Heavy Meson Pairs Research Articles

Model-independent predictions for decays of hidden-heavy hadrons into pairs of heavy hadrons

Hidden-heavy hadrons can decay into pairs of heavy hadrons through transitions from confining Born-Oppenheimer potentials to hadron-pair potentials with the same Born-Oppenheimer quantum numbers. The transitions are also constrained by conservation of angular momentum and parity. From these constraints, we derive model-independent selection rules for decays of hidden-heavy hadrons into pairs of heavy hadrons. The coupling potentials are expressed as sums of products of Born-Oppenheimer transition amplitudes and angular-momentum coefficients. If there is a single dominant Born-Oppenheimer transition amplitude, it factors out of the coupling potentials between hidden-heavy hadrons in the same Born-Oppenheimer multiplet and pairs of heavy hadrons in specific heavy-quark-spin-symmetry doublets. If furthermore the kinetic energies of the heavy hadrons are much larger than their spin splittings, we obtain analytic expressions for the relative partial decay rates in terms of Wigner 6j and 9j symbols. We consider in detail the decays of quarkonia and quarkonium hybrids into the lightest heavy-meson pairs. For quarkonia, our model-independent selection rules and relative partial decay rates agree with previous results from quark-pair-creation models in simple cases and give stronger results in other cases. For quarkonium hybrids, we find disagreement even in simple cases. Published by the American Physical Society 2024

TMD factorization for dijet and heavy-meson pair in DIS

We study a transverse momentum dependent (TMD) factorization framework for the processes of dijet and heavy-meson pair production in deep-inelastic-scattering in an electron-proton collider, considering the measurement of the transverse momentum imbalance of the two hard probes in the Breit frame. For the factorization theorem we employ soft-collinear and boosted-heavy-quark effective field theories. The factorized cross-section for both processes is sensitive to gluon unpolarized and linearly polarized TMD distributions and requires the introduction of a new soft function. We calculate the new soft function here at one-loop, regulating rapidity divergences with the δ-regulator. In addition, using a factorization consistency relation and a universality argument regarding the heavy-quark jet function, we obtain the anomalous dimension of the new soft function at two and three loops.

Calculation of Masses of Di-Mesons Consisting of a Pair of Heavy Mesons

In this paper, we study four-quark states as di-hadronic molecular states. For this purpose, we apply the Nikiforov–Uvarov method to solve the Schrödinger equation in the presence of the Woods–Saxon plus Coulomb-type potential and we obtain the binding energies and masses of heavy di-mesons. We calculate the root mean square (r.m.s) radius and the wave function for some observed tetraquarks.

Are the XYZ states unconventional states or conventional states with unconventional properties?

We discuss three possible scenarios for the interpretation of mesons containing a heavy quark and its antiquark near and above the first threshold for a decay into a pair of heavy mesons in a relative [Formula: see text]-wave. View I assumes that these thresholds force the quark potential to flatten which implies that while in these energy ranges molecular states may be formed, there should not be any quark–antiquark states above these thresholds. View II assumes that the main part of the interaction between two mesons is due to the poles which originate from the [Formula: see text] interaction. The properties of the [Formula: see text] mesons are strongly influenced by opening thresholds but the number of states is given by the quark model. In View III, both types of mesons are admitted also near and above the open flavor thresholds: [Formula: see text] mesons and dynamically generated mesons. Experimental consequences of these different views are discussed.

Heavy hybrids and tetraquarks in effective field theory

We report on an effective field theory (EFT) description of exotic quarkonia as bound states on the spectrum of hybrid and tetraquarks static energies. We provide expressions for hybrid and tetraquarks static energies in terms of Wilson loops. The former have been computed in quenched lattice calculations but the latter are yet unavailable. From the few simulations with dynamical light-quarks we argue that the overall picture from hybrid static energies does not change but additional states, such as heavy meson pairs, need to be considered for a full description. In this EFT framework for quarkonium hybrids, we report on recent results for mixing with standard quarkonium, spin-dependent contributions, and semi-inclusive decays.

