Hadron masses in lattice QCD

Light hadron spectrum and light quark masses from lattice QCD

Deriving the light hadron spectrum from first principles of QCD has been a fundamental issue in elementary particle physics since the mid-1970s, when QCD was established. With this goal in mind, we have carried out large-scale simulations of lattice QCD on the CPPACS computer. In this article, we present results for the light hadron spectrum derived in the quenched approximation to lattice QCD. We find that although the global structure of the observed spectrum is reproduced, the quenched spectrum systematically deviates from experiment when examined with an accuracy at better than a 10% level. Results for light quark masses are also reported. Another simulation of full QCD done recently (also on the CP-PACS computer) shows indications that the discrepancy observed in quenched QCD is significantly reduced by the introduction of two flavors of light dynamical quarks.

Calculation of the renormalized charmed-quark mass in lattice QCD

Light quark masses for dynamical, non-perturbatively O( a) improved Wilson fermions

It is shown that the mass difference between \ensuremath{\eta}\ensuremath{'} and pseudoscalar octet mesons can be calculated in quenched lattice QCD with the aid of a variant wall source technique. The estimated mass difference increases as the quark mass decreases, and its value extrapolated to the zero-quark-mass limit. ${\mathrm{m}}_{\mathrm{\ensuremath{\eta}}\ensuremath{'}}^{2}$-${\mathrm{m}}_{8}^{2}$=(750\ifmmode\pm\else\textpm\fi{}40 MeV${)}^{2}$, is close to the value determined from experiment (850 MeV${)}^{2}$. These results indicate that the long-standing U(1) problem could be solved in lattice QCD, with its essential part being understood within the quenched approximation. We also comment on implications of our results on spurious infrared divergences in quenched QCD.

A method for computing electromagnetic properties of hadrons in lattice QCD\nis described and preliminary numerical results are presented. The\nelectromagnetic field is introduced dynamically, using a noncompact\nformulation. Employing enhanced electric charges, the dependence of the\npseudoscalar meson mass on the (anti)quark charges and masses can be accurately\ncalculated. At $\\beta=5.7$ with Wilson action, the $\\pi^+-\\pi^0$ splitting is\nfound to be $4.9(3)$ MeV. Using the measured $K^0-K^+$ splitting, we also find\n$m_u/m_d = .512(6)$. Systematic errors are discussed.\n

We present results for the static interquark potential, lightest glueballs, light hadron spectrum, and topological susceptibility using a nonperturbatively improved action on a ${16}^{3}\ifmmode\times\else\texttimes\fi{}32$ lattice at a set of values of the bare gauge coupling and bare dynamical quark mass chosen to keep the lattice size fixed in physical units (\ensuremath{\sim}1.7 fm). By comparing these measurements with a matched quenched ensemble, we study the effects due to two degenerate flavors of dynamical quarks. With the greater control over residual lattice spacing effects which these methods afford, we find some evidence of charge screening and some minor effects on the light hadron spectrum over the range of quark masses studied ${(M}_{\mathrm{PS}}{/M}_{V}>~0.58,$ where PS denotes pseudoscalar and $V$ denotes vector). More substantial differences between quenched and unquenched simulations are observed in measurements of topological quantities.

Light hadron spectrum — MILC results with the Kogut-Susskind and Wilson actions

We present the final analysis of the light and strange hadron spectra from a full QCD lattice simulation with two degenerate dynamical sea quark flavours at $\beta = 5.6$ on a $16^3 \times 32$ lattice. Four sets of sea quark masses corresponding to the range $.69 \leq m_\pi/m_\rho \leq .83$ are investigated. For reference we also ran a quenched simulation at $\beta_{\sf eff} = 6.0$, which is the point of equal lattice spacing, $a_{\rho}^{-1}$. In the light sector, we find the chiral extrapolation to physical u- and d- masses to present a major source of uncertainty, comparable to the expected size of unquenching effects. From linear and quadratic fits we can estimate the errors on the hadron masses made from light quarks to be on a 15 % level prior to the continuum extrapolation. For the hadrons with strange valence quark content, the $N_F = 2$ approximation to QCD appears not to cure the well-known failure of quenched QCD to reproduce the physical $K-K^*$ splitting.

