arXiv subjects
Publications and source records attributed to E. Ruiz Arriola.
The renormalization of the NN interaction with the Chiral Two Pion Exchange Potential computed using relativistic baryon chiral perturbation theory is considered. The short distance singularity reduces the number of counter-terms to about a half as those in the heavy-baryon expansion. Phase shifts and deuteron properties are evaluated and a general overall agreement is observed.
We analyze how a short distance boundary condition for the Schrodinger equation must change as a function of the boundary radius by imposing the physical requirement of phase shift independence on the boundary condition. The resulting equation can be interpreted as a variable phase equation of a complementary boundary value problem. We discuss the corresponding infrared fixed points and the perturbative expansion around them generating a short distance modified effective range theory. We also discuss ultraviolet fixed points, limit cycles and attractors with a given fractality which take place for singular attractive potentials at the origin. The scaling behaviour of scattering observables can analytically be determined and is studied with some emphasis on the low energy nucleon-nucleon interaction via singular pion exchange potentials. The generalization to coupled channels is also studied.
We analyze the renormalization of the nucleon--nucleon interaction at low energies in coordinate space for both one and two pion exchange chiral potentials. The singularity structure of the long range potential and the requirement of orthogonality respectively determines, once renormalizability is imposed, the minimum and maximum number of counterterms allowed in the effective description of the nucleon--nucleon interaction in a non-perturbative context.
We address a possible relation between the expectation value of the Polyakov loop in pure gluodynamics and full QCD based on Polyakov Chiral Quark Models where constituent quarks and the Polyakov loop are coupled in a minimal way. To this end we use a center symmetry breaking Gaussian model for the Polyakov loop distribution which accurately reproduces gluodynamics data above the phase transition in terms of dimension 2 gluon condensate. The role played by the quantum and local nature of the Polyakov loop is emphasized.
We study the Nambu-Jona-Lasinio model with light and heavy quarks in a relativistic approach. We emphasize relevant regularization issues as well as the transition from light to heavy quarks. The approach of the electromagnetic meson form factor to the Isgur-Wise function in the heavy quark limit is also discussed.
We calculate deuteron positive and negative radial moments involving any bilinear function of the deuteron S and D wave functions for renormalized OPE and TPE chiral potentials. The role played by the strong singularities of the potentials at the origin and the short distance insensitivity of the results when the potentials are fully iterated is emphasized as compared to realistic potentials.
We describe results for the confinement-deconfinement phase transition as predicted by the Nambu--Jona-Lasinio model where the local and quantum Polyakov loop is coupled to the constituent quarks in a minimal way (PNJL). We observe that the leading correlation of two Polyakov loops describes the chiral transition accurately. The effects of the current quark mass on the transition are also analysed.
We extend the renormalization of the NN interaction with Chiral Two Pion Exchange Potential to the calculation of non-central partial wave phase shifts with total angular momentum j<=5 . The short distance singularity structure of the potential as well as the requirement of orthogonality conditions on the wave functions determines exactly the number of undetermined parameters after renormalization.
The renormalization of singular chiral potentials as applied to NN scattering and the structure of the deuteron is discussed. It is shown how zero range theories may be implemented non-perturbatively as constrained from known long range NN forces.
We describe how the inclusion of the gluonic Polyakov loop incorporates large gauge invariance and drastically modifies finite temperature calculations in chiral quark models after color neutral states are singled out. This generates an effective theory of quarks and Polyakov loops as basic degrees of freedom. We find a strong suppression of finite temperature effects in hadronic observables triggered by approximate triality conservation (Polyakov cooling), so that while the center symmetry breaking is exponentially small with the constituent quark mass, chiral symmetry restoration is exponentially small with the pion mass. To illustrate the point we compute some low energy observables at finite temperature and show that the finite temperature corrections to the low energy coefficients are $N_c$ suppressed due to color average of the Polyakov loop. Our analysis also shows how the phenomenology of chiral quark models at finite temperature can be made compatible with the expectations of chiral perturbation theory. The implications for the simultaneous center symmetry breaking-chiral symmetry restoration phase transition are also discussed.
We discuss convergence issues as well as short distance constraints on the deuteron wave functions based on chiral perturbation theory relevant to pion deuteron scattering. Non-analytical terms arise in the multiple scattering series for the pion-deuteron scattering length limiting the accuracy of the calculations. This result resembles similar findings in the structure of the NN interaction. The effects are found not to be numerically large. The iso-scalar $πN $ scattering length from the iso-vector one and the $πd$ scattering length yields values compatible with the experimental number and with much smaller errors.
