In this paper, we investigate operator product expansion for thermal correlation function of the two scalar currents. Due to breakdown of Lorentz invariance at finite temperature, more operators of the same dimension appear in the operator product expansion than at zero temperature. We calculated Wilson coefficients in the short distance expansion and obtain operator product expansion for thermal correlation function in terms of quark condensate, gluon condensate, quark energy density and gluon energy density.
Why the Pennington-Wilson expansion with real coefficients is of little use in the analysis of production processes
我们批判性地分析和评论的索赔M。R. Pennington和D. J. Wilson [arxiv：0711.3521].虽然我们大体上同意他们的明显的代数，但它显然不适用于我们的方程。此外，我们认为，相应的建议是没有用的生产数据分析。我们的方法，其中涉及复杂的，但纯粹的运动学系数的优点，进行了总结。
In this paper we construct the Wilson short distance operator product expansion for the gluon, quark and ghost propagators in QCD, including operators of dimension two and three, namely, A^2, m^2, m A^2, \ovlψ ψand m^3. We compute analytically the coefficient functions of these operators at three loops for all three propagators in the general covariant gauge. Our results, taken in the Landau gauge, should help to improve the accuracy of extracting the vacuum expectation values of these operators from lattice simulation of the QCD propagators.
The connected contribution to the kernel of the evolution equation for the 3-quark Wilson loop operator was derived within Balitsky high energy operator expansion. Its C-odd part was linearized and transferred to the momentum space.
We use AdS/QCD to analyze the quark and gluon scalar and pseudo-scalar condensates around static color sources described by a circular Wilson loop. We also derive the static dipole-dipole interactions between rectangular Wilson loops in AdS/QCD and discuss their relevance for static string interactions in QCD at strong coupling.
We study a scalar zero mode originated from extradimensional components of a gauge field in a six-dimensional theory compactified on a magnetized torus. We confirm it is a Nambu-Goldstone boson of the translational symmetry on the torus which is breaking spontaneously due to magnetic flux. We also show explicitly it is massless up to the two-loop level. Moreover, we discuss full order contributions by considering the effective potential.
At high energies particles move very fast so the proper degrees of freedom for the fast gluons moving along the straight lines are Wilson-line operators - infinite gauge factors ordered along the line. In the framework of operator expansion in Wilson lines the energy dependence of the amplitudes is determined by the rapidity evolution of Wilson lines. We present the next-to-leading order hierarchy of the evolution equations for Wilson-line operators.
In a torus compactification with magnetic flux, the scalar field generated from the higher dimensional gauge field becomes the Nambu-Goldstone boson of the translational symmetry in extra spaces and the mass of the scalar field is not allowed. In this paper, we explicitly show that the one-loop quantum correction to the mass of the scalar field is generated at fixed points in a case of an orbifold compactification $T^2/Z_2$ with magnetic flux. This is because the scalar field is a pseudo Nambu-Goldstone boson as a result of explicit breaking of the translational symmetry by the fixed points. T…
We derive a Wilson coefficient of a CP-violating purely gluonic dimension-6 operator called the Weinberg operator ($GG\tilde{G}$) generated by a scalar and two fermions at the two-loop level. We do not specify the representation of SU(3)$_c$ for the scalar and the fermions, and thus our result can be applied to a variety of models beyond the standard model. We estimate the nucleon EDMs induced by the Weinberg operator in some examples and discuss the importance of measuring EDMs. It is found that future measurements of the EDMs can probe physics at higher energy scale beyond the reach of colli…
We present 2+1 flavor Lattice QCD calculations of the nucleon scalar and tensor charges. Using the BMW clover-improved Wilson action with pion masses between 150 and 350 MeV and three source-sink separations between 0.9 and 1.4 fm, we achieve good control over excited-state contamination and extrapolation to the physical pion mass. As a consistency check, we also present results from calculations using unitary domain wall fermions with pion masses between 300 and 400 MeV, and using domain wall valence quarks and staggered sea quarks with pion masses between 300 and 600 MeV.
