\\end{document} invariant mass range. We extract the two-body branching ratios B(B(s)→ρϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{B}(B_{(s)}\\rightarrow \\rho \\phi )$$\\end{document} from the corresponding four-body decays B(s)→ρϕ→(ππ)(KK¯)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{(s)}\\rightarrow \\rho \\phi \\rightarrow (\\pi \\pi )(K \\bar{K})$$\\end{document} based on the narrow width approximation. The predicted B(Bs0→ρϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{B}(B^0_{s}\\rightarrow \\rho \\phi )$$\\end{document} agrees well with the current experimental data within errors. The longitudinal polarization fractions of the B(s)→ρϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{(s)}\\rightarrow \\rho \\phi $$\\end{document} decays are found to be as large as 90%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$90\\%$$\\end{document}, basically consistent with the previous two-body predictions within uncertainties. In addition to the direct CP asymmetries, the triple-product asymmetries (TPAs) originating from the interference among various helicity amplitudes are also presented for the first time. Since the Bs0→ρ0ϕ→(π+π-)(K+K-)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_s^0\\rightarrow \\rho ^0\\phi \\rightarrow (\\pi ^+\\pi ^-)(K^+K^-)$$\\end{document} decay is induced by both tree and penguin operators, the values of the AdirCP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{A}^\ extrm{CP}_\ extrm{dir}$$\\end{document} and AT-true1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{A}^{1}_{\ ext {T-true}}$$\\end{document} are calculated to be (21.8-3.3+2.7)%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(21.8^{+2.7}_{-3.3})\\%$$\\end{document} and (-10.23-1.56+1.73)%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(-10.23^{+1.73}_{-1.56})\\%$$\\end{document} respectively. While for pure penguin decays B0→ρ0ϕ→(π+π-)(K+K-)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^0\\rightarrow \\rho ^0\\phi \\rightarrow (\\pi ^+\\pi ^-)(K^+K^-)$$\\end{document} and B+→ρ+ϕ→(π+π0)(K+K-)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^+\\rightarrow \\rho ^+\\phi \\rightarrow (\\pi ^+\\pi ^0)(K^+K^-)$$\\end{document}, both the direct CP asymmetries and “true” TPAs are naturally expected to be zero in the standard model (SM) due to the absence of the weak phase difference. The “fake” TPAs requiring no weak phase difference are usually none zero for all considered decay channels. The sizable “fake” AT-fake1=(-20.92-2.80+6.26)%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{A}^{1}_{\ ext {T-fake}}=(-20.92^{+6.26}_{-2.80})\\%$$\\end{document} of the B0→ρ0ϕ→(π+π-)(K+K-)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^0\\rightarrow \\rho ^0\\phi \\rightarrow (\\pi ^+\\pi ^-)(K^+K^-)$$\\end{document} decay is predicted in the PQCD approach, which provides valuable information on the final-state interactions. The above predictions can be tested by the future LHCb and Belle-II experiments.

Study of Bs→ϕ(ρ0,ω) decays in the standard model and a family nonuniversal Z′ model

Within the QCD factorization approach, we employ the new results of form factors of Bs→ϕ and calculate the branching fractions, CP asymmetries (CPAs) and polarization fractions of the decay modes Bs→ϕ(ρ0,ω) in both the standard model (SM) and the family nonuniversal Z′ model. We find that in SM the above observables are relate to two parameters, ρH and ϕH, which characterize the end-point divergence in the hard spectator-scattering amplitudes. When setting ρH=0.5 and ϕH∈[−180,180]°, the theoretical uncertainties are large. By combining the experimental data, our results can be used to constrain these two parameters. Supposing ρH=0, we study the effects of the Z′ boson on the concerned observables. With the available branching fraction of Bs→ϕρ0, the possible ranges of parameter spaces are obtained. Within the allowed parameter spaces, the branching fraction of Bs→ϕω can be enlarged remarkably. Furthermore, the new introduced weak phase plays important roles in significantly affecting the CPAs and polarization fractions, which are important observables for probing the effects of NP. If these decay modes were measured in the on-going LHC-b and Belle-II experiments in the future, the peculiar deviation from SM could provide a signal of the family nonuniversal Z′ model, which can also be used to constrain the mass of Z′ boson in turn. Published by the American Physical Society 2024

