Hadron Mass Calculations Research Articles

Holographic picture of heavy vector meson melting

The fraction of heavy vector mesons produced in a heavy ion collision, as compared to a proton proton collision, serves as an important indication of the formation of a thermal medium, the quark gluon plasma. This sort of analysis strongly depends on understanding the thermal effects of a medium like the plasma on the states of heavy mesons. In particular, it is crucial to know the temperature ranges where they undergo a thermal dissociation, or melting. AdS/QCD models are know to provide an important tool for the calculation of hadronic masses, but in general are not consistent with the observation that decay constants of heavy vector mesons decrease with excitation level. It has recently been shown that this problem can be overcome using a soft wall background and introducing an extra energy parameter, through the calculation of correlation functions at a finite position of anti-de Sitter space. This approach leads to the evaluation of masses and decay constants of S wave quarkonium states with just one flavor dependent and one flavor independent parameters. Here we extend this more realistic model to finite temperatures and analyse the thermal behavior of the states $1S, 2S$ and $ 3S$ of bottomonium and charmonium. The corresponding spectral function exhibits a consistent picture for the melting of the states where, for each flavor, the higher excitations melt at lower temperatures. We estimate for these six states, the energy ranges in which the heavy vector mesons undergo a transition from a well defined peak in the spectral function to complete melting in the thermal medium. A very clear distinction between the heavy flavors emerges, with bottomonium state $\Upsilon (1S)$ surviving deconfinemet transition at temperatures much larger than the critical deconfinement temperature of the medium.

Parameter-free calculation of hadronic masses from instantons

We propose a non-perturbative calculation scheme which is based on the semi-classical approximation of QCD and can be used to evaluate quantities of interest in hadronic physics. As a first application, we evaluate the mass of the pion and of the nucleon. Such masses are related to a particular combination of Green functions which, in some limit, is dominated by the contribution of \emph{very small-sized} instantons. The size distribution of these pseudo-particles is determined by the 't Hooft tunneling amplitude formula and therefore our calculation is free from any model parameters. We prove that instanton forces generate a light pion and a nucleon with realistic mass ($M_n \sim 970 MeV$). In connection with sum-rules approaches, we discuss the overlap of instantons with pion and nucleon resonances.

Hadron mass extraction from lattice QCD

The extraction of quantities from lattice QCD calculations at realistic quark masses is of considerable importance. Whilst physical quark masses are some way off, the recent advances in the calculation of hadron masses within full QCD now invite improved extrapolation methods. We show that, provided the correct chiral behaviour of QCD is respected in the extrapolation to realistic quark masses, one can indeed obtain a fairly reliable determination of masses, the sigma commutator and the J parameter. We summarise these findings by presenting the nonanalytic behaviour of nucleon and rho masses in the standard Edinburgh plot.

Orderaimproved renormalization constants

We present nonperturbative results for the constants needed for on-shell O(a) improvement of bilinear operators composed of Wilson fermions. We work at {beta}=6.0 and 6.2 in the quenched approximation. The calculation is done by imposing axial and vector Ward identities on correlators similar to those used in standard hadron mass calculations. A crucial feature of the calculation is the use of nondegenerate quarks. We also obtain results for the constants needed for off-shell O(a) improvement of bilinears, and for the scale- and scheme-independent renormalization constants, Z{sub A}, Z{sub V}, and Z{sub S}/Z{sub P}. Several of the constants are determined using a variety of different Ward identities, and we compare their relative efficacies. In this way, we find a method for calculating c{sub V} that gives smaller errors than that used previously. Wherever possible, we compare our results with those of the ALPHA Collaboration (who use the Schro''dinger functional) and with one-loop tadpole-improved perturbation theory.

The sigma commutator from lattice QCD

As a direct source of information on chiral symmetry breaking within QCD, the sigma commutator is of considerable importance. Since hadron structure is a non-perturbative problem, numerical calculations on a space-time lattice are currently the only rigorous approach. With recent advances in the calculation of hadron masses within full QCD, it is of interest to see whether the sigma commutator can be calculated directly from the dependence of the nucleon mass on the input quark mass. We show that, provided the correct chiral behaviour of QCD is respected in the extrapolation to realistic quark masses, one can indeed obtain a fairly reliable determination of the sigma commutator using present lattice data. For two-flavour dynamical fermion QCD the sigma commutator lies between 45 and 55 MeV based on recent data from CP-PACS and UKQCD.

