The static potentials for quark-antiquark-gluon and 3-gluon systems are computed with lattice QCD methods. For the quark-antiquark-gluon hybrid meson the static potential is obtained for different values of the angle between the quark-gluon and antiquark-gluon segments. The simulations support the formation of an adjoint string for small angles, while for large angles, the adjoint string is replaced by two fundamental strings connecting the gluon and the quarks. For the 3-gluon glueball, we discuss the corresponding Wilson loops and show that the gluons are connected by fundamental strings when the gluons are far apart.
Time correlation functions of a hybrid exotic meson operator, with JPC=1-+, generated in quenched lattice QCD are subjected to a (Bayesian) maximum entropy analysis. Five distinct spectral levels are uncovered. Their extrapolation into the physical pion mass region suggests a possible relationship to experimentally known states pi1(1400) and pi1(1600), and also to a state in the 2 GeV region carrying the same quantum numbers.
A decay width calculation for a hybrid exotic meson h, with JPC=1-+, is presented for the channel h->pi+a1. This quenched lattice QCD simulation employs Luescher's finite box method. Operators coupling to the h and pi+a1 states are used at various levels of smearing and fuzzing, and at four quark masses. Eigenvalues of the corresponding correlation matrices yield energy spectra that determine scattering phase shifts for a discrete set of relative pi+a1 momenta. Although the phase shift data is sparse, fits to a Breit-Wigner model are attempted, resulting in a decay width of about 60 MeV when a…
We study exotic static 3-body potentials, utilizing generalized Wilson Loops in SU(3) lattice QCD. For the quark-antiquark-gluon techniques we address the angles of 0, 45, 60, 90, 120, 135 and 180 degrees, between the quark-gluon and the antiquark-gluon segments. We calculate the form of the static potential and discuss whether, or not, two-body interactions exist between the three different bodies, and study the existence of repulsion between the strings. We also perform a first study of the interactions in the system of three gluon.
A review of QCD-based theory approaches to study the heavy-flavor and exotic hadrons is given. The focus is on the results from lattice QCD and from lattice QCD complemented by effective field theories. Both approaches are first briefly introduced and applied in few examples. Then the status of various hadrons sectors is presented.
We review lattice QCD results for glueballs (including a discussion of mixing with scalar mesons), hybrid mesons and other exotic states (such as $B_s B_s$ molecules).
We analyze the theory of softly broken supersymmetric $QCD$. Exotic behavior like spontaneously broken baryon number, massless composite fermions and Seiberg's duality seems to persist also in the presence of (small) soft supersymmetry breaking. We argue that certain, specially tailored, lattice simulations may be able to detect the novel phenomena. Most of the exotic behavior does not survive the decoupling limit of large SUSY breaking parameters.
Using a new quark-field construction algorithm and a large variational basis of operators, we extract a highly excited isovector meson spectrum on dynamical anisotropic lattices. We show how carefully constructed operators can be used to reliably identify the continuum spin of extracted states, overcoming the reduced cubic symmetry of the lattice. Using this method we extract, with confidence, excited states, states with exotic quantum numbers (0+-, 1-+ and 2+-) and states of high spin, including for the first time in lattice QCD, spin-four states.
