arXiv subjects

Cesar Ayala

Publications and source records attributed to Cesar Ayala.

31 records · Page 2Linked to original sources

arXiv2018

Bjorken sum rule in QCD frameworks with analytic (holomorphic) coupling

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 (pQCD) in the same scheme. We apply them in order to verify the Bjorken sum rule within the range of energies available in the data collected by the experimental JLAB collaboration, i.e., $0.05 GeV^2 <Q^2< 3 GeV^2$ and compare the results with those obtained by using the perturbative QCD coupling. The results of the new frameworks with respective couplings (2$δ$ and 3$δ$) are in good agreement with the experimental data for $0.5 GeV^2<Q^2<3 GeV^2$ already when only one higher-twist term is used. In the low-$Q^2$ regime ($Q^2 \lesssim 1 GeV^2$) we use $χ$PT-motivated expression or an expression motivated by the light-front holography (LFH) QCD used earlier in the literature.

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arXiv2017

Nearly perturbative lattice-motivated QCD coupling with zero IR limit

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 motivated conditions. At high momenta it becomes the underlying perturbative coupling a(Q^2) to a very high precision. And at intermediate low squared momenta Q^2~1 GeV^2 it gives results consistent with the data of the semihadronic tau lepton decays as measured by OPAL and ALEPH. The coupling is constructed in a dispersive way, resulting as a byproduct in the holomorphic behavior of A(Q^2) in the complex Q^2-plane which reflects the holomorphic behavior of the spacelike QCD observables. Application of the Borel sum rules to tau-decay V+A spectral functions allows us to obtain values for the gluon (dimension-4) condensate and the dimension-6 condensate, which reproduce the measured OPAL and ALEPH data to a significantly better precision than the perturbative MSbar coupling approach.

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arXiv2017

QCD coupling which respects lattice restrictions at low energies

We consider a phenomenologycal parametrization of the QCD running coupling which arises from the dispersion relation respecting the holomorphic properties of the physical QCD observables in the complex momentum plane. The parameters are fixed by the following requirements: 1) at enough high energies, it reproduces the underlying perturbative coupling, 2) at intermediate energy momenta, it reproduces the experimental semihadronic tau decay ratio, and 3) in the deep IR regime, it satisfies the qualitative properties coming from recent lattice results. Finally, we apply this new coupling to low-energy available experimental data. In particular, to Borel sum rules for τ-decay, extracting the values of the dimension 4 and 6 condensates, to the V-channel Adler function, and to polarized Bjorken Sum Rule.

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arXiv2017

Lattice-motivated holomorphic nearly perturbative QCD

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 plane of the squared momenta, as dictated by the general principles of Quantum Field Theories. Further, we require the coupling to reproduce correctly the nonstrange semihadronic decay rate of tau lepton which is the best measured low-momentum QCD observable with small higher-twist effects. Subsequent application of the Borel sum rules to the V+A spectral functions of tau lepton decays, as measured by OPAL Collaboration, determines the values of the gluon condensate and of the V+A 6-dimensional condensate, and reproduces the data to a significantly higher precision than the usual MSbar running coupling.

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arXiv2016

The right top coupling in the aligned two-Higgs-doublet model

We compute the right top quark coupling in the aligned two-Higgs-doublet model. In the Standard Model the real part of this coupling is dominated by QCD-gluon-exchange diagram, but the imaginary part, instead, is purely electroweak at one loop. Within this model we show that values for the imaginary part of the coupling up to one order of magnitude larger than the electroweak prediction can be obtained. For the real part of the electroweak contribution we find that it can be up to three orders of magnitude larger than the standard model one. We also present detailed results of the one loop analytical computation.

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arXiv2016

Heavy quark potential from QCD-related effective coupling

We implement our past investigations in the quark-antiquark interaction through a non-perturbative running coupling defined in terms of a gluon mass function, similar to that used in some Schwinger-Dyson approaches. This coupling leads to a quark-antiquark potential, which satisfies not only asymptotic freedom but also describes linear confinement correctly. From this potential, we calculate the bottomonium and charmonium spectra below the first open flavor meson-meson thresholds and show that for a small range of values of the free parameter determining the gluon mass function an excellent agreement with data is attained.

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arXiv2016

Mass of the bottom quark from Upsilon(1S) at NNNLO: an update

We update our perturbative determination of MSbar bottom quark mass mb(mb), by including the recently obtained four-loop coefficient in the relation between the pole and MSbar mass. First the renormalon subtracted (RS or RS') mass is determined from the known mass of the Upsilon(1S) meson, where we use the renormalon residue Nm obtained from the asymptotic behavior of the coefficient of the 3-loop static singlet potential. MSbar mass is then obtained using the 4-loop renormalon-free relation between the RS (RS') and MSbar mass. We argue that the effects of the charm quark mass are accounted for by effectively using Nf=3 in the mass relations. The extracted value is mb(mb) = 4222(40) MeV, where the uncertainty is dominated by the renormalization scale dependence.