Stability of tetrons

We consider the interactions in a mesonic system, referred here to as ‘tetron’, consisting of two heavy quarks and two lighter antiquarks (which may still be heavy in the scale of QCD), i.e. generally QaQbq¯cq¯d, and study the existence of bound states below the threshold for decay into heavy meson pairs. At a small ratio of the lighter to heavier quark masses an expansion parameter arises for treatment of the binding in such systems. We find that in the limit where all the quarks and antiquarks are so heavy that a Coulomb-like approximation can be applied to the gluon exchange between all of them, such bound states arise when this parameter is below a certain critical value. We find the parametric dependence of the critical mass ratio on the number of colors Nc, and confirm this dependence by numerical calculations. In particular there are no stable tetrons when all constituents have the same mass. We discuss an application of a similar expansion in the large Nc limit to realistic systems where the antiquarks are light and their interactions are nonperturbative. In this case our findings are in agreement with the recent claims from a phenomenological analysis that a stable bbu¯d¯ tetron is likely to exist, unlike those where one or both bottom quarks are replaced by the charmed quark.

Mixing model for bottomoniumlike Zb resonances

The isovector bottomoniumlike exotic resonances $Z_b(10610)$ and $Z_b(10650)$ are very close to the thresholds of heavy meson pairs $B \bar B^* \, ( \bar B B^*)$ and $B^* \bar B^*$, and are naturally understood as `molecular' states made of the corresponding meson-antimeson pairs. The picture with a full separation of the two channels cannot be exact and a cross-feed between the states necessarily takes place. A simple model is considered here describing the mixing between the channels in terms of one parameter. The model reasonably describes the current data on the decays of the $Z_b$ resonances to bottomonium plus a pion and predicts the rate and a distinctive interference pattern for the decay $Z_b(10650) \to B \bar B^* \, ( \bar B B^*)$ as well as excess of the mass splitting between the resonances over the mass difference between $B^*$ and $B$ mesons.

Some properties of the states at the hidden-strangeness mixed 12++12− heavy meson pair threshold in e+e− annihilation

The threshold behavior of $e^+ e^-$ annihilation is considered in the channels $B_{s0} \bar B_s^* + c.c.$, $B_{s1} \bar B_s + c.c.$, and $B_{s1} \bar B_s^* +c.c.$, where $B_{s0}$ and $B_{s1}$ are the excited bottom-strange $J^P=0^+$ and $J^P = 1^+$ mesons. It is argued that due to the heavy quark spin symmetry (HQSS) only one coherent combination of the first two channels is produced in the $S$ wave as well as the third channel. Thus, if there exist threshold molecular peaks in the considered channels, only two of such peaks can be formed in the annihilation. The properties of such threshold states are discussed, including the heavy-light spin structure and the related transitions to bottomonium plus light mesons, as well as mixing with the channels with and without hidden strangeness.

Suppression and Two-Particle Correlations of Heavy Mesons in Heavy-Ion Collisions

We study the medium modification of heavy quarks produced in heavy-ion collisions. The evolution of heavy quarks inside the QGP is described using a modified Langevin framework that simultaneously incorporates their collisional and radiative energy loss. Within this framework, we provide good descriptions of the heavy meson suppression and predictions for the two-particle correlation functions of heavy meson pairs.

Hindered magnetic dipole transitions between P -wave bottomonia and coupled-channel effects

In the hindered magnetic dipole transitions of heavy quarkonia, the coupled-channel effects originating from the coupling of quarkonia to a pair of heavy and anti-heavy mesons can play a dominant role. Here, we study the hindered magnetic dipole transitions between two $P$-wave bottomonia, $\chi_b(n P)$ and $h_b(n^\prime P)$, with $n\neq n^\prime$. In these processes the coupled-channel effects are expected to lead to partial widths much larger than the quark model predictions. We estimate these partial widths which, however, are very sensitive to unknown coupling constants related to the vertices $\chi_{b0}(nP)B\bar B$. A measurement of the hindered M1 transitions can shed light on the coupled-channel dynamics in these transitions and hence on the size of the coupling constants. We also suggest to check the coupled-channel effects by comparing results from quenched and fully dynamical lattice QCD calculations.

ϒ(6S)and triangle singularity ine+e−→B1(5721)B¯→Zb(10610)π

We discuss the possibility that production of final states with bottomonium and light mesons at the peak $\Upsilon(6S)$ in the $e^+e^-$ annihilation at approximately 11.00 GeV is in fact due to a triangular singularity at the threshold of the heavy meson pair production $B_1(5721) \bar B + c.c.$ through the process $e^+e^- \to B_1(5721) \bar B \to Z_b(10610) \, \pi$. The presence of the hidden-bottom resonance $Z_b(10610)$ then explains the observed enhanced production of the final channels with both ortho- and para- bottomonium states, $\Upsilon(nS) \pi \pi$ and $h_b(kP) \pi \pi$. The discussed mechanism also predicts a distinct pattern for production of hidden-bottom states at the $\Upsilon(6S)$ energy that can be tested by experiment.

