Sum Rule Approach Research Articles

Heavy four-quark mesons [formula omitted]: Scalar particle

Parameters of the heavy four-quark scalar meson Tbcb‾c‾ with content bcb‾c‾ are calculated by means of the sum rule method. This structure is considered as a diquark-antidiquark state built of scalar diquark and antidiquark components. The mass and current coupling of Tbcb‾c‾ are evaluated in the context of the two-point sum rule approach. The full width of this tetraquark is estimated by taking into account two types of its possible strong decay channels. First class includes dissociation of Tbcb‾c‾ to mesons ηcηb, Bc+Bc−, Bc⁎+Bc⁎− and Bc+(13P0)Bc⁎−. Another type of processes are generated by annihilations b‾b→q‾q of constituent b-quarks which produces the final-state charmed meson pairs D+D−, D0D‾0, D⁎+D⁎−, and D⁎0D‾⁎0. Partial width all of these decays are found using the three-point sum rule method which is required to calculate strong couplings at corresponding meson-meson-tetraquark vertices. Predictions obtained for the mass m=(12697±90)MeV and width Γ[Tbcb‾c‾]=(142.4±16.9)MeV of this state are compared with alternative results, and are useful for further experimental investigations of fully heavy resonances.

Improved light-cone harmonic oscillator model for the ϕ -meson longitudinal leading-twist light-cone distribution amplitude and its effects to Ds+→ϕℓ+νℓ

In the present paper, we study the properties of ϕ-meson longitudinal leading-twist light-cone distribution amplitude ϕ2;ϕ∥(x,μ) by starting from a light-cone harmonic oscillator model for its wave function. To fix the input parameters, we derive the first ten order ξ moments of ϕ2;ϕ∥(x,μ) by using the QCD sum rules approach under the background field theory. The curves of ϕ2;ϕ∥(x,μ=2 GeV) tend to be a single-peak behavior, which is consistent with the latest lattice QCD result. To show how the twist-3 light-cone distribution amplitudes (LCDAs) affect the results, we consider two scenarios for the ϕ-meson chiral twist-3 LCDAs ϕ3;ϕ⊥(x) and ψ3;ϕ⊥(x), i.e., the ones using the Wandzura-Wilczek approximation with ϕ2;ϕ∥(x,μ) (S1) and the ones using self-consistent conformal expansion with second-order Gegenbauer moments a2;ϕ2 in this work (S2). As an application, we derive the Ds+→ϕ transition form factors (TFFs) by using the QCD light-cone sum rules. The TFFs at large recoil point for those two scenarios are given separately. As for the two TFF ratios γV and γ2, we obtain γV(S1)=1.755−0.005+0.008, γ2(S1)=0.852−0.133+0.135, γV(S2)=1.723−0.021+0.023, and γ2(S2)=0.785−0.104+0.100. After extrapolating those TFFs to the physically allowable region, we then obtain the transverse, longitudinal, and total decay widths for semileptonic decay Ds+→ϕℓ+νℓ. Then the branching fractions are B(S1)(Ds+→ϕe+νe)=(2.347−0.191+0.342)×10−3, B(S1)(Ds+→ϕμ+νμ)=(2.330−0.190+0.341)×10−3, B(S2)(Ds+→ϕe+νe)=(2.367−0.132+0.256)×10−3, and B(S2)(Ds+→ϕμ+νμ)=(2.349−0.132+0.255)×10−3, which show good agreement with the data issued by the BESIII, CLEO, and Collaborations. We finally calculate Ds+→ϕℓ+νℓ polarization and asymmetry parameters, which can be measured and tested in future experiments. Published by the American Physical Society 2024

Searching for |Vcd| through the exclusive decay [formula omitted] within QCD sum rules

