Modern Physics Letters A

A general introduction into the subject aimed at a general theoretical physics audience. We introduce the sign problem posed by finite density lattice QCD, and we discuss the main methods proposed to circumvent it, with emphasis on the imaginary chemical potential approach. The interrelation between Taylor expansion and analytic continuation from imaginary chemical potential is discussed in detail. The main applications to the calculation of the critical line, and to the thermodynamics of the hot and normal phase are reviewed.

This is a short overview of the lattice QCD simulations of finite density systems. We first describe a brief introduction of the lattice QCD at finite density, including the minimum necessary formulation, where we show why an annoying complex fermion determinant appears, and why in some cases it does not appear. Then we review several approaches of present and past days. We conclude possible directions of lattice QCD simulations at finite density in near future.

We apply the probability distribution function method to the study of chiral properties of QCD with quarks in the exact massless limit. A relation among the chiral condensate, zeros of the Bessel function and eigenvalue of Dirac operator is also given. The chiral condensate in this limit can be measured with small number of eigenvalues of the massless Dirac operator and without any ambiguous mass extrapolation. Results for lattice QCD with Kogut-Susskind quarks are shown.

In this proceeding we propose a new procedure to impose the Schrödinger functional Dirichlet boundary condition on the overlap Dirac operator and the domain-wall fermion using an orbifolding projection. With this procedure the zero mode problem with Dirichlet boundary condition can easily be avoided.

Tadpole improved Wilson quark actions with clover terms on anisotropic lattices are studied numerically. Using asymmetric lattice volumes, the pseudo-scalar meson dispersion relations are measured for 8 lowest lattice momentum modes with quark mass values ranging from the strange to the charm quark with various values of the gauge coupling β and 3 different values of the bare speed of light parameter ν. These results can be utilized to extrapolate or interpolate to obtain the optimal value for the bare speed of light parameter ν_opt(m) at a given gauge coupling for all bare quark mass values m. In particular, the optimal values of ν at the physical strange and charm quark mass are given for various gauge couplings. The lattice action with these optimized parameters can then be used to study physical properties of hadrons involving either light or heavy quarks.

In this paper, we studied the phase diagram of QCD at finite temperature T and chemical potential μ with 4 flavor Wilson quarks. The calculations are performed on a 8³ × 4 lattice using the imaginary chemical potential method. This method allows us to do large scale Monte Carlo simulations at imaginary chemical potential μ = iμ_I with μ_I < πT/3. By analytic continuation to the real chemical potential, the phase transition line on the (μ, T) plane can be determined.

Lattice QCD at finite temperature T and chemical potential μ is studied analytically in the strong coupling limit with overlap fermions. We start from the first order approximation of lattice action with generalized overlap (GO) fermions to derive an effective free energy written in terms of chiral condensate as a function of T and μ with the use of mean field approximation. We elucidate the phase structure on the (μ, T) plane and discover the tricritical point separating the first and the second order chiral phase transition. Discussion of the doubling problem and higher order terms are given.

We analyze the overlap fermion formulation expanded in powers of a hopping parameter in the strong coupling limit. The mass of the quasi-Goldstone pion is obtained. A random walk representation for the overlap fermion propagator is developed, to conclude that the expanded overlap fermion formulation, however, cannot be totally solve the fermion-doubling problem.

We discuss recent progress in the study of nuclear and neutron matter by combining chiral effective field theory with non-perturbative lattice methods. We present results for hot neutron matter at temperatures 20 to 40 MeV and densities below twice nuclear matter density. This proceedings article is a summary of results from work done in collaboration with Bugra Borasoy and Thomas Schaefer¹.

We discuss how the concept of the Monte Carlo Hamiltonian can be applied to lattice gauge theories.

We give the prediction for the ground and excited state masses of the charmonium hybrid mesons, 1^-+, 0^+-, 0^--, with exotic quantum numbers. We employ improved gluon and quark actions on anisotropic lattice, which reduce greatly the lattice artifacts, and lead to good signals. The data are extrapolated to the continuum limit, with finite size effects under well control. The ground state masses of 1^-+, 0^+-, 0^-- agree with our earlier results, where the mass of 0^-- were shown for the first time. And the excited state masses, reported for the first time here, are 6.450(190)GeV, 6.629(138)GeV and 8.487(201)GeV respectively.

By applying a spatially extended sink operator, the nucleon two-point functions are calculated in Coulomb gauge from quenched lattice QCD with overlap fermions. The Bethe-Salpeter wave functions of nucleon and Roper resonance are extracted at different quark masses. The typical size of nucleon is about 0.7 fm, which seems insensitive to the quark masses involved in this work. It is also found that the wave function of Roper has a radial node.