On the pair correlations of neutral K, D, B and BS mesons with close momenta produced in inclusive multiparticle processes

The phenomenological structure of inclusive cross-sections of the production of two neutral K mesons in collisions of hadrons and nuclei is investigated taking into account the strangeness conservation in strong and electromagnetic interactions. Relations describing the dependenceof the correlations of two short-lived and two long-lived neutral kaons KS∘KS∘,KL∘KL∘ and the correlations of “mixed” pairs KS∘KL∘ at small relative momenta upon the space-time parameters of the generation region of K∘ and K¯∘ mesons have been obtained. It is shown that under the strangeness conservation the correlation functions of the pairs KS∘KS∘ and KL∘KL∘, produced in the same inclusive process, coincide, and the difference between the correlation functions of the pairs KS∘KS∘ and KS∘KL∘ is conditioned exclusively by the production of the pairs of non-identical neutral kaons K∘K¯∘. Analogous correlations for the pairs of neutral heavy mesons D∘,B∘ and BS∘, generated in multiple processes with the charm (beauty) conservation, are analyzed, and differences from the case of neutral K mesons are discussed.

Production of heavy meson pairs in pp̄ collisions within a double handbag approach

We study the pair-production of heavy mesons in proton-antiproton annihilations within a perturbative QCD-motivated framework. In particular we investigate pp̄ → D0 within a double handbag approach, where a hard subprocess factorizes from soft hadronic matrix elements. The soft matrix elements can be parametrized by transition distribution amplitudes, which are off-diagonal in flavor space. The transition distribution amplitudes are modelled as overlaps of light-cone wave functions. We obtain rather robust model results for pp̄ → D0 cross sections, which are expected to be measured at the future detector at GSI-FAIR.

Production of Charged Heavy Quarkonium-Like States at the LHC and Tevatron

We study prompt hadroproduction of the charged bottomonium-like states Zb± (10610) and Zb± (10650), and the charged charmonium-like states Zc±(3900) and Zc±(4020), at the Tevatron and the LHC, provided that these states are S-wave hadronic molecules. Using two Monte Carlo event generators, Herwig and Pythia, to simulate the production of heavy meson pairs, we derive an order-of-magnitude estimate of the production rates for these four particles. Our estimates yield a cross section at the nb level for the Zb (10610) and Zb (10650). The results for the Zc (3900) and Zc (4020) are larger by a factor of 20–30. These cross sections are large enough to be observed, and measurements at hadron colliders in the future will supplement the study using electron-positron collisions, and therefore allow to explore the mysterious nature of these exotic states.

Isospin violation in the yield ofS-wave heavy meson pairs near threshold

We consider production of overall neutral pairs consisting of heavy $D^{(*)}$ or $B^{(*)}$ meson and antimeson in the processes, where the pair can be created in an $S$-wave, such as $e^+e^- \to \pi^0 \, D^* \bar D^{(*)}$ and $e^+e^- \to \gamma \, D^{(*)} \bar D^{(*)}$, and similar reactions with $B^{(*)}$ mesons. The ratio $R^{c/n}$ of the yield of pairs of charged mesons to that of neutral mesons near the threshold for the heavy pair is strongly affected by the isospin breaking due to the isotopic mass differences and due to the Coulomb interaction between the charged mesons. The actual behavior of the isospin breaking in $R^{c/n}$ is also sensitive to the strong interaction between the heavy mesons, so that experimental measurement of this ratio can be used as a probe of this strong interaction. We calculate $R^{c/n}$ at and very near the threshold in terms of the isotopic scattering lengths for the meson pairs. In particular we find that the yield of pairs of charged mesons does not go to zero at exactly the threshold, but rather starts with a finite step, whose height depends on the value of the scattering length in a particular channel.