We discuss the gauge symmetry breaking of six dimensional theories in flux compactification with a magnetic flux background and a constant vacuum expectation value (VEV) for the scalar fields, which are zero modes of extra spatial components of the gauge field. Although the effective potential for the scalar fields are known not to be generated classically and radiatively in a magnetic flux background only, the one-loop effective potential is shown to be generated by the effects of the non-zero constant VEV. As illustrations, we calculate the one-loop effective potential in SU(2) and SU(3) Yan…
We discuss properties of the $ε$-expansion in $d=4-ε$ dimensions. Using Lagrange inversion we write down an exact expression for the value of the Wilson-Fisher fixed point coupling order by order in $ε$ in terms of the beta function coefficients. The $ε$-expansion is combinatoric in the sense that the Wilson-Fisher fixed point coupling at each order depends on the beta function coefficients via Bell polynomials. Using certain properties of Lagrange inversion we then argue that the $ε$-expansion of the Wilson-Fisher fixed point coupling equally well can be viewed as a geometric expansion which …
Generalized susceptibilities of the net quark number have been proposed to be good probes for the transitions in the QCD phase diagram and for the search of a possible critical end point. In this article we explore a new strategy for computing quark number susceptibilities from lattice QCD via an expansion in the fugacity parameter $e^{μβ}$. All quark number related bulk observables are particularly easy to access in this approach and we present results for generalized quark number susceptibilities up to 4-th order. Ratios of these quantities are studied and compared with model calculations fo…
Parton distribution functions (PDFs) and light-cone distribution amplitudes (LCDAs) are central non-perturbative objects of interest in high-energy inelastic and elastic scattering, respectively. As a result, an ab-initio determination of these objects is highly desirable. In this paper we present theoretical details for the calculation of the PDFs and LCDAs using a heavy-quark operator product expansion method. This strategy was proposed in a previous paper [Phys. Rev. D 73, 014501 (2006)] for computing higher moments of the PDFs using lattice QCD. Its central feature is the introduction of a…
The equation of state (EoS), quark number density and susceptibility at nonzero quark chemical potential $μ$ are studied in lattice QCD simulations with a clover-improved Wilson fermion of 2-flavors and RG-improved gauge action. To access nonzero $μ$, we employ two methods : a multi-parameter reweighting (MPR) in $μ$ and $β$ and Taylor expansion in $μ/T$. The use of a reduction formula for the Wilson fermion determinant enables to study the reweighting factor in MPR explicitly and heigher-order coefficients in Taylor expansion free from errors of noise method, although calculations are limited…
The operator product expansion (OPE) for heavy-light-quark pseudoscalar mesons (D-mesons and B-mesons) in medium is determined, both for a moving meson with respect to the surrounding medium as well as for a meson at rest. First of all, the OPE is given in terms of normal-ordered operators up to mass dimension 5, and the mass of the heavy-quark and the mass of the light-quark are kept finite. The Wilson coefficients of such an expansion are infrared (IR) divergent in the limit of a vanishing light-quark mass. A consistent separation of scales necessitates an OPE in terms of non-normal-ordered …
Nucleon structure functions can be observed in Deep Inelastic Scattering experiments, but it is an outstanding challenge to confront them with fully non-perturbative QCD results. For this purpose we investigate the product of electromagnetic currents (with large photon momenta) between quark states (of low momenta). By means of an Operator Product Expansion the structure function can be decomposed into matrix elements of local operators, and Wilson coefficients. For consistency both have to be computed non-perturbatively. Here we present precision results for a set of Wilson coefficients. They…
Static QCD Potential at r < 1/Lambda_QCD: Perturbative expansion and operator-product expansion
我们以微扰QCD和OPE为基本理论工具，分析了距离为0.1fm < r <1fm的静态QCD势V_QCD（r）。我们收集最新的理论发展，并进行可靠而准确的分析。分析包括三个主要步骤：（1）研究V_QCD（r）微扰级数的高阶行为。(II)在OPE框架下，我们定义了两类Wilson系数的重整化格式。(III)我们比较了Wilson系数的数值微扰预言和V_QCD（r）的格点计算。我们进行拟合，同时确定非微扰的贡献和晶格尺度和Lambda_MSbar之间的关系。（简短版本）
We study the renormalisation of the non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric scalar field theory with the interaction $ϕ^2(iϕ)^\varepsilon$ using the Wilsonian approach and without any expansion in $\varepsilon$. Specifically, we solve the Wetterich equation in the local potential approximation, both in the ultraviolet regime and with the loop expansion. We calculate the scale-dependent effective potential and its infrared limit. The theory is found to be renormalisable at the one-loop level only for integer values of $\varepsilon$, a result which is not yet established within the $\va…
A major problem with periodic boundary condition on the gauge fields used in current lattice gauge theory simulations is the trapping of topological charge in a particular sector as the continuum limit is approached. To overcome this problem open boundary condition in the temporal direction has been proposed recently. One may ask whether open boundary condition can reproduce the observables calculated with periodic boundary condition. In this work we find that the extracted lowest glueball mass using open and periodic boundary conditions at the same lattice volume and lattice spacing agree for…
As an improvement of the QCD sum rule method to study modifications of light vector mesons in nuclear matter and/or at finite temperature, we calculate the Wilson coefficients of all independent gluonic non-scalar operators up to dimension 6 in the operator product expansion (OPE) of the vector channel for light quarks. To obtain the gluon part of the light quark OPE from the heavy quark one, we also compute the heavy quark expansion of the relevant quark condensates. Together with the results for the quark operators that are already available in the literature, this completes the OPE of the v…
We derive the perturbative expansion of Wilson loops to order g^4 in a SU(N) lattice gauge theory with twisted boundary conditions. Our expressions show that the thermodynamic limit is attained at infinite N for any number of lattice sites and allow to quantify the deviations from volume independence at finite large N as a function of the twist.