We analyze the consequences of the inclusion of the gluonic Polyakov loop in chiral quark models at finite temperature. Specifically, the low-energy effective chiral Lagrangian from two such quark models is computed. The tree level vacuum energy density, quark condensate, pion decay constant and Gasser-Leutwyler coefficients are found to acquire a temperature dependence. This dependence is, however, exponentially small for temperatures below the mass gap in the full unquenched calculation. The introduction of the Polyakov loop and its quantum fluctuations is essential to achieve this result and also the correct large $N_c$ counting for the thermal corrections. We find that new coefficients are introduced at ${\cal O}(p^4)$ to account for the Lorentz breaking at finite temperature. As a byproduct, we obtain the effective Lagrangian which describes the coupling of the Polyakov loop to the Goldstone bosons.
The leading- and higher-twist distribution amplitudes and light-cone wave functions of real and virtual photons are analyzed in chiral quark models. The calculations are performed in the nonlocal quark model based on the instanton picture of QCD vacuum, as well as in the spectral quark model and the Nambu--Jona-Lasinio model with the Pauli-Villars regulator, which both treat interaction of quarks with external fields locally. We find that in all considered models the leading-twist distribution amplitudes of the real photon defined at the quark-model momentum scale are constant or remarkably close to the constant in the $x$ variable, thus are far from the asymptotic limit form. The QCD evolution to higher momentum scales is necessary and we carry it out at the leading order of the perturbative theory for the leading-twist amplitudes. We provide estimates for the magnetic susceptibility of the quark condensate $χ_m$ and the coupling $f_{3γ}$, which in the nonlocal model turn out to be close to the estimates from QCD sum rules. We find the higher-twist distribution amplitudes at the quark model scale and compare them to the Wandzura-Wilczek estimates. In addition, in the spectral model we evaluate the distribution amplitudes and light-cone wave functions of the $ρ$-meson.
We analyze the renormalization of the NN interaction at low energies and the deuteron bound state through the Chiral Two Pion Exchange Potential assumed to be valid from zero to infinity. The short distance Van der Waals singularity structure of the potential as well as the requirement of orthogonality conditions on the wave functions determines that, after renormalization, in the 1S0 singlet channel and in the 3S1-3D1 triplet channel one can use the deuteron binding energy, the asymptotic D/S ratio and the S-wave scattering lengths as well as the chiral potential parameters as independent variables. We use then the asymptotic wave function normalization As of the deuteron and the singlet and triplet effective ranges to determine the chiral constants yielding c1, c3 and c4. The role of finite cut-off corrections, the loss of predictive power due to uncertainties in the input data and the connection to OPE distorted waves perturbative approaches is also discussed.
We show that recent available lattice data for the renormalized Polyakov loop above the deconfinement phase transition exhibit unequivocal inverse power temperature corrections driven by a dimension 2 gluon condensate. This simple ansatz provides a good overall description of the data throughout the deconfinement phase until near the critical temperature with just two parameters. One of the parameters is consistent with perturbation theory while a second, non perturbative, parameter provides a numerical value of the condensate which is close to existing zero and finite temperature determinations.
We describe how the coupling of the gluonic Polyakov loop to quarks solves different inconsistencies in the standard treatment of chiral quark models at finite temperature at the one quark loop level. Large gauge invariance is incorporated and an effective theory of quarks and Polyakov loops as basic degrees of freedom is generated. From this analysis we find a strong suppression of finite temperature effects in hadronic observables below the deconfinement phase transition triggered by approximate triality conservation in a phase where chiral symmetry is spontaneously broken (Polyakov cooling). We also propose a simple phenomenological model to describe the available lattice data for the renormalized Polyakov loop in the deconfinement phase. Our analysis shows that non perturbative contributions driven by dimension-2 gluon condensates dominate the behaviour of the Polyakov loop in the regime T_c < T < 6T_c.
The Polyakov loop is an order parameter to the confinement-deconfinement phase transition in pure gluodynamics. Recently a simple phenomenological model has been proposed to describe the available lattice data for the renormalized Polyakov loop in the deconfinement phase (hep-ph/0505215). These data exhibit unequivocal inverse power temperature corrections driven by a dimension two gluon condensate. The heavy quark free energy is also studied and compared to lattice data.
The low energy structure of the energy momentum tensor in several chiral quark models with SU(3) flavor symmetry is analyzed in the presence of external gravitational fields. To this end a derivative expansion in a curved four dimensional space time is considered. This allows us to compute the chiral coefficients $L_{11}$, $L_{12}$, and $L_{13}$, appearing when the model is coupled to gravity and related to space-time curvature properties.