Hadron mass calculations with Susskind and Wilson fermions in the fundamental-adjoint plane

We report the results of hadron mass calculations in the valence (quenched) approximation, on an 8³ × 16 lattice. For Wilson fermions with the standard Wilson action we find good agreement with results form the hopping parameter expansion on a 16⁴ lattice at β = 5.7, with only a small finite size effect in the anticipated direction. The proton-to-rho mass ration is however too high by 60% and the delta-proton mass difference is too small. We have repeated these calculations at two points of the same string tension in the plane of the fundamental and adjoint couplings, in an attempt to avoid the unphysical critical point there; within statistical errors the meson masses remain the same, there is an improvement in the delta-proton splitting and the proton mass decreases slightly, but not enough to produce agreement with experiment. The estimates of lines of constant string tension obtained as a preliminary to the mass calculation are in good agreement with weak coupling expansions at the larger β values and cross over towards strong coupling predictions around β = 5.7. Also, crude estimates reveal the disappearance of the specific heat peak as one moves away from the unphysical singularity. For Susskind fermions we find some measure of agreement with other results form a 10³ × 16 lattice, but large, apparently finite size, effects in the rho mass at low quark mass. Meson masses in lattice units disagree with the Wilson fermion results by as much as a factor of 2. This disagreement persists in the fundamental-adjoint plane, suggesting the importance of studying improved fermion actions. At β = 6.0, Wilson fermion results show clear finite size effects on the 8³ × 16 lattice.     

Determination of the renormalized heavy-quark mass in lattice QCD

We study on the lattice the correlator of heavy-quark currents in the vicinity of vanishing momentum. The renormalized charmed quark mass, the renormalized strong coupling constant and gluon condensate can be defined in terms of the derivatives of that correlator at zero momentum. We analyze quenched Monte Carlo data on a small 8³ × 16 lattice for β = 6. We generalize dispersion relations to the lattice theory in a simple way and use them successfully to fit both the short-distance part and long-distance part of the correlator in such a small volume.     

Nucleon wave functions from lattice-gauge theories: Measurements of baryonic operators

We present measurements of the matrix elements of certain 3-quark operators that govern the short-distance and light-cone properties of the proton wave function obtained on an 8³ × 16 lattice at β = 5.7 with Wilson fermions. Using these measurements we find the proton lifetime in the minimal SU(5) grand unified theory to be incompatible with the current experimental limits, in accord with another recent lattice calculation.     

Glueball masses and the loop-loop correlation functions

We analyse the pure gauge lattice QCD by measuring loop-loop correlation functions on a 12³×32 lattice at β=5.9. We select a set of operators given by the smearing procedure. We obtain a good estimate of the mass of the 0⁺⁺ state and for the string tension, and upper bounds for the masses of the 2⁺⁺ and the 1⁺⁻ states.     

Scaling in lattice QCD: Glueball masses and string tension

We study the scaling behaviour of lattice quantum chromodynamics by comparing the β dependence of the string tension and the 0⁺⁺ glueball mass. We use a source method at β=5.7, β=5.9 and β=6.1, on lattices from 9³· 24 to 16³· 32. Assuming a string tension of about (420 MeV)², the lattice spacing ranges from 0.16 to 0.08 fm. In order to separate finite volume from scaling violation effects we have compared data from lattices having approximately the same overall physical size at the different values of β. We find deviations from scaling to be very small.     

Hadronic spectroscopy in lattice QCD with dynamical staggered quark loops

We have made a high statistics hadron mass calculation at β = 5.4 on a 6³ × 24 lattice, for the two flavour fully coupled staggered QCD. We show that the systematic error of the pseudofermionic method is small for mass measurements. As has already been shown for Wilson fermions, we find that the effect of the quark loops can be readsorbed in a shift of the coupling constant. At the quark mass values (am) = 0.2, 0.1 we also find that the proton-rho mass ratio is no longer than in the quenched theory.     

High statistics study of the chiral condensate in quenched lattice QCD

We present the results of a high statistics study of the chiral condensate in quenched lattice QCD on an 8⁴ lattice at β = 5.4, 5.5, 5.6, 5.7, 5.8 and 6.0. We see clear evidence for deviation from asymptotic scaling in the range of β considered. Our results are in agreement with the behaviour anticipated from recent Monte Carlo renormalisation group studies of the β-function. We find indications of a common scaling behaviour for the condensate, the string tension and the deconfinement temperature.     