Revisit the heavy quarkonium double-gluon hybrid mesons with exotic quantum numbers

We revisit the masses of heavy quarkonium double-gluon hybrid mesons with exotic quantum numbers JPC = 1−+ and 2+− in the framework of the QCD sum rules. Considering the double-gluon hybrid meson operators in the octet-octet color structure, we have constructed two independent interpolating currents with JPC = 1−+ and five independent currents with JPC = 2+−. For the interpolating currents with antisymmetric glueball operator, there exist non-local divergences in one kind of additional Feynman diagrams of the tri-gluon condensate, which will give important contributions to the sum rule stabilities and mass predictions. We use the diagrammatic renormalization to cancel out such divergences. At the leading order of αs, the two-point correlation functions and spectral densities can be expressed in the analytic form of the generalized hypergeometric functions and Meijer’s G-functions. After performing the numerical analysis, we predict the masses of the 1−+ and 2+− charmonium double-gluon hybrid mesons to be around 6.1 − 7.2 GeV and 6.3 − 6.4 GeV, respectively. For the bottomonium systems, their masses are predicted to be 13.7 − 14.3 GeV and 12.6 − 13.3 GeV for the 1−+ and 2+− channels, respectively. Besides, it is possible to hunt for these charmonium hybrids in the radiative decays of bottomonium mesons in BelleII experiment. Further investigations on these hybrid states in various theoretical and phenomenological methods are also anticipated in the future.

0– – hidden-heavy tetraquark states via QCD sum rules* *Supported in part by the National Natural Science Foundation of China(12247113), the Project funded by China Postdoctoral Science Foundation (2022M723117), and the Specific Fund of Fundamental Scientific Research Operating Expenses for Undergraduate Universities in Liaoning Province, China (2024)

In this study, we evaluated the mass spectra of the prospective hidden-charm and hidden-bottom tetraquark states in molecular configuration via QCD sum rules. In our calculation, the nonperturbative condensate contributions are considered up to dimension eight in operator product expansion. It is found that there could exist 4 possible hidden-charm tetraquark states with masses , , , and GeV. Their corresponding hidden-bottom partners are found lying at , , , and GeV, respectively. The possible tetraquark decay modes were analyzed, which are expected to be measured in BESIII, BELLEII, and LHCb experiments.

Contributions of the subprocess K0*(1430)→Kη′ in the charmless three-body B meson decays

We study the contributions for Kη′ pair originating from the scalar intermediate state K0*(1430) in the three-body decays B→Kη′h (h=π, K) within the perturbative QCD approach. The contribution of K0*(1430)→Kη′ is described by the Flatté formula with coupled channels Kπ, Kη, and Kη′. The strong coupling constants gK0*Kη(′) are extracted from gK0*Kπ within flavor SU(3) symmetry. In spite of the strong depression by phase space near the threshold of Kη′, the CP averaged branching fractions for the B→K0*(1430)h→Kη′h decays are predicted to be on the order of 10−8 to 10−5, which are non-negligible for the corresponding three-body B decays. Since the Kη system is almost decoupled from the even-spin strange mesons under flavor SU(3) symmetry, those quasi-two-body B decays with subprocess K0*(1430)→Kη shall have quite small branching ratios and are not taken into account in this work. We also estimate that the branching fraction for K0*(1430)→Kη′ is about one fifth of that for K0*(1430)→Kπ. The predictions for the relevant decays are expected to be tested by the LHCb and Belle-II experiments in the future. Published by the American Physical Society 2024

Probing entanglement and testing Bell inequality violation with e+e−→τ+τ− at Belle II

