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 are evaluated from propagators for numerous quark momenta on the lattice, where the use of chiral fermions suppresses undesired operator mixing. This over-determines the Wilson coefficients, but reliable results can be extracted by means of a Singular Value Decomposition.
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）
The renormalization group relations for the higher-order hadronic vacuum polarization function perturbative expansion coefficients are studied. The folded recurrent and unfolded explicit forms of such relations are obtained. The explicit expression for the coefficients, which incorporate the contributions of the $π^{2}$-terms in the perturbative expansion of the R-ratio of electron-positron annihilation into hadrons, is derived at an arbitrary loop level. The obtained results can be employed as an independent crosscheck of the higher-order perturbative calculations of the hadronic vacuum polar…
The main objective of this thesis is to present a new analytical framework for low-energy QCD that goes under the name of massive, or "screened", perturbative expansion. The massive perturbative expansion is motivated by the phenomenon of dynamical mass generation, by which the gluons acquire a mass of the order of the QCD scale $Λ_{\text{QCD}}$ in the limit of vanishing momentum. It is a simple extension of ordinary perturbation theory that consists in a shift of the expansion point of the Yang-Mills perturbative series with the aim of treating the transverse gluons as massive already at tree…
We compute the static self-energy of SU(3) gauge theory in four spacetime dimensions to order α^{20} in the strong coupling constant. We employ lattice regularization to enable a numerical simulation within the framework of stochastic perturbation theory. We find perfect agreement with the factorial growth of high order coefficients predicted by the conjectured renormalon picture based on the operator product expansion.
Using numerical stochastic perturbation theory, we determine the first 35 infinite volume coefficients of the perturbative expansion in powers of the strong coupling constant $α$ of the plaquette in SU(3) gluodynamics. These coefficients are obtained in lattice regularization with the standard Wilson gauge action. The on-set of the dominance of the dimension four renormalon associated to the gluon condensate is clearly observed. We determine the normalization of the corresponding singularity in the Borel plane and convert this into the $\overline{\mathrm{MS}}$ scheme. We also comment on the im…
We determine the infinite volume coefficients of the perturbative expansions of the self-energies of static sources in the fundamental and adjoint representations in SU(3) gluodynamics to order α^{20} in the strong coupling parameter α. We use numerical stochastic perturbation theory, where we employ a new second order integrator and twisted boundary conditions. The expansions are obtained in lattice regularization with the Wilson action and two different discretizations of the covariant time derivative within the Polyakov loop. Overall, we obtain four different perturbative series. For all of…
The parametric error on the QCD-coupling can be a dominant source of uncertainty in several important observables. One way to extract the coupling is to compare high order perturbative computations with lattice evaluated moments of heavy quark two-point functions. The truncation of the perturbative series is a sizable systematic uncertainty that needs to be under control. In this contribution we give an update on our study arXiv:hep-lat/2203.07936v1 on this issue. We measure pseudo-scalar two-point functions in volumes of $L=2$ fm with twisted-mass Wilson fermions in the quenched approximation…
Perturbation theory is shown to be working in the IR limit of pure SU(3) Yang-Mills theory in Landau gauge by an unconventional setting of the perturbative expansion. A dynamical mass is predicted for the gluon and the lattice data are reproduced fairly well by a second-order expansion, without any free parameter. The effective running coupling is small in the IR and the approximation can be improved by inclusion of higher order terms.
Rigorous control of the non-perturbative corrections to the double expansion in $g$ and $g^2\ln(g)$ for the $ϕ^4_3$-trajectory in the hierarchical approximation
We study duality in $\mathcal{N}=1$ supersymmetric QCD in the non-Abelian Coulomb phase, order-by-order in scheme-independent series expansions. Using exact results, we show how the dimensions of various fundamental and composite chiral superfields, and the quantities $a$, $a/c$, and $b$ at superconformal fixed points of the renormalization group emerge in scheme-independent series expansions in the electric and magnetic theories. We further demonstrate that truncations of these series expansions to modest order yield very accurate approximations to these quantities.
The QCD-coupling is a necessary input in the computation of many observables, and the parametric error on input parameters can be a dominant source of uncertainty. The coupling can be extracted by comparing high order perturbative computations and lattice evaluated moments of mesonic two-point functions with heavy quarks, which provide a high energy scale for perturbation theory. The truncation of the perturbative series is an important systematic uncertainty. We report on our attempt to study this issue by measuring pseudo-scalar two-point functions in volumes of $L=2\, \text{fm}$ with twiste…
We review recent studies of the operator product expansion of the plaquette and of the associated determination of the gluon condensate. One first needs the perturbative expansion to orders high enough to reach the asymptotic regime where the renormalon behavior sets in. The divergent perturbative series is formally regulated using the principal value prescription for its Borel integral. Subtracting the perturbative series truncated at the minimal term, we obtain the leading non-perturbative correction of the operator product expansion, i.e. the gluon condensate, with superasymptotic accuracy.…
We construct a power series representation of the integrals of form \begin{equation} \text{log} \int dμ_{S}(ψ, \barψ) \hspace{0.05 cm} e^{f(ψ, \barψ, η, \barη)} \nonumber \end{equation} where $ψ, \barψ$ and $η, \barη$ are Grassmann variables on a finite lattice in $d \geqslant 2$. Our expansion has a local structure, is clean and provides an easy alternative to decoupling expansion and Mayer-type cluster expansions in any analysis. As an example, we show exponential decay of 2-point truncated correlation function (uniform in volume) in massive Gross-Neveu model on a unit lattice.