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arXiv2015

How to perform QCD analysis of DIS in Analytic Perturbation Theory

We apply (Fractional) Analytic Perturbation Theory (FAPT) to the QCD analysis of the nonsinglet nucleon structure function $F_2(x,Q^2)$ in deep inelastic scattering up to the next leading order and compare the results with ones obtained within the standard perturbation QCD. Based on a popular parameterization of the corresponding parton distribution we perform the analysis within the Jacobi Polynomial formalism and under the control of the numerical inverse Mellin transform. To reveal the main features of the FAPT two-loop approach, we consider a wide range of momentum transfer from high $Q^2\sim 100 {\rm GeV}^2$ to low $Q^2\sim 0.3 {\rm GeV}^2$ where the approach still works.

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arXiv2015

anQCD: Fortran programs for couplings at complex momenta in various analytic QCD models

We provide three Fortran programs which evaluate the QCD analytic (holomorphic) couplings $\mathcal{A}_ν(Q^2)$ for complex or real squared momenta $Q^2$. These couplings are holomorphic analogs of the powers $a(Q^2)^ν$ of the underlying perturbative QCD (pQCD) coupling $a(Q^2) \equiv α_s(Q^2)/π$, in three analytic QCD models (anQCD): Fractional Analytic Perturbation Theory (FAPT), Two-delta analytic QCD (2$δ$anQCD), and Massive Perturbation Theory (MPT). The index $ν$ can be noninteger. The provided programs do basically the same job as the Mathematica package anQCD.m in Mathematica published by us previously, Ref.[1], but are now written in Fortran.

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arXiv2015

anQCD: a Mathematica package for calculations in general analytic QCD models

We provide a Mathematica package that evaluates the QCD analytic couplings (in the Euclidean domain) $\mathcal{A}_ν(Q^2)$, which are analytic analogs of the powers $a(Q^2)^ν$ of the underlying perturbative QCD (pQCD) coupling $a(Q^2) \equiv α_s(Q^2)/π$, in three analytic QCD models (anQCD): Fractional Analytic Perturbation Theory (FAPT), Two-delta analytic QCD (2$δ$anQCD), and Massive Perturbation Theory (MPT). The analytic (holomorphic) running couplings $\mathcal{A}_ν(Q^2)$, in contrast to the corresponding pQCD expressions $a(Q^2)^ν$, reflect correctly the analytic properties of the spacelike observables ${\cal D}(Q^2)$ in the complex $Q^2$ plane as dictated by the general principles of quantum field theory. They are thus more suited for evaluations of such physical quantities, especially at low momenta $|Q^2| \sim 1 \ {\rm GeV}^2$.

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arXiv2014

Mathematica and Fortran programs for various analytic QCD couplings

We outline here the motivation for the existence of analytic QCD models, i.e., QCD frameworks in which the running coupling $A(Q^2)$ has no Landau singularities. The analytic (holomorphic) coupling $A(Q^2)$ is the analog of the underlying pQCD coupling $a(Q^2) \equiv α_s(Q^2)/π$, and any such $A(Q^2)$ defines an analytic QCD model. We present the general construction procedure for the couplings $A_ν(Q^2)$ which are analytic analogs of the powers $a(Q^2)^ν$. Three analytic QCD models are presented. Applications of our program (in Mathematica) for calculation of $A_ν(Q^2)$ in such models are presented. Programs in both Mathematica and Fortran can be downloaded from the web page: gcvetic.usm.cl.

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arXiv2014

The bottom quark mass from the $Υ(1S)$ system at NNNLO

We obtain an improved determination of the normalization constant of the first infrared renormalon of the pole mass (and the singlet static potential). For $N_f=3$ it reads $N_m=0.563(26)$. Charm quark effects in the bottom quark mass determination are carefully investigated. Finally, we determine the bottom quark mass using the NNNLO perturbative expression for the $Υ(1S)$ mass. We work in the renormalon subtracted scheme, which allows us to control the divergence of the perturbation series due to pole mass renormalon. Our result for the ${\overline {\rm MS}}$ mass reads ${\overline m}_{b}({\overline m}_{b})=4201(43)$ MeV.

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arXiv2014

Gluon Propagator in Fractional Analytic Perturbation Theory

We consider the gluon propagator in the Landau gauge at low spacelike momenta and with the dressing function $Z(Q^2)$ at the two-loop order. We incorporate the nonperturbative effects by making the (noninteger) powers of the QCD coupling in the dressing function $Z(Q^2)$ analytic (holomorphic) via the Fractional Analytic Perturbation Theory (FAPT) model, and simultaneously introducing the gluon dynamical mass in the propagator as motivated by the previous analyses of the Dyson-Schwinger equations. The obtained propagator has behavior compatible with the unquenched lattice data ($N_f=2+1$) at low spacelike momenta $0.4 \ {\rm GeV} < Q \lesssim 10$ GeV. We conclude that the removal of the unphysical Landau singularities of the powers of the coupling via the (F)APT prescription, in conjunction with the introduction of the dynamical mass $M \approx 0.62$ GeV of the gluon, leads to an acceptable behavior of the propagator in the infrared regime.

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