In this paper, we carry out an investigation into the semileptonic decays Ds+→K0ℓ+νℓ with ℓ=(e,μ) by employing the QCD light-cone sum rules approach. The vector transition form factor (TFF) f+Ds+K0(q2) for Ds+→K0 decay is calculated while considering its next-to-leading order contribution. Subsequently, we briefly introduce the twist-2, 3 kaon distribution amplitudes, which are calculated by using QCD sum rules within the framework of the background field theory. At the large recoil point, the TFF has f+Ds+K0(0)=0.692−0.026+0.027. Then, we extrapolate f+Ds+K0(q2) to the whole physical q2-region via the simplified z(q2,t)-series expansion, and the behavior of TFF f+Ds+K0(q2) is exhibited in the numerical results part, including the theoretical and experimental predictions for comparison. In addition, we compute the differential branching fraction B(Ds+→K0ℓ+νℓ) with the electron and muon channels, which are expected to be B(Ds+→K0e+νe)=3.379−0.275+0.301×10−3 and B(Ds+→K0μ+νμ)=3.351−0.273+0.299×10−3 as well as contained other results for comparison. Our results show good agreement with the BESIII measurements and theoretical predictions. Furthermore, we present our prediction with respect to the CKM matrix element |Vcd| by using the B(Ds+→K0e+νe) result from BESIII Collaboration, yielding |Vcd|=0.221−0.010+0.008. Finally, we provide the ratio between Ds+→K0e+νe and Ds+→ηe+νe channels, i.e.RK0/ηe=0.144−0.020+0.028.

Parameters of the tensor tetraquark [formula omitted]

The mass and width of the tensor tetraquark T=bbc‾c‾ with spin-parity JP=2+ are calculated in the context of the QCD sum rule method. The tetraquark T is modeled as a diquark-antidiquark state built of components bTCγμb and c‾γνCc‾T with C being the charge conjugation matrix. The mass m=(12.795±0.095)GeV of the exotic tensor meson T is found by means of the two-point sum rule approach. Its full width Γ is evaluated by considering processes T→Bc−Bc−, Bc−Bc⁎−, and Bc⁎−Bc⁎−. Partial widths of these decays are computed by means of the three-point sum rule approach which is used to determine the strong couplings at relevant tetraquark-meson-meson vertices. Predictions obtained for the width ΓT=55.5−9.9+10.6MeV, as well as the mass of the tetraquark T can be useful in investigations of fully heavy four-quark mesons.

Probing the inverse moment of Bs-meson distribution amplitude via Bs→ ηs form factors

We investigate the inverse moment of the Bs-meson light-cone distribution amplitude (LCDA), denoted as λBs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\lambda}_{B_s} $$\\end{document} and defined within the heavy quark effective theory, through the calculation of Bs → ηs form factors. The presence of the s-quark inside the Bs-meson dictates a notable departure of approximately 20% in the λBs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\lambda}_{B_s} $$\\end{document} value compared to the non-strange case λBq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\lambda}_{B_q} $$\\end{document}, as computed within the QCD sum rule approach, albeit with significant uncertainty. First, we compute the decay constant of the ηs-meson utilizing two-point sum rules while retaining finite s-quark mass contributions. Next, we constrain the parameter λBs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\lambda}_{B_s} $$\\end{document} by calculating Bs → ηs form factors within the light-cone sum rule approach, using Bs-meson LCDAs, and leveraging Lattice QCD estimates at zero momentum transfer from the HPQCD collaboration. Our findings yield λBs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\lambda}_{B_s} $$\\end{document} = 480 ± 92 MeV when expressing the Bs-meson LCDAs in the Exponential model, consistent with previous QCD sum rule estimate yet exhibiting a 1.5-fold improvement in uncertainty. Furthermore, we compare the form factor predictions, based on the extracted λBs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\lambda}_{B_s} $$\\end{document} value, with earlier analyses for other channels such as Bs → Ds and Bs → K.

Superfluid excitations in rotating two-dimensional ring traps

We studied a rotating Bose–Einstein condensate confined in ring trap configurations that can be produced starting with a bubble trap confinement, approximated by a Mexican hat and shift harmonic oscillator potentials. Using a variational technique and perturbation theory, we determined the vortex configurations in this system by varying the interparticle interaction and the angular velocity of the atomic cloud. We found that the phase diagram of the system has macrovortex structures for small positive values of the interaction parameter, and the charge of the central vortex increases with rotation. Strengthening the atomic interaction makes the macrovortex unstable, and it decays into multiple singly charged vortices that arrange themselves in a lattice configuration. We also look for experimentally realizable methods to determine the vortex configuration without relying upon absorption imaging since the structures are not always visible in the latter. More specifically, we study how the vortex distribution affects the collective modes of the condensate by solving the Gross–Pitaevskii equation numerically and by analytical predictions using the sum-rule approach for the frequencies of the modes. These results reveal important signatures to characterize the macrovortices and vortex lattice transitions in the experiments.