We present a feasibility study to probe quantum entanglement and Bell inequality violation in the process e+e−→τ+τ− at a center-of-mass energy of s=10.579 GeV. The sensitivity of the analysis is enhanced by applying a selection on the scattering angle ϑ in the τ+τ− center-of-mass frame. We analyze events in which both τ leptons decay to hadrons, using a combination of decay channels τ−→π−ντ, τ−→π−π0ντ, and τ−→π−π+π−ντ. The spin orientation of the τ leptons in these decays is reconstructed using the polarimeter-vector method. Assuming a dataset of 200 million τ+τ− events and accounting for experimental resolutions, we expect the observation of quantum entanglement and Bell inequality violation by the Belle-II experiment will be possible with a significance well in excess of five standard deviations. Published by the American Physical Society 2024

The ρ(770, 1450) → ωπ contributions for three-body decays B→D¯∗ωπ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ B\ o {\\overline{D}}^{\\left(\\ast \\right)}\\omega \\pi $$\\end{document}

The decays B→D¯∗ωπ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ B\ o {\\overline{D}}^{\\left(\\ast \\right)}\\omega \\pi $$\\end{document} are very important for the investigation of ρ excitations and the test of factorization hypothesis for B meson decays. The B+→D¯∗0ωπ+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {B}^{+}\ o {\\overline{D}}^{\\left(\\ast \\right)0}\\omega {\\pi}^{+} $$\\end{document} and B0 → D(*)−ωπ+ have been measured by different collaborations but without any predictions for their observables on theoretical side. In this work, we study the contributions of ρ(770, 1450) → ωπ for the cascade decays B+→D¯∗0ρ+→D¯∗0ωπ+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {B}^{+}\ o {\\overline{D}}^{\\left(\\ast \\right)0}{\\rho}^{+}\ o {\\overline{D}}^{\\left(\\ast \\right)0}\\omega {\\pi}^{+} $$\\end{document}, B0 → D(*)−ρ+ → D(*)−ωπ+ and Bs0→Ds∗−ρ+→D∗−ωπ+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {B}_s^0\ o {D}_s^{\\left(\\ast \\right)-}{\\rho}^{+}\ o {D}^{\\left(\\ast \\right)-}\\omega {\\pi}^{+} $$\\end{document}. We introduce ρ(770, 1450) → ωπ subprocesses into the distribution amplitudes for ωπ system via the vector form factor Fωπ(s) and then predict the branching fractions for the first time for concerned quasi-two-body decays with ρ(770, 1450) → ωπ, as well as the corresponding longitudinal polarization fractions ΓL/Γ for the cases with the vector D¯∗0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\overline{D}}^{\\ast 0} $$\\end{document} or Ds∗−\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {D}_{(s)}^{\\ast -} $$\\end{document} in their final states. The branching fractions of these quasi-two-body decays are predicted at the order of 10−3, which can be detected at the LHCb and Belle-II experiments. The predictions for the decays B0 → D*−ρ(770)+ → D*−ωπ+ and B0 → D*−ρ(1450)+ → D*−ωπ+ agree well with the measurements from Belle Collaboration. In order to avoid the pollution from annihilation Feynman diagrams, we recommend to take the Bs0→Ds∗−ρ7701450+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {B}_s^0\ o {D}_s^{\\ast -}\\rho {\\left(770,1450\\right)}^{+} $$\\end{document} decays, which have only emission diagrams at quark level, to test the factorization hypothesis for B decays.