Hadron Mass and the Properties of Nuclear Matter in the Quark Bag Models**The project supported by National Natural Science Foundation of China (Grant No. 19775072) and the Natural Science Foundation of Guangdong Province of China (Grant No. 970130)

The MIT bag model, chiral bag model and cloudy bag model are revisited. A typical work on the hadron mass calculation by chiral bag model and cloudy bag model is shown in more details with the quark-quark-pi vertex correction and quark self-energy being emphasized. More details are given to review the quark-meson coupling model and its application in nuclear matter. We put forth the Lagrangian of the quark-meson coupling model and studied the possibility of using the model to calculate the hadron mass.

Lattice QCD calculations of the sigma commutator

As a direct source of information on chiral symmetry breaking within QCD, the sigma commutator is of considerable importance. With recent advances in the calculation of hadron masses within full QCD it is of interest to see whether the sigma commutator can be calculated directly from the dependence of the nucleon mass on the input quark mass. We show that provided the correct chiral behaviour of QCD is respected in the extrapolation to realistic quark masses one can indeed obtain a fairly reliable determination of the sigma commutator using present lattice data. Within two-flavour, dynamical-fermion QCD the value obtained lies in the range 45 to 55 MeV.

Quenched staggered light hadron spectroscopy from 48 3 × 64 at β = 6.5

We report our light hadron mass calculation based on an increased statistics of 250 quenched gauge configurations on a 48 3 × 64 lattice at β = 6.5. Quark propagators are calculated for each of these configurations with staggered wall source and point sink at quark mass values of m q = 0.01, 0.005, 0.00125. and 0.0125. We also did additional calculations to improve our understanding of systematic biases arising from autocorrelation, source size, and propagator calculations. Our earlier conclusions that the flavor symmetry breaking is reduced and the ratio m N m ϱ (∼1.25(4)) is small remains robust.

Quenched KS light hadron mass at β = 6.5 on a 64 × 48 3 lattice

We report our quenched staggered light hadron mass calculation at the coupling of β = 6.5 on a 48 3 × 64 lattice, based on an increased statistics of two hundred gauge configurations. Staggered quark wall sources with mass of m q a = 0.01, 0.005, 0.0025 and 0.00125 are used. Flavor symmetry is restored for pion and ϱ meson. The lattice scale is estimated to be a −1 = 3.7(2) GeV.

Hadron masses and decay constants with Wilson quarks at beta =5.85 and 6.0.

We present results of a high statistics calculation of hadron masses and meson decay constants in the quenched approximation to lattice QCD with Wilson quarks at $\beta=$ 5.85 and 6.0 on $24^3 \times 54$ lattices. We analyze the data paying attention in particular to the systematic errors due to the choice of fitting range and due to the contamination from excited states. We find that the systematic errors for the hadron masses with quarks lighter than the strange quark amount to 1 --- 2 times the statistical errors. When the lattice scale is fixed from the $\rho$ meson mass, the masses of the $\Omega^{-}$ baryon and the $\phi$ meson at two $\beta$'s agree with experiment within about one standard deviation. On the other hand, the central value of the nucleon mass at $\beta=6.0$ (5.85) is larger than its experimental value by about 15\% (20\%) and that of the $\Delta$ mass by about 15\% (4\%): Even when the systematic errors are included, the baryon masses at $\beta=6.0$ do not agree with experiment. Vector meson decay constants at two values of $\beta$ agree well with each other and are consistent with experiment for a wide range of the quark mass, when we use current renormalization constants determined nonperturbatively by numerical simulations. The pion decay constant agrees with experiment albeit with large errors. Results for the masses of excited states of the $\rho$ meson and the nucleon are also presented.

Light hadron masses with 4-GeV cutoff and L = 2.4 fm

We discuss preliminary results from our quenched light hadron mass calculation on a $48^3 \times 64$ lattice at the coupling of $\beta = 6.5$. Staggered quarks with masses of $m_q = 0.01, 0.005, 0.0025$ and $0.00125$ are used.

QCD spectroscopy

I review recent work on the calculation of hadron masses, decay constants and wave functions.

Simulations of 2-flavor QCD on a 324 lattice at β = 5.7

Abstract We report on the large volume, hadron mass calculations in full QCD with 2-flavor staggered fermions currently being performed on the Columbia 256-node parallel supercomputer. The calculations are being done at β = 5.7 with quark masses of ma = 0.01 and 0.025 on a 324 volume using the hybrid algorithm.

