2 pages, 1 figure (double), to appear in the Proceedings of the VIII Latin American Symposium on Nuclear Physics and Applications, Santiago, Chile, 15-19 December 2009. Poster presented by H. E. Martinez
We consider a modification of the Minimal Analytic (MA) coupling of Shirkov and Solovtsov. This modified MA (mMA) coupling reflects the desired analytic properties of the space-like observables. We show that an approximation by Dirac deltas of its discontinuity function $ρ$ is equivalent to a Padé (rational) approximation of the mMA coupling that keeps its analytic structure. We propose a modification to mMA that, as preliminary results indicate, could be an improvement in the evaluation of low-energy observables compared with other analytic couplings.
Borel-Pade vs Borel-Weniger method: a QED and a QCD example
最近，文献[1]（Jentschura et al.）的作者提出了Weniger（delta层序）方法。用于量子场论中截断微扰级数的重新表示。这些作者提出的数值证据表明，这种方法比帕德逼近更好地工作时，我们resum一个函数的奇异性在博雷尔平面，但不是在正轴上。我们在这里提出的数值证据表明，在这种情况下，Borel-帕德的组合方法比它的模拟Borel-Weniger更好地工作，它可能会更好地工作或在某些情况下，当有奇点的正轴上的Borel平面。
Previously developed Pade-related method of resummation for QCD observables, which achieves exact renormalization-scale-invariance, is extended so that the scheme-invariance is obtained as well. The dependence on the leading scheme parameter $c_2$ is eliminated by a variant of the method of the principle of minimal sensitivity. The subleading parameter $c_3$ in the approximant is then fixed in such a way that the correct known location of the leading infrared renormalon pole is reproduced. Thus, $beta$-functions which go beyond the last perturbatively calculated order in the observable are use…
A method of resummation of truncated perturbation series, related to diagonal Padé approximants but giving results independent of the renormalization scale, was developed more than ten years ago by us with a view of applying it in perturbative QCD. We now apply this method in analytic QCD models, i.e., models where the running coupling has no unphysical singularities, and we show that the method has attractive features such as a rapid convergence. The method can be regarded as a generalization of the scale-setting methods of Stevenson, Grunberg, and Brodsky-Lepage-Mackenzie. The method involve…
We propose a novel Bayesian method to analytically continue observables to real baryochemical potential $μ_B$ in finite density QCD. Taylor coefficients at $μ_B=0$ and data at imaginary chemical potential $μ_B^I$ are treated on equal footing. We consider two different constructions for the Padé approximants, the classical multipoint Padé approximation and a mixed approximation that is a slight generalization of a recent idea in Padé approximation theory. Approximants with spurious poles are excluded from the analysis. As an application, we perform a joint analysis of the available continuum ex…
The use of Pade approximants for the description of QCD matrix elements is discussed in this talk. We will see how they prove to be an extremely useful tool, specially in the case of resonant amplitudes. It will allow the inclusion of high-energy Euclidian data to improve the determination of low-energy properties, such as the quadratic vector radius. This does not mean that the rational approximations can be arbitrarily employed for the extraction of any desired hadronic parameter. A discussion about the validity, limitations and possible issues of the Pade analysis is carried on along the pa…
We consider the ``modified Minimal Analytic'' (mMA) coupling that involves an infrared cut to the standard MA coupling. The mMA coupling is a Stieltjes function and, as a consequence, the paradiagonal Pade approximants converge to the coupling in the entire $Q^2$-plane except on the time-like semiaxis below the cut. The equivalence between the narrow width approximation of the discontinuity function of the coupling, on the one hand, and this Pade (rational) approximation of the coupling, on the other hand, is shown. We approximate the analytic analogs of the higher powers of mMA coupling by ra…
A method of evaluation of spacelike QCD observables ${\cal D}(Q^2)$ is developed, motivated by the renormalon structure of these quantities. A related auxiliary quantity ${\widetilde {\cal D}}(Q^2)$ is introduced, which is renomalization scale independent only at the one-loop level, and a large-$β_0$-type renormalon motivated ansatz is made for the Borel transform of this quantity. This leads to a `dressed' Borel transform of the considered observable ${\cal D}(Q^2)$. From there, a Neubert-type distribution is obtained for the observable. The described method is then applied to the massless Ad…
On the Parameters of the QCD-Motivated Potential in the Relativistic Independent Quark Model
在相对论独立夸克模型的框架下，基于$1^{--}$介子质量谱计算了QCD激发的静态势参数和夸克质量。计算得到了束缚势系数为（$0.197\pm 0.005) GeV$ {}^2 $. for quark- antiquark interaction independently on their flavours. The dependence of the quasi-Coulombic potential strength on the interaction distance are consistent with the QCD-motivated behaviour. The $ q \bar q $-separations are evaluated and the $ e^+e^-$。
MSbar-like schemes in QCD have in general the running coupling which contains Landau singularities, i.e., singularities outside the timelike semi-axis, at low squared momenta. As a consequence, evaluation of the spacelike quantities, such as current correlators, in terms of (powers of) such a coupling then results in quantities which contradict the basic principles of Quantum Field Theories. On the other hand, in those QCD frameworks where the running coupling remains finite at low squared momenta (IR freezing), the coupling usually does not have Landau singularities in the complex plane of th…
The results presented in this paper differ from our previous unsuccessful attempt to predict the rapidity distribution at $W = 7 \,TeV$. The original version of our model (GLMM) only summed a particular class of Pomeron diagrams (enhanced diagrams). We believe that this was the reason for our failure to describe the $7 \,TeV$ inclusive LHC data. We have developed a new approach (GLM) that also includes the summation of the semi-enhanced diagrams.This contribution is essential for a successful description of the inclusive distributions, which is presented here.