String tension,gluebal masses and finite size effects in lattice SU(3)

We estimate the string tension by looking at Wilson loops and measuring the correlation between Wilson lines at g² = 1.0 for lattice SU(3). The bound $\text{Λ}{}_{\mathrm{<mtext>L</mtext>}}\text{σ}\text{?0.0087 ± 0.0011}$ is larger than the previous results. The mass of the 0⁺⁺ glueball is also estimated. The finite size effects on these quantities are shown to be large by comparing results on a 6³ × 10 lattice with those on 9⁴ lattice.     

Calculation of the hadron spectrum in lattice QCD

We present Monte Carlo results for the hadron mass-spectrum in lattice SU(3) using the Wilson action and the quenched approximation. We show that on a 6³· 10 lattice at β=6.0, there exist long-lived metastable states of the gauge-field, characterized by the eigenvalues of Z(3) and associated with the first-order deconfining phase transition. The hadron masses are very different in these state if the quark paths that wind around the lattice are not removed. We demonstrate two methods which eliminate a significant fraction of such quark paths. The final results for hadron masses do not agree with the experimental values. We find that the π and ?, as well as the proton and the Δ are degenerate.     

Electric field gradient at 12 N implanted into ZnO

The nuclear quadrupole interaction of short-lived β-emitter ¹²N(I?=?1, T _1/2?=?11 ms) implanted into a ZnO single crystal has been studied by means of the β-NMR method. We have observed a quadrupole splitting of ¹²N in ZnO at room temperature, from which the electric field gradient (EFG) q?=?+?(8.6 ±1.1) ×10¹⁹ V/m² was deduced assuming axially symmetric EFG with respect to the crystalline c axis. A first principle calculation does not reproduce the data under assumption of the lattice location of ¹²N at the oxygen substitutional site.     

Few-Baryon Interactions from Lattice QCD

We report the recent progress on the determination of three-nucleon forces (3NF) in lattice Quantum Chromodynamics (QCD). We utilize the Nambu–Bethe–Salpeter wave function to define the potential in quantum field theory, and extract two-nucleon forces and 3NF on equal footing. The enormous computational cost for calculating multi-baryon correlators on the lattice is drastically reduced by developing a novel contraction algorithm (the unified contraction algorithm). Quantum numbers of the three-nucleon system are chosen to be (I, J ^P ) = (1/2, 1/2⁺) (the triton channel), and we extract 3NF in which three nucleons are aligned linearly with an equal spacing. Lattice QCD simulations are performed using N _f = 2 dynamical clover fermion configurations at the lattice spacing of a = 0.156fm on a 16³ × 32 lattice with a large quark mass corresponding to m _π = 1.13 GeV. Repulsive 3NF is found at short distance.     

Interatomic force constants studies of AMF3perovskite-type crystals (A = K,Rb; M = Mg,Ni, Co,Zn, Mn)

A simple model involving only three force constants allows us to evaluate the short range interactions in perovskite fluorides from the experimental values of the elastic constants and the lattice parameters of these compounds. The results indicate that the A-F bonds are quite central in character whereas the M-F bonds are axially symmetric; thus the short range A-F interactions are assumed to have the Born-Mayer form:ZZZZZBy studying the variations of the force constants with respect to the lattice parameter r, it is determined that ρ = 0·232 , λ = 2·8 × 10^?8 ergs for K⁺-F^?; ρ = 0·232 , λ = 4·1 × 10^?8 ergs for Rb⁺-F^?; λ₂, ρ₂ and ρ₂ are respectively 6·9 × 10^?10 ergs, 0·34 , 0·98for Co²⁺-F^? and 2·9 × 10^?10 ergs, 0·46 , 1·40for Mn²⁺-F^?. Taking into account both the short range repulsive potential and the long range electrostatic potential we can study the variations of the lattice energy as a function of r near the equilibrium position and deduce a theoretical value of the lattice distance. In spite of the simplicity of the model, the discrepancy between the experimental and the theoretical values is less than 10 per cent for all the compounds.     

Inverse Raman spectrum of the ν1-fundamental of CF4

We have obtained fully resolved spectra of the ν₁ (Q-branch) band of CF₄ at a pressure of 4 Torr using a variation of stimulated Raman spectroscopy. With an experimental resolution of ≤0.004 cm^?1, no detectable tensor splitting of the rotational levels exists up to J = 55. The spectrum is readily fit with a band origin α = 909.0720 cm^?1 and a single rotational term β ? β₀ = ?3.417 × 10^?1cm^?1. We have also observed an underlying hot band, which we tentatively assign as the ν₁ + ν₂ ← ν₂ transition, with α′ = 909.1997 cm^?1 and (β ? β₀)′ = ?3.405 × 10^?4cm^?1.     

