Decoupling of heavy quarks in mass-independent momentum subtraction schemes

Heavy quark decoupling in Quantum Chromodynamics (QCD) defined by mass-independent momentum subtraction (MOM) is investigated. The coefficients of the functions which allow for twoloop matching of the QCD parameters below and above a heavy quark threshold are calculated for some MOM schemes. The resulting numerical relations between the QCD scales and between the renormalization group invariant light-quark mass parameters off andf?1 flavour QCD are given.     

Quark Gluon Condensate,Virtuality and Susceptibility of QCD Vacuum

We study vacuum of QCD in this work. The structure of non-local quark vacuum condensate, values of various local quark and gluon vacuum condensates, quark-gluon mixed vacuum condensate, quark and gluon virtuality in QCD vacuum state, quark dynamical mass and susceptibility of QCD vacuum state to external field are predicted by use of the solutions of Dyson-Schwinger equations in “rainbow” approximation with a modeling gluon propagator and three different sets of quark-quark interaction parameters. Our theoretical predictions are in good agreement with the correspondent empirical values used widely in literature, and many other theoretical calculations. The quark propagator and self-energy functions are also obtained from the numerical solutions of Dyson-Schwinger equations. This work is centrally important for studying non-perturbative QCD, and has many important applications both in particle and nuclear physics.     

Ratio of a strange quark mass ms to up or down quark mass mu,d predicted by a quark propagator in the frameworkof the chiral perturbation theory

Based on the fully dressed quark propagator and chiral perturbation theory, we study the ratio of the strange quark mass m_s to up or down quark mass m_u,d. The ratio is related to the determination of quark masses which are fundamental input parameters of QCD Lagrangian in the Standard Model of particle physics and can not be directly measured since the quark is confined within a hadron. An accurate determination of these QCD free parameters is extremely important for both phenomenological and theoretical applications. We begin with a brief introduction to the non-perturbation QCD theory, and then study the mass ratio in the framework of the chiral perturbation theory (χ PT) with a parameterized fully dressed quark propagator which describes confining fully dressed quark propagation and is analytic everywhere in the finite complex p²-plane and has no Lehmann representation so there are no quark production thresholds in any theoretical calculations of observable data. Our prediction for the ratio m_s/m_u,d is consistent with other model predictions such as Lattice QCD, instanton model, QCD sum rules and the empirical values used widely in the literature. As a by-product of this study, our theoretical results, together with other predictions of physical quantities that used this quark propagator in our previous publications, clearly show that the parameterized form of the fully dressed quark propagator is an applicable and reliable approximation to the solution of the Dyson-Schwinger Equation of quark propagator in the QCD.     

自能函数和夸克的动力学质量(英文)

研究夸克的质量是QCD研究中的一个非常重要问题。因为, 夸克质量是标准模型的基本输入参数, 准确地确定这些参数无论对于唯象的应用还是对于理论的应用都是极其重要的。基于参数化的完全穿衣服的夸克传播子, 研究了自能函数和夸克的动力学质量。理论预言了夸克质量和自能函数, 其结果与文献中的经验值相符合, 也与Dyson Schwinger方程解一致。反过来这也说明了参数化的夸克传播子是成功和可靠的。Study of mass of quark is one of the most important issues in the investigation of QCD. Because masses of quarks are fundamental QCD input parameters of standard Model, and an accurate determination of these parameters is extremely important for both phenomenological and theoretical applications. Based on the parameterized fully dressed quark propagator proposed by us, the theoretical predictions of the masses of quarks are predicted in this short note. The effective quark mass is defined by the scalar self energy function Bf(p2) and vector self energy function Af(p2). The results of our calculations are in agreement with the empirical values used widely in literature and also show that the parameterized form of quark propagator is an applicable and reliable approximation.     

Calculating infrared contributions to vacuum expectation values of gluonic and quark fields

Based on the infrared asymptotics of the lower QCD Green's functions obtained before, we propose a definition and elaborate a technique for calculating non-perturbative vacuum expectations of gluon and quark fields. In our calculations, we use only the known QCD parameters: constitutent quark masses, the confining potential slope and the QCD parameter Γ. The values obtained for the vacuum expectations agree well with experiment.     

Heavy quark effects on the parameters of quantum chromodynamics defined by minimal subtraction

We report a complete two-loop calculation of the relations for matching the parameters of MS renormalized QCD below and above a certain heavy quark threshold and we investigate the implications of these relations for the QCD scale Λ and the scale-invariant quark masses.     

Truncation of QCD with four-quark interaction

We examine conditions for models with fourquark interaction and a finite cutoff to be a reasonable approximation to the QCD at low energies. The flavourdependent part of QCD vacuum energy is identified with an effective potential for quark model. The independence on the cutoff and the scale anomaly of QCD is exploited in the quark sector to establish the scaling law for QCD-motivated effective coupling constants. On the contrary the insensitivity of effective potential in respect to intrinsic field dilatations leads to a selection rule for parameters of quark models to make a truncation of QCD.     

On the quark mass dependence of the parameters of quantum chromodynamics

The running coupling constant and quark masses in QCD are calculated in the one-loop approximation using the 3-gluon vertex to define the coupling constant. Our results differ for finite quark masses from those reported previously in the literature. We discuss the origin of this apparent discrepancy. We also make some comments on the gauge dependence of the QCD parameters.     

