After presenting the motivations to explore the low-lying scalar mesons such as the $σ$, $a_0$ and $κ$ in the unquenched as well as quenched lattice QCD, we review the works done by our collaboration (SCALAR Collaboration) with a what-to-do-next list. We briefly mention the imporatance to explore the $N_c$ dependence of and possible effects of the $U_A(1)$ anomaly to the properties the low-lying scalar mesons.
In situations where the low lying eigenmodes of the Dirac operator are suppressed one observed degeneracies of some meson masses. Based on these results a hidden symmetry was conjectured, which is not a symmetry of the Lagrangian but emerges in the quantization process. We show here how the difference between classes of meson propagators is governed by the low modes and shrinks when they disappear.
We present preliminary results for the B meson decay constant and masses of low-lying heavy-light mesons in the static limit. Calculations were performed on the lattice in the quenched approximation using multistate smearing functions generated from a Hamiltonian for a spinless relativistic quark. The 2S--1S and 1P--1S mass splittings are measured. Using the 1P--1S charmonium splitting to set the overall scale, the ground state decay constant, f_B, is 319 +- 11 (stat) MeV.
The lowest eigenmodes of the Dirac operator are related to the dynamical breaking of the chiral symmetry in Quantum Chromodynamics (QCD). In our work we construct quark propagators which exclude a varying number of the lowest Dirac eigenmodes and study the influence thereof on meson correlators and the meson spectrum. That procedure partially restores the chiral symmetry (in the valence sector) and we observe degeneracies in the spectrum while confinement seems not to be affected.
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.
We compute the low energy mass spectrum of lattice QCD in the large $N_C$ limit. Expanding around a gauge-invariant ground state, which spontaneously breaks the discrete chiral symmetry, we derive an improved strong-coupling expansion and evaluate, for any value of $N_C$, the masses of the low-lying states in the unflavored meson spectrum. We then take the 't Hooft limit by rescaling $g^2 N_C\to g^2$; the 't Hooft limit is smooth and no arbitrary parameters are needed. We find, already at the fourth order of the strong coupling perturbation theory, a very good agreement between the results of …
Using lattice QCD simulation in the quenched approximation, we study the $κ$ meson, which is ^3P_0 in the quark model, and compare experimental and other lattice data. The $κ$ is the lowest scalar meson with strangeness and constitutes the scalar nonet. The obtained mass is much higher than the recent experimental value, and therefore the $κ(800)$ is difficult to consider as a simple two-body constituent-quark structure, and may have another unconventional structure.
We study the isoscalar and isovector $J=0,1$ mesons with the overlap operator within two flavour lattice QCD. After subtraction of the lowest-lying Dirac eigenmodes from the valence quark propagator all disconnected contributions vanish and all possible point-to-point $J=0$ correlators become identical, signaling a simultaneous restoration of both $SU(2)_L \times SU(2)_R$ and $U(1)_A$ symmetries. The ground states of the $π,σ,a_0,η$ mesons do not survive this truncation. All possible $J=1$ states have a very clean exponential decay and become degenerate, demonstrating a $SU(4)$ symmetry of a d…
We argue that in generic AdS/QCD models (confining gauge theories dual to string theory on a weakly-curved background), the couplings g_{rho HH} of any rho meson to any hadron H are quasi-universal, lying within a narrow band near m(rho)^2/f(rho). The argument relies upon the fact that the rho is the lowest-lying state created by a conserved current, and the detailed form of the integrals which determine the couplings in AdS/QCD. Quasi-universality holds even when rho-dominance is violated. The argument fails for all other hadrons, except the lowest-lying spin-two hadron created by the energy-…
Lattice QCD allows us to probe the low-lying hadron spectrum in finite-volume using a basis of single- and multi-hadron interpolating operators. Here we examine the effect of including tetraquark operators on the spectrum in the scalar meson sectors containing the $K_0^*(700)$ ($κ$) and the $a_0(980)$ in $N_f = 2 + 1$ QCD, with $m_π\approx 230$ MeV. Preliminary results of additional finite-volume states found using tetraquark operators are shown, and possible implications of these states are discussed.
We present a quenched calculation of meson correlators with the overlap fermion at very small masses 2.6--13 MeV. In this region the pion Compton wavelength is larger than our lattice size L\simeq 1.23fm and the system is in the so-called epsilon-regime of chiral perturbation theory. We found that the scalar and pseudo-scalar correlators are precisely approximated by a few hundred low-lying fermion eigenmodes in this regime, whereas axial-vector correlator receives significant contributions from higher eigenmodes. We also measure the disconnected pseudo-scalar correlator, which is well saturat…
We present a calculation of the spectrum of low-lying D and D_s mesons calculated on 2+1 flavor configurations with Clover-Wilson quarks generated by the PACS-CS collaboration. S- and P-wave states are explored for pion masses down to 156MeV, including some excited states. As a benchmark, a calculation of the low-lying charmonium spectrum is performed. While the charmonium results agree favorably with experiment, noticeable differences remain for charmed mesons in channels where resonances close to multi-particle thresholds exist.
