The hidden-charm pentaquark and tetraquark states

A large number of experimental discoveries especially in the heavy quarkonium sector that did not at all fit to the expectations of the until then very successful quark model led to a renaissance of hadron spectroscopy Among various explanations of the internal structure of these excitations, hadronic molecules, being analogues of light nuclei, play a unique role since for those predictions can be made with controlled uncertainty We review experimental evidences of various candidates of hadronic molecules, and methods of identifying such structures Nonrelativistic effective field theories are the suitable framework for studying hadronic molecules, and are discussed in both the continuum and finite volumes Also pertinent lattice QCD results are presented Further, we discuss the production mechanisms and decays of hadronic molecules, and comment on the reliability of certain assertions often made in the literature

Hadronic molecules

Quantum chromodynamics (QCD), the generally accepted theory for strong interactions, describes the interactions between quarks and gluons. The strongly interacting particles that are seen in nature are hadrons, which are composites of quarks and gluons. Since QCD is a strongly coupled theory at distance scales that are characteristic of observable hadrons, there are no rigorous, first-principle methods to derive the spectrum and properties of the hadrons from the QCD Lagrangian, except for lattice QCD simulations that are not yet able to cope with all aspects of complex and short-lived states. Instead, a variety of “QCD inspired” phenomenological models have been proposed. Common features of these models are predictions for the existence of hadrons with substructures that are more complex than the standard quark-antiquark mesons and the three-quark baryons of the original quark model that provides a concise description of most of the low-mass hadrons. Recently, an assortment of candidates for nonstandard multiquark mesons, meson-gluon hybrids, and pentaquark baryons that contain heavy (charm or bottom) quarks has been discovered. Here the experimental evidence for these states is reviewed and some general comparisons of their measured properties with standard quark model expectations and predictions of various models for nonstandard hadrons are made. The conclusion is that the spectroscopy of all but the simplest hadrons is not yet understood.

https://link.aps.org/accepted/10.1103/RevModPhys.90.015003

Nonstandard heavy mesons and baryons: Experimental evidence

Heavy-quark QCD exotica

Pentaquark and Tetraquark states

We present the results of a lattice calculation of tetraquark states with quark contents ${q}_{1}{q}_{2}\overline{Q}\overline{Q},{q}_{1},{q}_{2}\ensuremath{\subset}u,d,s,c$ and $Q\ensuremath{\equiv}b$, $c$ in both spin-0 ($J=0$) and spin-1 ($J=1$) sectors. This calculation is performed on three dynamical ${N}_{f}=2+1+1$ highly improved staggered quark ensembles at lattice spacings of about 0.12, 0.09, and 0.06 fm. We use the overlap action for light to charm quarks, while a nonrelativistic action with nonperturbatively improved coefficients with terms up to $\mathcal{O}({\ensuremath{\alpha}}_{s}{v}^{4})$ is employed for the bottom quark. While considering charm or bottom quarks as heavy, we calculate the energy levels of various four-quark configurations with light quark masses ranging from the physical strange quark mass to that of the corresponding physical pion mass. This enables us to explore the quark mass dependence of the extracted four-quark energy levels over a wide range of quark masses. The results of the spin-1 states show the presence of ground state energy levels which are below their respective thresholds for all the light flavor combinations. Further, we identify a trend that the energy splittings, defined as the energy difference between the ground state energy levels and their respective thresholds, increase with decreasing the light quark masses and are maximum at the physical point for all the spin-1 states. The rate of increase is, however, dependent on the light quark configuration of the particular spin-1 state. We also present a study of hadron mass relations involving tetraquarks, baryons, and mesons arising in the limit of infinitely heavy quarks and find that these relations are more compatible with the heavy quark limit in the bottom sector but deviate substantially in the charm sector. The ground state spectra of the spin-0 tetraquark states with various flavor combinations are seen to lie above their respective thresholds.

Study of doubly heavy tetraquarks in Lattice QCD

We report the ground state masses of hadrons containing at least one charm and one bottom quark using lattice quantum chromodynamics. These include mesons with spin ($J$) and parity ($P$), (${J}^{P}$): ${0}^{\ensuremath{-}}$, ${1}^{\ensuremath{-}}$, ${1}^{+}$, and ${0}^{+}$ and the spin $1/2$ and $3/2$ baryons. Among these hadrons, only the ground state of ${0}^{\ensuremath{-}}$ is known experimentally, and therefore our predictions provide important information for the experimental discovery of all other hadrons with these quark contents.

https://link.aps.org/pdf/10.1103/PhysRevLett.121.202002

Precise Predictions of Charmed-Bottom Hadrons from Lattice QCD.

We perform a lattice study of charmonium-like mesons with ${J}^{\mathrm{PC}}={1}^{++}$ and three quark contents $\overline{c}c\overline{d}u$, $\overline{c}c(\overline{u}u+\overline{d}d)$ and $\overline{c}c\overline{s}s$, where the later two can mix with $\overline{c}c$. This simulation with ${N}_{f}=2$ and ${m}_{\ensuremath{\pi}}\ensuremath{\simeq}266\text{ }\text{ }\mathrm{MeV}$ aims at the possible signatures of four-quark exotic states. We utilize a large basis of $\overline{c}c$, two-meson and diquark-antidiquark interpolating fields, with diquarks in both antitriplet and sextet color representations. A lattice candidate for $X(3872)$ with $I=0$ is observed very close to the experimental state only if both $\overline{c}c$ and $D{\overline{D}}^{*}$ interpolators are included; the candidate is not found if diquark-antidiquark and $D{\overline{D}}^{*}$ are used in the absence of $\overline{c}c$. No candidate for neutral or charged $X(3872)$, or any other exotic candidates are found in the $I=1$ channel. We also do not find signatures of exotic $\overline{c}c\overline{s}s$ candidates below 4.2 GeV, such as $Y(4140)$. Possible physics and methodology related reasons for that are discussed. Along the way, we present the diquark-antidiquark operators as linear combinations of the two-meson operators via the Fierz transformations.

X (3872 ) and Y (4140 ) using diquark-antidiquark operators with lattice QCD

The spectrum of excitations of triply-charmed baryons is computed using lattice QCD including dynamical light quark fields. The spectrum obtained has baryonic states with well-defined total spin up to 7/2 and the low-lying states closely resemble the expectation from models with an SU(6) x O(3) symmetry. As a result, energy splittings between extracted states, including those due to spin-orbit coupling in the heavy quark limit are computed and compared against data at other quark masses.

Spectroscopy of doubly-charmed baryons from lattice QCD

Slovenian Research Agency ARRS; Austrian Science Fund [FWF:I1313-N27]; Deutsche Forschungsgemeinschaft [SFB/TRR 55]; U.S. Department of Energy [DE-AC05-06OR23177]

M. Padmanath

Papers

Study of doubly heavy tetraquarks in Lattice QCD

Precise Predictions of Charmed-Bottom Hadrons from Lattice QCD.

X (3872 ) and Y (4140 ) using diquark-antidiquark operators with lattice QCD

Spectroscopy of doubly-charmed baryons from lattice QCD

Pion-nucleon scattering in the Roper channel from lattice QCD