Low-temperature structural phase transitions of TbB4 and ErB4 studied by high resolution X-ray diffraction and profile analysis

The isostructural rare earth tetraborides TbB₄ and ErB₄ of tetragonal space group P4/mbm undergo structural phase transitions to orthorhombic symmetry around T = 80 K and T = 15 K, respectively. The lattice distortions have been investigated by individual peak profile analysis performed on high-precision X-ray data. The experimental and analytical processing is outlined. The deviations from a tetragonal cell at 4.2 K are 2 × 10⁻² Å for TbB₄ and 3 × 10⁻³ Å for ErB₄. The relative volume change between 300 and 4.2 K is less than 10⁻³ in the TbB₄ lattice and 2.3 × 10⁻³ in ErB₄.The tetragonal to orthorhombic distortions are discussed in the context of the antiferromagnetic phase transitions of TbB₄ at T_N = 43 K and of ErB₄ at T_N = 13 K. The relationship between the structural and magnetic phase transitions differs for the two compounds. In TbB₄, the structural transition, which occurs at a definitely higher temperature than the magnetic ordering, is assumed to be driven by a strong electron-lattice coupling or by an electronic quadrupole-quadrupole interaction. In ErB₄, the structural distortion is attributed to magnetostrictive effects occurring simultaneously with the magnetic ordering process.     

锗、硅、锑化铟和砷化镓的热膨涨——用X射线衍射法测量

本工作是用X射线衍射法测量锗、硅和合金InSb及GaAs在不同温度的点阵常数,观察它们的热膨涨,并求得它们的膨涨系数。     

Dynamical quark effects on the hadronic spectrum and qq-potential in lattice QCD

The results of a calculation which incorporates virtual quark-antiquark pairs at a coupling of β=5.7 and quark mass of 0.05 are compared with those of two quenched simulations at β=5.895 and 6. The inclusion of the dynamical quark produces no effects in the hadron mass spectrum besides an overall shift in the coupling. In contrast, the Wilson lopp factors show a non-trivial effect, in the form of a flattening of the heavy quark potential. All three studies were carried out on a 10³·32 lattice.     

U(3) four-dimensional lattice gauge theory and Monte Carlo calculations

Monte Carlo results for the pure U(3) lattice gauge theory on a 6⁴ lattice are reported. Wilson loops and the string tension are presented. The first-order phase transition in U(3) is reflected quite clearly in a discontinuity in the string tension at β = β_c. The U(1) factor of U(3) is extracted using the determinant of the Wilson loops. As expected, the U(1) component appears to deconfine at the phase transition..     

The thermodynamics of SU(3) lattice gauge theory with a light isodoublet of quarks

Using hybrid differential equations with stochastic pseudo-fermion fields, we simulated SU(3) lattice gauge theory with a light isodoublet of quarks on a 4 × 8³ lattice. The bare quark mass is 0.0125 in lattice units which corresponds to 7.75 MeV if the finite temperature chiral transition occurs at T_c=155 MeV as suggested by phenomenology. The transition is first order and metastable states are found over a narrow range in temperature. Results for 4⁴ lattices are also presented for 2 and 3 light flavors.     

Analytic expressions for energy centroids and widths in the microscopic collective model

Analytic formulae are given for the U(3) centroids of the collective Bohr-Mottelson potential in the microscopic collective model. In particular, formulae are reported for the centroids of the quadratic [Q · Q ～ β²] and cubic [Q · (Q × Q ～ β³cos 3γ] rotational scalars in the microscopic quadrupole operator. Favorable comparisons for ground-state intensities are achieved between shell-model diagonalizations and statistical predictions based upon the gaussian approximation to the energy density. These results suggest that statistical measures can be used reliably for truncation of the infinite-dimensional representation spaces of the microscopic symplectic collective theory.     

Elastic constants of solid krypton at T = 77 K determined by inelastic neutron scattering

Long-wavelength acoustic phonons have been studied for each of the [ζ00]T, [ζ00]L, [ζζ0]L and [ζζ0]T₁ branches in solid Kr at T = 77 K by means of inelastic neutron scattering utilizing ‘cold neutrons’ as they are available in the long-wave length tail of the pile spectrum. The raw data have been corrected for resolution effects taking into account the curvature of the dispersion surface and variation of mode eigenvectors. It has turned out, that this yields appreciable shifts of the raw data. The results of our experiment give c₁₁ = 4·25 ± 0·10, c₄₄ = 2·04 ± 0·03, c₁₂ = 2·82 ± 0·12 and a value for B = (c₁₁ + 2c₁₂)/3 = 3·30 ± 0·09 × 10¹⁰ dyne/cm². Available thermodynamic data for Kr gives a derived value for B^ad = 2·58 ± 0·06 × 10¹⁰ dyne/cm² indicating a large difference between zero sound and first sound in solid Kr at high temperatures.