Strong Coupling Lattice QCD Research Articles

Anisotropic Goldstone bosons of strong-coupling lattice QCD at high density

We calculate the spectrum of excitations in strong-coupling lattice QCD in a background of fixed baryon density, at a substantial fraction of the saturation density. We employ a next-nearest-neighbor fermion formulation that possesses the SU(N_f)xSU(N_f) chiral symmetry of the continuum theory. We find two types of massless excitations: type I Goldstone bosons with linear dispersion relations and type II Goldstone bosons with quadratic dispersion relations. Some of the type I bosons originate as type II bosons of the nearest-neighbor theory. Bosons of either type can develop anisotropic dispersion relations, depending on the value of N_f and the baryon density.

Order from disorder in lattice QCD at high density

We investigate the properties of the ground state of strong coupling lattice QCD at finite density. Our starting point is the effective Hamiltonian for color singlet objects, which looks at lowest order as an antiferromagnet, and describes meson physics with a fixed baryon number background. We concentrate on uniform baryon number backgrounds (with the same baryon number on all sites), for which the ground state was extracted in an earlier work, and calculate the dispersion relations of the excitations. Two types of Goldstone boson emerge. The first, antiferromagnetic spin waves, obey a linear dispersion relation. The others, ferromagnetic magnons, have energies that are quadratic in their momentum. These energies emerge only when fluctuations around the large-N_c ground state are taken into account, along the lines of ``order from disorder'' in frustrated magnetic systems. Unlike other spectrum calculations in order from disorder, we employ the Euclidean path integral. For comparison, we also present a Hamiltonian calculation using a generalized Holstein-Primakoff transformation. The latter can only be constructed for a subset of the cases we consider.

Spontaneous symmetry breaking in strong-coupling lattice QCD at high density

We determine the patterns of spontaneous symmetry breaking in strong-coupling lattice QCD in a fixed background baryon density. We employ a next-nearest-neighbor fermion formulation that possesses the ${SU(N}_{f})\ifmmode\times\else\texttimes\fi{}{SU(N}_{f})$ chiral symmetry of the continuum theory. We find that the global symmetry of the ground state varies with ${N}_{f}$ and with the background baryon density. In all cases the condensate breaks the discrete rotational symmetry of the lattice as well as part of the chiral symmetry group.

Existence of Baryons, Baryon Spectrum and Mass Splitting in Strong Coupling Lattice QCD

We consider a functional integral formulation for one-flavor lattice Quantum Chromodynamics in d=2,3 space dimensions and imaginary time, and work in the regime of the small hopping parameter , and zero plaquette coupling. Following the standard construction, this model exhibits positivity which is used to obtain the underlying physical Hilbert space . Then, using a Feynman-Kac formalism, we write the correlation functions for the model as functional integrals over the space of Grassmannian (fermionic) fields for one quark specie and the SU(3) gauge fields. We determine the energy-momentum spectrum associated with gauge invariant local baryon (anti-baryon) fields which are composites of three quark (anti-quark) fields. With the associated correlation functions, we establish a Feynman-Kac formula, and a spectral representation for the Fourier transform of the two-point functions. This representation allows us to show that baryons and anti-baryons arise as tightly bound, bound states of three (anti-)quarks. Labelling the components of the baryon fields by s=3/2,1/2,-1/2,-3/2, we show that the baryon and anti-baryon mass spectrum only depends on |s|, and the associated masses are given by M s = −3lnκ+r s (κ), where r s (κ) is real analytic in κ, for each d=2,3. The mass splitting is M 3/2 −M 1/2 =18κ6, for d=2 and, if any, is at least of (κ7), for d=3. In the subspace o ⊂ generated by an odd number of fermions, the baryon and anti-baryon energy-momentum dispersion curves are isolated up to near the baryon-meson threshold −5lnκ (upper gap property), identical and are determined up to (κ5). The symmetries of coordinate reflections, spatial lattice rotations, parity and charge conjugation are established for the correlation functions, and are shown to be implemented on by unitary (anti-unitary, for time reversal) operators.

Lattice gauge theory with baryons at strong coupling

We study the effective Hamiltonian for strong-coupling lattice QCD in the case of non-zero baryon density. In leading order the effective Hamiltonian is a generalized antiferromagnet. For naive fermions, the symmetry is U(4N_f) and the spins belong to a representation that depends on the local baryon number. Next-nearest-neighbor (nnn) terms in the Hamiltonian break the symmetry to U(N_f) x U(N_f). We transform the quantum problem to a Euclidean sigma model which we analyze in a 1/N_c expansion. In the vacuum sector we recover spontaneous breaking of chiral symmetry for the nearest-neighbor and nnn theories. For non-zero baryon density we study the nearest-neighbor theory only, and show that the pattern of spontaneous symmetry breaking depends on the baryon density.