Tensor Susceptibilities of QCD Vacuum and Parameterized Quark Propagator

Based on the parameterized fully dressed quark propagator proposed by us, the tensor susceptibilities of QCD vacuum and quark vacuum condensates are investigated. Our predicted values of the tensor susceptibilities are in agreement with those predicted by many other theoretical models with QCD feature. The results also show that the tensor susceptibility of QCD vacuum strongly depends on flavor of quark but not sensitive to variation of quark vacuum condensates. However, the quark vacuum condensate is very sensitive to the change of cut-off-parameter μ^2 of the integration, that is, it depends on the separation point of perturbative and non-perturbative QCD region. The successful predictions clearly indicate the extensive validity of our parameterized fully dressed quark propagator used here.     

Renormalized Wick expansion for a modified PQCD

The renormalization scheme for the Wick expansion of a modified version of the perturbative QCD introduced in previous works is discussed. Massless QCD is considered by implementing the usual multiplicative scaling of the gluon and quark wave functions and vertices. However, also massive quark and gluon counterterms are allowed in this massless theory since the condensates are expected to generate masses. A natural set of expansion parameters of the physical quantities is introduced: the coupling itself and the two masses m_q and m_g associated to quarks and gluons, respectively. This procedure allows one to implement a dimensional transmutation effect through these new mass scales. A general expression for the new generating functional in terms of the mass parameters m_q and m_g is obtained in terms of integrals over arbitrary but constant gluon or quark fields in each case. Further, the one loop potential is evaluated in more detail in the case when only the quark condensate is retained. This lowest order result again indicates the dynamical generation of quark condensates in the vacuum.     

Sum rules and analyticity in QCD

QCD sum rules of Shifman, Vainstein and Zakharov are investigated from the point of view of analytical extrapolations: in the weighted sum rule the analyticity connects the low energy hadron parameters with the high energy QCD parameters (coupling constant, quark masses, condensate parameters). It is shown that the optimal weight function in the sum rule is prescribed by the errors of the input information. The optimal tests of analyticity are proposed and applied (under some simplifying assumptions) to the vector and pseudoscalar charmonium channels.     

Minimal subtraction and the decoupling of heavy quarks for arbitrary values of the gauge parameter

The decoupling of a heavy quark is investigated to two loops for QCD renormalized by minimal subtraction. It is shown that the heavy quark effects can be absorbed into an effective coupling constant, an effective gauge parameter and effective masses for the light quarks. The relations between these effective parameters and the parameters of the full theory are gauge invariant. In terms of the effective parameters the theory satisfies renormalization group equations which refer only to the light degrees of freedom.     

Renormalization of QCD Coupling Constant in Terms of Physical Quantities

A renormalization scheme is suggested where QCDinput parameters — quark mass and couplingconstant — are expressed in terms ofgauge-invariant and infrared-stable quantities. For theQCD charge renormalization the quark anomalous electromagnetic moment isused. It turns out that in the renormalization procedureQED and QCD do not differ. The examination of the quarkscattering amplitude indicates confinement phenomena inQCD.     

Vacuum condensates of QCD

We study the properties of QCD vacuum state in this paper. The     

QCD finite energy sum rule calculation of the K → vacuum weak amplitude

The kaon-to-vacuum weak amplitude is discussed using the QCD finite energy sum rule approach. Its structure in terms of quark masses and other parameters of the theory is elucidated. Numerical estimates are also given.     

Vacuum condensates of QCD

We study the properties of QCD vacuum state in this paper. The values of various local quark vacuum condensates, quark-gluon mixed vacuum condensates, and the structure of non-local quark vacuum condensate are predicted by the solution of Dyson-Schwinger Equations in "rainbow" approximation with three sets of different parameters for effective gluon propagator. The light quark virtuality is also obtained in a consistent way. Our all theoretical results here are in good agreement with the empirical values used widely in literature and many other theoretical calculations.     

非微扰QCD真空中夸克真空凝聚的结构(英文)

基于Dyson-Schwinger方程(DSEs)所确定的夸克传播子和算符成积展开(OPE),在彩虹近似下,预言了QCD真空中非定域夸克真空凝聚的结构。这种结构由夸克自能函数Af和Bf决定,通过数值求解DSEs就可以得到这些自能函数。但是,直接数值求解DSEs方程非常复杂,这里采用Roberts和Williams提出的参数化方法,用参数化的夸克传播函数σf v(p2)和σf s(p2)计算夸克自能函数。同时,也计算了定域的夸克真空凝聚值,夸克胶子混合的真空凝聚值,以及夸克的虚度。理论预言和计算结果均与标准QCD求和定则、格点QCD和瞬子模型的理论结果大致相符。和这些模型的结果相比,参数化方法得到的轻夸克(u,d,s)的定域真空凝聚偏大,这主要是由于模型依赖导致的。与u,d夸克相比,s夸克的真空凝聚比较大,这是因为s夸克自身质量较大的缘故。当然,Roberts-Williams参数化的夸克传播子只是一个经验公式,只能近似描述夸克的传播。     

Phase structure of two-flavor QCD at finite chemical potential

We study the phase diagram of two-flavor QCD at imaginary chemical potentials in the chiral limit. To this end we compute order parameters for chiral symmetry breaking and quark confinement. The interrelation of quark confinement and chiral symmetry breaking is analyzed with a new order parameter for the confinement phase transition. We show that it is directly related to both the quark density as well as the Polyakov loop expectation value. Our analytical and numerical results suggest a close relation between the chiral and the confinement phase transition.     

On the bare pomeron graph in two-dimensional QCD

We present a detailed study of the bare pomeron graph in two-dimensional QCD in the 1/N_c approximation. The absence of a new singularity unrelated to quark parameters is derived. The “cylinder” graph is shown to induce renormalization of the vertex and intercept associated with quark andti-quark exchange in the vacuum channel.