The six quark state(uuddss) called H dibaryon(J^P = 0⁺,S = -2) has been calculated to study its existence and stability. The simulations are performed in quenched QCD on 8³ × 24 and 16³ × 48 anisotropic lattices with Symanzik improved gauge action and Clover fermion action. The gauge coupling is β = 2.0 and aspect ratio ξ = a_s/a_t = 3.0. Preliminary results indicate that mass of H dibaryon is 2134(100)Mev on 8³ × 24 lattice and 2167(59)Mev on 16³ × 48 respectively. It seems that the radius of H dibaryon is very large and the finite size effect is very obvious.

We calculate the glueball 〈gg〉 wavefunction and mass in SU(3) Lattice gauge with improved gauge actions on the anisotropic lattice. All simulations are performed on the cluster of our lab. We have measured the scalar and tensor glueball wavefunction. At the same time, we have briefly calculated the glueball mass as for a consistent check.

We investigate color superconductivity and chiral symmetry restoration at finite temperature and baryon density in the frame of standard two flavor Nambu–Jona-Lasinio model. We derive the diquark mass in RPA, discuss its constraint on the coupling constant in the diquark channel, and find a strong competition between the two phase transitions when the coupling constant is large enough.

The perturbative QCD approach is based on k_T factorization, including the Sudakov form factors so that to avoid the endpoint singularity. In this approach, we calculate the charmless B decays like B → ππ decays etc. to produce the right number of branching ratios and also CP asymmetry parameters. For final states with at least one charmed meson, like B → Dπ decays, our results also agree with the experiments.

In the mean field approximation of the relativistic σ-ω-ρ model, the magnetic fields are incorporated, and it's influence on the properties of n-p-e neutron star matter are studied. When the strength of the magnetic field is weaker than ~10¹⁸G, the particles' fractions and chemical potentials, matter's energy density and pressure hardly change with the magnetic field; when the strength of the magnetic field is stronger than ~10²⁰G, the above quantities change with the magnetic field evidently. Furthermore, the pressure is studied in both thermodynamics and hydrodynamics. The difference between these two ways exits in the high density region, that is, the thermal self-consistency may not be satisfied in this region if the magnetic field is considered.

Accurate to the first order in the uniform angular velocity, the general relativistic frame dragging effect of the moments of inertia and the radii of gyration of two kinds of neutron stars are calculated in a relativistic σ – ω model. The calculation shows that the dragging effect will diminish the moments of inertia and radii of gyration.

We investigate the isospin chemical potential effect in the frame of SU(2) Nambu-Jona-Lasinio model. When the isospin chemical potential is less than the vacuum pion mass, the phase structure with two chiral phase transition lines does not happen due to U_A(1) breaking of QCD. When the isospin chemical potential is larger than the vacuum pion mass, the ground state of the system is a Bose-Einstein condensate of charged pions.

The historical and geometrical origin of Gauge Transformation and Yang's phase loop of gauge theory are discussed. In the present talk, we present the following points: 1. Parallel transport of a vector; 2. Weyl 1918 gauge transformation 3. Concept of non-integrable phase factor; 4. Berry's quantum geometrical phase; 5. Parallel transport of quantum state vector produces the phase physics.

We first briefly review tests on CPT invariance based on the consequences of the CPT theorem and then present some possible CPT tests due to exotic models in which some of the CPT conditions are lost, such as those without hermiticity.

Processes of the form are studied via a technique that may be viewed as an adaptation of time-honored Dalitz plot analyses. X_i and X_j are new heavy states (with i,j = 1…n), which may be identical or distinct; and and are necessarily distinct Standard Model (SM) fermion pairs whose invariant masses can be measured. A Dalitz-like plot of said invariant masses, vs., exhibits a topology connected to the masses and specific decay chains of X_i and X_j. Aside from relatively minor details, observed patterns consist of a collection of box and wedge shapes. This collection is model-dependent: comparison of the observed pattern to the possibilities for a specific model yields information on which new particle pair combinations are actually being produced, information beyond that extractable from conventional one-dimensional invariant mass distributions. The technique is illustrated via application to the Minimal Supersymmetric Standard Model (MSSM) process . Here the heavy states are neutralinos (i = 2,3,4) — note is excluded — which are produced in gluino/squark cascade decay chains. Even with fairly modest expectations for the LHC performance during the first few years, this method still provides substantial insight into the neutralino mass spectrum and couplings if gluino/squark masses are relatively low (≃ 400 GeV).

We report recent analysis of one-loop scattering amplitudes in N=4 super Yang-Mills theories, in the paradigm of maximally helicity violating Feynman diagrams. Non-planar amplitudes are found to be related to planar ones in the same manners as those in conventional field theory. More so, there are are very limited number of loop integrals to be evaluated. For a process with n external particles, there are only [n/2]-1 generically independent integrals.

