Large-Nc Regge models and the condensate
We explore the role of the gluon condensate in matching Regge models to the operator product expansion of meson correlators.
hep-ph↗
arXiv subjects
Enrique Ruiz Arriola
Publications and source records attributed to Enrique Ruiz Arriola.
Confined Chiral Solitons in the Spectral Quark Model
Chiral solitons with baryon number one are investigated in the Spectral Quark Model. In this model the quark propagator is a superposition of complex-mass propagators weighted with a suitable spectral function. This technique is a method of regularizing the effective quark theory in a way preserving many desired features crucial in analysis of solitons. We review the model in the vacuum sector, stressing the feature of the absence of poles in the quark propagator. We also investigate in detail the analytic structure of meson two-point functions. We provide an appropriate prescription for constructing valence states in the spectral approach. The valence state in the baryonic soliton is identified with a saddle point of the Dirac eigenvalue treated as a function of the spectral mass. Due to this feature the valence quarks never become unbound nor dive into the negative spectrum, hence providing stable solitons as absolute minima of the action. This is a manifestation of the absence of poles in the quark propagator. Self-consistent mean field hedgehog solutions are found numerically and some of their properties are determined and compared to previous chiral soliton models. Our analysis constitutes an involved example of a treatment of a relativistic complex-mass system.
hep-ph↗
Pion-photon Transition Distribution Amplitudes in the Spectral Quark Model
The vector and axial pion-photon transition distribution amplitudes are analyzed in the Spectral Quark Model. We proceed by the evaluation of double distributions through the use of a manifestly covariant calculation based on the alpha representation of propagators. As a result polynomiality is incorporated and calculations become rather simple. Explicit formulas, holding at the low-energy quark-model scale, are obtained. The corresponding form factors for the anomalous decay pi0 -> gamma gamma* and the radiative pion decays are also evaluated and confronted with the data.
hep-ph↗
Dimension-2 condensates, zeta-regularization and large-Nc Regge Models
Dimension-2 and -4 gluon condensates are re-analyzed in large-Nc Regge models with the zeta-function regularization which preserves the spectrum in any q qbar channel separately. We demonstrate that the signs and magnitudes of both condensates can be properly described within the framework.
hep-ph↗
Pion transition form factor and distribution amplitudes in large-Nc Regge models
We analyze the pi -> gamma* gamma* amplitude in the framework of radial Regge models in the large-Nc limit. With the assumption of similarity of the asymptotic Regge rho and omega meson spectra we find that the pion distribution amplitude is constant in the large-$N_c$ limit at the scale Q0 where the QCD radiative corrections are absent -- a result found earlier in a class of chiral quark models. We discuss the constraints on the couplings from the anomaly and from the limit of large photon virtualities, and find that the coupling of the pion to excited rho and omega mesons must be asymptotically constant. We also discuss the effects of the QCD evolution on the pion electromagnetic transition form factor. Finally, we use the Regge model to evaluate the slope of the form factor at zero momentum and compare the value to the experiment, finding very reasonable agreement.
hep-ph↗
Dimension-two gluon condensate from large-Nc Regge models
It is shown that in the large-N_c limit radial Regge trajectories give rise in a natural way to the presence of the dimension-2 gluon condensate, , in meson correlators. We match these models to QCD and provide estimates for in terms of other physical quantities. In particular, in the simplest strictly linear radial Regge model with equal residues is proportional to the pion decay constant squared. However, the linear model fails a consistency condition based on matching the short- and long-distance string tensions, nor reproduces the phenomenological values of the gluon condensates. On the contrary, in Regge models departing from strict linearity one may reproduce both the consistency condition and the signs of condensates. We demonstrate this in a simple explicit model.
