Heavy Antiquark Research Articles

Heptaquarks with two heavy antiquarks in a simple chromomagnetic model

We investigate the symmetry property and the stability of the heptaquark containing two identical heavy antiquarks using color-spin interaction. We construct the wave function of the heptaquark from the Pauli exclusion principle in the SU(3) breaking case. The stability of the heptaquark against the strong decay into one baryon and two mesons is discussed in a simple chromomagnetic model. We find that $q^2 s^3 \bar{s}^2$ with $I=0,S=\frac{5}{2}$ is the most stable heptaquark configuration that could be probed by reconstructing the $\Lambda+\phi+\phi$ invariant mass.

Fate of in-medium heavy quarks via a Lindblad equation

What is the dynamics of heavy quarks and antiquarks in a quark gluon plasma? Can heavy-quark bound states dissociate? Can they (re)combine? These questions are addressed by investigating a Lindblad equation that describes the quantum dynamics of the heavy quarks in a medium. The Lindblad equations for a heavy quark and a heavy quark-antiquark pair are derived from the gauge theory, following a chain of well-defined approximations. In this work the case of an abelian plasma has been considered, but the extension to the non-abelian case is feasible. A one-dimensional simulation of the Lindblad equation is performed to extract information about bound-state dissociation, recombination and quantum decoherence for a heavy quark-antiquark pair. All these phenomena are found to depend strongly on the imaginary part of the inter-quark potential.

Single electrons from heavy-flavor mesons in relativistic heavy-ion collisions

We study the single electron spectra from $D-$ and $B-$meson semileptonic decays in Au+Au collisions at $\sqrt{s_{\rm NN}}=$200, 62.4, and 19.2 GeV by employing the parton-hadron-string dynamics (PHSD) transport approach that has been shown to reasonably describe the charm dynamics at RHIC and LHC energies on a microscopic level. In this approach the initial heavy quarks are produced by using the PYTHIA which is tuned to reproduce the FONLL calculations. The produced heavy quarks interact with off-shell massive partons in QGP with scattering cross sections which are calculated in the dynamical quasi-particle model (DQPM). At energy densities close to the critical energy density the heavy quarks are hadronized into heavy mesons through either coalescence or fragmentation. After hadronization the heavy mesons interact with the light hadrons by employing the scattering cross sections from an effective Lagrangian. The final heavy mesons then produce single electrons through semileptonic decay. We find that the PHSD approach well describes the nuclear modification factor $R_{\rm AA}$ and elliptic flow $v_2$ of single electrons in d+Au and Au+Au collisions at $\sqrt{s_{\rm NN}}=$ 200 GeV and the elliptic flow in Au+Au reactions at $\sqrt{s_{\rm NN}}=$ 62.4 GeV from the PHENIX collaboration, however, the large $R_{\rm AA}$ at $\sqrt{s_{\rm NN}}=$ 62.4 GeV is not described at all. Furthermore, we make predictions for the $R_{\rm AA}$ of $D-$mesons and of single electrons at the lower energy of $\sqrt{s_{\rm NN}}=$ 19.2 GeV. Additionally, the medium modification of the azimuthal angle $\phi$ between a heavy quark and a heavy antiquark is studied. We find that the transverse flow enhances the azimuthal angular distributions close to $\phi=$ 0 because the heavy flavors strongly interact with nuclear medium in relativistic heavy-ion collisions and almost flow with the bulk matter.

String dynamics and metastability of all-heavy tetraquarks

Multiquark states have been advocated to explain recent experimental data in the heavy-light sector, and there are already speculations about multiquarks containing only heavy quarks and antiquarks. With a rigorous treatment of the four-body problem in current quark models, full-charm $(cc\bar c\bar c)$ and full-beauty $(bb\bar b\bar b)$ tetraquarks are found to be unbound. Thus their stability should rely on more subtle effects that are not included in the simple picture of constituent quarks. The case of $(bc\bar b\bar c)$ might be more favorable if the naive color-additive model of confinement is replaced by a string-inspired interaction.

Tetraquark bound states and resonances in a unitary microscopic quark model: A case study of bound states of two light quarks and two heavy antiquarks

We address $qq\overline{Q}\overline{Q}$ exotic tetraquark bound states and resonances with a fully unitarized and microscopic quark model. We propose a triple string flip-flop potential, inspired by lattice QCD tetraquark static potentials and flux tubes, combining meson-meson and double Y potentials. Our model includes the color excited potential, but neglects the spin-tensor potentials, as well as all the other relativistic effects. To search for bound states and resonances, we first solve the two-body mesonic problem. Then we develop fully unitary techniques to address the four-body tetraquark problem. We fold the four-body Schr\odinger equation with the mesonic wave functions, transforming it into a two-body meson-meson problem with nonlocal potentials. We find bound states for some quark masses, including the one reported in lattice QCD. Moreover, we also find resonances and calculate their masses and widths, by computing the $T$ matrix and finding its pole positions in the complex energy plane, for some quantum numbers. However, a detailed analysis of the quantum numbers where binding exists shows a discrepancy with recent lattice QCD results for the $ll\overline{b}\overline{b}$ tetraquark bound states. We conclude that the string flip-flop models need further improvement.

