arXiv subjects

E. Ruiz Arriola

Publications and source records attributed to E. Ruiz Arriola.

At least 163 records · Page 9Linked to original sources

arXiv2001

The Inverse Amplitude Method in $ππ$ Scattering in Chiral Perturbation Theory to Two Loops

The inverse amplitude method is used to unitarize the two loop $ππ$ scattering amplitudes of SU(2) Chiral Perturbation Theory in the $I=0,J=0$, $I=1,J=1$ and $I=2,J=0$ channels. An error analysis in terms of the low energy one-loop parameters $\bar l_{1,2,3,4,}$ and existing experimental data is undertaken. A comparison to standard resonance saturation values for the two loop coefficients $\bar b_{1,2,3,4,5,6} $ is also carried out. Crossing violations are quantified and the convergence of the expansion is discussed.

hep-ph↗

arXiv2001

Parton distributions for the pion in a chiral quark model

Parton distributions for the pion are studied in a chiral quark model characterized by a quark propagator for which a spectral representation is assumed. Electromagnetic and chiral symmetry constraints are imposed through the relevant Ward-Takahashi identities for flavoured vertex functions. Finiteness of the theory, requires the spectral function to be non-positive definite. Straightforward calculation yields the result that the pion structure function becomes one in the chiral limit, regardless of the details of the spectral function. LO and NLO evolution provide a satisfactory description of phenomenological parameterizations of the valence distribution functions but fails to describe gluon and sea distributions.

hep-ph↗

arXiv2000

Chiral Perturbation Theory and Unitarization

We review our recent work on unitarization and chiral perturbation theory both in the $ππ$ and the $πN$ sectors. We pay particular attention to the Bethe-Salpeter and Inverse Amplitude unitarization methods and their recent applications to $ππ$ and $πN$ scattering.

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arXiv2000

Bethe-Salpeter Approach for the $P_{33}$ Elastic Pion-Nucleon Scattering in Heavy Baryon Chiral Perturbation Theory

Heavy Baryon Chiral Perturbation Theory (HBChPT) to leading order provides a kernel to solve the Bethe-Salpeter equation for the $P_{33}$ ($Δ(1232)$-channel) $π-N$ system, in the infinite nucleon mass limit. Crossed Born terms include, when iterated within the Bethe-Salpeter equation, both {\it all} one- and {\it some} two-pion intermediate states, hence preserving elastic unitarity below the two-pion production threshold. This suggests searching for a solution with the help of dispersion relations and suitable subtraction constants, when all in-elasticities are explicitly neglected. The solution allows for a successful description of the experimental phase shift from threshold up to $\sqrt{s}=1500$ MeV in terms of four subtraction constants. Next-to-leading order HBChPT calculations are also used to estimate the unknown subtraction constants which appear in the solution. Large discrepancies are encountered which can be traced to the slow convergence rate of HBChPT.

hep-ph↗

arXiv2000

Improved Unitarized Heavy Baryon Chiral Perturbation Theory for $πN $ Scattering

We show how the unitarized description of pion nucleon scattering within Heavy Baryon Chiral Perturbation Theory can be considerably improved, by a suitable reordering of the expansion over the nucleon mass. Within this framework, the $Δ$ resonance and its associated pole can be recovered from the chiral parameters obtained from low-energy determinations. In addition, we can obtain a good description of the six $S$ and $P$ wave phase shifts in terms of chiral parameters with a natural size and compatible with the Resonance Saturation Hypothesis.

hep-ph↗

arXiv2000

Error estimates for pi-pi scattering threshold parameters in Chiral Perturbation Theory to two loops

Using the analysis of ChPT to two loops, we perform an error analysis of the threshold and low energy parameters, based on the uncertainties for the one loop low energy parameters and the resonance saturation mechanism. Different sets of one loop low energy constants have been considered.Thus, the predictive power of the effective field theory is quantified on the basis of the present experimental uncertainties.

hep-ph↗

arXiv2000

Bethe-Salpeter Approach for Unitarized 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 in the two particle irreducible amplitude and the propagators accomplishing exact elastic unitarity at any step. Renormalizability of the amplitudes can be achieved by allowing for an infinite set of counter-terms as it is the case in ordinary Chiral Perturbation Theory. Crossing constraints can be imposed on the parameters to a given order. Within this framework, we calculate the leading and next-to-leading contributions to the elastic $ππ$ scattering amplitudes, for all isospin channels, and to the vector and scalar pion form factors in several renormalization schemes. A satisfactory description of amplitudes and form factors is obtained. In this latter case, Watson's theorem is automatically satisfied. From such studies we obtain a quite accurate determination of some of the ChPT $SU(2)-$low energy parameters (${\bar l}_1 - {\bar l}_2 = -6.1\er{0.1}{0.3} $ and ${\bar l}_6= 19.14 \pm 0.19$). We also compare the two loop piece of our amplitudes to recent two--loop calculations.

