arXiv subjects
Publications and source records attributed to J. Rodríguez-Quintero.
We briefly report on a recent computation, with the help of a fruitful algebraic model, sketching the pion valence dressed-quark generalized parton distribution and, very preliminary, discuss on a possible avenue to get reliable results in both Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) and Efremov-Radyushkin-Brodsky-Lepage (ERBL) kinematial regions.
We sketch here an approach to the computation of generalised parton distributions (GPDs), based upon a rainbow-ladder (RL) truncation of QCD's Dyson-Schwinger equations and exemplified via the pion's valence dressed-quark GPD, $H_π^{\rm v}(x,ξ,t)$. Our analysis focuses on the case of zero skewness, $ξ=0$, and underlines that the impulse-approximation used hitherto to define the pion's valence dressed-quark GPD is generally invalid owing to omission of contributions from the gluons which bind dressed-quarks into the pion. A simple correction enables us to identify a practicable improvement to the approximation for $H_π^{\rm v}(x,0,t)$, expressed as the Radon transform of a single amplitude. Therewith we obtain results for $H_π^{\rm v}(x,0,t)$ and the associated impact-parameter dependent distribution, $q_π^{\rm v}(x,|\vec{b}_\perp|)$, which provide a qualitatively sound picture of the pion's dressed-quark structure at an hadronic scale.
We compute the pion quark Generalized Parton Distribution H and quark Double Distributions F and G in a coupled Bethe-Salpeter and Dyson-Schwinger approach in terms of quark flavors or isospin states. We use simple analytic expressions inspired by the numerical resolution of Dyson-Schwinger and Bethe-Salpeter equations. We explicitly check the support and polynomiality properties, and the behavior under charge conjugation or time invariance of our model. We obtain analytic expressions for the pion Double Distributions and Generalized Parton Distribution at vanishing pion momentum transfer at a low scale. Our model compares very well to experimental pion form factor or Parton Distribution Function data. This paper is the first stage of a GPD-modeling program which will be pursued by incorporating more realistic solutions of the Bethe-Salpeter and Dyson-Schwinger equations.
Exploiting the recent lattice results for the infrared gluon propagator with light dynamical quarks, we solve the gap equation for the quark propagator. We thus model the chiral symmetry breaking mechanism with increasing number of flavours and study confinement (intimately tied with the analytic properties of QCD Schwinger functions) order parameters. We obtain, with this approach, clear signals of chiral symmetry restoration and deconfinement when the number of light quark flavors exceeds a critical value of $N_f^c \approx 8 \pm 1$, in agreement with the state-of-the-art direct lattice analysis of chiral symmetry restoration in QCD.
This paper reports on the determination of $α_S$ from lattice simulations with 2+1+1 twisted-mass dynamical flavours {\it via} the computation of the ghost-gluon coupling renormalized in the MOM Taylor scheme. A high-statistics sample of gauge configurations, used to evaluate the coupling from ghost and gluon propagators, allows for the appropriate update of previous results, now performing an improved analysis of data with reduced statistical errors and the systematical uncertainties under a better control.
This letter reports on the first computation, from data obtained in lattice QCD with $u,d,s$ and $c$ quarks in the sea, of the running strong coupling via the ghost-gluon coupling renormalized in the MOM Taylor scheme. We provide with estimates of $\ams(m_τ^2)$ and $\ams(m_Z^2)$ in very good agreement with experimental results. Including a dynamical c quark makes safer the needed running of $\ams$.
We present a lattice calculation of the renormalized running coupling constant in symmetric (MOM) and asymmetric ($\widetilde{\rm MOM}$) momentum substraction schemes including $u$, $d$, $s$ and $c$ quarks in the sea. An Operator Product Expansion dominated by the dimension-two $\langle A^2\rangle$ condensate is used to fit the running of the coupling. We argue that the agreement in the predicted $\langle A^2\rangle$ condensate for both schemes is a strong support for the validity of the OPE approach and the effect of this non-gauge invariant condensate over the running of the strong coupling.
We exploit the recent lattice results for the infrared gluon propagator with light dynamical quarks and solve the gap equation for the quark propagator. Chiral symmetry breaking and confinement (intimately tied with the analytic properties of QCD Schwinger functions) order parameters are then studied.
This letter reports on a new procedure for the lattice spacing setting that takes advantage of the very precise determination of the strong coupling in Taylor scheme. Although it can be applied for the physical scale setting with the experimental value of $Λ_{\overline{\rm MS}}$ as an input, the procedure is particularly appropriate for relative "calibrations". The method is here applied for simulations with four degenerate light quarks in the sea and leads to prove that their physical scale is compatible with the same one for simulations with two light and two heavy flavours.
Gluon and ghost propagators data, obtained in Landau gauge from lattice simulations with two light and two heavy dynamical quark flavours ($N_f$=2+1+1), are described here with a running formula including a four-loop perturbative expression and a nonperturbative OPE correction dominated by the local operator $A^2$. The Wilson coefficients and their variation as a function of the coupling constant are extracted from the numerical data and compared with the theoretical expressions that, after being properly renormalized, are known at ${\cal O}(α^4)$. As also $Λ_{\msbar}$ is rather well known for $N_f$=2+1+1, this allows for a precise consistency test of the OPE approach in the joint description of different observables.
