Masses Of Excited States Research Articles

Gauge invariant smearing and the extraction of excited state masses using Wilson fermions at β = 6.2

We present an investigation of gauge invariant smearing for Wilson fermions on a 24 3 × 48 lattice at β = 6.2. We demonstrate a smearing algorithm that allows a substantial improvement in the determination of the baryon spectrum obtained using propagators smeared at both source and sink, at only a small computational cost. We investigate the matrix of correlators constructed from local and smeared operators, and are able to expose excited states of both the mesons and baryons.

Leptonic decay constants of heavy mesons in QCD

A formula for calculating the axial decay constant of heavy-light quark mesons has been obtained by means of the QCD sum rules. The calculations are based on the use of the excited state mass spectrum of the corresponding system. The calculated values for the charmed mesons are f D = 145 MeV and f F = 160 MeV. For B and B s mesons, the dependencies of the decay constants on the b-quark mass are presented. At m b = 4.55 GeV the results are f B = 165 MeV and f B s = 177 MeV.

Improved methods for computing masses from numerical simulations

An important advance in the computation of hadron and glueball masses has been the introduction of non-local operators. This talk summarizes the critical signal-to-noise ratio of glueball correlation functions in the continuum limit, and discusses the case of (q q and qqq) hadrons in the chiral limit. A new strategy for extracting the masses of excited states is outlined and tested. The lessons learned here suggest that gauge-fixed momentum-space operators might be a suitable choice of interpolating operators.

Stochastic mechanics of Abelian lattice theories

A stochastic equation for lattice theories is written, which describes a Markov process on a space lattice evolving in (stochastic) time. At the cost of requiring the construction of the drift function this reduces one dimension in numerical simulations, as compared to Monte Carlo methods. The drift can be obtained either from the asymptotic solution of an auxiliary equation or from a ground state ansatz. It is shown that for Abelian theories a drift can be constructed from ground state ansatze which are exact eigenstates of Hamiltonians with the same continuum limit as the Kogut-Susskind Hamiltonian. Lattice observables may be obtained from stochastic time correlations. In addition, a new method is obtained to measure the lowest excited state (mass gap) from the exit times of the stochastic process from a bounded region. In some cases the mass gap may be obtained at weak coupling from the theory of small random perturbations of dynamical systems.

An algorithm for high-order strong-coupling expansions: The mass gap in 3d pure Z 2 lattice gauge theory

An effecient description of all clusters contributing to the strong coupling expansion of the mass gap in three-dimensional pure Z 2 lattice gauge theory is presented. This description is correct to all orders in the strong coupling expansion and is chosen in such a way that it remains valid in four dimensions for gauge group Z 2. Relying on this description an algorithm has been constructed which generates and processes all the contributing graphs to the exact strong coupling expansion of the mass gap in the three-dimensional model in a fully automatic fashion. A major component of this algorithm can also be used to generate exact strong coupling expansions for the free energy logZ. The algorithm is correct to any order; thus the order of these expansions is only limited by the available computing power. The presentation of the algorithm is such that it can serve as a guidline for the construction of a generalized one which would also generate exact strong coupling expansions for the masses of low-lying excited states of four-dimensional pure Yang-Mills theories.

Methods in hamiltonian lattice field theory (I). Connected diagram expansions

Connected diagram expansions in hamiltonian lattice field theory are discussed, using a formalism due to Goldstone, together with the method of cumulant expansions. Connected diagram rules are derived for the ground-state energy, the axial string tension in a gauge model, and for excited state masses.

Quark masses from regularized integrals of vector current spectral functions

We give estimates of quark masses from a comparison of two methods of regularizing the coefficient of the Schwinger term. The masses of the first radial excited states of ϱ, ω, and ϕ would have to be slightly higher than indicated by the new Orsay data for this method to yield real solutions for the masses of theu, d, ands quarks.

Some Empirical Systematics of the Pion-Nucleon System

Several empirical systematics of the quantum numbers and masses of the nuclear excited states in meson( rature of the d )nucleon resonances are given. A possible selection rule is suggested. The representation of the nucleon isobars presented are based upon purely empirical rules that may lead to a better understanding of the meson( rature of the d )-nucleon interaction. (C.E.S.)