Study of four-body decays B(s)→(ππ)(ππ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{(s)} \\rightarrow (\\pi \\pi )(\\pi \\pi )$$\\end{document} in the perturbative QCD approach

In this work, we make a systematical study on the four-body B(s)→(ππ)(ππ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{(s)} \\rightarrow (\\pi \\pi )(\\pi \\pi )$$\\end{document} decays in the perturbative QCD (PQCD) approach, where the ππ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi \\pi $$\\end{document} invariant mass spectra are dominated by the vector resonance ρ(770)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho (770)$$\\end{document} and the scalar resonance f0(980)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_0(980)$$\\end{document}. We improve the Gengenbauer moments for the longitudinal P-wave two-pion distribution amplitudes (DAs) by fitting the PQCD factorization formulas to measured branching ratios of three-body and four-body B decays. With the fitted Gegenbauer moments, we make predictions for the branching ratios and direct CP asymmetries of four-body B(s)→(ππ)(ππ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{(s)} \\rightarrow (\\pi \\pi )(\\pi \\pi )$$\\end{document} decays. As a by-product, we extract the branching ratios of two-body B(s)→ρρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{(s)} \\rightarrow \\rho \\rho $$\\end{document} from the corresponding four-body decay modes and calculate the relevant polarization fractions. We find that the B(B0→ρ+ρ-)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{B}(B^0 \\rightarrow \\rho ^+\\rho ^-)$$\\end{document} is consistent with the previous theoretical predictions and data. The leading-order PQCD calculations of the B(B+→ρ+ρ0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{B}(B^+\\rightarrow \\rho ^+\\rho ^0)$$\\end{document}, B(B0→ρ0ρ0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{B}(B^0\\rightarrow \\rho ^0\\rho ^0)$$\\end{document} and the f0(B0→ρ0ρ0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_0(B^0\\rightarrow \\rho ^0\\rho ^0)$$\\end{document} are a bit lower than the experimental measurements, which should be further examined. It is shown that the direct CP asymmetries are large when both tree and penguin contributions are comparable to each other, but small for the tree-dominant or penguin-dominant processes. In addition to the direct CP asymmetries, the “true” and “fake” triple-product asymmetries (TPAs) originating from the interference among various helicity amplitudes in the B(s)→(ππ)(ππ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{(s)}\\rightarrow (\\pi \\pi )(\\pi \\pi )$$\\end{document} decays are also analyzed. The sizable averaged TPA AT-true1,ave=25.26%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{A}_{\ ext {T-true}}^{1, \ ext {ave}}=25.26\\%$$\\end{document} of the color-suppressed decay B0→ρ0ρ0→(π+π-)(π+π-)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^0\\rightarrow \\rho ^0\\rho ^0 \\rightarrow (\\pi ^+\\pi ^-)(\\pi ^+\\pi ^-)$$\\end{document} is predicted for the first time, which deviates a lot from the so-called “true” TPA AT-true1=7.92%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {A}_\ ext {T-true}^1=7.92\\%$$\\end{document} due to the large direct CP violation. A large “fake” TPA AT-fake1=24.96%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {A}_\ ext {T-fake}^1=24.96\\%$$\\end{document} of the decay B0→ρ0ρ0→(π+π-)(π+π-)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^0\\rightarrow \\rho ^0\\rho ^0 \\rightarrow (\\pi ^+\\pi ^-)(\\pi ^+\\pi ^-)$$\\end{document} is also found, which indicates the significance of the final-state interactions. The predictions in this work can be tested by LHCb and Belle-II experiments in the near future.

Mass predictions of triply heavy hybrid baryons via QCD sum rules

In this article, we study the mass spectrum of the low-lying triply heavy hybrid baryon, which consists of three valence heavy quarks in a color octet and one valence gluon, with spin-parity J^P=(frac{1}{2})^+ via QCD sum rules. This is the first study on the triply heavy hybrid baryons in the framework of QCD sum rules. After performing the QCD sum rule analysis, we find that the mass of cccg hybrid baryon lies in M_{cccg}= 5.91–6.13 GeV. As a byproduct, the mass of the triply bottom hybrid baryon state is extracted to be around M_{bbbg}= 14.62–14.82 GeV. The contributions up to dimension eight at the leading order of alpha _s (LO) in the operator product expansion are taken into account in the calculation. The triply charmed hybrid baryon predicted in this work can decay into one doubly charmed baryon and one charmed meson. Especially, we propose to search for cccg hybrid baryon with J^{P}= (1/2)^+ in the P-wave decay channels Xi _{cc}^{++} D^0, Xi _{cc}^{+} D^+, and Xi _{ccs}^{+} D_s^+, which may be accessible in future BelleII, Super-B, PANDA, and LHCb experiments.