Mass spectra of heavy hybrid quarkonia and [formula omitted] mesons

Masses and current couplings of the charmonium and bottomonium hybrids c‾gc and b‾gb with spin-parities JPC=0++,0+−,0−+,0−− and 1++,1+−,1−+,1−− are calculated using QCD two-point sum rule method. Computations are performed by taking into account gluon condensates up to dimension 12 including terms ∼〈gs3G3〉2. The parameters of the bottom-charm hybrids b‾gc with quantum numbers JPC=0+,0−,1+, and 1− are calculated as well. In computations the dominance of the pole contribution to sum rule results is ensured. It is demonstrated that all charmonia hybrids decay strongly to two-meson final states. The bottomonium hybrids 0−+ and 1−+ as well as the bottom-charm hybrid mesons 0−(+) and 1−(+) may be stable against strong two-meson decay modes. Results of the present work are compared with ones obtained using the sum rule and alternative approaches. Our predictions for parameters of the heavy hybrid mesons may be useful to study their various decay channels which are important for interpretation of ongoing and future experiments.

Non-factorisable contributions of strong-penguin operators in Λb→ Λℓ+ℓ− decays

We investigate for the first time a certain class of non-factorisable contributions of the four-quark operators O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}3−6 in the weak effective Hamiltonian to the Λb → Λℓ+ℓ− decay amplitude. We focus on the case where a virtual photon is radiated from one of the light constituents of the Λb baryon, in the kinematic situation of large hadronic recoil with an energetic Λ baryon in the final state. The effect on the suitably defined “non-local form factors” is calculated using the light-cone sum rule approach for a correlator with an interpolating current for the light Λ baryon. We find that this approach requires the introduction of new soft functions that generalise the standard light-cone distribution amplitudes (LCDAs) for the heavy Λb baryon. We give a heuristic discussion of their properties and a model that relates them to the standard LCDAs. Within this framework, we provide numerical results for the size of the non-local form factors considered.

ρ-meson longitudinal leading-twist distribution amplitude revisited and the D→ρ semileptonic decay* *Supported in part by the National Natural Science Foundation of China (12265009, 12265010, 12147102), the Project of Guizhou Provincial Department of Science and Technology (ZK[2021]024, ZK[2023]142), the Project of Guizhou Provincial Department of Education (KY[2021]030) and the Chongqing Graduate Research and Innovation Foundation (ydstd1912)

Motivated by our previous study [Phys. Rev. D 104(1), 016021 (2021)] on the pionic leading-twist distribution amplitude (DA), we revisit the ρ-meson leading-twist longitudinal DA in this study. A model proposed by Chang based on the Dyson-Schwinger equations is adopted to describe the behavior of . However, the ξ-moments of are calculated with the QCD sum rules in the framework of the background field theory. The sum rule formulas for these moments are improved. More accurate values for the first five nonzero ξ-moments at the typical scale are given, e.g., at , , , , , and . By fitting these values with the least squares method, the DSE model for is determined. By taking the left-handed current light-cone sum rule approach, we obtain the transition form factor in the large recoil region, i.e., , , and , and the ratio , . After extrapolating with a rapidly converging series based on -expansion, we present the -independent decay width for the semileptonic decays . Finally, the branching fractions are , , , and .

Constraining inverse moment of B-meson distribution amplitude using Lattice QCD data

We constrain the inverse moment of the B-meson light-cone distribution amplitude (LCDA), λB in heavy quark effective theory, using form factor estimates from Lattice QCD collaboration. The estimation of the parameter λB has, until now, relied solely on QCD sum rule methods and deals with significant uncertainty. In this work, we express the form factors for the B→K channel, calculated within the light-cone sum rule (LCSR) approach, in terms of the B-meson LCDAs. By incorporating recent Lattice results from the HPQCD collaboration for the B→K form factors at zero momentum transfer (q2 = 0), we impose constraints on this parameter. Consequently, we achieve a twofold reduction in uncertainty compared to the QCD sum rule estimate, yielding λB=338±68 MeV, when the B-meson LCDAs are expressed in the Exponential model. Additionally, we compare the form factor predictions, using the constrained λB value, with the earlier analyses for other channels as well, such as B→π and B→D.