hep-ph↗

arXiv2000

Unitarized Heavy Baryon Chiral Perturbation Theory and the $Δ$ Resonance in $πN $ Scattering

Based on the recent phenomenological analysis done by M. Mojzis, Eur. Phys. Jour. {\bf C2} (1998) 182, of $πN $ scattering within the framework of Heavy Baryon Chiral Perturbation Theory we predict, after a suitable unitarization of the amplitude, the $Δ$ resonance at $\sqrt{s} = M_Δ= 1238 \er{22}{18}{\rm MeV} $ and with a width of $ Γ_Δ= 150 \er{43}{31} {\rm MeV} $ in excellent agreement with the experimental numbers. The error bars reflect only the uncertainties in the low energy parameters as determined from an extrapolation to threshold of experimental data. We also describe satisfactorily, within errors, the phase shifts up to $\sqrt{s} \sim 1300 {\rm MeV} $.

hep-ph↗

arXiv1999

Anomalies for Nonlocal Dirac Operators

The anomalies of a very general class of non local Dirac operators are computed using the $ζ$-function definition of the fermionic determinant and an asymmetric version of the Wigner transformation. For the axial anomaly all new terms introduced by the non locality can be brought to the standard minimal Bardeen's form. Some extensions of the present techniques are also commented.

hep-th↗

arXiv1999

On the Structure Functions of Mesons and Baryons in a Chiral Quark Model

This research summarizes work done by myself (Nucl.Phys.{\bf A641} (1998)461), or in collaboration with R. M. Davidson (Phys.Lett.{\bf B348}(1995)163) and H. Weigel and L. Gamberg (Nucl.Phys.{\bf B560}(1999)xx). I will discuss several topics related with the computation of structure functions in the quark model in general and its perturbative evolution. In particular, I address this topic in the Nambu-Jona-Lasinio model of hadrons, where the nucleon is constructed as a soliton. I show that the handling of the regularization procedure is crucial in order to obtain exact scaling in the Bjorken limit and fulfillment of sum rules. I also include some problems concerning the general validity of quark model calculations.

hep-ph↗

arXiv1999

Hadron Structure Functions in a Chiral Quark Model: Regularization, Scaling and Sum Rules

We provide a consistent regularization procedure for calculating hadron structure functions in a chiral quark model. The structure functions are extracted from the absorptive part of the forward Compton amplitude in the Bjorken limit. Since this amplitude is obtained as a time-ordered correlation function its regularization is consistently determined from the regularization of the bosonized action. We find that the Pauli-Villars regularization scheme is most suitable because it preserves both the anomaly structure of QCD and the leading scaling behavior of hadron structure functions in the Bjorken limit. We show that this procedure yields the correct pion structure function. In order to render the sum rules of the regularized polarized nucleon structure functions consistent with their corresponding axial charges we find it mandatory to further specify the regularization procedure. This specification goes beyond the double subtraction scheme commonly employed when studying static hadron properties in this model. In particular the present approach serves to determine the regularization prescription for structure functions whose leading moments are not given by matrix elements of local operators. In this regard we conclude somewhat surprisingly that in this model the Gottfried sum rule does not undergo regularization.

hep-ph↗

arXiv1998

Chiral and scale anomalies of non local Dirac operators

The chiral and scale anomalies of a very general class of non local Dirac operators are computed using the $ζ$-function definition of the fermionic determinant. For the axial anomaly all new terms introduced by the non locality are shown to be removable by counterterms and such counterterms are also explicitly computed. It is verified that the non local Dirac operators have the standard minimal anomaly in Bardeen's form.

hep-th↗

arXiv1996

Elimination of the vacuum instability for finite nuclei in the relativistic $σ$-$ω$ model

The $σ$-$ω$ model of nuclei is studied at leading order in the $1/N$ expansion thereby introducing the self consistent Hartree approximation, the Dirac sea corrections and the one fermion loop meson self energies in a unified way. For simplicity, the Dirac sea is further treated within a semiclassical expansion to all orders. The well-known Landau pole vacuum instability appearing in this kind of theories is removed by means of a scheme recently proposed in this context. The effect of such removal on the low momentum effective parameters of the model, relevant to describe nuclear matter and finite nuclei, is analyzed. The one fermion loop meson self energies are found to have a sizeable contribution to these parameters. However, such contribution turns out to come mostly from the Landau poles and is thus spurious. We conclude that the fermionic loop can only be introduced consistently in the $σ$-$ω$ nuclear model if the Landau pole problem is dealt with properly.