We compute, for the first time using lattice QCD methods, radiative transition rates involving excited charmonium states, states of high spin and exotics. Utilizing a large basis of interpolating fields we are able to project out various excited state contributions to three-point correlators computed on quenched anisotropic lattices. In the first lattice QCD calculation of the exotic 1-+ eta_c1 radiative decay, we find a large partial width Gamma(eta_c1 -> J/psi gamma) ~ 100 keV. We find clear signals for electric dipole and magnetic quadrupole transition form factors in chi_c2 -> J/psi gamma,…
We present a spectrum of highly excited charmonium mesons up to around 4.5 GeV calculated using dynamical lattice QCD. Employing novel computational techniques and the variational method with a large basis of carefully constructed operators, we extract and reliably identify the continuum spin of an extensive set of excited states, states with exotic quantum numbers (0+-, 1-+, 2+-) and states with high spin. Calculations are performed on two lattice volumes with pion mass approximately 400 MeV and the mass determinations have high statistical precision even for excited states. We discuss the re…
We explore the spectrum of excited and exotic bottomonia using lattice QCD. Highly excited states are identified with masses up to 11,000 MeV, many of which can be grouped into supermultiplets matching those of the quark model while exotic spin--parity--charge-conjugation quantum numbers $J^{PC}=0^{+-},\,1^{-+},\,2^{+-}$ that cannot be formed from $\bar{q}q$ alone are also identified. Single-meson operator constructions are used that have good $J^{PC}$ in the continuum, these are found to overlap well onto heavy quark states with $J\le4$. A continuum $J^{PC}$ is assigned to each level, based o…
We extend Seiberg's qualitative picture of the behavior of supersymmetric QCD to nonsupersymmetric models by adding soft supersymmetry breaking terms. In this way, we recover the standard vacuum of QCD with $N_f$ flavors and $N_c$ colors when $N_f < N_c$. However, for $N_f \geq N_c$, we find new exotic states---new vacua with spontaneously broken baryon number for $N_f = N_c$, and a vacuum state with unbroken chiral symmetry for $N_f > N_c$. These exotic vacua contain massless composite fermions and, in some cases, dynamically generated gauge bosons. In particular Seiberg's electric-magnetic d…
We present highly-excited charmonium, $D_s$ and $D$ meson spectra from dynamical lattice QCD calculations with light quarks corresponding to $M_π \sim 240$ MeV and compare these to previous results with $M_π \sim 400$ MeV. Utilising the distillation framework, large bases of carefully constructed interpolating operators and a variational procedure, we extract and reliably identify the continuum spin of an extensive set of excited mesons. These include states with exotic quantum numbers which, along with a number with non-exotic quantum numbers, we identify as having excited gluonic degrees of …
We review selected lattice results on the charmonium spectrum and first attempts to search for the existence of exotic states. The hadro-quarkonium model was proposed to interpret some of the exotic states as a quarkonium core inside a hadron. We present a lattice study of the hadro-quarkonium model in the limit of static quarks. The charm quark decouples in low energy observables and binding energies of charmonium. In a model calculation we are able to evaluate the corrections to decoupling of the charm quark in the continuum.
We report our present status of on-going project on the measurement of the static quark potential in 2+1 flavour domain wall QCD with various improved gauge actions and couplings. Lattice spacing determined from Sommer scale on these ensembles are from 1.6 GeV to 2.0 GeV for $16^3 \times 32$ lattice with fifth dimension size 8. We also examine size of discretization error from scaling of a pair of dimensionless quantities, $(r_0 m_π)^2$ and $r_0 m_ρ$, and found small scaling violation.
The generalization of the Feynman-Hellmann theorem for resonance states in quantum field theory is derived. On the basis of this theorem, a criterion is proposed to study the possible exotic nature of certain hadronic states emerging in QCD. It is shown that this proposal is supported by explicit calculations in Chiral Perturbation Theory and by large-$N_c$ arguments. Analyzing recent lattice data on the quark mass dependence in the pseudoscalar, vector meson, baryon octet and baryon decuplet sectors, we conclude that, as expected, these are predominately quark-model states, albeit the correct…
The ground and first excited states of the hybrid charmonium ${\bar c} c g$, with non-exotic quantum numbers $J^{PC}=0^{-+}$, $1^{--}$ and $1^{++}$ are investigated using quenched lattice QCD. They are completely ignored in the literature, only because their ground states are degenerate with $η_c$, $J/ψ$, and $χ_{c1}$, and are difficult to be distinguished from these conventional charmonium mesons in experiment. However, we observe strong gluonic radial excitations in the first excited states; We predict that their masses are 4.352(225)GeV, 4.379(149)GeV and 7.315(257)GeV, completely different…
We compute the static-light meson spectrum using two-flavor Wilson twisted mass lattice QCD. We have considered five different values for the light quark mass corresponding to 300 MeV < m_PS < 600 MeV. We have extrapolated our results, to make predictions regarding the spectrum of B and B_s mesons.