Recent results from the 256-node columbia machine

The two major calculations currently underway on the Columbia machine are a two flavor simulation using staggered fermions on a 32 4 lattice with quark masses of 0.025 and 0.01 and an eight flavor calculation on 16 3 × N t lattices for N t = 4, 8, 16 and 32 using a dynamical quark mass of 0.015 and a variety of valence quark masses. These eight flavor calculations suggest a quite complex phase structure for eight flavor QCD including a strong, first order bulk transition for β = 4.59(2). Questions related to the zero quark mass limit of our earlier 16 3 × 32 hadron mass calculations are also discussed.

Hadron masses in QCD with two flavors of dynamical fermions at beta =5.7.

A hadron mass calculation is reported using two flavors of dynamical, staggered fermions with masses of {ital ma}=0.01, 0.015, 0.02, and 0.025 on a 16{sup 3}{times}32 lattice. The masses of hadrons containing valence quarks with {ital ma}=0.004, 0.07, 0.1, 0.14, and 0.25 were also computed to study the limit {ital ma}{r arrow}0 and the strange particle spectrum. For {ital ma}=0.01, the mass ratio {ital m}{sub {ital N}}/{ital m}{sub {rho}}=1.527(11) is 25% larger than experiment while the results {ital f}{sub {pi}}/{ital m}{sub {rho}}=0.14(1) and ({ital m}{sub {ital K}}{sup 2}{minus}{ital m}{sub {pi}}{sup 2})/({ital m}{sub {ital K}}{sup *}{minus}{ital m}{sub {rho}}){ital m}{sub {rho}}=2.25(3) agree somewhat better.

Hadron mass calculations with lattice constituent quarks

The author extends previous work through a series of exploratory mass calculations of relevance to meson spectroscopy. He considers a definition for a kinetic quark mass and the order-1/ma2 correction to the qq static potential due to creation and annihilation of virtual qq pairs. He also obtains the spectrum of his order-1/ma2 meson effective Hamiltonian in a reduced basis of states consisting of a static quark and antiquark separated by one lattice spacing, with the gluonic field in its ground state.

Hadron masses in 2-flavor QCD at β = 5.7

High statistics hadron mass calculations of full QCD with 2-flavor staggered fermions are performed on the Columbia 16GFLOP parallel supercomputer. At β = 5.7 with ma = 0.01 and 0.025 on a 16 3 × 32 lattice using the hybrid algorithm, the restoration of flavor symmetry is easily recognized. However, the mass ratio of the nucleon to the rho is still found to be too high, even when the valence quark mass is reduced to m v a = 0.004. The results at ma = 0.025 with various quenched strange quark masses indicate that better mass ratios of strange hadrons to the nucleon are possible at m s a = 0.1. We also find a factor of two reduction in the errors for the ϱ and nucleon masses by averaging over many time slices in each configuration.

Study of the hadron mass spectrum with dynamical kogut-susskind fermions

Status report is made of a hadron mass calculation with two flavors of dynamical Kogut-Susskind quarks on a lattice of sizes 8 4 – 20 4 and β = 5.5 – 5.7 at m q a = 0.01 and 0.02. Size effects in hadron masses are appreciable at least up to a 16 4 lattice at β = 5.7 and m q a = 0.01. Restoration of flavor symmetry with an increasing β is observed in the pion channel. Various ϱ and nucleon operators give consistent values for their masses. Signal for the Δ baryon is observed, whose mass is larger than that of nucleon by about 10% at β = 5.7 and m q a = 0.01.

QCD with dynamical fermions

We present our latest hadron mass calculations for four flavors of staggered fermions on a 24 × 16 3 lattice at quark mass ma = 0.010 and β = 5.35. Our work clearly shows a systematic tendency for the nucleon to ϱ meson mass ratio to decrease below the naive quark model value of 3 2 as the zero quark mass limit is approached. This completes an extensive study of hadron spectroscopy using the pseudofermion method at numerous quark mass values for β = 5.20 and β = 5.35. We also present initial results of our new Hybrid Monte Carlo analysis at β = 5.35 and ma = 0.025 on the 24 × 16 3 lattice. We discuss the performance of the algorithm on this lattice, and we measure hadron masses and the interquark potential. Where we can compare results, we find good agreement with our earlier pseudofermion calculations.

The finite temperature phase transition in four flavour QCD on an 8×12 3 lattice

We present results of a numerical study of lattice QCD with four dynamical flavours of staggered fermions, performed by using a hybrid Monte Carlo algorithm on an 8×12 3 lattice. We find a rapid change in the average value of the Polyakov loop at β c=5.25±0.025 for a quark mass ma=0.025; at this mass value, the behaviour of the chiral order parameter, 〈 ΨΨ〉 does not yet allow an independent determination of the transition point. Using existing hadron mass calculations, the value of β c we have obtained here would lead to a transition temperature T∼100 MeV.