Full QCD light hadron spectrum from the CP-PACS

We show results for the $\ensuremath{\Upsilon}$ spectrum calculated in lattice QCD including for the first time vacuum polarization effects for light $u$ and $d$ quarks as well as $s$ quarks. We use gluon field configurations generated by the MILC collaboration. The calculations compare the results for a variety of $u$ and $d$ quark masses, as well as making a comparison to quenched results (in which quark vacuum polarization is ignored) and results with only $u$ and $d$ quarks. The $b$ quarks in the $\ensuremath{\Upsilon}$ are treated in lattice Nonrelativistic QCD through NLO in an expansion in the velocity of the $b$ quark. We concentrate on accurate results for orbital and radial splittings where we see clear agreement with experiment once $u$, $d$ and $s$ quark vacuum polarization effects are included. This now allows a consistent determination of the parameters of QCD. We demonstrate this consistency through the agreement of the $\ensuremath{\Upsilon}$ and $B$ spectrum using the same lattice bare $b$ quark mass. A one-loop matching to continuum QCD gives a value for the $b$ quark mass in full lattice QCD for the first time. We obtain ${m}_{b}^{\overline{\mathrm{MS}}}({m}_{b}^{\overline{\mathrm{MS}}})=4.4(3)\text{ }\text{ }\mathrm{GeV}$. We are able to give physical results for the heavy quark potential parameters, ${r}_{0}=0.469(7)\text{ }\text{ }\mathrm{fm}$ and ${r}_{1}=0.321(5)\text{ }\text{ }\mathrm{fm}$. Results for the fine structure in the spectrum and the $\ensuremath{\Upsilon}$ leptonic width are also presented. We predict the $\ensuremath{\Upsilon}\ensuremath{-}{\ensuremath{\eta}}_{b}$ splitting to be 61(14) MeV, the ${\ensuremath{\Upsilon}}^{\ensuremath{'}}\ensuremath{-}{\ensuremath{\eta}}_{b}^{\ensuremath{'}}$ splitting as 30(19) MeV and the splitting between the ${h}_{b}$ and the spin-average of the ${\ensuremath{\chi}}_{b}$ states to be less than 6 MeV. Improvements to these calculations that will be made in the near future are discussed.

An important tool for the analysis of results of numerical simulations of lattice QCD is chiral perturbation theory. In the Wilson chiral perturbation theory the effects of the finite lattice spacingaare taken into account. In recent years the effects of isospin splitting on the masses of hadrons have been investigated in the Monte Carlo simulations. Correspondingly, in this paper we derive the expansions of the masses of the pseudoscalar mesons in chiral perturbation theory at next-to-leading order for twisted mass lattice QCD with three light quark flavours, taking the mass difference between the up- and downquarks into account. The results include terms up to ordersmq2in the quark masses,Δm2in the mass splitting between up- and downquarks, anda2in the lattice spacing, respectively.

Light hadron spectrum with two flavors of O(a) improved dynamical quarks: final results from JLQCD

Hadron mass calculations are carried out in lattice QCD on a 9/sup 3/ x 18 lattice for flavor-nonsinglet mesons and baryons. Dynamical quark loops are fully incorporated with the Langevin technique. The contribution of dynamical quark loops significantly modifies the hadron masses in lattice units, but its dominant part can be absorbed into a shift of the coupling constant for the quark mass range we explored.

Through the embedding of superconformal quantum mechanics into AdS space, it is possible to construct an effective supersymmetric QCD light-front Hamiltonian for hadrons, which includes a spin-spin interaction between the hadronic constituents. A specific breaking of conformal symmetry determines a unique effective quark-confining potential for light hadrons, as well as remarkable connections between the meson, baryon, and tetraquark spectra. The pion is massless in the chiral limit and has no supersymmetric partner. The excitation spectra of relativistic light-quark meson, baryon and tetraquark bound states lie on linear Regge trajectories with identical slopes in the radial and orbital quantum numbers. Although conformal symmetry is strongly broken by the heavy quark mass, the basic underlying supersymmetric mechanism, which transforms mesons to baryons (and baryons to tetraquarks) into each other, still holds and gives remarkable connections across the entire spectrum of light, heavy-light and double-heavy hadrons. Here we show that all the observed hadrons can be related through this effective supersymmetric QCD, and that it can be used to identify the structure of the new charmonium states.