Formula omitted] from QCD Laplace sum rule

We present a review of our recent works on heavy-light exotic states, with new compact integrated expressions of the spectral functions at lowest order (LO) of perturbative (PT) QCD and up to d=6 condensates of the Operator Product Expansion (OPE). Including higher order (HO) PT corrections, which we have estimated by assuming the factorization of the molecule/four-quark spectral functions, we evaluate masses and couplings with the Laplace sum rules (LSR) and finite energy (FESR) QCD spectral sum rules (QSSR) approaches. Our optimal results based on stability criteria are summarized and compared with experimental candidates and some LO QSSR results. We conclude that, our predicted spectra, do not confirm that the X(5568) is a pure molecule or a four-quark state. The masses of the XZ observed states are compatible with (almost) pure JPC=1+±,0++ molecule or/and four-quark states. The SU3 corrections on the meson masses are tiny: ≤10% (respectively ≤3%) for the c (respectively b)-quark channel but can be large for the couplings (≤20%). We expect that the resonance near the D−K+ threshold can be originated from the 0+(D−K+) molecule and/or D−K+ scattering. The X0(2900), XJ(3150) (if J = 0), X1(2900) and the XJ(3350) (if J = 1) can emerge from a minimal mixing model between tetramoles and first radial excitation. The Zc(3900,4025,4040,4430) and Zcs(3983) spectra are well reproduced by the molecules and tetramoles candidates, or radial excitation.

Resonance X(7300): excited 2S tetraquark or hadronic molecule χc1χc1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _{c1}\\chi _{c1}$$\\end{document}?

We explore the first radial excitation X4c∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_{\ extrm{4c}}^{*}$$\\end{document} of the fully charmed diquark-antidiquark state X4c=ccc¯c¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_{\ extrm{4c}}=cc{\\overline{c}}{\\overline{c}} $$\\end{document} built of axial-vector components, and the hadronic molecule M=χc1χc1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {M}} =\\chi _{c1}\\chi _{c1}$$\\end{document}. The masses and current couplings of these scalar states are calculated in the context of the QCD two-point sum rule approach. The full widths of X4c∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_{\ extrm{4c}}^{*}$$\\end{document} and M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {M}}$$\\end{document} are evaluated by taking into account their kinematically allowed decay channels. We find partial widths of these processes using the strong couplings gi∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_i^{*}$$\\end{document} and Gi(∗)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G_i^{(*)}$$\\end{document} at the X4c∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_{\ extrm{4c}}^{*}$$\\end{document}(M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {M}}$$\\end{document} )-conventional mesons vertices computed by means of the QCD three-point sum rule method. The predictions obtained for the parameters m=(7235±75)MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m=(7235 \\pm 75)~ \ extrm{MeV}$$\\end{document}, Γ=(144±18)MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma =(144 \\pm 18)~\ extrm{MeV}$$\\end{document} and m~=(7180±120)MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\widetilde{m}}=(7180 \\pm 120)~\ extrm{MeV}$$\\end{document}, Γ~=(169±21)MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\widetilde{\\Gamma }}=(169 \\pm 21)~\ extrm{MeV}$$\\end{document} of these structures, are compared with the experimental data of the CMS and ATLAS Collaborations. In accordance to these results, within existing errors of measurements and uncertainties of the theoretical calculations, both the excited tetraquark and hadronic molecule may be considered as candidates to the resonance X(7300). Detailed analysis, however, demonstrates that the preferable model for X(7300) is an admixture of the molecule M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {M}}$$\\end{document} and sizeable part of X4c∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_{\ extrm{4c}}^{*}$$\\end{document}.

Fully charmed resonance X(6900) and its beauty counterpart

The fully heavy scalar tetraquarks T4Q=QQQ‾Q‾, (Q=c,b) are explored in the context of QCD sum rule method. We model T4Q as diquark-antidiquark systems composed of pseudoscalar constituents, and calculate their masses m(′) and couplings f(′) within the two-point sum rule approach. Our results m=(6928±50)MeV and m′=(18858±50)MeV for masses of the tetraquarks T4c and T4b prove that they can decay to hidden-flavor heavy mesons. The full width Γ4c of the T4c is evaluated by taking into account the decay channels T4c→J/ψJ/ψ, J/ψψ′, ηcηc, ηcηc(2S), ηcχc1(1P), and χc0χc0. The partial widths of these processes depend on strong couplings gi at vertices T4cJ/ψJ/ψ, T4cJ/ψψ′ etc., which are computed using the QCD three-point sum rule method. The decay T4b→ηbηb is used to find the width Γ4b of the T4b. The predictions for m and Γ4c=(128±22)MeV are compared with parameters of the fully charmed resonances reported by the LHCb, ATLAS, and CMS Collaborations. Based on this analysis, we interpret the tetraquark T4c as a candidate to the resonance X(6900). The mass m′ and width Γ4b=(94±28)MeV of the exotic meson T4b can be used in future experimental investigations of these states.