hep-ph↗
Landau-gauge condensates from the quark propagator on the lattice
We compute the dimension-2 condensate, , and the dimension-4 mixed condensate, <\bar q A q>, from the recent quenched lattice results for the quark propagator in the Landau gauge. We fit the lattice data to the Operator Product Expansion in the "fiducial" region 1.2 GeV < Q < 3 GeV. Our result for the dynamical gluon mass at the scale of 10 GeV^2 is m_A=600-650 MeV, in agreement with independent determinations. For the mixed Landau gauge condensate of dimension-4 we get alpha_s <\bar q g A q> = (-0.11 +/- 0.03) GeV^4. This value is an order of magnitude larger than the gluon condensate.
hep-ph↗
Application of chiral quark models to high-energy processes
We discuss the predictions of chiral quark models for basic pion properties entering high-energy processes: generalized parton distributions (GPD's) and unintegrated parton distributions (UPD's). We stress the role of the QCD evolution, necessary to compare the predictions to data.
hep-ph↗
Kwiecinski evolution of unintegrated parton distributions
The Kwiecinski evolution of unintegrated parton distributions (UPDs) in the transverse-coordinate space is analyzed with the help of the Mellin transform. Numerical results are presented for the unintegrated pion distributions with a simple valence-like initial condition at the low scale, which follows from chiral large-Nc quark models. The effect of spreading of UPDs in the transverse momentum with the increasing scale is confirmed, with growing asymptotically as Q^2 alpha(Q^2). Formal aspects of the equations, such as the limits of UPDs at x -> 0, x -> 1, and at low and large b, are straightforward to obtain with our method.
hep-ph↗
Solution of the Kwiecinski evolution equations for unintegrated parton distributions using the Mellin transform
The Kwiecinski equations for the QCD evolution of the unintegrated parton distributions in the transverse-coordinate space (b) are analyzed with the help of the Mellin-transform method. The equations are solved numerically in the general case, as well as in a small-b expansion which converges fast for b Lambda_QCD sufficiently small. We also discuss the asymptotic limit of large bQ and show that the distributions generated by the evolution decrease with b according to a power law. Numerical results are presented for the pion distributions with a simple valence-like initial condition at the low scale, following from chiral large-N_c quark models. We use two models: the Spectral Quark Model and the Nambu--Jona-Lasinio model. Formal aspects of the equations, such as the analytic form of the b-dependent anomalous dimensions, their analytic structure, as well as the limits of unintegrated parton densities at x -> 0, x -> 1, and at large b, are discussed in detail. The effect of spreading of the transverse momentum with the increasing scale is confirmed, with growing asymptotically as Q^2 alpha(Q^2). Approximate formulas for for each parton species is given, which may be used in practical applications.
hep-ph↗
Impact-Parameter Dependence of the Diagonal GPD of the Pion from Chiral Quark Models
We analyze the impact-parameter dependent diagonal non-singlet generalized parton distribution of the pion in two distinct chiral quark models: the Spectral Quark Model and the Nambu-Jona-Lasinio model. Leading-order perturbative QCD evolution from the low quark-model scale to higher scales is carried out with the help of the inverse Mellin transform. The model agrees very reasonably with the recent results from transverse-lattice calculations, while the forward parton distribution agrees with the experimental data.
hep-ph↗
Impact-parameter dependence of the generalized parton distribution of the pion in chiral quark models
We compute the off-forward diagonal non-singlet generalized parton distribution of the pion in two distinct chiral quark models: the Nambu-Jona-Lasinio model with the Pauli-Villars regulator and the Spectral Quark Model. The analysis is carried out in the impact-parameter space. Leading-order perturbative QCD evolution is carried out via the inverse Mellin transform in the index space. The model predictions agree very reasonably with the recent results from transverse-lattice calculations, reproducing qualitatively both the Bjorken-x and the impact-parameter dependence of the data.