Decay of the pseudoscalar glueball into vector, axial-vector, scalar and pseudoscalar mesons

We resume the investigation of the ground-state pseudoscalar glueball, J^{PC}=0^{-+}, by computing its two- and three-body decays into vector and axial-vector quark-antiquark meson fields additional to scalar and pseudoscalar mesons through the construction of an interaction chiral Lagrangian that produces these decays. We evaluate the branching ratio, via a parameter-free calculation, by setting the mass of the pseudoscalar glueball to 2.6 GeV as predicted by lattice QCD simulations. We duplicate the computation for the branching ratios for a pseudoscalar glueball mass 2.37 GeV which matches to the measured mass of the resonance X(2370) in the BESIII experiment. The present channels and states are potentially reached and are interesting for the running BESIII and Belle-II experiments and the planned PANDA experiment at FAIR/GSI which will be able to detect the pseudoscalar glueball within the accessible energy range.

The natures of recently observed states η1(1855) and X(2600)

We examine the tetraquark and trigluon glueball interpretations of the newly observed resonances η1(1855) and X(2600) by BESIII Collaboration, respectively. Our numerical results indicate that η1(1855) could be embedded into the [1c]s¯s⊗[1c]q¯q configuration and X(2600) is consistent with the mass of the 2−+ trigluon glueball. The possible decay channels of the correlative hadronic states are analyzed, which are crucial in decoding the internal structures of η1(1855) and X(2600), and are hopefully measurable in BESIII, BEllEII, PANDA, and LHCb experiments.

Phenomenological studies on neutral B-meson decays into J/psi f_1 and eta _c f_1

The axial-vector mesons f_1(1285) and f_1(1420) are particularly viewed as the mixtures of flavor states f_n and f_s with mixing angle varphi . In order to determine this angle, we study the B_{d,s}^0rightarrow J/psi f_1(1285,1420) and B_{d,s}^0rightarrow eta _c f_1(1285,1420) decays in perturbative QCD (PQCD) approach, including the effects of vertex corrections, nonfactorizable diagrams and penguin operators. Not only the branching fractions, but also the direct CP asymmetries and the polarization fractions are calculated. It is found that the branching fractions of these decays are large enough to be measured in the running LHCb and Belle-II experiments. Moreover, in comparison with the observed {mathcal {B}}(B_{d,s}^0 rightarrow J/psi f_1(1285)), B_s^0 rightarrow (J/psi , eta _c) f_1(1420) decays have large branching fractions, which could be measured promisingly through f_1(1420) rightarrow K_S^0 K^pm pi ^mp in experiments. We also propose several ratios that could be used to further constrain the absolute value of the mixing angle varphi , but its sign cannot be determined yet in these decays. The direct CP asymmetries of these decays indicate the penguin pollution in the B_d^0 rightarrow (J/psi , eta _c) f_1 decays cannot be neglected. We acknowledge that there are large theoretical uncertainties arising from the distribution amplitudes of axial-vector mesons and charmonium states, and more precise nonperturbative parameters are called. The comparisons between our results and future experimental data would help us to understand the nature of f_1 states and to test the PQCD approach.

