Hadronic Molecules Research Articles

Isospin violation effect and three-body decays of the Tcc+ state

In this work, we make a study of the Tcc+ state observed by the LHCb collaboration in 2021. In obtaining the effective potentials using the one-boson-exchange potential model we use an exponential form factor and find that, in the short and medium range, the contributions of the π, ρ, and ω exchanges are comparable while in the long range the pion-exchange contribution is dominant. Based on the assumption that Tcc+ is a loosely bound state of D*D, we focus on its three-body decay using the meson-exchange method. Considering that the difference between the thresholds of D*+D0 and D*0D+ is even larger than the binding energy of Tcc+, the isospin-breaking effect is amplified by the small binding energy of Tcc+. Explicitly including such an isospin-breaking effect we obtain, by solving the Schrödinger equation, that the probability of the isoscalar component is about 91% while that of the isovector component is around 9% for Tcc+. Using the experimental value of the mass of Tcc+ as an input, we obtain the wave function of Tcc+ and further obtain its width via the three-body hadronic as well as the radiative decays. The total width we obtain is in agreement with the experimental value of the LHCb measurement with a unitarized Breit-Wigner profile. Conversely, the current results support the conclusion that Tcc+ is a hadronic molecule of D*D. Published by the American Physical Society 2024

Pole structure of Pψ N(4312)+ via machine learning and uniformized S-matrix

Abstract We probed the pole structure of the Pψ N(4312)+ using a trained deep neural network. The training dataset was generated using uniformized independent S-matrix poles to ensure that the resulting interpretation is as model-independent as possible. To prevent possible ambiguity in the interpretation of the pole structure, we included the contribution from the off-diagonal elements of the S-matrix. Our trained model favors a possible three-pole structure of Pψ N(4312)+ signal, with one pole on each of the unphysical sheets. The two poles on two different Riemann sheets can be associated with a pole-shadow pair which is a characteristic of a true resonance. On the other hand, the last isolated pole is most likely associated with the coupled-channel effect in the meson-baryon system. The combined effect of these poles produced a peak below the ΣcD threshold which mimics the line shape of a hadronic molecule.

Analysis of DD* and D¯(*)Ξcc(*) molecule by one boson exchange model based on heavy quark symmetry

Numerous exotic hadrons with heavy quarks have been reported in the experiments. In such states, symmetries of heavy quarks are considered to play a significant role. In particular, the superflavor symmetry, or also called the heavy quark antidiquark symmetry is one of the interesting symmetries, which links a quark Q to an antidiquark Q¯Q¯ having the same color representation as Q. In this paper, we study a D¯Ξcc molecular state as a superflavor partner of the doubly charmed tetraquark Tcc reported by LHCb recently. Tcc locating slightly below the DD* threshold is a candidate of the hadronic molecule. Thus by replacing the singly charmed meson D(*) with the doubly charmed baryon Ξcc(*), superflavor symmetry predicts the existence of the D¯(*)Ξcc(*) bound state. We employ the one boson exchange model respecting with the heavy quark spin symmetry where the parameter is obtained to reproduce the Tcc binding energy. We apply this model with superflavor symmetry to the D¯(*)Ξcc(*) molecule and predict a bound state with I(JP)=0(12−). If the pentaquark state corresponding to D¯(*)Ξcc(*) molecular state is observed in future experiments as predicted in this work, it is more likely that Tcc is a DD* molecular state. Published by the American Physical Society 2024

Heavy exotic hadrons near thresholds: [formula omitted] and its partners

Recent accelerator experiments have reported unexpected states known as exotic hadrons, whose properties cannot be explained by the conventional picture. In 2022, the LHCb collaboration reported the doubly charmed tetraquark Tcc+ which is a genuine exotic states whose minimal quark content is ccūd̄. We consider the Tcc state as a DD∗ hadronic molecule. The one meson exchange potentials are employed as for the hadron interactions, and a bound state properties is investigated. Furthermore, the superflavor symmetry predicts a new pentaquark state D̄Ξcc from Tcc, which is obtained by replacing a D(∗) meson with a Ξcc(∗) baryon. We also study a possible existence of the D̄Ξcc bound state, and its properties.