We compute the full non-perturbative ghost and gluon two-point Green functions by using gauge field configurations with $\nf=2$ and $\nf=2+1+1$ twisted-mass quark flavours. We use simulations with several different light quark masses, heavy quark masses close to that of the strange and charm quarks, and lightest pseudoscalar masses ranging from 270 to 510 [MeV]. Quark flavour effects on both the gluon and the ghost propagators are then investigated in a wide range of momenta, bridging the deep infrared and intermediate momenta domain of QCD interactions in the presence of dynamical quarks. The ghost-gluon vertex is also indirectly probed through a consistency requirement among the lattice data for the gluon and ghost propagators and the ghost propagator Schwinger-Dyson equation. The effective full QCD coupling is finally constructed, and its dependence on the presence of dynamical fermions scrutinized.
Either by solving the ghost propagator DSE or through a one-loop computation in the RGZ (Refined Gribov-Zwanziger) formalism, we show that a non-trivial ghost-gluon vertex is anyhow required to obtain a ghost propagator prediction compatible with the available corresponding lattice data in the SU(3) case. For the necessary gluon propagator input, we present RGZ tree level fits which account well for the gluon lattice data. Interestingly, this propagator can be rewritten in terms of a running gluon mass. A comparison of both DSE and RGZ results for the ghost propagator is furthermore provided. We also briefly discuss the connection between the RGZ and the OPE $d=2$ gluon condensate.
This paper is a first report on the determination of $Λ_{\msbar}$ from lattice simulations with 2+1+1 twisted-mass dynamical flavours {\it via} the computation of the ghost-gluon coupling renormalized in the MOM Taylor scheme. We show this approach allows a very good control of the lattice artefacts and confirm the picture from previous works with quenched and ${\rm N}_f$=2 twisted-mass field configurations which prove the necessity to include non-perturbative power corrections in the description of the running. We provide with an estimate of $Λ_{\msbar}$ in very good agreement with experimental results. To our knowledge it is the first calculation with a dynamical charm quark which makes the running up to $α_s(M_Z)$ much safer.
This brief note is devoted to a study of genuine non-perturbative corrections to the Landau gauge ghost-gluon vertex in terms of the non-vanishing dimension-two gluon condensate. We pay special attention to the kinematical limit which the bare vertex takes for its tree-level expression at any perturbative order, according to the well-known Taylor theorem. Based on our OPE analysis, we also present a simple model for the vertex, in acceptable agreement with lattice data.
We review the infrared properties of the pure Yang-Mills correlators and discuss recent results concerning the two classes of low-momentum solutions for them reported in literature; i.e. decoupling and scaling solutions. We will mainly focuss on the Landau gauge and pay special attention to the results inferred from the analysis of the Dyson-Schwinger equations of the theory and from "{\it quenched}" lattice QCD. The results obtained from properly interplaying both approaches are strongly emphasized.
We study the genuine non-perturbative corrections to the Landau gauge ghost-gluon vertex in terms of the non-vanishing dimension-two gluon condensate, and prove these corrections to give account of current SU(2) lattice data for the vertex with different kinematical configurations in the domain of intermediate momenta, roughly above 2-3 GeV. Based on this OPE analysis, we also present a simple model for the vertex, in acceptable agreement with the lattice data also in the IR domain. The necessity of a non-vanishing dimension-two gluon condensate will be also investigated through the analysis of the running coupling defined by the ghost-gluon vertex in Taylor kinematics.
We study RI/MOM renormalization constants of bilinear quark operators for $N_f=4$ and the strong coupling constant for $N_f=2+1+1$ using Wilson twisted-mass fermions. We use the "egalitarian" method to remove H(4) hypercubic artifacts non-perturbatively, which enables us to study physical quantities in a wide range of momenta. We then apply OPE in studying the running behavior of $Z_q$ and $α_s$, from which we are able to extract the Landau gauge dimension-two gluon condensate $ $ which is of phenomenological interest.
Both regular (the zero-momentum ghost dressing function not diverging), also named decoupling, and critical (diverging), also named scaling, Yang-Mills propagators solutions can be obtained by analyzing the low-momentum behaviour of the ghost propagator Dyson-Schwinger equation (DSE) in Landau gauge. The asymptotic expression obtained for the regular or decoupling ghost dressing function up to the order ${\cal O}(q^2)$ fits pretty well the low-momentum ghost propagator obtained through the numerical integration of the coupled gluon and ghost DSE in the PT-BFM scheme. Furthermore, when the size of the coupling renormalized at some scale approaches some critical value, the PT-BFM results seems to tend to the the scaling solution as a limiting case. This critical value of the coupling is compared with the lattice estimate for the Yang-Mills QCD coupling and the latter is shown to lie much above the former.