In this article a systematic quantitative analysis of the isoscalar bosonic states is performed in the framework of supersymmetric light front holographic QCD. It is shown that the spectroscopy of the $η$ and $h$ mesons can be well described if one additional mass parameter -- which corresponds to the hard breaking of chiral $U(1)$ symmetry in standard QCD -- is introduced. The mass difference of the $η$ and $η'$ isoscalar mesons is then determined by the strange quark mass content of the $η'$. The theory also predicts the existence of isoscalar tetraquarks which are bound states of diquarks a…
We calculate the static quark and anti-quark potential both in quenched and two-flavor dynamical quark lattice QCD using DBW2 gauge and domain-wall quark actions. Lattice spacings from Sommer scale are determined. We find (i) mixing of excited states is different in between quenched and dynamical, (ii) lattice spacing $a_{r_0}\sim a_{m_ρ}$ in dynamical and (iii) coefficient of Coulomb term being $α_{N_f=0}<α_{N_f=2}$ at $a^{-1}\sim$ 2 GeV.
We study lattice QCD in the limit that the quark mass and chemical potential are simultaneously made large, resulting in a controllable density of quarks which do not move. This is similar in spirit to the quenched approximation for zero density QCD. In this approximation we find that the deconfinement transition seen at zero density becomes a smooth crossover at any nonzero density, and that at low enough temperature chiral symmetry remains broken at all densities.
We perform the first study for the static penta-quark (5Q) potential in lattice QCD with $β$=6.0 and $16^3 \times 32$ at the quenched level. Accurate results of the 5Q potential are extracted from the 5Q Wilson loop using the smearing method, which enhances the ground-state component. The tetra-quark potential for the $\rm QQ$-$\rm {\bar Q}{\bar Q}$ system is also studied in lattice QCD. The multi-quark potentials are found to be well described as a sum of the one-gluon-exchange Coulomb term and the multi-Y linear confinement term based on the flux-tube picture.
We study lattice QCD in the limit that the quark mass and chemical potential are simultaneously made large, resulting in a controllable density of quarks which do not move; this is similar in spirit to the quenched approximation for zero density QCD. In this approximation we find that the deconfinement transition seen at zero density becomes a smooth crossover for any nonzero density at which we simulated, and that at low enough temperature chiral symmetry remains broken at all densities.
We present results for the static-light meson from unquenched lattice QCD. The unquenched gauge configurations were generated using the non-perturbatively improved clover action. At the fixed lattice spacing of 0.1 fm the lightest sea quark mass used is a third of the strange quark mass. A comparison is made between heavy-light chiral perturbation theory and the f_B^(static) decay constant. The mass of the bottom quark is also reported: m_b(m_b) = 4.25(2)(11) GeV, where the first error is statistical and the last error is the systematic uncertainty.
We present results from a detailed study of singlet free energies in full QCD with realistic quark masses. An improved scheme for the non-perturbative renormalization of the Polyakov loop is used and we compare its temperature dependence for QCD with different flavor content. We also analyze screening masses extracted from singlet free energies at various temperatures close to and above the QCD transition temperature. We conclude that the temperature dependence of screening masses is well described by perturbation theory up to a non-perturbative pre-factor. An effective running coupling has be…
We extract to high statistical precision an excited spectrum of single-particle isoscalar mesons using lattice QCD, including states of high spin and, for the first time, light exotic JPC isoscalars. The use of a novel quark field construction has enabled us to overcome the long-standing challenge of efficiently including quark-annihilation contributions. Hidden-flavor mixing angles are extracted and while most states are found to be close to ideally flavor mixed, there are examples of large mixing in the pseudoscalar and axial sectors in line with experiment. The exotic JPC isoscalar states a…
We study the phase structure of effective models of finite-density QCD using analytic and lattice simulation techniques developed for the study of non-Hermitian and $\mathcal{PT}$-symmetric QFTs. Finite-density QCD is symmetric under the combined operation of the charge and complex conjugation operators $\mathcal{CK}$, which falls into the class of so-called generalized $\mathcal{PT}$ symmetries. We show that $\mathcal{PT}$-symmetric quantum field theories can support patterned ground-state field configurations in the vicinity of a critical endpoint. We apply our methods to a lattice heavy qua…
Lattice QCD approach to study the hadronic resonances and exotic hadrons is described at an introductory level. The main challenge is that these states decay strongly via one or more decay channels, and they often lie near thersholds. Specific results for conventional and exotic hadrons are shown to illustrate the current status.