Zb states as the mixture of the molecular and diquark-anti-diquark components within the effective field theory

In this study, we reconsider the states Zb(10610) and Zb(10650) by investigating the presence of diquark-anti-diquark components as well as the hadronic molecule components in the framework of effective field theory. The different masses of pseudoscalar mesons such as π0, η8, and η0, as well as vector mesons like ρ0 and ω violate the Okubo-Zweig-Iizuka (OZI) rule that is well depicted under the [U(3)L⊗U(3)R]global⊗[U(3)V]local symmetry. To account for the contribution of intermediate bosons of heavy masses within the one-boson-exchange model, we introduce an exponential form factor instead of the commonly used monopole form factor in the past. By solving the coupled-channel Schrödinger equation with the Gaussian expansion method, our numerical results indicate that the Zb(10610) and Zb(10650) states can be explained as hadronic molecules slightly mixing with diquark-anti-diquark states. Published by the American Physical Society 2024

Predicting isovector charmonium-like states from X(3872) properties

Using chiral effective field theory, we predict that there must be isovector charmonium-like DD¯∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ D{\\overline{D}}^{\\ast } $$\\end{document} hadronic molecules with JPC = 1++ denoted as Wc1. The inputs are the properties of the X(3872), including its mass and the ratio of its branching fractions of decays into J/ψρ0 and J/ψω. The predicted states are virtual state poles of the scattering matrix, pointing at a molecular nature of the X(3872) as well as its spin partners. They should show up as either a mild cusp or dip at the DD¯∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ D{\\overline{D}}^{\\ast } $$\\end{document} thresholds, explaining why they are elusive in experiments. The so far negative observation also indicates that the X(3872) is either a bound state with non-vanishing binding energy or a virtual state, only in these cases the X(3872) signal dominates over that from the Wc10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {W}_{c1}^0 $$\\end{document}. The pole positions are 3881.2−0.0+0.8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {3881.2}_{-0.0}^{+0.8} $$\\end{document}−i1.6−0.9+0.7\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ i{1.6}_{-0.9}^{+0.7} $$\\end{document} MeV for Wc10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {W}_{c1}^0 $$\\end{document} on the fourth Riemann sheet of the D0D¯∗0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {D}^0{\\overline{D}}^{\\ast 0} $$\\end{document}-D+D∗− coupled-channel system, and 3866.9−7.7+4.6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {3866.9}_{-7.7}^{+4.6} $$\\end{document}− i(0.07 ± 0.01) MeV for Wc1±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {W}_{c1}^{\\pm } $$\\end{document} on the second Riemann sheet of the DD¯∗±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\left(D{\\overline{D}}^{\\ast}\\right)}^{\\pm } $$\\end{document} single-channel system. The findings imply that the peak in the J/ψπ+π− invariant mass distribution is not purely from the X(3872) but contains contributions from Wc10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {W}_{c1}^0 $$\\end{document} predicted here. The states should have isovector heavy quark spin partners with JPC = 0++, 2++ and 1+−, with the last one corresponding to Zc. We suggest to search for the charged 0++, 1++ and 2++ states in J/ψπ±π0.

Revealing the mystery of the double charm tetraquark in pp collision

A novel approach is proposed to probe the nature of the double charm tetraquark through the prompt production asymmetry between Tc¯c¯-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{\\bar{c}\\bar{c}}^-$$\\end{document} and Tcc+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{cc}^+$$\\end{document} in pp collisions. When comparing two theoretical pictures, i.e. the compact tetraquark and hadronic molecular pictures, we find that the former one exhibits a significantly larger production asymmetry, enabling the unambiguous determination of the tetraquark’s internal structure. Additionally, distinctive differences in the transverse momentum and rapidity distributions of Tc¯c¯-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{\\bar{c}\\bar{c}}^-$$\\end{document} and Tcc+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{cc}^+$$\\end{document} cross sections emerge, particularly at pT≈2GeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_\ extrm{T}\\approx 2~\ extrm{GeV}$$\\end{document} and y≈±6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$y\\approx \\pm 6$$\\end{document} at a center-of-mass energy of 14TeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$~\ extrm{TeV}$$\\end{document}. The insignificant asymmetry in hadronic molecular picture is because that hadronic molecules are produced in hadronic phase, where the phase space of their constituents needs to be taken into account rigorously. Our work can be extended to the exploration of other double heavy tetraquark candidates, offering a versatile approach to advance our understanding of exotic hadrons.