Rapid thermal co-annihilation through bound states in QCD

The co-annihilation rate of heavy particles close to thermal equilibrium, which plays a role in many classic dark matter scenarios, can be "simulated" in QCD by considering the pair annihilation rate of a heavy quark and antiquark at a temperature of a few hundred MeV. We show that the so-called Sommerfeld factors, parameterizing the rate, can be defined and measured non-perturbatively within the NRQCD framework. Lattice measurements indicate a modest suppression in the octet channel, in reasonable agreement with perturbation theory, and a large enhancement in the singlet channel, much above the perturbative prediction. The additional enhancement is suggested to originate from bound state formation and subsequent decay. Making use of a Green's function based method to incorporate thermal corrections in perturbative co-annihilation rate computations, we show that qualitative agreement with lattice data can be found once thermally broadened bound states are accounted for. We suggest that our formalism may also be applicable to specific dark matter models which have complicated bound state structures.

Towards a Theoretical Understanding of theXYZMesons from QCD

The XYZ mesons are mesons that contain a heavy quark and antiquark but have properties that seem to require additional constituents. Some of them are electrically charged, so they must be tetraquark mesons whose additional constituents are a light quark and antiquark. The list of XYZ mesons has grown to about two dozen over the last decade. A promising approach to understanding these mesons within QCD is the Born-Oppenheimer approximation, which reduces the problem to the solution of the Schrodinger equation in potentials that can be calculated using lattice QCD. The Born-Oppenheimer approximation has not yet revealed the pattern of the XYZ mesons, but it provides a compelling framework for understanding them from the fundamental theory.

Quarkonium hybrids with nonrelativistic effective field theories

We construct a nonrelativistic effective field theory description of heavy quarkonium hybrids from QCD. We identify the symmetries of the system made of a heavy quark, a heavy antiquark, and glue in the static limit. Corrections to this limit can be obtained order by order in an expansion in the inverse of the mass $m$ of the heavy quark. At order $1/m$ in the expansion, we obtain at the level of potential Non-Relativistic QCD a system of coupled Schr\"odinger equations that describes hybrid spin-symmetry multiplets, including the mixing of different static energies into the hybrid states, an effect known as $\Lambda$-doubling in molecular physics. In the short distance, the static potentials depend on two nonperturbative parameters, the gluelump mass and the quadratic slope, which can be determined from lattice calculations. We adopt a renormalon subtraction scheme for the calculation of the perturbative part of the potential. We numerically solve the coupled Schr\"odinger equations and obtain the masses for the lowest lying spin-symmetry multiplets for $c\bar{c}$, $b\bar{c}$, and $b\bar{b}$ hybrids. The $\Lambda$-doubling effect breaks the degeneracy between opposite parity spin-symmetry multiplets and lowers the mass of the multiplets that get mixed contributions of different static energies. We compare our findings to the experimental data, direct lattice computations, sum rules calculations, and discuss the relation to the Born-Oppenheimer approximation.

Quarkonia disintegration due to time dependence of the qq̄ potential in relativistic heavy-ion collisions

Rapid thermalization in ultra-relativistic heavy-ion collisions leads to fast changing potential between a heavy quark and antiquark from zero temperature potential to the finite temperature one. Time-dependent perturbation theory can then be used to calculate the survival probability of the initial quarkonium state. In view of very short time scales of thermalization at relativistic heavy-ion collider (RHIC) and large hadron collider (LHC) energies, we calculate the survival probability of [Formula: see text] and [Formula: see text] using sudden approximation. Our results show that quarkonium decay may be significant even when temperature of quark–gluon plasma (QGP) remains low enough so that the conventional quarkonium melting due to Debye screening is ineffective.