Using conventional constituent-quark model, $I=1/2$ scalar $κ$, vector $K^\ast(892)$, and axial vector $K_1$ mesons are studied in the asqtad-improved staggered fermion with the wall-source and point-sink interpolators. The mass ratio of $m_κ/m_{K^\ast(892)}$ is numerically confirmed to vary apparently with quark mass, and the experimental ordering $m_{K^\ast(892)} > m_κ$ is elegantly hold when the light $u/d$ quark masses are sufficiently small, while the valence strange quarks are fixed to its physical values. We also get reasonable signals for $K_1$ meson suggested by SCALAR Collaboration f…
Lattice calculations allow us to probe the low-lying, non-perturbative spectrum of QCD using first principles numerical methods. Here we present the low-lying spectrum in the scalar sector with vacuum quantum numbers including, in fully dynamical QCD for the first time, the mixing between glueball, q-qbar, and meson-meson operators.
Smooth transitions from hadronic matter to hot and dense matter of quantum chromodynamics accompany continuous transformations in effective degrees of freedom. The microscopic descriptions should include relativistic quarks interacting inside of hadrons. In this work we construct a schematic constituent quark model with relativistic kinematics which captures the global trends of meson spectra in the light, strange, and charm quark sectors. We examine the roles of the scalar- and vector-confining potentials as well as semishort range correlations in estimating the strength of central, spin-spin…
Results are presented for the low-lying spectrum of D and D_s mesons calculated in lattice QCD using 2+1 flavor Clover-Wilson configurations made available by the PACS-CS collaboration. For the heavy quark, the Fermilab method is employed. The main focus is S- and P-wave states of charmed and charmed-strange mesons, where previous lattice QCD results have been mostly from quenched calculations. In addition to the ground states, some excited states are extracted. To check the method, calculations of the charmonium spectrum are also carried out. For charmonium, the low-lying spectrum agrees favo…
Chiral symmetry breaking in Quantum Chromodynamics is associated with the low lying spectral modes of the Dirac operator according to the Banks-Casher relation. Here we study how removal of a variable number of low lying modes from the valence quark sector affects the masses of the ground states and first excited states of baryons and mesons in two flavor lattice QCD.
Physics of the low-lying and high-lying hadrons in the light flavor sector is reviewed. While the low-lying hadrons are strongly affected by the spontaneous breaking of chiral symmetry, in the high-lying hadrons the chiral symmetry is restored. A manifestation of the chiral symmetry restoration in excited hadrons is a persistence of the chiral multiplet structure in both baryon and meson spectra. Meson and baryon chiral multiplets are classified. A relation between the chiral symmetry restoration and the string picture of excited hadrons is discussed.
We explore, by a rather peculiar limit of QCD sum rules subject to a Borel transformation (realized by allowing the related Borel mass parameter to approach infinity), how the small difference of the masses of up and down quark translates into the leptonic decay constants of pseudoscalar or vector heavy-light mesons. For the charmed and bottom mesons, we find that the decay constants of their lowest-lying charged and neutral representatives should differ by an amount of the order of 1 MeV.
We present results for the low-lying spectrum of D and D_s mesons from a lattice QCD calculation on 2+1 flavor Clover-Wilson configurations generated by the PACS-CS collaboration. In particular S- and P-wave states of charmed and charmed-strange mesons are explored for pion masses down to 156MeV. For the heavy quark, the Fermilab method is employed. In addition to ground states, some excited states are extracted using the variational method. To check our setup, calculations of the charmonium spectrum are also carried out. For charmonium, the low-lying spectrum agrees favorably with experiment.…
We consider effective theory treatment for the lowest-lying $S$- and $P$-wave states of charmed mesons. In our analysis, quantum corrections and contributions from leading chiral and heavy quark symmetry breakings are taken into account. The heavy meson mass expressions have abundance parameters, low-energy constants, in comparison to the measured charmed mesons masses. The experimental and lattice QCD data on charmed meson spectroscopy are used to extract, for the first time, the numerical values of the full set of low-energy constants of the effective chiral Lagrangian. Our results on these …
Some meson correlation functions have a large contribution from the low lying eigenmodes of the Dirac operator. The contribution of these eigenmodes can be averaged over all positions of the source. This can improve the signal in these channels significantly. We test the method for meson two-point functions.
We present our preliminary results on the determination of the low lying meson spectrum for pure gauge theory in the large $N$ limit. Some results are also shown for the theory with two flavours of quarks in the adjoint representation.