Since gluons in QCD are interacting fundamental constituents just as quarks are, we expect that in addition to mesons made from a quark and an antiquark, there should also be glueballs and hybrids (bound states of quarks, antiquarks and gluons). In general, these states would mix strongly with the conventional q-bar-q mesons. However, they can also have exotic quantum numbers inaccessible to q-bar-q mesons. Confirmation of such states would give information on the role of "dynamical" color in low energy QCD. In the quenched approximation we present a lattice calculation of the masses of mesons…
Lattice QCD studies of the $Δ$ baryon resonance and the $K_0^\ast(700)$ and $a_0(980)$ meson resonances: the role of exotic operators in determining the finite-volume spectrum
In this work we investigate the $X(3872)$ meson with quantum numbers $J^{PC}=1^{++}$ in the framework of the thermal QCD sum rules method. We use a diquark-antidiquark current with the corresponding quantum numbers and calculate the two-point correlation function including contributions of non-perturbative condensates up to six dimensions. Analysis of the obtained thermal sum rule allows us to study contributions of a medium to the mass and coupling constant of the $X(3872)$ resonance. Our numerical calculations demonstrate that the mass and the meson-current coupling constant are insensitive …
We present the first determination of the hadronic decays of the lightest exotic $J^{PC}=1^{-+}$ resonance in lattice QCD. Working with SU(3) flavor symmetry, where the up, down and strange quark masses approximately match the physical strange-quark mass giving $m_π\sim 700$ MeV, we compute finite-volume spectra on six lattice volumes which constrain a scattering system featuring eight coupled channels. Analytically continuing the scattering amplitudes into the complex energy plane, we find a pole singularity corresponding to a narrow resonance which shows relatively weak coupling to the open …
We compute the purely gluonic contribution to the static QCD potential at three--loop order. This completes the computation of the static potential at this order.
Inspired by $P_c(4380)$ and $P_c(4450)$ recently observed by LHCb, a QCD sum rule investigation is performed, by which they can be identified as exotic hidden-charm pentaquarks composed of an anti-charmed meson and a charmed baryon. Our results suggest that $P_c(4380)$ and $P_c(4450)$ have quantum numbers $J^P=3/2^-$ and $5/2^+$, respectively. Furthermore, two extra hidden-charm pentaqurks with configurations $\bar{D}Σ_c^*$ and $\bar{D}^*Σ_c^*$ are predicted, which have spin-parity quantum numbers $J^P=3/2^-$ and $J^P=5/2^+$, respectively. As an important extension, the mass predictions of hid…
We resum the leading ultrasoft logs of the singlet and octet static QCD potentials within potential NRQCD. We then obtain the complete three-loop renormalization group improvement of the singlet QCD static potential. The discrepancies between the perturbative evaluation and the lattice results at short distances are slightly reduced.
Using pNRQCD and known results for the field strength correlator, we calculate the ultrasoft contribution to the QCD static energy of a quark-antiquark pair at short distances at NNNNLO in alpha_s. At the same order, this provides the logarithmic terms of the singlet static potential in pNRQCD and the log alpha_s terms of the static energy.
We analyze the static QCD potential V_QCD(r) in the distance region 0.1 fm < r < 1 fm using perturbative QCD and OPE as basic theoretical tools. We assemble theoretical developments up to date and perform a solid and accurate analysis. The analysis consists of 3 major steps: (I) We study large-order behavior of the perturbative series of V_QCD(r) analytically. (II) In the frame of OPE, we define two types of renormalization schemes for the leading Wilson coefficient. (III) We compare numerically perturbative predictions of the Wilson coefficient and lattice computations of V_QCD(r). We perform…
We present a general class of operators resembling compact tetraquarks which have a range of colour-flavour-spin structures, transform irreducibly under the symmetries of the lattice and respect other relevant symmetries. These constructions are demonstrated in lattice QCD calculations with light quarks corresponding to $m_π=$ 391 MeV. Using the distillation framework, correlation functions involving large bases of meson-meson and tetraquark operators are computed in the isospin-1 hidden-charm and doubly-charmed sectors, and finite-volume spectra are extracted with the variational method. We f…
The status and prospects for investigations of exotic and conventional hadrons with lattice QCD are discussed. The majority of hadrons decay strongly via one or multiple decay-channels, including most of the experimentally discovered exotic hadrons. Despite this difficult challenge, the properties of several hadronic resonances have been determined within lattice QCD. To further discern the spectroscopic properties of various hadrons and to help resolve their nature we present our suggestions for future analytic and lattice studies.