Heavy quark pair production in high energy pA collisions: Open heavy flavors

We study open heavy flavor meson production in proton-nucleus (pA) collisions at RHIC and LHC energies within the Color Glass Condensate framework. We use the unintegrated gluon distribution at small Bjorken's x in the proton obtained by solving the Balitsky-Kovchegov equation with running coupling correction and constrained by global fitting of HERA data. We change the initial saturation scale of the gluon distribution for the heavy nucleus. The gluon distribution with McLerran-Venugopalan model initial condition is also used for comparison. We present transverse momentum spectra of single D and B productions in pA collisions, and the so-called nuclear modification factor. The azimuthal angle correlation of open heavy flavor meson pair is also computed to study the modification due to the gluon saturation in the heavy nucleus at the LHC.

Systematic study of the singularity mechanism in heavy quarkonium decays

We investigate in detail the role of heavy meson loops in the transition from JPC=1−− sources to candidates for QCD “exotics”, such as Zc(3900), Zb(10610) and Zb′(10650). We demonstrate that, if a vector state strongly couples to a heavy meson pair in an S-wave and this system decays to another heavy meson pair (e.g. via pion emission), again in an S-wave, the pertinent diagrams get enhanced significantly, if the intermediate states are (near) on-shell and have small relative momenta. In a limited kinematic range this mechanism generates “singularity regions” that lead to the creation of a large number of low-energy heavy meson pairs, providing an ideal environment for the formation of hadron–hadron bound states or resonances. For instance, we predict that the signals for Zb and Zb′ should be a lot stronger in ϒ(6S) decays due to this mechanism, if these states are indeed hadron–hadron resonances. The findings of this work should be valuable for deepening our understanding of the nature of the mentioned states.

Zc(3900)—what is inside?

The models for the internal structure of the newly found four-quark charmoniumlike resonance ${Z}_{c}(3900)$ are discussed: the molecular model as well as the hadro-charmonium and tetraquark schemes. It is argued that it would be possible to resolve between these models by combining measurements of the quantum numbers of the resonance and of its decay rates into yet unseen channels $\ensuremath{\pi}{\ensuremath{\psi}}^{\ensuremath{'}}$, $\ensuremath{\pi}{h}_{c}$, $\ensuremath{\rho}{\ensuremath{\eta}}_{c}$ and into pairs of heavy mesons ${D}^{*}\overline{D}$ and $D{\overline{D}}^{*}$. The models also predict different related four-quark states, which can be sought for in the existing and future data.

Enhanced mixing of partial waves near threshold for heavy meson pairs and properties ofZb(10610)andZb(10650)resonances

The mixing of $S\mathrm{\text{\ensuremath{-}}}D$ partial waves for the heavy meson pairs in the decays $\ensuremath{\Upsilon}(5S)\ensuremath{\rightarrow}[{B}^{*}\overline{B}+\mathrm{c}.\mathrm{c}.]\ensuremath{\pi}$ and $\ensuremath{\Upsilon}(5S)\ensuremath{\rightarrow}{B}^{*}{\overline{B}}^{*}\ensuremath{\pi}$ is considered. It is argued that this mixing, enhanced by the heavy meson mass, is calculable as dominated by a rescattering through pion exchange if the production of the heavy mesons is dominated by $S$-wave ``molecular'' resonances ${Z}_{b}(10610)$ and ${Z}_{b}(10650)$. The effect of the mixing grows with the c.m. energy $E$ in each channel over the threshold, and may reach $10\textdiv{}20%$ in the rate at the upper end of applicability of the discussed approach, $E\ensuremath{\sim}15\text{ }\text{ }\mathrm{MeV}$. It is also argued that the mixing is likely to reach maximum at an energy approximately equal to the mass gap between the thresholds.

A Mechanism for Hadron Molecule Production in <i>pp</i>(<i>p</i>) Collisions

The problem of understanding loosely bound hadron molecules prompt production at hadron colliders is still open: how is it possible that meson molecules with binding energy compatible with zero could be formed within the bulk of the hadrons ejected in very high energy collisions? Monte Carlo simulations have been performed in the literature, leading to production cross sections, two orders of magnitude which were smaller than the experimental value. One possible mechanism to reduce this gap could be final state interactions of heavy mesons, but a precise evaluation of such effect is challenged by the presence of pions between the molecular constituents. In this paper, we present a new mechanism by using precisely such comoving pions. Heavy meson pairs can indeed slow down because of elastic scattering with surrounding pions. The number of low-relative-momentum meson pairs increases, thereby enhancing prompt production cross section. In this preliminar simulation, we show that an enhancement of 100 is indeed possible.