Meson Pairs Research Articles

Tetraquarks from intrinsic heavy quarks

A number of new tetraquark candidate states containing from one to four charm or anticharm quarks have been observed recently. Many of these new states have been discovered at the LHC. The production of these states via intrinsic charm in the proton is investigated. The tetraquark masses obtained in this approach, while dependent on the internal transverse momenta of the partons in the state, are shown to agree well with the measured masses. These calculations can provide some insight into the nature of the tetraquark candidates, whether as a bound meson pair or as a looser configuration of four individual partons. The kinematic distributions of these states as a function of rapidity and transverse momentum are also studied. The possible cross sections for these states are finally considered, with a comparison to the X(3872) pT distributions from p+p collisions at s=13 TeV. Published by the American Physical Society 2024

Diabatic dynamical diquark bound states: Mass corrections and widths

Using the diabatic formalism, which generalizes the adiabatic approximation in the Born-Oppen-heimer formalism, we apply well-known Hamiltonian methods to calculate the effect of open di-meson thresholds that lie well below the mass of elementary cc¯qq¯′, cc¯ss¯, and cc¯qs¯ tetraquark bound states. We compute the resulting mass shifts for these states, as well as their decay widths to the corresponding meson pairs. Each mass eigenstate, originally produced using a bound-state approximation under the diabatic formalism, consists of an admixture of a compact diquark-antidiquark configuration (an eigenstate of the original dynamical diquark model) with an extended di-meson configuration induced by the nearest threshold. We compare our results with those from our recent work that employs a scattering formalism, and find a great deal of agreement, but also comment upon interesting discrepancies between the two approaches. Published by the American Physical Society 2024

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.

Charmonium χc0 and χc2 resonances in coupled-channel scattering from lattice QCD

In order to explore the spectrum of hidden-charm scalar and tensor resonances, we study meson-meson scattering with JPC=0++,2++ in the charmonium energy region using lattice QCD. Employing a light-quark mass corresponding to mπ≈391 MeV, we determine coupled-channel scattering amplitudes up to around 4100 MeV considering all kinematically relevant channels consisting of a pair of open-charm mesons or a charmonium meson with a light meson. A single isolated scalar resonance near 4000 MeV is found with large couplings to DD¯, DsD¯s and the kinematically closed D*D¯* channel. A single tensor resonance at a similar mass couples strongly to DD¯, DD¯* and D*D¯*. We compare the extracted resonances to contemporary experimental candidate states, previous lattice results and theoretical modeling. In contrast to several other studies, we do not find any significant feature in the scalar amplitudes between the ground state χc0(1P) and the resonance found around 4000 MeV. Published by the American Physical Society 2024

Scalar and Tensor Charmonium Resonances in Coupled-Channel Scattering from Lattice QCD

We determine JPC=0++ and 2++ hadron-hadron scattering amplitudes in the charmonium energy region up to 4100 MeV using lattice QCD, a first-principles approach to QCD. Working at mπ≈391 MeV, more than 200 finite-volume energy levels are computed and these are used in extensions of the Lüscher formalism to determine infinite-volume coupled-channel scattering amplitudes. We find that this energy region contains a single χc0 and a single χc2 resonance. Both are found as pole singularities on the closest unphysical Riemann sheet, just below 4000 MeV with widths around 70 MeV. The largest couplings are to kinematically closed D*D¯* channels in S-wave, and couplings to several decay channels consisting of pairs of open-charm mesons are found to be large and significant in both cases. Above the ground state χc0, no other scalar bound states or near-DD¯ threshold resonances are found, in contrast to several theoretical and experimental studies. Published by the American Physical Society 2024

NLO QCD corrections to the Bc -pair hadroproduction

The Bc meson pair, including pairs of pseudoscalar states and vector states, productions in proton-proton collisions are investigated at the next-to-leading order (NLO) accuracy in the nonrelativistic quantum chromodynamics factorization formalism. The corresponding cross sections at the Large Hadron Collider (LHC) with s=14 TeV are evaluated. Numerical results indicate that the NLO corrections are substantial, and even dominate over the leading order contributions. Considering the predicted cross sections are sizable, the Bc-pair production is expected to be observable at the high-luminosity LHC experiment. Published by the American Physical Society 2024