We revisit the static potential for the $Q Q \bar Q \bar Q$ system using SU(3) lattice simulations, studying both the colour singlets groundstate and first excited state. We consider geometries where the two static quarks and the two anti-quarks are at the corners of rectangles of different sizes. We analyse the transition between a tetraquark system and a two meson system with a two by two correlator matrix. We compare the potentials computed with quenched QCD and with dynamical quarks. We also compare our simulations with the results of previous studies and analyze quantitatively fits of our…
These talks review and summarize our results in [1,2] on $XYZ$-like spectra obtained from QCD Laplace Sum Rules in the chiral limit at next-to-next-leading order (N2LO) of perturbation theory (PT) and including leading order (LO) contributions of dimensions $d\leq 6-8$ non-perturbative condensates. We conclude that the observed $XZ$ states are good candidates for $1^{+}$ and $0^+$ molecules or / and four-quark states while the predictions for $1^-$ and $0^-$ states are about 1.5 GeV above the $Y_{c,b}$ experimental candidates and hadronic thresholds. We (numerically) find that these exotic mol…
We compute the static energy of QCD at short distances at next-to-next-to-next-to leading-logarithmic accuracy in terms of the three-loop singlet potential. By comparing our results with lattice data we extract the value of the unknown piece of the three-loop singlet potential.
The static QCD potential is analyzed in operator-product-expansion within potential-NRQCD framework when r << 1/Lambda_{QCD}. We show that the leading short-distance contribution to the potential, defined as a perturbatively computable Wilson coefficient, can be expressed, up to O(r^2), as a ``Coulomb+linear'' potential. It coincides with the ``Coulomb+linear'' potential obtained previously from the renormalon-dominance hypothesis. Non-perturbative contributions are of order r^2 and subleading.
Chiral symmetry restoration high in the hadron spectra is expected but it remains to be confirmed both in lattice QCD computations and in experiments. Recently, a theorem was derived, relating chiral symmetry restoration high in the hadron spectra to the spontaneous generation of the dynamical quark mass in QCD. We refine the theorem in the case of static-light mesons. Utilizing chiral quark model computations and lattice QCD results for the spectrum of mesons composed by a static antiquark and a light quark, we explore chiral symmetry restoration in the spectrum and the quark running mass m(k…
We study the free energy of a static quark anti-quark pair at finite temperature in three flavor QCD with degenerate quark masses using N_tau=4 and 6 lattices with Asqtad staggered fermion action. The static free energy was calculated for different values of the quark mass and the entropy contribution at large distances has been extracted. We also calculate the renormalized Polyakov loop following the approach by Kaczmarek et al.
We review how lattice QCD can contribute to the prediction and the comprehension of tetraquarks, pentaquarks and related exotic hadrons, with at least one heavy quark. We include all families of exotic hadrons, except for the quarkless glueballs and the hexaquarks which are related to nuclear physics. Since the discovery of quarks and the development of the QCD theory, there has been a large interest in exotic hadrons, initiated by the tetraquark models developed by Jaffe in 1977. Lattice QCD, being a first principle approach to solve non-perturbative QCD, has been crucial not only to compute …
We study $I=0$ quarkonium resonances decaying into pairs of heavy-light mesons using static-static-light-light potentials from lattice QCD. To this end, we solve a coupled channel Schrödinger equation with a confined quarkonium channel and channels with a heavy-light meson pair to compute phase shifts and $\mbox{T}$ matrix poles for the lightest decay channel. We discuss our results for $S$, $P$, $D$ and $F$ wave states in the context of corresponding experimental results, in particular for $Υ(10753)$ and $Υ(10860)$.
I report on a lattice computation of the energy of a system of two light quarks and two static antiquarks as a function of the separation of the static antiquarks. In terms of hadrons such a system corresponds to a pair of B mesons and its energy to the hadronic potential. I present selected results for different isospin, spin and parity combinations of the individual B mesons mainly focusing on those channels relevant to determine, whether two B mesons may form a bound tetraquark state.