Extractions of |Vub|/|Vcb| from a combined study of the exclusive bto u(c){ell}^{-}{overline{nu}}_{ell } decays

We have extracted the ratio |Vub|/|Vcb| from a combined study of the available inputs on overline{B}to left(pi, rho, omega right){ell}^{-}{overline{nu}}_{ell } and overline{B}left({overline{B}}_sright)to left({D}^{left(ast right)},{D}_s^{left(ast right)}right){ell}^{-}{overline{nu}}_{ell } left(ell =mu textrm{or} eright) decays. We have done our analysis with and without the inclusion of the available experimental results on the branching fraction mathcal{BR}left({overline{B}}_sto {K}^{+}{mu}^{-}{overline{nu}}_{mu}right) or the ratio of the rates Gamma left({overline{B}}_sto {K}^{+}{ell}^{-}{overline{nu}}_{ell}right)/Gamma left({overline{B}}_sto {D}_s^{+}{ell}^{-}{overline{nu}}_{ell}right) . We have used all the available experimental data on the branching fractions in different q2-bins, the available theory inputs on the form factors from lattice and the light cone sum rule (LCSR) approach; analysed the data in different possible scenarios and presented the results. From a combined analysis of all the b → cℓ−νℓ exclusive decays, we have obtained |Vcb| = (40.5 ± 0.6) × 10−3 and from all the b → uℓ−νℓ modes, we obtain |Vub| = (3.46 ± 0.12) × 10−3 which changes to |Vub| = (3.51 ± 0.13) × 10−3 after dropping mathcal{BR}left({overline{B}}_sto {K}^{+}{mu}^{-}{overline{nu}}_{mu}right) . We hence report the values of the ratio |Vub|/|Vcb| = 0.085 ± 0.003 and 0.087 ± 0.003 with and without the input from {overline{B}}_sto {K}^{+}{mu}^{-}{overline{nu}}_{mu } modes, respectively. We have also predicted the ratio Gamma left({overline{B}}_sto {K}^{+}{ell}^{-}{overline{nu}}_{ell}right)/Gamma left({overline{B}}_sto {D}_s^{+}{ell}^{-}{overline{nu}}_{ell}right) using the fit results. In addition, we provide the predictions of mathcal{BR}left({overline{B}}_sto {K}^{+}{mu}^{-}{overline{nu}}_{mu}right) and mathcal{BR}left(overline{B}to left(rho, omega right){ell}^{-}{overline{nu}}_{ell}right) in the Standard Model (SM) in small q2-bins.

Modeling the resonance Tcs0a(2900)++ as a hadronic molecule D*+K*+

The doubly charged scalar resonance $T_{cs0}^{a}(2900)^{++}$ is studied in the context of the hadronic molecule model. We consider $ T_{cs0}^{a}(2900)^{++}$ as a molecule $M=D^{\ast +}K^{\ast +}$ composed of vector mesons, and calculate its mass, current coupling and full width. The spectroscopic parameters of $M$, i.e., its mass and current coupling, are found by means of the QCD two-point sum rule method by taking into account vacuum expectation values of quark, gluon and mixed operators up to dimension $10$. The width of the molecule $M$ is evaluated through the calculations of the partial widths of the decay channels $M \to D_{s}^{+}\pi^{+}$, $M \to D_{s}^{\ast +}\rho^{+}$, and $M \to D^{\ast +}K^{\ast +}$. Partial widths of these processes are determined by strong couplings $g_1$, $g_2$, and $g_3$ of particles at vertices $ MD_{s}^{+}\pi^{+} $, $MD_{s}^{\ast +}\rho^{+}$, and $M D^{\ast +}K^{\ast +}$ , respectively. We calculate the couplings $g_i$ by employing the QCD light-cone sum rule approach and technical tools of the soft-meson approximation. Predictions obtained for the mass $m=(2924 \pm 107)~\mathrm{ MeV}$ and width $\Gamma=(123 \pm 25)~\mathrm{MeV}$ of the hadronic molecule $ M$ allow us to consider it as a possible candidate of the resonance $ T_{cs0}^{a}(2900)^{++}$.