Exclusive production of double light neutral mesons at the e+e− colliders

In this work we investigate the exclusive production of a pair of light neutral mesons in e+e− annihilation, where the final state bears an even C-parity. The production processes can be initiated via the photon fragmentation or the nonfragmentation mechanism. While the fragmentation contribution can be rigorously accounted, the nonfragmentation contributions are calculated within the framework of collinear factorization, where only the leading-twist light-cone distribution amplitudes (LCDAs) of mesons are considered. Mediately solely by the nonfragmentation mechanism, the production rates of double light neutral pseudoscalar mesons are too small to be observed at the commissioning e+e− facilities. In contrast, the production rates of a pair of light neutral vector mesons are greatly amplified owing to the significant kinematic enhancement brought by the fragmentation mechanism. It is found that, at s=3.77 GeV, after including the destructive interference between the nonfragmentation and fragmentation contributions, the production rates for e+e−→ρ0ρ0 and ρ0ω can be lowered by about 10% and 30% relative to the fragmentation predictions. Future precise measurement of these exclusive double neutral vector meson production channels at BESIII experiment may provide useful constraints on the LCDAs of light vector mesons. Published by the American Physical Society 2024

Hidden-flavor four-quark states in the charm and bottom region

We discuss the spectrum and the internal composition of ground and excited four-quark states in the charm and bottom energy region. To this end we extend previous calculations within the framework of the relativistic four-body Faddeev-Yakubovsky equation to include quantum numbers with JPC=0++,0−+,1−−,1+− and 1++ and study their internal composition in terms of heavy-light meson pairs, hadroquarkonia and diquark-antidiquark clusters. We observe similar patterns in the charm and bottom energy region with different compositions of the four-quark states depending on JPC quantum numbers. Most notably, we find that all states with C·P=+1 are dominated by heavy-light meson contributions, whereas for axial-vector states with JPC=1+− including the Zc(3900) we find a much more complicated picture depending on the flavor content. We systematically compare our results for the spectrum with existing experimental results and provide predictions for future analyses. Published by the American Physical Society 2024

Dynamical generation of the scalar f0(500) , f0(980) , and K0*(700) resonances in the Ds+→K+π+π− reaction

We develop a model aimed at understanding the three mass distributions of pairs of mesons in the Cabibbo-suppressed Ds+→K+π+π− decay recently measured with high statistics by the BESIII collaboration. The largest contributions to the process come from the Ds+→K+ρ0 and Ds+→K*0π+ decay modes, but the Ds+→K0*(1430)π+ and Ds+→K+f0(1370) modes also play a moderate role and all of them are introduced empirically. Instead, the contribution of the f0(500), f0(980), and K0*(700) resonances is introduced dynamically by looking at the decay modes at the quark level, hadronizing qq¯ pairs to give two mesons, and allowing these mesons to interact, for which we follow the chiral unitary approach, to finally produce the K+π+π− final state. While the general features of the mass distributions are fairly obtained, we pay special attention to the specific effects created by the light scalar resonances, which are visible in the low mass region of the π+π−(f0(500)) and K+π−(K0*(700)) mass distributions and a narrow peak for π+π− distribution corresponding to f0(980) excitation. The contribution of these three resonances is generated by only one parameter. We see the agreement found in these regions as further support for the nature of the light scalar states as dynamically generated from the interaction of pseudoscalar mesons. Published by the American Physical Society 2024

First observation of Λc+→ΛK+π0 and evidence of Λc+→ΛK+π+π−

We present the first observation of the singly Cabibbo-suppressed decay Λc+→ΛK+π0 with a significance of 5.7σ and the first evidence of Λc+→ΛK+π+π− decay with a significance of 3.1σ, based on e+e− annihilation data recorded by the BESIII detector at the BEPCII collider. The data correspond to an integrated luminosity of 6.4 fb−1, in the center-of-mass energy range from 4.600 to 4.950 GeV. We determine the branching fractions of Λc+→ΛK+π0 and Λc+→ΛK+π+π− relative to their Cabibbo-favored counterparts to be B(Λc+→ΛK+π0)B(Λc+→Λπ+π0)=(2.09±0.39stat±0.07syst)×10−2 and B(Λc+→ΛK+π+π−)B(Λc+→Λπ+π+π−)=(1.13±0.41stat±0.06syst)×10−2, respectively. Moreover, by combining our measured result with the world average of B(Λc+→Λπ+π0), we obtain the branching fraction B(Λc+→ΛK+π0)=(1.49±0.27stat±0.05syst±0.08ref)×10−3. This result significantly departs from theoretical predictions based on quark SU(3) flavor symmetry, which is underpinned by the presumption of meson pair S-wave amplitude dominance. Published by the American Physical Society 2024

Why quarkonium hybrid coupling to two S -wave heavy-light mesons is not suppressed

