Local Correlation among the Chiral Condensate, Monopoles, and Color Magnetic Fields in Abelian Projected QCD

Using the lattice gauge field theory, we study the relation among the local chiral condensate, monopoles, and color magnetic fields in quantum chromodynamics (QCD). First, we investigate idealized Abelian gauge systems of (1) a static monopole–antimonopole pair and (2) a magnetic flux without monopoles, on a four-dimensional Euclidean lattice. In these systems, we calculate the local chiral condensate on quasi-massless fermions coupled to the Abelian gauge field, and find that the chiral condensate is localized in the vicinity of the magnetic field. Second, using SU(3) lattice QCD Monte Carlo calculations, we investigate Abelian projected QCD in the maximally Abelian gauge, and find clear correlation of distribution similarity among the local chiral condensate, monopoles, and color magnetic fields in the Abelianized gauge configuration. As a statistical indicator, we measure the correlation coefficient r, and find a strong positive correlation of r≃0.8 between the local chiral condensate and an Euclidean color-magnetic quantity F in Abelian projected QCD. The correlation is also investigated for the deconfined phase in thermal QCD. As an interesting conjecture, like magnetic catalysis, the chiral condensate is locally enhanced by the strong color-magnetic field around the monopoles in QCD.

Recovering the Lattice From Its Random Perturbations

Given a $d$-dimensional Euclidean lattice we consider the random set obtained by adding an independent Gaussian vector to each of the lattice points. In this note we provide a simple procedure that recovers the lattice from a single realization of the random set.

Reconstruction of smeared spectral functions from Euclidean correlation functions

We propose a method to reconstruct smeared spectral functions from two-point correlation functions measured on the Euclidean lattice. An arbitrary smearing function can be considered as long as it is smooth enough to allow an approximation using Chebyshev polynomials. We test the method with numerical lattice data of charmonium correlators. The method provides a framework to compare lattice calculation with experimental data including excited-state contributions without assuming quark–hadron duality.

Extraction of bare form factors for Bs →Kℓν decays in nonperturbative HQET

We discuss the extraction of the ground state [Formula: see text] matrix elements from Euclidean lattice correlation functions. The emphasis is on the elimination of excited state contributions. Two typical gauge-field ensembles with lattice spacings 0.075, 0.05 fm and pion masses 330, 270 MeV are used from the O[Formula: see text]-improved CLS 2-flavor simulations and the final state momentum is [Formula: see text] GeV. The b-quark is treated in HQET including the [Formula: see text] corrections. Fits to two-point and three-point correlation functions and suitable ratios including summed ratios are used, yielding consistent results with precision of around 2% which is not limited by the [Formula: see text] corrections but by the dominating static form factors. Excited state contributions are under reasonable control but are the bottleneck towards precision. We do not yet include a specific investigation of multi-hadron contaminations, a gap in the literature which ought to be filled soon.

Variational structure of Luttinger–Ward formalism and bold diagrammatic expansion for Euclidean lattice field theory

The Luttinger–Ward functional was proposed more than five decades ago and has been used to formally justify most practically used Green’s function methods for quantum many-body systems. Nonetheless, the very existence of the Luttinger–Ward functional has been challenged by recent theoretical and numerical evidence. We provide a rigorously justified Luttinger–Ward formalism, in the context of Euclidean lattice field theory. Using the Luttinger–Ward functional, the free energy can be variationally minimized with respect to Green’s functions in its domain. We then derive the widely used bold diagrammatic expansion rigorously, without relying on formal arguments such as partial resummation of bare diagrams to infinite order.