Meson Molecules Research Articles

Production of meson molecules in ultraperipheral heavy ion collisons

In this work we present a calculation of exotic charmonium production in ultraperipheral collisions, in which the exotic state is explicitly treated as a meson molecule. Our formalism is general, but we focus on the lightest possible exotic charmonium state: a D+D− molecular bound state. It was proposed some time ago, and it has been an object of experimental searches. Here we study the production of the open charm pair in the process γγ→D+D−. Then we use a prescription to project the free pair |D+D−⟩ onto a bound state at the amplitude level and compute the cross section of the process γγ→B (where B is the bound state). Finally, we convolute this last cross section with the equivalent photon distributions coming from the projectile and target in an ultraperipheral collision and find the AA→AAB cross section, which, for Pb−Pb collisions at sNN=5.02 TeV, is of the order of 3 μb. Published by the American Physical Society 2024

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.

Mass Spectra of Mesonic Molecules at Finite Temperature

At a finite temperature, exotic hadronic systems, mass spectrum was studied using the quark structure and the radial Schrödinger equation with the Cornell interaction potential representing the hadronic interaction. The projective unitary representation has been used in the study of hadronic ground states in physics. A relativistic bound state's mass spectrum with temperature dependence is shown to have a unique feature. The resulting values are compared to experimental and theoretical values, and the study showed a high level of conformity with additional values wherever feasible.

The nature of X(3872) from high-multiplicity pp collisions

The structure of exotic resonances that do not trivially fit the usual quark model expectations has been a matter of intense scientific debate during the last two decades. A possible way of estimating the size of these states is to study their behavior when immersed in QCD matter. Recently, LHCb has measured the relative abundance of the exotic X(3872) over the ordinary psi (2S). We use the comover interaction model to study the yield of a compact X(3872). To confirm the reliability of the model in high-multiplicity pp collisions, we describe the suppression of excited over ground Upsilon states. With this at hand, we show that the size of the compact X(3872) would be slightly larger than that of the psi (2S). If the X(3872) is instead assumed to be a meson molecule of large size, we argue that its evolution in QCD matter should be described via a coalescence model, as suggested by data on deuteron production. We show that the predictions of this model for the X(3872) are in contrast with data.

Disentangling different structures in heavy-light four-quark states

Models proposed to explain recently discovered heavy-light four-quark states already assume certain internal structures, i.e. the (anti)quark constituents are grouped into diquark/antidiquark clusters, heavy-meson/light-meson clusters (hadrocharmonium) or heavy-light meson molecules. We propose and use an approach to four-quark states based on Dyson-Schwinger and Bethe-Salpeter equations that has the potential to discriminate between these models. We study the masses of heavy-light $cq\bar{q}\bar{c}$ and $cc\bar{q}\bar{q}$ four-quark states with $q=u,d,s$ and quantum numbers $I(J^{PC})=0(1^{++}),1(1^{+-}),0(0^{++})$ and $1(0^+),0(1^+),1(1^+)$. We identify the dominant components of the ground states with these quantum numbers and suggest candidates for corresponding experimental states. Most notably, we find strong heavy-light meson-meson and negligible diquark-antidiquark components in all $cq\bar{q}\bar{c}$ states, whereas for $cc\bar{q}\bar{q}$ states diquarks are present. A potential caveat in the $I=0$ channels is the necessary but costly inclusion of $c\bar{c}$ components which is relegated to future work.

Collision dynamics and reactions of fractional vortex molecules in coherently coupled Bose-Einstein condensates

Coherently coupled two-component Bose-Einstein condensates (BEC) exhibit vortex confinement resembling quark confinement in Quantum Chromo Dynamics (QCD). Fractionally quantized vortices winding only in one of two components are attached by solitons, and they cannot stably exist alone. Possible stable states are "hadrons" either of mesonic type, i.e., molecules made of a vortex and anti-vortex in the same component connected by a soliton, or of baryonic type, i.e., molecules made of two vortices winding in two different components connected by a soliton. Mesonic molecules move straight with a constant velocity while baryonic molecules rotate. We numerically simulate collision dynamics of mesonic and baryonic molecules and find that the molecules swap a partner in collisions in general like chemical and nuclear reactions, summarize all collisions as vortex reactions, and describe those by Feynman diagrams. We find a selection rule for final states after collisions of vortex molecules, analogous to that for collisions of hadrons in QCD.