nucl-th↗

arXiv1996

Baryons as non-topological chiral solitons

The present review gives a survey of recent developments and applications of the Nambu--Jona-Lasinio model with $N_f=2$ and $N_f=3$ quark flavors for the structure of baryons. The model is an effective chiral quark theory which incorporates the SU(N$_f$)$_L\otimes$SU(N$_f$)$_R\otimes$U(1)$_V$ approximate symmetry of Quantum chromodynamics. The approach describes the spontaneous chiral symmetry breaking and dynamical quark mass generation. Mesons appear as quark-antiquark excitations and baryons arise as non-topological solitons with three valence quarks and a polarized Dirac sea. For the evaluation of the baryon properties the present review concentrates on the non-linear Nambu--Jona-Lasinio model with quark and Goldstone degrees of freedom which is identical to the Chiral quark soliton model obtained from the instanton liquid model of the QCD vacuum. In this non-linear model, a wide variety of observables of baryons of the octet and decuplet is considered. These include, in particular, electromagnetic, axial, pseudoscalar and pion nucleon form factors and the related static properties like magnetic moments, radii and coupling constants of the nucleon as well as the mass splittings and electromagnetic form factors of hyperons. Predictions are given for the strange form factors, the scalar form factor and the tensor charge of the nucleon.

hep-ph↗

arXiv1996

Semiclassical treatment of the Dirac sea contribution for finite nuclei

Dirac sea corrections for bulk properties of finite nuclei are computed within a self-consistent scheme in the $σ$-$ω$ model. The valence part is treated in the Hartree approximation whereas the sea contribution is evaluated semiclassically up to fourth order in $\hbar$. Numerically, we find a quick convergence of the semiclassical expansion; the fourth order contributing much less than one percent to the binding energy per nucleon.

nucl-th↗

arXiv1995

Chiral anomaly and nucleon properties in the Nambu--Jona-Lasinio model with vector mesons

We consider the extended SU(3) Nambu and Jona-Lasinio model with explicit vector couplings in the presence of external fields. We study the chiral anomaly in this model and its implications on the properties of the nucleon described as a chiral soliton of three valence quarks bounded in mesonic background fields. For the model to reproduce the QCD anomaly it is necessary to subtract suitable local and polynomial counterterms in the external and dynamical vector and axial-vector fields. We compute the counterterms explicitly in a vector gauge invariant regularization, and obtain modifications to the total effective action and vector and axial currents. We study the numerical influence of those counterterms in the two flavour version of model with dynamical $σ,π, ρ, A $ and $ω$ mesons. We find that, for time independent hedgehog configurations, the numerical effects in the nucleon mass, the isoscalar nucleon radius and the axial coupling constant are negligibly small.

nucl-th↗

arXiv1994

Wigner transformation for the determinant of Dirac operators

We use the $ζ$-function regularization and an integral representation of the complex power of a pseudo differential operator, to give an unambiguous definition of the determinant of the Dirac operator. We bring this definition to a workable form by making use of an asymmetric Wigner representation. The expression so obtained is amenable to several treatments of which we consider in detail two, the inverse mass expansion and the gradient expansion, with concrete examples. We obtain explicit closed expressions for the corresponding Seeley-DeWitt coefficients to all orders. The determinant is shown to be vector gauge invariant and to posses the correct axial and scale anomalies. The main virtue of our approach is that it is conceptually simple and systematic and can be extended naturally to more general problems (bosonic operators, gravitational fields, etc). In particular, it avoids defining the real and imaginary parts of the effective action separately. In addition, it does not reduce the problem to a bosonic one to apply heat kernel nor performs further analytical rotations of the fields to make the Dirac operator Hermitian. We illustrate the flexibility of the method by studying some interesting cases.

hep-th↗

arXiv1994

Semiclassical expansions up to $\hbar^4$-order in relativistic nuclear physics

We present the first calculation of the $\hbar^4$-Wigner--Kirkwood corrections to a relativistic system of fermions in the presence of external scalar and vector potentials. The method we propose allows to compute efficiently semiclassical corrections to one body operators such as mean energies and local densities. It also preserves gauge invariance and produces explicitly convergent results despite some apparent divergencies at the classical turning points. As a byproduct we obtain the $\hbar^4$ corrections stemming from the polarization of the Dirac sea. We apply our results to the relativistic $σ$-$ω$ Lagrangian in the Hartree valence approximation. We compare the semiclassical expansion with the exact result and with the Strutinsky average whenever it can be obtained. We find that the $\hbar^4 $ corrections are much smaller than typical shell effects. Our results provide convincing arguments to neglect higher than second order $\hbar$ effects in the Wigner--Kirkwood scheme to relativistic nuclear physics in the mean field approximation.

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