Reduced Dirac-Kähler lattice fermion action

It is shown that the lattice Dirac-Kähler action is reducible under a chiral-like transformation. This provides a new lattice fermion action for spinors that have 2^d−1 components (instead of 2^d), with the property that, in the free case, each component satisfies the lattice euclidean Klein-Gordon equation. Reflection positivity is satisfied on the lattice, thus assuring a (positive) physical Hilbert space. In d = 4 dimensions the spinors have 8 components, and the correct physical chiral anomaly in the continuum limit. The action is suitable for QCD quarks which, in the continuum limit, are described by Dirac spinors that occur in flavor doublets.     

A numerical study of Langevin QCD with dynamical quarks

QCD with four flavours of dynamical staggered quarks of mass ma=0.1 is simulated on a 4⁴ lattice, using two versions of the second order Langevin algorithm with bilinear noise: the naive version and one which compensates for the non-integrable term which appears to first order in the discrete Langevin time step size. Comparison with the results of an exact numerical computation of the fermion determinant reveals that these algorithms yield accurate results only at rather small values of the step size. The correction due to the non-integrable term is quantitatively unimportant for such step sizes.     

Baryon spectrum in quenched QCD on a 164 lattice

We report a result of computation of baryon masses in quenched QCD using 32nd order numerical hopping parameter expansion on a 16⁴ lattice. It is demonstrated that at β = 5.4 and β = 5.7 the baryon mass calculation becomes feasible at this order in K. Influence of statistics, finite size effects are briefly discussed.     

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.     

Constituent gluon interpretation of glueballs and gluelumps

Arguments are given that support the interpretation of the lattice QCD glueball and gluelump spectra in terms of bound states of massless constituent gluons with helicity 1. In this scheme, we show that the mass hierarchy of the currently known gluelumps and glueballs is mainly due to the number of constituent gluons and can be understood within a simple flux tube model. It is also argued that the lattice QCD 0^+- glueball should be seen as a four-gluon bound state. We finally predict the mass of the 0^- state, not yet computed in lattice QCD.     

Hard-thermal-loop QCD trace anomaly

In this proceedings I summarize results of QCD trace anomaly from recent three-loop hard-thermal-loop perturbation theory (HTLpt) calculations. I focus on the trace anomaly scaled by T ² for pure-glue and N _f = 3 QCD. The comparison to available lattice data suggests that for pure-glue QCD agreement between HTLpt results and lattice data for the trace anomaly begins at temperatures above 8 T _c while when including quarks (N _f = 3) agreement begins already at temperatures above 2 T _c . The results in both cases indicate that at very high temperatures the T ²-scaled trace anomaly increases with temperature in accordance with the predictions of HTLpt.     

Low energy QCD predictions from non perturbative methods

We show that by using lattice results about the euclidean ?-propagator, it is possible to give theoretical predictions on the low energy behavior of thee ⁺ e ^?→had. cross section. Furthermore, we present a comparison of perturbative QCD results (plus certain sum rules corrections) with non perturbative results from the lattice in the intermediate energy region.     

Meson-meson potentials from lattice QCD and inverse scattering

Potentials between light-light and heavy-light mesons are computed from meson-meson Green’s functions in the framework of quenched lattice QCD with Kogut-Susskind fermions. Comparisons with a full QCD simulation and a simulation using an O(a ²) tree-level and tadpole improved gauge action show that dynamic quarks and lattice discretization errors have no drastic influence. Calculations from inverse scattering theory propose a similar shape for $K\bar K$ potentials, whereas a good qualitative agreement with ππ potentials could not be obtained.     

Properties of hot and dense nuclear matter in a mixed phase

The QCD phase transition is treated within a statistical model taking into account the coexistence of interacting quark-gluon and hadron phases. Being in agreement with the recent lattice QCD data, this statistical mixed phase model predicts that the “softest point” of the equation of state, resulting in the longest-lived fireball effect, is atε _{sp ≈ 0.35}GeV/fm³. It is shown that this “softest point” is washed out at the baryon densities higher than the normal nuclear density. The approach is extended to include strangeness. Attention is drawn to the study of signatures for forming the mixed quark-hadron phase of nuclear matter in the collision energy rangeE _lab ≈ 2–10 GeV/A.     

Normalization of currents in lattice QCD

The normalization of vector and axial vector currents in lattice QCD with Wilson's fermion method is discussed and the numerical values of the multiplicative constants are computed to order g² and for g² → ∞.     

