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.
We present a formulation to give renormalon-free predictions consistently with fixed order perturbative results. The formulation has a similarity to Lee's method in that the renormalon-free part consists of two parts: one is given by a series expansion which does not contain renormalons and the other is the real part of the Borel integral of a singular Borel transform. The main novel aspect is to evaluate the latter object using a dispersion relation technique, which was possible only in the large-$β_0$ approximation. Here, we introduce an "ambiguity function," which is defined by inverse Mell…
According to standard lore, perturbative series of super-renormalizable theories have only instanton singularities. In this paper we show that two-dimensional scalar theories with a spontaneously broken $O(N)$ symmetry at the classical level, which are super-renormalizable, have an IR renormalon singularity at large $N$. Since perturbative expansions in these theories are made around the "false vacuum" in which the global symmetry is broken, this singularity can be regarded as a manifestation of the non-perturbative absence of Goldstone bosons. We conjecture that the Borel singularity in the g…
I discuss various situations in which perturbative expansions are used in Yang-Mills theories with asymptotic freedom and establish the limits of its applicability.
We propose a simple and easy-to-implement scheme for a renormalon-free gluon condensate (GC) matrix element, which is analogous to implementations of short-distance heavy-quark mass renormalization schemes existing in the literature already for a long time. Because the scheme is based on a perturbative subtraction at the level of the matrix element, with a freely adaptable infrared factorization scale, it can be implemented with little effort for any observable where the GC is relevant. The scheme depends on the renormalon norm of the GC which has to be supplemented independently. We apply the…
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.…
Power corrections and renormalon resummation for the average thrust
红外功率修正的平均推力< T >在e+e-湮灭的框架下分析的重整化，激发类似的骨架膨胀QED和BLM方法。通过对“重胶子”的重整化积分，得到了一个重整化方案不变的结果。我们发现，一个已知的次领先阶（NLO）的计算和实验之间的差异的主要部分可以解释由高阶微扰项的再确认。这一事实并不排除红外有限耦合解释与一个实质性的1/Q功率项。将正则化微扰和加上1/Q项与实验数据拟合得到alpha_s^{MSbar}（M_Z）=0.110 \pm 0.006。
In a recent work by some of us it was shown that the long-standing discrepancy between the QCD perturbation series for the inclusive hadronic tau decay rate computed in the CIPT and FOPT expansion approaches can be understood from the fact that CIPT has an infrared (IR) sensitivity that it not compatible with the standard form of the operator production expansion (OPE). For concrete IR renormalon models for the QCD Adler function the resulting CIPT-FOPT discrepancy, the asymptotic separation, can be calculated analytically from the Borel representation of the CIPT series expansion. If the know…
As higher order perturbative series are available, it is becoming necessary to include nonperturbative effects in QCD calculations using the OPE. In order to systematically determine nonperturbative effects and to incorporate them into theoretical calculations, the renormalon problem should be resolved. We use a renormalon subtraction method utilizing Fourier transform to determine nonperturbative matrix elements of HQET, $\barΛ$ and $μ_π^2$. This is the first determination performed with subtraction of the $u=1$ renormalon.
In integrable field theories in two dimensions, the Bethe ansatz can be used to compute exactly the ground state energy in the presence of an external field coupled to a conserved charge. We generalize previous results by Volin and we extract analytic results for the perturbative expansion of this observable, up to very high order, in various asymptotically free theories: the non-linear sigma model and its supersymmetric extension, the Gross--Neveu model, and the principal chiral field. We study the large order behavior of these perturbative series and we give strong evidence that, as expected…
We study the free energy of integrable, asymptotically free field theories in two dimensions coupled to a conserved charge. We develop methods to obtain analytic expressions for its trans-series expansion, directly from the Bethe ansatz equations, and we use this result to determine the structure of its Borel singularities. We find a new class of infrared renormalons which does not fit the traditional expectations of renormalon physics proposed long ago by 't Hooft and Parisi. We check the existence of these new singularities with detailed calculations based on the resurgent analysis of the pe…
Precise theoretical predictions are a key ingredient for an accurate determination of the structure of the Langrangian of particle physics, including its free parameters, which summarizes our understanding of the fundamental interactions among particles. Furthermore, due to the absence of clear new-physics signals, precise theoretical calculations are required in order to pin down possible subtle deviations from the Standard Model predictions. The error associated with such calculations must be scrutinized, as non-perturbative power corrections, dubbed infrared renormalons, can limit the ultim…