Analysis of CKM-favored quasi-two-body B rightarrow D (Rrightarrow ) K pi decays in PQCD approach

LHCb Collaboration studied the resonant structure of B_srightarrow overline{D}^0K^-pi ^+ decays using the Dalitz plot analysis technique, based on a data sample corresponding to an integrated luminosity of 3.0textrm{fb}^{-1} of pp collision. The K^-pi ^+ components have been analyzed in the amplitude model, where the decay amplitude is modeled to be the resonant contributions with respect to the intermediate resonances K^*(892), K_0^*(1430) and K_2^*(1430). Motivated by the experimental results, we investigate the CKM-favored quasi-two-body B rightarrow overline{D}^0Kpi decays in the framework of the perturbative QCD (PQCD) approach. We calculate the the branching fractions by introducing the appropriate wave functions of Kpi pair. Our results are in agreement well the available data, and others can be tested in LHCb and Belle-II experiments. Using the narrow-width-approximation, we also extract the branching fractions of the corresponding two-body Brightarrow {overline{D}} R decays, which agree to the previous theoretical calculations and the experimental data within the errors. There are no CP asymmetries in these decays in the standard model, because these decays are all governed by only the tree operators.

Gluonic nature of the newly observed state X(2600)

Motivated by the newly observed resonance $X(2600)$ by BESIII Collaboration, we examine the trigluon glueball interpretation for it in the framework of QCD sum rules. We evaluate the mass spectra of the trigluon glueballs with quantum numbers $0^{-+}$ and $2^{-+}$ up to dimension 8 condensate in the operator product expansion. Our numerical results indicate that the mass of the $2^{-+}$ trigluon glueball is about $2.66\pm 0.06$ GeV, which is consistent with the mass of the X(2600) within the uncertainties, while $0^{-+}$ has a mass of $2.01\pm0.14$ GeV. The possible decay channels of the $2^{-+}$ state are analyzed, which are crucial in decoding $X(2600)$'s internal structure and are hopefully measurable in BESIII, BEllEII, PANDA, and LHCb experiments.

Belle II sensitivity to long–lived dark photons

In this letter we point out that the BelleII experiment has a unique sensitivity to visibly decaying long-lived dark photons. Concentrating on the signatures with a single high-energy photon in association with a displaced pair of charged particles, we find that BelleII will be able to probe large regions of parameter space that cannot be covered by any other running or proposed experimental facility. While the signature with charged muons or pions in the final state is expected to be background-free after all selections are applied, the case of final state electrons is more involved and requires an in-depth study. We discuss possible ways to further suppress backgrounds and the corresponding experimental prospects.

Resonances ρ(1450)+ and ρ(1700)+ in B → DKKdecays * *Supported by the National Natural Science Foundation of China (11947011), the Natural Science Foundation of Jiangsu Province (BK20191010) and the Scientific Research Foundation of Nanjing Institute of Technology (YKJ201854)

The contributions for the kaon pair from the intermediate states and in the decays , , and are analyzed within the perturbative QCD factorization approach. The decay amplitudes for all concerned decays in this work are dominated by the factorizable Feynman diagrams with the emission of the kaon pair, and the charged ρ mesons should be of great importance in the channel of the related three-body B decays. Moreover, these quasi-two-body decays are CKM-favored, and the relevant branching ratios are predicted to be in the order of , which have the potential to be measured by experiments. It is also shown that the contributions of the subprocesses for the three-body B meson decays are considerable according to the total three-body branching fractions presented by Belle. Therefore, the decays , , and can be employed to study the properties of and in the LHCb and Belle-II experiments.

Charmless Quasi-Two-Body B Decays in Perturbative QCD Approach: Taking B ⟶ K R ⟶ K + K − as Examples

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 ⟶ K R ⟶ 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 -wave functions of kaon-pair with different waves are introduced. By keeping the transverse momenta, all possible diagrams including the hard spectator diagrams and annihilation ones can be calculated in PQCD approach. Most results are well consistent with the current measurements from BaBar, Belle, and LHCb experiments. Moreover, under the narrow-width approximation, we can extract the branching fractions of the two-body decays involving the resonant states and also predict the branching fractions of the corresponding quasi-two-body decays B ⟶ K R ⟶ π + π − . All predictions are expected to be tested in the ongoing LHCb and Belle-II experiments.