We discuss, how to study $I = 0$ quarkonium resonances decaying into pairs of heavy-light mesons using static potentials from lattice QCD. These static potentials can be obtained from a set of correlation functions containing both static and light quarks. As a proof of concept we focus on bottomonium with relative orbital angular momentum $L = 0$ of the $\bar{b} b$ pair corresponding to $J^{P C} = 0^{- +}$ and $J^{P C} = 1^{- -}$. We use static potentials from an existing lattice QCD string breaking study and compute phase shifts and $\mbox{T}$ matrix poles for the lightest heavy-light meson-m…
We systematically re-examine the extraction of the masses and couplings of the 1^{-+} hybrid, four-quark and molecule mesons from QCD spectral sum rules (QSSR). To NLO for the perturbative and power corrections, the hybrid mass is M_H=1.81(6) GeV and M_H < 2.2(2) GeV from the positivity of the spectral function. In the same way, but to LO, the four-quark state mass is M_{4q}= 1.70(4) GeV and M_{4q} < 2.4(1) GeV, while the molecule mass is about 1.3(1) GeV. The observed π_1(1400) and π_1(1600) might be explained by a two-component mixing with the set of input masses (1.2-1.3 ; 1.70-1.74) GeV an…
The definition of the quark-antiquark static potential is given within an effective field theory framework. The leading infrared divergences of the static singlet potential in perturbation theory are explicitly calculated.
We estimate the potential energy for a system of three static gluons in Lattice QCD. This is relevant for the different models of three-body glueballs have been proposed in the literature, either for gluons with a constituent mass, or for massless ones. A Wilson loop adequate to the static hybrid three-body system is developed. We study different spacial geometries, to compare the starfish model with the triangle model, for the three-gluon potential. We also study two different colour structures, symmetric and antisymmetric, and compare the respective static potentials. A first simulation is p…
Recent results on meson spectroscopy from lattice QCD are reviewed. The emphasis is on interesting states near thresholds like $Z_c^+(3900)$, $X(3872)$ and $D_{s0}^*(2317)$. Another focus is on the meson resonances in light, strange and charm sector, where the resonance masses as well as the strong decay widths are extracted from the lattice.
We discuss properties of 1^{-+} exotic mesons within the framework of the QCD field-theoretic approach. We estimate the mass of the lowest-lying 1^{-+} exotic meson using renormalization-improved QCD sum rules, and find that the mass lies around $1.26\pm 0.15$ GeV, in good agreement with the $π_1(1400)$ data. This state should be expected in QCD. We find that the mass for the lowest-lying strange 1^{-+} meson is $1.31\pm 0.19$ GeV. Our result hints that the K^*(1410) may be the lowest-lying 1^{-+} nonet state.
I consider two cases where QCD string is described by an effective theory of long strings: the static potential and meson scattering amplitudes in the Regge regime. I show how they can be solved in the mean-field approximation, justified by the large number of space-time dimensions, and argue that it turns out to be exact. I compare contributions from QCD string and perturbative QCD and discuss experimental consequences for the scattering amplitudes.
In previous works we predicted the existence of a $\bar b \bar b u d$ tetraquark with quantum numbers $I(J^P) = 0(1^+)$ using the static approximation for the $\bar b$ quarks and neglecting heavy spin effects. Since the binding energy is of the same order as expected for these heavy spin effects, it is essential to include them in the computation. Here we present a corresponding method and show evidence that binding is only slightly weakened and that the $\bar b \bar b u d$ tetraquark persists.
Comparing perturbative calculations with a lattice computation of the static energy in quantum chromodynamics at short distances, we obtain a determination of the strong coupling alpha_s. Our determination is performed at a scale of around 1.5 GeV (the typical distance scale of the lattice data) and, when evolved to the Z-boson mass scale M_Z, it corresponds to alpha_s(M_Z)=0.1156^{+0.0021}_{-0.0022}.
We study correlation functions of various static meson operators of size r at non-zero temperature in 2+1 flavor QCD, including Coulomb gauge fixed operators and Wilson loops with smeared spatial parts. The numerical calculations are performed on 24^3x6 lattices using highly improved staggered quark action. We discuss possible implications of our findings on the temperature dependence of the static energy of QQbar pair.