The positive-parity nucleon spectrum is explored in $2 + 1$-flavour lattice QCD in a search for new low-lying energy eigenstates near the energy regime of the Roper resonance. In addition to conventional three-quark operators, we consider novel, local five-quark meson-baryon type interpolating fields that hold the promise to reveal new eigenstates that may have been missed in previous analyses. Drawing on phenomenological insight, five-quark operators based on $σ{N}$, $π{N}$ and $a_0{N}$ channels are constructed. Spectra are produced in a high-statistics analysis on the PACS-CS dynamical gauge…
We have calculated the masses of bound states numerically in N = 1 supersymmetric Yang-Mills theory with gauge group SU(2). Using the suitably optimised variational method with an operator basis consisting of smeared Wilson loops and mesonic operators, we are able to obtain the masses of the ground states and first excited states in the scalar, pseudoscalar and spin-1/2 sectors. Extrapolated to the continuum limit, the corresponding particles appear to be approximately mass degenerate and to fit into the predicted chiral supermultiplets. The extended operator basis including both glueball-like…
The precision of lattice QCD calculations has been steadily improving for some time and is now approaching, or has surpassed, the 1% level for multiple quantities. At this level QED effects, i.e. the fact that quarks carry electric as well as color charge, come into play. In this report we will summarise results from the first lattice QCD+QED computations of the properties of ground-state charmonium and bottomonium mesons by the HPQCD Collaboration.
The low energy mass spectrum of QCD in the large $N_C$ limit is computed. The low-lying states in the meson spectrum are explicitly evaluated up to the fourth order in the strong coupling perturbative expansion. The 't Hooft limit is smooth and the meson masses are in very good agreement with the experimental values.
We compute the B^*Bπcoupling \hat{g}_{\infty} for static heavy-light meson using all-to-all propagators. It is shown that low-mode averaging with 100 low-lying eigenmodes indeed improves the signal for the 2-point and 3-point functions for heavy-light meson significantly. Our study suggests that the all-to-all propagator will be a very efficient method for high precision computation of the B^*Bπcoupling especially in unquenched QCD where the number of configurations is limited.
Physics of the low-lying and high-lying hadrons in the light flavors sector is reviewed. While the low-lying hadrons are strongly affected by both $U(1)_A$ and spontaneous $SU(2)_L \times SU(2)_R$ breakings, in the high-lying hadrons these symmetries are restored. A manifestation is a persistence of the chiral multiplet structure in both baryon and meson spectra. A fundamental origin of this phenomenon is that effects of quantum fluctuations of both quark and gluon fields must vanish at large $n$ or $J$ and a semiclassical description becomes adequate. A relation between the chiral symmetry re…
The structure of the lightest positive-parity charmed mesons from LQCD
CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所，中国科学院理论物理重点实验室）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Peng Huanwu Collaborative Center for Research and Education, Beihang University（北京航空航天大学鹏程协同创新中心）
We present results for excited meson spectra from $N_f=2$ clover-Wilson configurations provided by the CP-PACS Collaboration. In our study we investigate both low and high spin mesons. For spin-0 and spin-1 mesons, we are especially interested in the excited states. To access these states we construct several different interpolators from quark sources of different spatial smearings and calculate a matrix of correlators. For this matrix we then solve a generalized eigenvalue problem. For spin-2 and spin-3, we extract only the lowest lying states.
We study light scalar mesons with particular focus on the a_0(980) using lattice QCD with 2+1+1 dynamical quark flavors. To investigate the structure of these scalar mesons and to identify, whether a sizeable tetraquark component is present, we use a large set of operators, including diquark-antidiquark, mesonic molecule and two-meson operators. We find that the low-lying states overlap essentially exclusively with two-meson states. This indicates that in the channels investigated no tightly bound four-quark states of either molecular or diquark-antidiquark type exist.
We present results for f_B and masses of low-lying heavy-light mesons. Calculations were performed in the quenched approximation using multistate smearing functions generated from a spinless relativistic quark model Hamiltonian. Beta values range from 5.7 to 6.3, and light quark masses corresponding to pion masses as low as 300 MeV are computed at each value. We use the 1P--1S charmonium splitting to set the overall scale.
We present the current results of our simulations of N=1 supersymmetric Yang-Mills theory on a lattice. The masses of the gluino-glue particle, the a-eta-prime, the a-f0 meson, and the scalar glueball are obtained at finer lattice spacing than before, and extrapolations towards vanishing gluino mass are made. The calculations employ different levels of stout smearing. The statistical accuracy as well as the control of finite size effects and lattice artefacts are better than in previous investigations. Taking the statistical and systematic uncertainties into account, the extrapolations towards…
We present results of a high-statistics study of scalar and pseudoscalar meson propagators in quenched QCD at two values of lattice spacing, beta = 5.7 and 5.9, with clover-improved Wilson fermions. The study of the chiral limit is facilitated by the pole-shifting ansatz of the modified quenched approximation. Pseudoscalar masses and decay constants are determined as a function of quark mass and quenched chiral log effects are estimated. A study of the flavor singlet eta prime hairpin diagram yields a precise determination of the eta prime mass insertion. The corresponding value of the quenche…