hep-ph↗
Spectral quark model and low-energy hadron phenomenology
We propose a spectral quark model which can be applied to low energy hadronic physics. The approach is based on a generalization of the Lehmann representation of the quark propagator. We work at the one-quark-loop level. Electromagnetic and chiral invariance are ensured with help of the gauge technique which provides particular solutions to the Ward-Takahashi identities. General conditions on the quark spectral function follow from natural physical requirements. In particular, the function is normalized, its all positive moments must vanish, while the physical observables depend on negative moments and the so-called log-moments. As a consequence, the model is made finite, dispersion relations hold, chiral anomalies are preserved, and the twist expansion is free from logarithmic scaling violations, as requested of a low-energy model. We study a variety of processes and show that the framework is very simple and practical. Finally, incorporating the idea of vector-meson dominance, we present an explicit construction of the quark spectral function which satisfies all the requirements. The corresponding momentum representation of the resulting quark propagator exhibits only cuts on the physical axis, with no poles present anywhere in the complex momentum space. The momentum-dependent quark mass compares very well to recent lattice calculations. A large number of predictions and relations can be deduced from our approach for such quantities as the pion light-cone wave function, non-local quark condensate, pion transition form factor, pion valence parton distribution function, etc.
hep-ph↗
Pion light-cone wave function and pion distribution amplitude in the Nambu-Jona-Lasinio model
We compute the pion light-cone wave function and the pion quark distribution amplitude in the Nambu-Jona-Lasinio model. We use the Pauli-Villars regularization method and as a result the distribution amplitude satisfies proper normalization and crossing properties. In the chiral limit we obtain the simple results, namely phi_pi(x)=1 for the pion distribution amplitude, and = -M / f_pi^2 for the second moment of the pion light-cone wave function, where M is the constituent quark mass and f_pi is the pion decay constant. After the QCD Gegenbauer evolution of the pion distribution amplitude good end-point behavior is recovered, and a satisfactory agreement with the analysis of the experimental data from CLEO is achieved. This allows us to determine the momentum scale corresponding to our model calculation, which is close to the value Q_0 = 313 MeV obtained earlier from the analogous analysis of the pion parton distribution function. The value of is, after the QCD evolution, around (400 MeV)^2. In addition, the model predicts a linear integral relation between the pion distribution amplitude and the parton distribution function of the pion, which holds at the leading-order QCD evolution.
hep-ph↗
The $S_{11}- N$(1535) and $-N$(1650) Resonances in Meson-Baryon Unitarized Coupled Channel Chiral Perturbation Theory
The $s-$wave meson-baryon scattering is analyzed for the strangeness S=0 sector in a Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry. Four channels have been considered: $πN$, $ηN$, $K Λ$, $K Σ$. The needed two particle irreducible matrix amplitude is taken from lowest order Chiral Perturbation Theory in a relativistic formalism and low energy constants are fitted to the elastic $πN $ phase-shifts and the $π^- p \to ηn$ and $π^- p \to K^0 Λ$ cross section data. The position of the complex poles in the second Riemann sheet of the scattering amplitude determine masses and widths of the $S_{11}-$ $N$(1535) and $-N$(1650) resonances, in reasonable agreement with experiment. A good overall description of data, from $πN$ threshold up to 2 GeV, is achieved keeping in mind that the two pion production channel has not been included.
hep-ph↗
Bethe-Salpeter Approach for Meson-Meson Scattering in Chiral Perturbation Theory
The Bethe-Salpeter equation restores exact elastic unitarity in the s- channel by summing up an infinite set of chiral loops. We use this equation to show how a chiral expansion can be undertaken by successive approximations to the potential which should be iterated. Renormalizability of the amplitudes in a broad sense can be achieved by allowing for an infinite set of counter-terms as it is the case in ordinary Chiral Perturbation Theory. Within this framework we calculate the $ππ$ scattering amplitudes both for s- and p-waves at lowest order in the proposed expansion where a successful description of the low-lying resonances ($σ$ and $ρ$) and threshold parameters is obtained. We also extract the SU(2) low energy parameters ${\bar l}_{1,2,3,4}$ from our amplitudes.
nucl-th↗