Spectrum of molecular hexaquarks

We investigate the mass spectra of molecular-type hexaquark states in the dibaryon systems. These systems are composed of the charmed baryons [Σc(*),Ξc(′,*)], doubly charmed baryons [Ξcc(*)], and hyperons [Σ(*),Ξ(*)]. We consider all possible combinations of particle-particle and particle-antiparticle pairs, including the S-wave spin multiplets in each combination. We establish the underlying connections among the molecular tetraquarks, pentaquarks, and hexaquarks with the effective quark-level interactions. We find that the existence of molecular states in DD*, DD¯*, and ΣcD¯(*) systems leads to the emergence of a large number of deuteronlike hexaquarks in the heavy flavor sectors. Currently, there have been several experimental candidates for molecular tetraquarks and pentaquarks. The experimental search for near-threshold hexaquarks will further advance the establishment of the underlying dynamical picture of hadronic molecules and deepen our understanding of the role of spin-flavor symmetry in near-threshold residual strong interactions. Published by the American Physical Society 2024

Role of hidden-color components in the tetraquark mixing model

Multiquarks can have two-hadron components and hidden-color components in their wave functions. The presence of two-hadron components in multiquarks introduces a potential source of confusion, particularly with respect to their resemblance to hadronic molecules. On the other hand, hidden-color components are essential for distinguishing between multiquarks and hadronic molecules. In this work, we study the hidden-color components in the wave functions of the tetraquark mixing model, a model that has been proposed as a suitable framework for describing the properties of two nonets in the JP=0+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J^{P}=0^{+}$$\\end{document} channel: the light nonet [a0(980)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a_{0} (980)$$\\end{document}, K0∗(700)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K_{0}^{*} (700)$$\\end{document}, f0(500)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{0} (500)$$\\end{document}, 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}] and the heavy nonet [a0(1450)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a_{0} (1450)$$\\end{document}, K0∗(1430)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K_{0}^* (1430)$$\\end{document}, f0(1370)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{0} (1370)$$\\end{document}, f0(1500)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{0} (1500)$$\\end{document}]. Our analysis reveals a substantial presence of hidden-color components within the tetraquark wave functions. To elucidate the impact of hidden-color components on physical quantities, we conduct computations of the hyperfine masses, ⟨VCS⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle V_{CS}\\rangle $$\\end{document}, for the two nonets, considering scenarios involving only the two-meson components and those incorporating the hidden-color components. We demonstrate that the hidden-color components constitute an important part of the hyperfine masses, such that the mass difference formula, ΔM≈Δ⟨VCS⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta M\\approx \\Delta \\langle V_{CS}\\rangle $$\\end{document}, which has been successful for the two nonets, cannot be achieved without the hidden-color contributions. This can provide another evidence supporting the tetraquark nature of the two nonets.

Production of hidden-heavy and double-heavy hadronic molecules at the Z factory of CEPC

With a clean environment and high collision energy, the Circular Electron Positron Collider (CEPC) would be an excellent facility for heavy flavor physics. Using the Monte Carlo event generator ythia, we simulate the production of the charmed (bottom) hadron pairs in the electron-positron collisions at the Z factory of CEPC, and the inclusive production rates for typical candidates of the hidden/double-charm and hidden/double-bottom S-wave hadronic molecules are estimated at an order-of-magnitude level with the final state interactions after the hadron pair production. The predicted cross sections for the hidden-charm meson-meson molecules X(3872) and Zc(3900) are at pb level, which are about two to three orders of magnitude larger than the production cross sections for the double-charm meson-meson molecules Tcc and Tcc*, as the double-charmed ones require the production of two pairs of cc¯ from the Z boson decay. The production cross sections for the hidden-charm pentaquark states Pc and Pcs as meson-baryon molecules are a few to tens of fb, which are about one magnitude larger than those of the possible hidden-charm baryon-antibaryon and double-charm meson-baryon molecules. In the bottom sector, the production cross sections for the Zb states as B(*)B¯* molecules are about tens to hundreds of fb, indicating 106–107 events from a two-year operation of CEPC, and the expected events from the double-bottom molecules are about 2–5 orders of magnitude smaller than the Zb states. Our results shows great prospects of probing heavy exotic hadrons at CEPC. Published by the American Physical Society 2024

Production of singly charm pentaquarks from meson-baryon interactions in B -meson decay

In the paper, we discuss the possible interpretation of the JP=1/2− singly charm pentaquark as hadronic molecules. With the effective Lagrangian method, we further analyze the production properties of singly charm pentaquark from decays of B meson, including strong coupling constants and production branching ratios of the charm pentaquark. Our numerical results show that the branching ratio of production of pentaquark from B meson can reach to order of 10−6. Published by the American Physical Society 2024