Charm-meson triangle singularity in e+e− annihilation into D*0D¯0+γ

We calculate the cross section for $e^+ e^-$ annihilation into $D^{*0} \bar D^0 +\gamma$ at center-of-mass energies near the $D^{*0} \bar D^{*0}$ threshold under the assumption that $X(3872)$ is a weakly bound charm meson molecule. The Dalitz plot has a $\bar D^{*0}$ resonance band in the squared invariant mass $t$ of $\bar D^0 \gamma$. In the limit as the decay width of the $D^{*0}$ goes to 0, the Dalitz plot also has a narrow band in the squared invariant mass $u$ of $D^{*0} \bar D^0$ from a charm-meson triangle singularity. At the physical value of the $D^{*0}$ width, the narrow band reduces to a shoulder. Thus the triangle singularity cannot be observed directly as a peak in a differential cross section as a function of $u$. It may however be observed indirectly as a local minimum in the $t$ distribution for events with $u$ below the triangle singularity. The minimum is produced by the Schmid cancellation between triangle loop diagrams and a tree diagram. The observation of this minimum would support the identification of $X(3872)$ as a weakly bound charm meson molecule.

X(3872) in the molecular model

We discuss methods and approaches for describing molecular states in the spectrum of heavy quarks and investigate various properties of the exotic charmonium-like state X(3872) in detail in the framework of the mesonic molecule model.

Threshold effects and the line shape of the X(3872) in effective field theory

Latest measurements suggest that the X(3872) mass lies less than 200 keV away from the D0-Dbar0* threshold, reenforcing its interpretation as a loosely-bound mesonic molecule. This observation implies that in processes like D0-Dbar0-pi0 production, threshold effects could disguise the actual pole position of the X(3872). We propose a new effective field theory with D0, Dbar0 and pi0 degrees of freedom for the X(3872), considering Galilean invariance to be an exact symmetry. The D0* enters as a D0-pi0 p-wave resonance, allowing for a comprehensive study of the influence of pion interactions on the X(3872) width. We calculate relations between the mass of the X(3872), its width, and its line shape in D0-Dbar0-pi0 production up to next-to-leading order. Our results provide a tool for the extraction of the X(3872) pole position from the experimental data near threshold.

X(4260) revisited: A coupled channel perspective

We calculate the probabilities of various charmed meson molecules for $X(4260)$ under the framework of ${}^3P_0$ model. The results indicate that even though heavy quark spin symmetry forbids $S$ wave coupling of $D_1\bar{D}$ to the ${}^3S_1$ charmonia ($\psi(nS)$), the $D$ wave coupling is allowed and not negligible. Under this symmetry, the $D_1\bar{D}$ can couple to ${}^3D_1$ charmonia ($\psi(nD)$) via both $S$ and $D$ wave, and the overall coupling is around three times larger than that of $\psi(nS)$. The $X(4260)$ cannot be a pure molecule but a mixture of a charmonium and various charmed meson components. Since the $D_1\bar{D}$ couples strongly to $\psi(nD)$, our results suggest that in the $D_1\bar{D}$ molecular picture, the charmonium core of $X(4260)$ is $\psi(nD)$ instead of $\psi(nS)$. As a result, the experimental fact that the $R$ ratio has a dip around 4.26 GeV can be understood in the $D_1\bar{D}$ molecular picture of the $X(4260)$.

Investigating efficient methods for computing four-quark correlation functions

We discuss and compare the efficiency of various methods, combinations of point-to-all propagators, stochastic timeslice-to-all propagators, the one-end trick and sequential propagators, to compute two-point correlation functions of two-quark and four-quark interpolating operators of different structure including quark–antiquark type, mesonic molecule type, diquark–antidiquark type and two-meson type. Although we illustrate our methods in the context of the a0(980), they can be applied for other multi-quark systems, where similar diagrams appear. Thus our results could provide helpful guidelines on the choice of methods for correlation function computation for future lattice QCD studies of meson–meson scattering and possibly existing tetraquark states.

Exploring X(5568) as a meson molecule

The parameters, i.e. the mass and current coupling of the exotic X(5568) state observed by the D0 Collaboration as well as the decay width of the process \( X \rightarrow B_s^{0}\pi^{+}\), are explored using the \( B\overline{K}\) molecule assumption on its structure. Employed computational methods include QCD two-point and light-cone sum rules, the latter being considered in the soft-meson approximation. The obtained results are compared with the data of the D0 Collaboration as well as with the predictions of the diquark-antidiquark model. This comparison strengthens a diquark-antidiquark picture for the X(5568) state rather than a meson molecule structure.