A0(980)-meson twist-2 distribution amplitude within the QCD sum rules and investigation of D → a0(980)(→ηπ)e+νe

In this paper, moments of a0(980)-meson twist-2 light-cone distribution amplitudes were deeply researched by using QCD sum rules approach within background field theory. Up to 9th-order accuracy, we present 〈ξ2;a0n〉|μ0 at the initial scale μ0=1GeV, i.e. 〈ξ2;a01〉|μ0=−0.307(43), 〈ξ2;a03〉|μ0=−0.181(34), 〈ξ2;a05〉|μ0=−0.078(28), 〈ξ2;a07〉|μ0=−0.049(26), 〈ξ2;a09〉|μ0=−0.036(24), respectively. An improved light-cone harmonic oscillator model for a0(980)-meson twist-2 light-cone distribution amplitudes is adopted, where its parameters are fixed by using the least squares method based on the 〈ξ2;a0n〉|μ0, and their goodness of fit reach to 95.4%. Then, we calculate the D→a0(980) transition form factors within the light-cone sum rules approach, and at largest recoil point, we obtain f+D→a0(0)=1.058−0.035+0.068 and f−D→a0(0)=0.764−0.036+0.044. As a further application, the branching fractions of the D→a0(980)ℓν¯ℓ semileptonic decays are given. Taking the decay a0(980)→ηπ into consideration, we obtain B(D0→a0(980)−(→ηπ−)e+νe)=(1.330−0.134+0.216)×10−4, B(D+→a0(980)0(→ηπ0)e+νe)=(1.675−0.169+0.272)×10−4, which are consistent with the BESIII collaboration and PDG data within errors. Finally, we present the angle observables of forward-backward asymmetries, q2-differential flat terms and lepton polarization asymmetry of the semileptonic decay D→a0(980)ℓν¯ℓ.

Axial Collective Mode of a Dipolar Quantum Droplet

In this work, we investigate the ground state properties and collective excitations of a dipolar Bose–Einstein condensate that self-binds into a quantum droplet, stabilized by quantum fluctuations. We demonstrate that a sum rule approach can accurately determine the frequency of the low energy axial excitation, using properties of the droplet obtained from the ground state solutions. This excitation corresponds to an oscillation in the length of the filament-shaped droplet. Additionally, we evaluate the static polarizabilities, which quantify change in the droplet dimensions in response to a change in harmonic confinement.

Exotics from QCD Sum Rules

Many new exotic states in the charmonium mass region were discovered in the last decades by BaBar, Belle, CLEO-c, CDF, DØ, BESIII, LHCb and CMS Collaborations. We use the QCD Sum Rule approach to study some of these states.

Light-cone sum rule analysis of semileptonic decays varLambda _b^0 rightarrow varLambda _c^+ ell ^- {overline{nu }}_ell

In this work, we analyze the semileptonic decay processes of varLambda _b rightarrow varLambda _c in the light-cone sum rule approach. In order to calculate the form factors of the varLambda _b baryon transition matrix element, we use the light-cone distribution amplitudes of varLambda _b obtained from the QCD sum rule in the heavy quark effective field theory framework. With the calculation of the six form factors of the varLambda _b rightarrow varLambda _c transition matrix element, the differential decay widths of varLambda _b^0 rightarrow varLambda _c^+ ell ^- {overline{nu }}_ell (ell = e, ~mu , ~tau ) and their absolute branching fractions are obtained. Additionally, the ratio of R(varLambda _c^+) equiv {mathcal {B}}r(varLambda _b^0 rightarrow varLambda _c^+ tau ^- {overline{nu }}_tau )/{mathcal {B}}r(varLambda _b^0 rightarrow varLambda _c^+ mu ^- {overline{nu }}_mu ) is also obtained in this work. Our results are in accord with the newest experimental result and other theoretical calculations and predictions.

Dipole modes of a trapped bosonic mixture: Fate of the sum-rule approach

We present a general discussion of the dipole modes of a heteronuclear bosonic mixture in a harmonic trap by comparing the prediction of the sum-rule approach with full Gross-Pitaevskii (GP) calculations. Yet in the range of interaction in which the mixture is miscible and stable at the mean field level, $g_{12}^2<g_{11}g_{22}$, we find that there are regimes where the sum rules displays significant deviations from the GP solution. We provide an interpretation for this behavior in terms of the Ehrenfest approach, which we show to be equivalent to the sum-rule approach for dipole excitations.