We examine the couplings of quarkonium hybrids to heavy-light meson pairs in the Born-Oppenheimer approximation for QCD. The lowest hybrid multiplets consist of bound states of the Πu and Σu− potentials. We find that the Σu− potential can couple to pairs of S-wave mesons through string breaking, while the Πu potential cannot. From this observation, we derive model-independent selection rules that contradict previous expectations that quarkonium hybrids are forbidden to decay into pairs of S-wave mesons. These Born-Oppenheimer selection rules are consistent with the partial decay widths of the lowest charmonium hybrid with exotic quantum numbers JPC=1−+ recently calculated using lattice QCD. Published by the American Physical Society 2024

Charmed meson pair production in high‐energy pp$$ pp $$ collisions within the QCD color dipole approach

AbstractA study of double‐charmed meson production in high‐energy proton–proton collisions at the Large Hadron Collider is presented. Considering the color dipole formalism developed in the transverse momentum representation along with the double parton scattering mechanism, predictions are made for the transverse momentum differential cross section for different pairs of ‐mesons. The theoretical results cover the center‐of‐mass energy and forward rapidities available by the LHCb experiment. The proton–proton results considering different unintegrated gluon distributions are compared to the respective data collected at the LHC.

Decays of fully beauty scalar tetraquarks to BqB¯q and Bq*B¯q* mesons

Decays of the fully beauty four-quark structures X4b and T4b to B meson pairs are investigated in the framework of the QCD three-point sum rule method. We model the scalar exotic mesons X4b and T4b as diquark-antidiquark systems composed of the axial-vector and pseudoscalar diquarks, respectively. The masses m=(18540±50) MeV and m˜=(18858±50) MeV of these compounds calculated in our previous articles fix possible decay channels of these particles. In the present work, we consider their decays to BqB¯q and Bq*B¯q* (q=u, d, s, c) mesons. In the case of X4b, the mass of which is below the 2ηb threshold, these channels determine essential part of its full width Γ4b. The tetraquark T4b can decay to the pair ηbηb; therefore, partial widths of processes with B(B*) mesons in the final state permit us to refine our estimate for the full width of this particle. The predictions Γ4b=(9.6±1.1) MeV and Γ˜4bFull=(144±29) MeV obtained in this article can be used in future experimental investigations of four b-quark mesons. Published by the American Physical Society 2024

Measurement of branching fractions and direct CP asymmetries for B→Kπ and B→ππ decays at Belle II

We report measurements of the branching fractions and direct CP asymmetries of the decays B0→K+π−, B+→K+π0, B+→K0π+, and B0→K0π0, and use these for testing the standard model through an isospin-based sum rule. In addition, we measure the branching fraction and direct CP asymmetry of the decay B+→π+π0 and the branching fraction of the decay B0→π+π−. The data are collected with the elle II detector from e+e− collisions at the ϒ(4S) resonance produced by the SuperKEKB asymmetric-energy collider and contain 387×106 bottom-antibottom meson pairs. Signal yields are determined in two-dimensional fits to background-discriminating variables, and range from 500 to 3900 decays, depending on the channel. We obtain −0.03±0.13±0.04 for the sum rule in agreement with the standard model expectation of zero and with a precision comparable to the best existing determinations. Published by the American Physical Society 2024

Theoretical interpretation of the Ξ(1620)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi (1620)$$\\end{document} and Ξ(1690)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi (1690)$$\\end{document} resonances seen in Ξc+→Ξ-π+π+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi _c^+ \\rightarrow \\Xi ^- \\pi ^+ \\pi ^+$$\\end{document} decay

We study the Belle reaction Ξc+→Ξ-π+π+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi _c^+ \\rightarrow \\Xi ^- \\pi ^+ \\pi ^+$$\\end{document} looking at the mass distribution of π+Ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi ^+ \\Xi $$\\end{document}, where clear signals for the Ξ(1620)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi (1620)$$\\end{document} and Ξ(1690)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi (1690)$$\\end{document} resonances are seen. These two resonances are generated dynamically from the interaction in coupled channels of πΞ,K¯Λ,K¯Σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi \\Xi , {\\bar{K}} \\Lambda , {\\bar{K}} \\Sigma $$\\end{document} and ηΞ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta \\Xi $$\\end{document} within the chiral unitary approach. Yet, the weak decay process at the quark level, together with the hadronization to produce pairs of mesons, does not produce the ππΞ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi \\pi \\Xi $$\\end{document} final state. In order to produce this state one must make transitions from the K¯Λ,K¯Σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\bar{K}} \\Lambda , {\\bar{K}} \\Sigma $$\\end{document} and ηΞ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta \\Xi $$\\end{document} components to πΞ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi \\Xi $$\\end{document}, and this interaction is what produces the resonances. So, the reaction offers a good test for the molecular picture of these resonances. Adding the contribution of the Ξ∗(1530)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi ^*(1530)$$\\end{document} and some background we are able to get a good reproduction of the mass distribution showing the signatures of the two resonances as found in the experiment.