Chiral drag force

We provide a holographic evaluation of novel contributions to the drag force acting on a heavy quark moving through strongly interacting plasma. The new contributions are chiral in the sense that they act in opposite directions in plasmas containing an excess of left- or right-handed quarks. The new contributions are proportional to the coefficient of the axial anomaly, and in this sense also are chiral. These new contributions to the drag force act either parallel to or antiparallel to an external magnetic field or to the vorticity of the fluid plasma. In all these respects, these contributions to the drag force felt by a heavy quark are analogous to the chiral magnetic effect (CME) on light quarks. However, the new contribution to the drag force is independent of the electric charge of the heavy quark and is the same for heavy quarks and antiquarks, meaning that these novel effects do not in fact contribute to the CME current. We show that although the chiral drag force can be non-vanishing for heavy quarks that are at rest in the local fluid rest frame, it does vanish for heavy quarks that are at rest in a suitably chosen frame. In this frame, the heavy quark at rest sees counterpropagating momentum and charge currents, both proportional to the axial anomaly coefficient, but feels no drag force. This provides strong concrete evidence for the absence of dissipation in chiral transport, something that has been predicted previously via consideration of symmetries. Along the way to our principal results, we provide a general calculation of the corrections to the drag force due to the presence of gradients in the flowing fluid in the presence of a nonzero chemical potential. We close with a consequence of our result that is at least in principle observable in heavy ion collisions, namely an anticorrelation between the direction of the CME current for light quarks in a given event and the direction of the kick given to the momentum of all the heavy quarks and antiquarks in that event.

Relationship between quark-antiquark potential and quark-antiquark free energy in hadronic matter**Supported by National Natural Science Foundation of China (11175111)

In high-temperature quark-gluon plasma and its subsequent hadronic matter created in a high-energy nucleus-nucleus collision, the quark-antiquark potential depends on the temperature. The temperature-dependent potential is expected to be derived from the free energy obtained in lattice gauge theory calculations. This requires one to study the relationship between the quark-antiquark potential and the quark-antiquark free energy. When the system's temperature is above the critical temperature, the potential of a heavy quark and a heavy antiquark almost equals the free energy, but the potential of a light quark and a light antiquark, of a heavy quark and a light antiquark and of a light quark and a heavy antiquark is substantially larger than the free energy. When the system's temperature is below the critical temperature, the quark-antiquark free energy can be taken as the quark-antiquark potential. This allows one to apply the quark-antiquark free energy to study hadron properties and hadron-hadron reactions in hadronic matter.

Azimuthal correlations of heavy quarks in Pb + Pb collisions ats=2.76TeV at the CERN Large Hadron Collider

In this paper we study the azimuthal correlations of heavy quarks in Pb+Pb collisions with $\sqrt{s}=2.76$ TeV at LHC. Due to the interaction with the medium heavy quarks and antiquarks are deflected from their original direction and the initial correlation of the pair is broadened. We investigate this effect for different transverse momentum classes. Low-momentum heavy-quark pairs lose their leading order back-to-back initial correlation, while a significant residual correlation survives at large momenta. Due to the larger acquired average deflection from their original directions the azimuthal correlations of heavy-quark pairs are broadened more efficiently in a purely collisional energy loss mechanism compared to including radiative corrections. This discriminatory feature survives when next-to-leading order production processes are included.

Born-Oppenheimer approximation for theXYZmesons

Many of the XYZ mesons discovered in the last decade can be identified as bound states in Born-Oppenheimer (B-O) potentials for a heavy quark and antiquark. They include quarkonium hybrids, which are bound states in excited flavor-singlet B-O potentials, and quarkonium tetraquarks, which are bound states in flavor-nonsinglet B-O potentials. We present simple parameterizations of the deepest flavor-singlet B-O potentials. We infer the deepest flavor-nonsinglet B-O potentials from lattice QCD calculations of static adjoint mesons. Selection rules for hadronic transitions are used to identify XYZ mesons that are candidates for ground-state energy levels in the B-O potentials for charmonium hybrids and tetraquarks. The energies of the lowest-energy charmonium hybrids are predicted by using the results of lattice QCD calculations to calculate the energy splittings between the ground states of different B-O potentials and using the Schroedinger equation to determine the splittings between energy levels within a B-O potential.

Selection Rules for Hadronic Transitions ofXYZMesons

Many of the XYZ mesons discovered in the last decade can be identified as bound states of a heavy quark and antiquark in Born-Oppenheimer (BO) potentials defined by the energy of gluon and light-quark fields in the presence of static color sources. The mesons include quarkonium hybrids, which are bound states in excited flavor-singlet BO potentials, and quarkonium tetraquarks, which are bound states in BO potentials with light-quark+antiquark flavor. The deepest hybrid potentials are known from lattice QCD calculations. The deepest tetraquark potentials can be inferred from lattice QCD calculations of static adjoint mesons. Selection rules for hadronic transitions are derived and used to identify XYZ mesons that are candidates for ground-state energy levels in the BO potentials for charmonium hybrids and tetraquarks.