We present the effective chiral Lagrangian of mesons (peusodoscalars, vectors and axial-vectors) obtained in the chiral limit by using two approaches. The first approach is based on symmetries: the explicit global chiral symmetry and hidden local chiral symmetry. In this approach, it is noticed that there are in general fourteen interacting terms up to the dimension-four of covariant derivative for meson fields rather than the usual eleven interacting terms given in literature from hidden local symmetry approach. Of particular, the additional terms are found to be very important for understanding the vector meson dominance and providing consistent predictions on the decay rates of a₁ → γπ and a₁ → ρπ as well as for resulting a consistent effective chiral Lagrangian with chiral perturbation theory. The second approach is motivated from the chiral symmetry of chiral quarks and the bound state solutions of nonperturbative QCD at low energy and large N_c. The second approach is more fundamental in the sense that it is based on the QCD Lagrangian of quarks and only relies on two basic parameters in addition to the ones in the standard model. As a consequence, it allows us to extract, in terms of only two basic parameters, all the fourteen parameters in the more general effective Lagrangian constructed from symmetries in the first approach. It is surprising to note that except the necessity of three additional new interacting terms introduced in this paper, the resulting values of the coupling constants for other three interacting terms at the dimension-four are also quite different from the ones given in the literature. It is likely that the structures of the effective chiral Lagrangian for the dimension-four given in the literatures by using hidden local symmetry are incomplete and consequently the resulting coulpings are not reliable. It is shown that the more general effective chiral Lagrangian given in the present paper shall provide a more consistent prediction for all the low energy phenomenology of ρ - a₁ system and result in a more consistent description on the low energy behavior of light flavor mesons. Its fourteen parameters up to the dimension-four of covariant derivative may be uniquely determined from the effective chiral theory based on the second approach, which is consistent with the chiral perturbation theory.

In the nonsymmetric gravitational theory (NGT) the space-time metric g_μν departs from the flat-space Minkowski form η_μν such that it is no longer symmetric, i.e.g_μν ≠ g_νμ. We find that in the most conservative such scenario coupled to quantum field theory, which we call Minimally Nonsymmetric Quantum Field Theory (MNQFT), there are experimentally measurable consequences similar to those from noncommutative quantum field theory (NCQFT). This can be expected from the Seiberg-Witten map which has recently been interpreted as equating gauge theories on noncommutative spacetimes with those in a field dependent gravitational background. In particular, in scattering processes such as the pair annihilation e⁺e^- → γγ, both theories make the same striking prediction that the azimuthal cross section oscillates in ϕ. However the predicted number of oscillations differs in the two theories: MNQFT predicts between one and four, whereas NCQFT has no such restriction.

We explore the nature of the σ or f₀(600) meson using large N_c technique, assuming that the σ pole dominates low energy physics in the IJ=00 channel. We trace the N_c dependence of the σ pole position using [1,1] Padé approximation of SU(3) chiral amplitude, [1,2] Padé approximation of SU(2) chiral amplitudes, and the PKU parametrization form. We find that in all 3 cases the σ pole moves to the real axis of the complex s-plane. Finally we construct a pedagogical example using the SU(2) Padé amplitude to show that when the analyticity property of the scattering amplitude is violated, it is possible that the σ pole resides on the complex s plane when N_c is large.

In view of the general holographic principle between gauge theories and gravity, We calculate the mass spectra of several typical QCD₄ glueballs in term of AdS₆AdS-Schwarzschild black hole metric of Einstein gravity theory. The obtained mass spectra are numerically in consistent with those from the AdS₇ × S⁴ black hole metric of the 11-dimensional supergravity. Besides, by separating the thermal circle from the extra dimensions, we find a novel exact Dp-brane solution of Type IIB supergravity, which might provide a scenario for studying the non-perturbative dynamics of QCD₄ from the perspective of Type IIB supergravity.

We examine the ground state properties of a dimerized ferromagnetic S = 1 Ising chain with single-ion crystal fields by mapping the model onto the dimerized S = 1/2 Ising chain with transverse fields. We show that the system exhibits a series of Ising transitions depending on the dimerization strength of the crystal fields, while the critical points can be determined exactly.

The deformed t-J lattice model is defined by replacing the fermion operators by the deformed Hubbard operators in the t-term but without changing the J-term in the conventional t-J model. The physics of this model was argued to be continuously connected to those of the t-J one when the deformation parameter λ varies from zero to unit. In this paper, by using the bosonization field theory and renormalization group technique, we study the phase diagram of the one dimension deformed t-J model in the regime where λ and J/t are both positively small but comparable to each other. By explicitly incorporating the contributions from the deformation-induced six-particle term and the antiferromagnetic exchange interaction, we find that at half-filling the system shows three distinct ground states characterized by the Luttinger liquid, the spin-density-wave and the bond-order-wave, respectively. These results indicate that the ground state phases of the deformed t-J model is neither connected smoothly to those of the system at λ = 1 nor to those of the conventional t-J model.

The S=1/2 Heisenberg chain with bond alternation and randomness of antiferromagnetic (AFM) and ferromagnetic (FM) interactions is investigated by quantum Monte Carlo simulations of loop/cluster algorithm. Our results have shown interesting finite temperature magnetic properties of this model. The relevance of our study to former investigation results is discussed.