Doubly heavy dibaryons as seen by string theory

We propose the stringy description of the system consisting of two heavy and four light quarks in the case of two light flavors of equal mass. As an application, we consider the three low-lying Born-Oppenheimer potentials as a function of the heavy quark separation. Our analysis shows that the ground state potential is described in terms of both hadroquarkonia and hadronic molecules. A connected string configuration makes the dominant contribution to the potential of an excited state at small separations, and for separations larger than 0.1 fm, it exhibits the diquark-diquark-diquark structure [Qq][Qq][qq]. For better understanding the quark organization inside the system, we introduce several critical separations related to the processes of string reconnection, breaking and junction annihilation. We also discuss the simplest string configurations including the five-string junctions and their implications for the system, in particular the emergence of composite quark objects different from diquarks and the process of junction fusion. Published by the American Physical Society 2024

Spectrum of the molecular pentaquarks

We investigate the mass spectrum of the molecular pentaquarks composed of a baryon and a meson. We establish the underlying relations among the near-threshold interactions of the molecular tetraquark and pentaquark systems. We find the existence of the molecule candidates in the ΣcD¯(*), DD*, and DD¯* systems indicates a substantial presence of the hadronic molecules in the heavy baryon plus heavy meson systems ( refers to the hadrons with the c and/or s quarks). We make an exhaustive prediction of the possible bound/virtual molecular states in the systems: Σc(*)D¯(*), Σc(*)D(*), Ξc(′,*)D¯(*), Ξc(′,*)D(*), Σc(*)K*, Σc(*)K¯*, Ξc(′,*)K*, Ξc(′,*)K¯*, Ξcc(*)D¯(*), Ξcc(*)D(*), Ξcc(*)K*, Ξcc(*)K¯*, Σ(*)D¯(*), Σ(*)D(*), Ξ(*)D¯(*), Ξ(*)D(*), Σ(*)K*, Σ(*)K¯*, Ξ(*)K*, Ξ(*)K¯*. Hunting for the predicted states in experiments will significantly deepen our understanding of the formation mechanism of the hadronic molecules, and shed light on the manifestation of flavor symmetry in the low-energy residual strong interactions. Published by the American Physical Society 2024

The effect of cutoff dependence on heavy quark spin symmetry partners

Hadron spectroscopy is revealed by observing heavy resonances. Among various explanations of the internal structure of these hadronic states, hadronic molecules play a unique role. For hadronic molecules, which are associated with meson–meson or meson–baryon interactions, the [Formula: see text] cutoff is a significant factor in determining the composite states’ binding energies and overall properties. The cutoff becomes important when it comes to the location of hadronic molecules’ masses because it influences the predictions. From this perspective, in the light of cutoff dependency, heavy quark spin partners of near-threshold the [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] resonances, which are considered as hadronic molecules, are examined.

Hints of the JPC = 0−− and 1−−[formula omitted] molecules in the J/ψ → ϕηη′ decay

The primary objective of this study is to investigate hadronic molecules of K⁎K¯1(1270) using a one-boson-exchange model, which incorporates exchanges of vector and pseudoscalar mesons in the t-channel, as well as the pion exchange in the u-channel. Additionally, careful consideration is given to the three-body effects resulting from the on-shell pion originating from K1(1270)→K⁎π. Then the BESIII data of the J/ψ→ϕηη′ process is fitted using the K⁎K¯1(1270) scattering amplitude with JPC=0−− or 1−−. The analysis reveals that both the JPC=0−− and 1−− assumptions for K⁎K¯1(1270) scattering provide good descriptions of the data, with similar fit qualities. Notably, the parameters obtained from the best fits indicate the existence of K⁎K¯1(1270) bound states, denoted by ϕ(2100) and ϕ0(2100) for the 1−− and 0−− states, respectively. The current experimental data, including the η polar angular distribution, cannot distinguish which K⁎K¯1(1270) bound state contributes to the J/ψ→ϕηη′ process, or if both are involved. Therefore, we propose further explorations of this process, as well as other processes, in upcoming experiments with many more J/ψ events to disentangle the different possibilities.

Coupled-channel description of charmed heavy hadronic molecules within the meson-exchange model and its implication

Motivated by the first observation of the double-charm tetraquark Tcc+(3875) by the LHCb Collaboration, we investigate the nature of Tcc+ as an isoscalar DD* hadronic molecule in a meson-exchange potential model incorporated by the coupled-channel effects and three-body unitarity. The D0D0π+ invariant mass spectrum can be well-described and the Tcc+ pole structure can be precisely extracted. Under the hypothesis that the interactions between the heavy flavor hadrons can be saturated by the light meson-exchange potentials, the near-threshold dynamics of Tcc+ can shed light on the binding of its heavy-quark spin symmetry (HQSS) partner D*D* (I=0) and on the nature of other heavy hadronic molecule candidates such as X(3872) and Zc(3900) in the charmed-anticharmed systems. The latter states can be related to Tcc+ in the meson-exchange potential model with limited assumptions based on the SU(3) flavor symmetry relations. The combined analysis, on the one hand, indicates the HQSS breaking effects among those HQSS partners, and on the other hand, highlights the role played by the short and long-distance dynamics for the near threshold D(*)D(*) and D(*)D¯(*)+c.c. systems. Published by the American Physical Society 2024