Effective field theory investigations of the XYZ puzzle

Quantum Chromodynamics, the theory of strong interactions, predicts several types of bound states. Among them are conventional mesons (qq̅) and baryons (qqq), which have been the only states observed in experiments for years. However, in the last decade, many states that do not fit this picture have been observed at B-factories (BaBar, Belle and CLEO), at τ-charm facilities (CLEO-c, BESIII) and also at proton-proton colliders (CDF, D0, LHCb, ATLAS, CMS). There is growing evidence that at least some of the new charmonium- and bottomonium-like states, the so-called XYZ mesons, are new forms of matter such as quark-gluon hybrids, mesonic molecules or different arrangements of tetraquarks, pentaquarks... Effective Field Theories (EFTs) have been constructed for heavy-quark-antiquark bound states, but a general study of the XYZ mesons within the same framework has not yet been done. The scope of this conference proceedings is to discuss the possibilities we have in developing novel EFTs that, characterizing the conventional quarkonium states, facilitate also the systematic and model-independent description of the new exotic matter, in particular, the hybrid mesons.

Tetraquarks in the 1/N expansion and meson-meson resonances

Diquarks are found to have the right degrees of freedom to describe the tetraquark poles in hidden-charm to open-charm meson-meson amplitudes. Compact tetraquarks result as intermediate states in non-planar diagrams of the 1/N expansion and the corresponding resonances are narrower than what estimated before. The proximity of tetraquarks to meson-thresholds has an apparent role in this analysis and, in the language of meson molecules, an halving rule in the counting of states is obtained.

The light scalar mesons as tetraquarks

We present a numerical solution of the four-quark Bethe–Salpeter equation for ground-state scalar tetraquarks with JPC=0++. We find that the four-body equation dynamically generates pseudoscalar-meson poles in the Bethe–Salpeter amplitude. The resulting tetraquarks are genuine four-quark states that are dominated by pseudoscalar meson–meson correlations. Diquark–antidiquark contributions are subleading because of their larger mass scale. In the light quark sector, the sensitivity of the tetraquark wave function to the pion poles leads to an isoscalar tetraquark mass Mσ∼350 MeV which is comparable to that of the σ/f0(500). The masses of its multiplet partners κ and a0/f0 follow a similar pattern. This provides support for a tetraquark interpretation of the light scalar meson nonet in terms of ‘meson molecules’.

Determination of the structure of the [formula omitted] in [formula omitted] collisions

Currently, the structure of the X(3872) meson is unknown. Different competing models of the cc¯ exotic state X(3872) exist, including the possibilities that this state is either a mesonic molecule with dominating D0D¯⁎0+c.c. composition, a cc¯qq¯ tetraquark, or a cc¯-gluon hybrid state. It is expected that the X(3872) state is rather strongly coupled to the p¯p channel and, therefore, can be produced in p¯p and p¯A collisions at PANDA. We propose to test the hypothetical molecular structure of X(3872) by studying the D or D¯⁎ stripping reactions on a nuclear residue.

Charm tetraquarks in a non-relativistic quark model

New charmonium states have been discovered since 2003. Although some of them can be explained as cc states, others do not fit in the predictions of that spectrum. Exotic models have been proposed to explain these new states, regarded now as multiquark states in the charm sector. In this work we focus on two of the most discussed models: the tetraquark, which consists on a diquark-antidiquark system, and the meson molecule, which is a weakly bound state of two mesons. We have developed a non-relativistic approach to study exotic heavy hadron spectroscopy, where the four body system is considered as three subsequent two- body systems. We solve numerically the Schroedinger equation using an effective Cornell-like potential to model the two-body interaction in each step of the tetraquark calculation, and a Yukawa-like potential to describe the meson molecule.

Probing the nature of [formula omitted] states via the [formula omitted] decay

The nature of the so-called XYZ states is a long-standing problem. It has been suggested that such particles may be described as compact four-quark states or loosely bound meson molecules. In the present work we analyze the Zc(′)→ηcρ decay using both approaches. Such channel might provide useful insights on the nature of the Zc(′), helping discriminating between the two different models.

Molecular interpretation of the supercharmonium state Z(4475)

Charm meson molecule (c\bar n)(n\bar c) assignments for the supercharmonium state Z(4475) are considered, both on general grounds and in the context of specific pion exchange models. Two possible charm molecule assignments for the JP = 1+, Z(4475) are considered here, involving respectively a radially and an orbitally excited charm meson. In each assignment, a lower-mass isosinglet charm molecule state is predicted. For both the Z(4475) and the Y(4260), measurement of the ratios of the branching fractions to D \bar D plus n pions is recommended as a test of the nature of these states.

Observation of Structures in the J/ψϕ Mass Spectrum at CMS

Observation of charmonium like new states since 2003, which do not fit into conventional quark model renewed the interest in exotic states. Many models like meson molecule, tetraquark, and quark-gluon hybrid are proposed to explain the observed charmonium spectroscopy. The observation of Y(3940)[1] near the J/ψω threshold motivated the searches for similar structures near J/ψϕ threshold. In this proceeding, we summarize the recent developments on the observation of a peaking structure in the J/ψϕ mass spectrum from B± → J/ψϕK± decay.