Normalizing the renormalization group analysis of deep inelastic leptoproduction

The nucleon matrix elements of the leading twist non-singlet operators which arise in the standard QCD analysis of leptoproduction are computed in an improved version of the bag model. QCD radiative corrections are used to evolve the bag predictions which are applicable at a low value of Q² to a high Q² regime where they can be compared with moments of non-singlet structure functions. The agreement with data is good and suggests that higher twist effects are not large.     

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.     

Glueball masses and string tension Smeared loop-loop correlation functions

By using results obtained by the Ape Collaboration [1] we study the glueball spectrum and the string tension in lattice QCD by analyzing correlation functions between operators. We use and discuss the smearing method. We consider a 5³ × 16 lattice at β = 5.6 as a test case, and a 12³ × 32 lattice at β = 5.9 in order to compare with the old wall results of ref. [3]. We study the structure of the excited states.     

Valence quark distributions in the soliton bag model

Valence quark distributions are calculated in a momentum projected version of the soliton bag model. These distributions are evolved to Q²=15 GeV² using QCD perturbation theory, where they are compared with experiment. Substantial agreement is achieved.     

Effective lagrangian and dynamical symmetry breaking in strongly coupled lattice QCD

A method is proposed for computing effective lagrangians in QCD with N colors using lattice regularization. The meson field lagrangian is worked out in detail in the strong coupling limit with various lattice fermion formulations. For generalized Susskind fermions the spontaneous breakdown U(n) ? U(n) → U(n) (diagonal) is found at large N and a generalized version of the non-linear σ model emerges in a natural way. The Nambu-Goldstone spectrum is investigated and a continuous transition is made to Wilson fermions, for which the effective potential and the ππ scattering amplitude are tested on chiral symmetry. Large d (=dimension) approximations are compared with the large N limit and applied to N = 3.     

Magnetic moments of negative parity baryons from the effective Hamiltonian approach to QCD

The magnetic moments of the S ₁₁(1535) and S ₁₁(1650) baryons are studied in the framework of the relativistic three-quark Hamiltonian derived in the Field Correlation Method. The baryon magnetic moments are expressed via the average current quark energies which are defined by the fundamental QCD parameters: the string tension σ, the quark masses, and the strong coupling constant α _s . The resulting magnetic moments for the J ^P = 1/2^? nucleons are compared both to model calculations and to those from lattice QCD.     

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.     

The relationship between chemical and tracer diffusion coefficients of aliovalent ions in an ionic lattice

The theoretical model developed by Lidiard was extended to describe the relationship between the chemical and tracer diffusion coefficients of aliovalent ions in an ionic lattice.It is shown that the relationship between the chemical diffusion coefficient, D, and the tracer diffusion coefficient, D¹, is D = 2D¹ if the migration of dimers is the principal mechanism of transport and for the migration of trimers D = 3D¹ if the concentration of impurity ion is relatively small. These relationships are valid regardless of the charge of the aliovalent or lattice ions.The chemical diffusion coefficients of Cr³⁺ in Cr-doped MgO were determined for three different temperatures, 1656, 1717 and 1768K, and for the concentration region 2.5×10^?2?2.8×10^?1 mole% Cr₂O₃. Using previously determined values for the tracer diffusion coefficient of ⁵¹Cr in Cr-doped MgO it was found that for the temperature and concentration region investigated D = (2.00±0.17)D¹ which indicates that diffusion proceeds primarily by the migration of dimers.     

Interface tension in the Polyakov loop model

The interface tension of the Polyakov loop model is calculated by Monte Carlo simulation. The form of the operator measuring the tension is derived from QCD in the strong coupling limit. The result is αa ³=0.0255±0.0003 in terms of the lattice constanta. The interface profile is also calculated and the spatial extent of the interface is estimated to be 10 lattice spacings. The result implies that the phase transition in the Polyakov loop model is of first order.     

Phase diagrams in nonlocal Polyakov-Nambu-Jona-Lasinio models constrained by lattice QCD results

Based on lattice QCD-adjusted SU(2)f nonlocal Polyakov-Nambu-Jona-Lasinio (PNJL) models, we investigate how the location of the critical endpoint in the QCD phase diagram depends on the strenght of the vector meson coupling, as well as the Polyakov-loop (PL) potential and the form factors of the covariant model. The latter are constrained by lattice QCD data for the quark propagator. The strength of the vector coupling is adjusted such as to reproduce the slope of the pseudocritical temperature for the chiral phase transition at low chemical potential extracted recently from lattice QCD simulations. Our study supports the existence of a critical endpoint in the QCD phase diagram albeit the constraint for the vector coupling shifts its location to lower temperatures and higher baryochemical potentials than in the case without it.