In this paper we construct a model that satisfies the theoretical requisites of high energy soft interactions, based on two ingredients:(i) the results of N=4 SYM, which at present is a unique theory that allows one to deal with a large coupling constant; and (ii) the requirement of matching with high energy QCD. In accordance with these ideas, we assume that the soft Pomeron intercept is rather large, and the slope of the Pomeron trajectory is equal to zero. We derive analytical formulae that sum both enhanced and semi-enhanced diagrams for elastic and diffractive amplitudes. We fit the avail…
We extend our two component Pomeron model (GLMM) for soft high energy scattering to single inclusive cross sections. We present a suitable formulation which also includes the semi enhanced Pomeron-particle vertex corrections. The available data on single inclusive density $(1/σ_{in})dσ/dy$ in the c.m. energy range of 200-1800 GeV, including the just published Alice Collaboration point at 900 GeV,and the CMS collaboration measurements at 900 and 2360 GeV are well reproduced by our model. We also present predictions covering the complete LHC energy range which can be readily tested in the early …
In this paper we present a self consistent theoretical approach for the calculation of the Survival Probability for central dijet production . These calculations are performed in a model of high energy soft interactions based on two ingredients:(i) the results of N=4 SYM, which at the moment is the only theory that is able to deal with a large coupling constant; and (ii) the required matching with high energy QCD. Assuming, in accordance with these prerequisites, that soft Pomeron intercept is rather large and the slope of the Pomeron trajectory is equal to zero, we derive analytical formulae …
We present an updated version of a QCD coupling which fulfills various physically motivated conditions: at high momenta it practically coincides with the perturbative QCD (pQCD) coupling; at intermediate momenta it reproduces correctly the physics of the semihadronic tau decay; and at very low momenta it is suppressed as suggested by large-volume lattice calculations. An earlier presented analysis is updated here in the sense that the Adler function, in the regime $|Q^2| \lesssim 1 \ {\rm GeV}^2$, is evaluated by a renormalon-motivated resummation method. This Adler function is then used here …
We analyze general convergence properties of the Taylor expansion of observables to finite chemical potential in the framework of an effective 2+1 flavor Polyakov-quark-meson model. To compute the required higher order coefficients a novel technique based on algorithmic differentiation has been developed. Results for thermodynamic observables as well as the phase structure obtained through the series expansion up to 24th order are compared to the full model solution at finite chemical potential. The available higher order coefficients also allow for resummations, e.g. Pade series, which improv…
Newer lattice results indicate that, in the Landau gauge at low spacelike momenta, the gluon propagator and the ghost dressing function are finite nonzero. This leads to a definition of the QCD running coupling, in a specific scheme, that goes to zero at low spacelike momenta. We construct a running coupling which fulfills these conditions, and at the same time reproduces to a high precision the perturbative behavior at high momenta. The coupling is constructed in such a way that it reflects qualitatively correctly the holomorphic (analytic) behavior of spacelike observables in the complex pla…
The product of the gluon dressing function and the square of the ghost dressing function in the Landau gauge can be regarded to represent, apart from the inverse power corrections 1/Q^{2n}, a nonperturbative generalization A(Q^2) of the perturbative QCD running coupling a(Q^2)=alpha_s(Q^2)/pi. Recent large volume lattice calculations for these dressing functions indicate that the coupling defined in such a way goes to zero as A(Q^2)~Q^2 when the squared momenta Q^2 go to zero (Q^2<<1 GeV^2). In this work we construct such a QCD coupling A(Q^2) which fulfills also various other physically motiv…
The product of the gluon dressing function and the square of the ghost dressing function in the Landau gauge can be regarded to represent, apart from the inverse power corrections $1/Q^{2 n}$, a nonperturbative generalization $A(Q^2)$ of the perturbative QCD running coupling $a(Q^2)$ ($\equiv α_s(Q^2)/π$). Recent large volume lattice calculations for these dressing functions strongly indicate that such a generalized coupling goes to zero as $A(Q^2) \sim Q^2$ when the squared momenta $Q^2$ go to zero ($Q^2 \ll 1 \ {\rm GeV}^2$). We construct such a QCD coupling $A(Q^2)$ which fulfills also vari…
We investigate the Bjorken polarized sum rule (BSR) in three approaches to QCD with analytic (holomorphic) coupling: Analytic Perturbation Theory (APT), Two-delta analytic QCD (2$δ$anQCD), and Three-delta lattice-motivated analytic QCD in the three-loop and four-loop MOM scheme (3l3$δ$anQCD, 4l3$δ$anQCD). These couplings do not have unphysical (Landau) singularities, and have finite values when the transferred momentum goes to zero, which allows us to explore the infrared regime. With the exception of APT, these theories at high momenta practically coincide with the underlying perturbative QCD…
Perturbative QCD (pQCD) running coupling a(Q^2) (=alpha_s(Q^2)/pi) is expected to get modified at low spacelike momenta 0 < Q^2 < 1 GeV^2 so that, instead of having unphysical (Landau) singularities it remains smooth and finite there, due to infared (IR) fixed point. This behavior is suggested by: Gribov-Zwanziger approach, Dyson-Schwinger equations (DSE) and other functional methods, lattice calculations, light-front holographic mapping AdS/CFT modified by a dilaton background, and by most of the analytic (holomorphic) QCD models. All such couplings, A(Q^2), differ from the pQCD couplings a(Q…