Heavy-quark spin symmetry breaking in the Born-Oppenheimer approximation

Heavy-quark spin symmetry is explicitly broken by the mass splitting between a heavy-light pseudoscalar meson and its vector partner. This fact plays a pivotal role in the physics of states whose mass lies close to the threshold of an open-flavor meson pair, like X(3872). We show that this source of heavy-quark spin symmetry breaking can be systematically included within the diabatic representation of the Born-Oppenheimer approximation. We verify that including all the appropriate coupled channels guarantees conservation of total angular momentum, parity, and charge-conjugation parity. This marks a fundamental step towards a unified, first-principles study of quarkonia and meson molecules with hidden flavor.

Quantum oscillons may be long-lived

Hertzberg has constructed a quantum oscillon that decays into pairs of relativistic mesons with a power much greater than the radiation from classical oscillon decay. This result is often construed as a proof that quantum oscillons decay quickly, and so are inconsequential. We apply a construction similar to Hertzberg’s to the quantum kink. Again it leads to a rapid decay via the emission of relativistic mesons. However, we find that this is the decay of a squeezed kink state to a stable kink state, and so it does not imply that the quantum kink is unstable. We then consider a time-dependent solution, which may be an oscillon, and we see that the argument proceeds identically.

Kinematical higher-twist corrections in γ*→M1M2γ : Neutral meson production

We carry out the calculation of kinematical higher-twist corrections to the cross section of $\gamma^* \to M_1 M_2 \gamma$ up to twist 4, where $M_i$ is a scalar or pseudoscalar neutral meson. The three independant helicity amplitudes are presented in terms of the twist-2 generalized distribution amplitudes (GDAs), which are important non-perturbative quantities for understanding the 3D structure of hadrons. Since this process can be measured by BESIII in $e^+ e^-$ collisions, we perform the numerical estimate of the kinematical higher-twist corrections by using the kinematics of BESIII. We adopt the $\pi \pi$ GDA extracted from Belle measurements and the asymptotic $\pi \pi$ GDA to study the size of the kinematical corrections in the case of pion meson pair, and a model $\eta \eta$ GDA is used to see the impact of target mass corrections $\mathcal O(m^2/s)$ for $\gamma^* \to \eta \eta \gamma$. Our results show that the kinematical higher-twist corrections account for $\sim 20\%$ of the cross sections at BESIII on the average, and it is necessary to include them if one tries to extract GDAs from experimental measurements precisely. We also comment the case of $\pi^0 \eta$ production which is important for the search of hybrid mesons.

Exclusive photoproduction of B_{c}^{pm } and bottomonia pairs

In this paper we analyze the photoproduction of heavy quarkonia pairs which include b-quarks, such as B_{c}^{+}B_{c}^{-}-mesons or charmonium-bottomonium pairs. Compared to charmonia pair production, these channels get contributions only from some subsets of diagrams, and thus allow for a better theoretical understanding of different production mechanisms. In contrast to the production of hidden-flavor quarkonia, for the production of B_{c}-meson pairs there are no restrictions on internal quantum numbers in the suggested mechanisms. Using the Color Glass Condensate approach, we estimated numerically the production cross-sections in the kinematics of the future electron–hadron colliders and the ultraperipheral collisions at LHC. We found that the production of J/psi ,eta _{c} and B_{c}^{+}B_{c}^{-} meson pairs are the most promising channels for studies of quarkonia pair production.

X(3872) , X(4014) , and their bottom partners at finite temperature

The properties of the $X(3872)$ and its spin partner, the $X(4014)$, are studied both in vacuum and at finite temperature. Using an effective hadron theory based on the hidden-gauge Lagrangian, the $X(3872)$ is dynamically generated from the $s$-wave rescattering of a pair of pseudoscalar and vector charm mesons. By incorporating the thermal spectral functions of open charm mesons, the calculation is extended to finite temperature. Similarly, the properties of the $X(4014)$ are obtained out of the scattering of charm vector mesons. By applying heavy-quark flavor symmetry, the properties of their bottom counterparts in the axial-vector and tensor channels are also predicted. All the dynamically generated states show a decreasing mass and acquire an increasing decay width with temperature, following the trend observed in their meson constituents. These results are relevant in relativistic heavy-ion collisions at high energies, in analyses of the collective medium formed after hadronization or in femtoscopic studies, and can be tested in lattice-QCD calculations exploring the melting of heavy mesons at finite temperature.