Productions of Ds0*(2317) and Ds1(2460) in B(s) and Λb(Ξb) decays

Recent studies show that Ds0*(2317) and Ds1(2460) contain large molecular components. In this work, we employ the naive factorization approach to calculate the production rates of Ds0*(2317) and Ds1(2460) as hadronic molecules in B(s) and Λb(Ξb) decays, where their decay constants are estimated in the effective Lagrangian approach. With the so-obtained decay constants fDs0*(2317) and fDs1(2460), we calculate the branching fractions of the b-meson decays B(s)→D¯(s)(*)Ds0* and B(s)→D¯(s)(*)Ds1 and the b-baryon decays Λb(Ξb)→Λc(Ξc)Ds0* and Λb(Ξb)→Λc(Ξc)Ds1. Our results show that the production rates of Ds0*(2317) and Ds1(2460) in the Bs, Λb, and Ξb decays are large enough that future experiments could observe them. In particular, we demonstrate that one can extract the decay constants of hadronic molecules via the triangle mechanism because of the equivalence of the triangle mechanism to the tree diagram established in calculating the decays B→D¯(*)Ds0*(2317) and B→D¯(*)Ds1(2460). Published by the American Physical Society 2024

Analysis of Tcc and Tbb based on the hadronic molecular model and their spin multiplets

Tcc(ccu¯d¯)+ has been reported by the LHCb experiment in 2022. The analysis using the Breit-Wigner parametrization found the small binding energy, 0.273 MeV, which is measured from the threshold of D*+D0. In this paper, we consider Tcc as a DD* hadronic molecule as a deuteronlike state. The one-boson exchange model is employed as for the heavy meson interactions, where we determine the cutoff parameter Λ to reproduce the reported binding energy of Tcc with I(JP)=0(1+). We discuss the properties of the bound state and also search for Tcc with quantum numbers other than 0(1+). Furthermore, we analyze Tbb as a bottom counterpart of Tcc, which involves two bottom quarks, and obtain several bound states. Finally, we consider the light-cloud basis for wave functions of the doubly heavy tetraquarks in the heavy quark limit. Using the basis, we find the spin multiplets of their bound states, indicating the spin structures of diquarks in Tcc and Tbb with the finite quark masses. Published by the American Physical Society 2024

Predictions for feed-down enhancements at the ΛcD¯ and ΛcD¯* thresholds via the triangle and box singularities

We demonstrate that triangle singularity (TS) and box singularity (BS) mechanisms can produce unique narrow enhancements at the ΛcD¯ and ΛcD¯* thresholds in the invariant mass spectra of J/ψp and J/ψpπ, respectively. Taking into account that such mechanisms only depend on the initial Σc(*)D¯(*) interactions near threshold within the TS or BS kinematic regimes, the ΛcD¯ and ΛcD¯* threshold enhancements can also acquire contributions from both the heavier pentaquark decays and the Σc(*)D¯(*) scatterings of the continuum as a feed-down phenomenon. A search for these structures in the J/ψp and J/ψpπ spectra in both exclusive and semi-inclusive processes will provide a crucial evidence for the hadronic molecule nature of these observed pentaquarks and clarify the role played by the TS and BS in the near-threshold dynamics. Published by the American Physical Society 2024

Production of the X(4014) as the Spin-2 Partner of X(3872) in e + e − Collisions

In 2021, the Belle collaboration reported the first observation of a new structure in the ψ(2S)γ final state produced in the two-photon fusion process. In the hadronic molecule picture, this new structure can be associated with the shallow isoscalar D*D¯* bound state and as such is an excellent candidate for the spin-2 partner of the X(3872) with the quantum numbers J PC = 2++ conventionally named X 2. In this work we evaluate the electronic width of this new state and argue that its nature is sensitive to its total width, the experimental measurement currently available being unable to distinguish between different options. Our estimates demonstrate that the planned Super τ-Charm Facility offers a promising opportunity to search for and study this new state in the invariant mass distributions for the final states J/ψγ and ψ(2S)γ.