Conformal symmetry of the Lange–Neubert evolution equation

The Lange–Neubert evolution equation describes the scale dependence of the wave function of a meson built of an infinitely heavy quark and light antiquark at light-like separations, which is the hydrogen atom problem of QCD. It has numerous applications to the studies of B-meson decays. We show that the kernel of this equation can be written in a remarkably compact form, as a logarithm of the generator of special conformal transformation in the light-ray direction. This representation allows one to study solutions of this equation in a very simple and mathematically consistent manner. Generalizing this result, we show that all heavy–light evolution kernels that appear in the renormalization of higher-twist B-meson distribution amplitudes can be written in the same form.

Color spin wave functions of heavy tetraquark states

Using the variational method, we calculate the mass of the J^P=1^+ (ud)bar(bb) tetraquark containing two identical heavy antiquarks in a nonrelativistic potential model with color confinement and spin hyperfine interaction. In particular, we extend a previous investigation of the model by Brink and Stancu by investigating the effect of including the color anti-sextet component of the diquark configuration as well as using several more Gaussian parametrization for the L=0 part of the spatial wave function. We find that for the heavy tetraquark, the 6bar{6} component among the color singlet bases is negligible and that the previously used specific Gaussian spatial configuration is good enough in obtaining the ground state energy.

$\bar{D}$ and B nuclei with one pion exchange potential

We discuss the possible existence of exotic dibaryons with a heavy antiquark, being realized three-body systems, [Formula: see text] and B(*)NN. These are genuinely exotic states with no quark-antiquark annihilation. We consider the heavy quark spin symmetry and chiral symmetry, and introduce the one pion exchange potential between a [Formula: see text] meson and a nucleon N. As for the NN interaction, we employ the Argonne [Formula: see text] potential. By solving the coupled-channel equations for PNN and [Formula: see text], we find bound and resonant states near the thresholds both in charm and bottom sectors.

Exotic dibaryons with a heavy antiquark

We discuss the possible existence of exotic dibaryons with a heavy antiquark, being realized three-body systems, Dbar^(*)NN and B^(*)NN. These are genuinely exotic states with no quark-antiquark annihilation. We consider the heavy quark spin and chiral symmetries, and introduce the one pion exchange potential between a Dbar^(*) (B^(*)) meson and a nucleon N. As for the NN interaction, we employ the Argonne v^\prime_8 potential. By solving the coupled-channel equations for PNN and P^* NN (P^(*)=Dbar^(*) and B^(*)), we find bound states for (I,J^P)=(1/2,0^-) as well as resonant states for (I,J^P)=(1/2,1^-) both in Dbar^(*)NN and B^(*)NN systems. We also discuss the heavy quark limit, and find that the spin degeneracy is realized in the bound states with (I,J^P)=(1/2,0^-) and (1/2,1^-).

Lattice QCD signal for a bottom-bottom tetraquark

Utilizing lattice QCD results for the potential of two static antiquarks and two dynamical quarks as well as quark model techniques for the dynamics of two heavy antiquarks in a cloud of two light quarks, we are provided with an accurate framework for the study of possibly existing heavy-heavy-light-light tetraquarks. Among the possible quantum numbers of such a system, we find binding in only one channel, the scalar isosinglet. Solving the Schroedinger equation for the displacement of the heavy antiquarks and taking systematic errors into account, we find an antibottom-antibottom-light-light bound state with a confidence level of around 1.8 sigma ... 3.0 sigma and binding energy of approximately 30 MeV ... 57 MeV.

ND¯system: A challenge forP¯ANDA

We study the $N \bar D$ system by means of a chiral constituent quark model. This model, tuned in the description of the baryon and meson spectra as well as the $NN$ interaction, provides parameter-free predictions for the charm -1 two-hadron systems. The presence of a heavy antiquark makes the interaction rather simple. We have found sharp quark-Pauli effects in some particular channels, generating repulsion, due to lacking degrees of freedom to accommodate the light quarks. Our results point to the existence of an attractive state, the $\Delta \bar D^*$ with $(T,S)=(1,5/2)$, presenting a resonance close to threshold. It would show up in the scattering of $\bar D$ mesons on nucleons as a D wave state with quantum numbers $(T)J^P=(1)5/2^-$. This resonance resembles our findings in the $\Delta\Delta$ system, that offered a plausible explanation to the cross section of double-pionic fusion reactions through the so-called {\it ABC} effect. The study of the interaction of $D$ mesons with nucleons is a goal of the $\bar {\rm P}$ANDA Collaboration at the European facility FAIR and, thus, the present theoretical study is a challenge to be tested at the future experiments.