Quark Cluster Model and Confinement

How confinement of quarks is implemented for multi-hadron systems in the quark cluster model is reviewed. In order to learn the nature of the confining interaction for fermions we first study 1+1 dimensional QED and QCD, in which the gauge field can be eliminated exactly and generates linear interaction of fermions. Then, we compare the two-body potential model, the flip-flop model and the Born-Oppenheimer approach in the strong coupling lattice QCD for the meson-meson system. Having shown how the long-range attraction between hadrons, van der Waals interaction, shows up in the two-body potential model, we discuss two distinct attempts beyond the two-body potential model: one is a many-body potential model, the flip-flop model, and the other is the Born-Oppenheimer approach in the strong coupling lattice QCD. We explain how the emergence of the long-range attraction is avoided in these attempts. Finally, we present the results of the application of the flip-flop model to the baryon-baryon scattering in the quark cluster model.

Form factors for semileptonic decays of heavy-light hadrons

The strong coupling lattice QCD solution \cite{APtifr} for the Isgur-Wise functions, parametrising the semileptonic decay form factors of hadrons containing a single heavy quark, is reviewed. Several useful features connected with the result are pointed out.

The spectrum of the Kazakov-Migdal model

Gross has found an exact expression for the density of eigenvalues in the simplest version of the Kazakov-Migdal model of induced QCD. In this paper we compute the spectrum of small fluctuations around Gross' semi-circular solution. By solving Migdal's wave equation we find a string-like spectrum which, in four dimensions, corresponds to the infinite tower of mesons in strong coupling lattice QCD with adjoint matter. In one dimension our formula reproduces correctly the well-known spectrum of the hermitian matrix model with a harmonic oscillator potential. We comment on the relevance of our results to the possibility of the model describing extended objects in more than one dimension.

Gauge dependence of effective quark mass and matrix elements in gauge fixed large N strong coupling lattice QCD

In conjunction with recent numerical λ∂ 0 A 0+ Λ· A =0 “λ-gauge” results reported in a companion paper, we construct an → ∞ Wilson loop picture of λ-gauge fixing in which (i) the λ-gauge expectation value of a link chain C is the weighted sum over Wilson loops made by joining to C all selfavoiding chains C̃ closing C. (ii) Wieghts A C ̄ , containing all the λ-dependence, are given by the β = 0 λ-gauge epectation value of c̃. (iii) A C ̃ equals path-products of coefficients from the trace expansion of the gauge fixing Boltzmann weight. From (ii) and (iii) we deduce formulas for β = 0 quark matrix elements. We find that M q λ decreases with increasing λ; the quark propagator dispersion relation is not covariant when λ ≠ 1; and Δ = 1 2 matching coefficients are λ-dependent. These strong coupling features are qualitatively consistent with numerical β = 5.7 and 6.0 results briefly described here for comparison purposes but mainly presented in a companion paper.

Quark confinement and number of flavors in strong coupling lattice QCD.

The problem of whether there is a constraint on the number of flavors for quark confinement in QCD is numerically investigated on a lattice with Wilson fermions as quarks. It is shown that even in the strong coupling limit, when the number of flavors exceeds 7, quarks are not confined and chiral symmetry is not spontaneously broken for light quarks.

Formula omitted]p annihilation into mesons in the 3P 0 model with a planar quark-diagram topology, and in the flux-tube model

The foundation of the 3P 0 model with a planar quark-diagram topology, which is called the A2 model and the A3 model, in the p p annihilation into two mesons and into three mesons, respectively, are studied in the flux-tube model. The flux-tube model is based on the strong coupling lattice QCD theory, and we calculate the amplitudes of a flux-tube breaking into two flux tubes and into three flux tubes numerically and compare with their continuum limits which can be calculated analytically. The strength of the flux-tube breaking is compared with the empirical strength of the 3P 0 model.

Weak interaction matrix elements in strong coupling lattice QCD

Amplitude of many non-leptonic processes require a non-perturbative calculation of matrix elements between pseudo-Goldstone boson states, after the standard perturbation theory in the Electro-Weak sector. Several such matrix elements are estimated using the techniques of strong coupling lattice QCD.