arXiv subjects
Publications and source records attributed to M. R. Robilotta.
Chiral symmetry allows two and three nucleon forces to be treated in a single theoretical framework. We discuss two new features of this research programme at $\cO(q^4)$ and the consistency of the overall chiral picture.
In the rest frame of a many-body system, used in the calculation of its static and scattering properties, the center of mass of a two-body subsystem is allowed to drift. We show, in a model independent way, that drift corrections to the nucleon-nucleon potential are relatively large and arise from both one- and two-pion exchange processes. As far as chiral symmetry is concerned, corrections to these processes begin respectively at $\cO(q^2)$ and $\cO(q^4)$. The two-pion exchange interaction also yields a new spin structure, that promotes the presence of $P$ waves in trinuclei and is associated with profile functions which do not coincide with neither central nor spin-orbit ones. In principle, the new spin terms should be smaller than the $\cO(q^3)$ spin-orbit components. However, in the isospin even channel, a large contribution reverts this expectation and gives rise to the prediction of important drift effects.
We review the main achievements of the research programme for the study of nuclear forces in the framework of chiral symmetry and discuss some problems which are still open.
Chiral symmetry and unitarization are combined into generalized Breit-Wigner expressions describing scalar resonances, which contain free parameters and allow flexible descriptions of masses, widths and pole positions. This theoretical tool is especially designed to be used in analyses of low-energy data.
We use a configuration space chiral model in order to evaluate nucleon and delta sigma-terms. Analytic expressions are consistent with chiral counting rules and give rise to expected non-analytic terms in the chiral limit. We obtain the results $σ_N=46$ MeV and $σ_Δ=32$ MeV, which are very close to values extracted from experiment and produced by other groups.
The linear $\s$-model is used to study the effects of chiral symmetry in unitarized amplitudes incorporating scalar resonances. When just a single resonance is present, we show that the iteration of a chiral tree amplitude by means of regularized two-pion loops preserves the smallness of $\p\p$ interaction at low energies and estimate the importance of pion off-shell contributions. The inclusion of a second resonance is performed by means of a chiral extension of the linear $\s$-model lagrangian. The new $\p\p$ ampitude at tree level complies with low-energy theorems, depends on a mixing angle and has a zero for a given energy between the resonance masses. The unitarization of this amplitude by means of two-pion loops preserves both its chiral low energy behavior and the position of this zero confirming, in a lagrangian framework, conclusions drawn previously by Törnqvist. Finally, we approximate and generalize our results and give a friendly expression that can be used in the parametrization of $N$ coupled scalar resonances.
The chiral two-pion exchange nucleon-nucleon interaction has nowadays a rather firm conceptual basis, but depends on low-energy constants, which may be extracted from fits to data. In order to facilitate this kind of application, we present here a parametrized version of our relativistic expansion of this component of the force to $O(q^4)$, performed recently.
The $D^*Dπ$ form factor is evaluated at low and moderate $Q^2$ in a hadronic loop model, for off-shell $D$ mesons. The results contain arbitrary constants, which are fixed so as to match previous QCD sum rule calculations valid at higher $Q^2$. The form factor obtained in this way was used to extract the coupling constant, which is in very good agreement with the experimental value.
We present a relativistic procedure for the chiral expansion of the two-pion exchange component of the $NN$ potential, which emphasizes the role of intermediate $πN$ subamplitudes. The relationship between power counting in $πN$ and $NN$ processes is discussed and results are expressed directly in terms of observable subthreshold coefficients. Interactions are determined by one- and two-loop diagrams, involving pions, nucleons, and other degrees of freedom, frozen into empirical subthreshold coefficients. The full evaluation of these diagrams produces amplitudes containing many different loop integrals. Their simplification by means of relations among these integrals leads to a set of intermediate results. Subsequent truncation to $O(q^4)$ yields the relativistic potential, which depends on six loop integrals, representing bubble, triangle, crossed box, and box diagrams. The bubble and triangle integrals are the same as in $πN$ scattering and we have shown that they also determine the chiral structures of box and crossed box integrals. Relativistic threshold effects make our results to be not equivalent with those of the heavy baryon approach. Performing a formal expansion of our results in inverse powers of the nucleon mass, even in regions where this expansion is not valid, we recover most of the standard heavy baryon results. The main differences are due to the Goldberger-Treiman discrepancy and terms of $O(q^3)$, possibly associated with the iteration of the one-pion exchange potential.
We evaluate the long range part of the hyperon form factors and their contribution to elastic pion-hyperon scattering.
We perform a non-perturbative calculation of the $J/Ψ-π$ cross section using a $SU(2)\times SU(2)$ effective Lagrangian. Our results differ from those of previous calculations, specially in the description of vertices involving pions.
The central two-pion exchange NN potential at large distances is studied in the framework of relativistic chiral symmetry and related directly to the nucleon scalar form factor, which describes the mass density of its pion cloud. This relationship is well supported by phenomenology and allows the dependence of the asymptotic potential on the nucleon mass to be assessed. Results in the heavy baryon limit are about 25% larger than those corresponding to the empirical nucleon mass in the region of physical interest. This indicates that it is very important to keep this mass finite in precise descriptions of the NN system and supports the efficacy of the relativistic chiral framework. One also estimates the contribution of subleading effects and presents a simple discussions of the role of the quark condensate in this problem.
We study the changes produced by the deuteron on the QCD quark condensate by means the Feynman-Hellmann theorem and find that the pion mass dependence of the pion-nucleon coupling could play an important role. We also discuss the relation between the many body effect of the condensate and the meson exchange currents, as seen by photons and pions. For pion probes, the many-body term in the physical amplitude differs significantly from that of soft pions, the one linked to the condensate. Thus no information about the many-body term of the condensate can be extracted from the pion-deuteron scattering length. On the other hand, in the Compton amplitude, the relationship with the condensate is a more direct one.
We show that the tail of the chiral two-pion exchange nucleon-nucleon potential is proportional to the $πN$ scalar form factor and discuss how it can be translated into effective scalar meson interactions. We then construct a kernel for the process $NN\toπNN$, due to the exchange of two pions, which may be used in either three body forces or pion production in NN scattering. Our final expression involves a partial cancellation among three terms, due to chiral symmetry, but the net result is still important. We also find that, at large internucleon distances, the kernel has the same spatial dependence as the central NN potential and we produce expressions relating these processes directly.
The exchange of a single pion does not contribute to $Nα$ scattering, due to the isoscalar nature of the target. Therefore peripheral $Nα$ scattering may be used to probe existing models for the two-pion exchange component of the $NN$ potential. In a recent work we have considered this possibility using an effective $Nα$ interaction based on two-body forces only. In the present communication we discuss the role played by the two-pion exchange three-nucleon force, since its range is comparable to the two-pion exchange potential (TPEP).
The leading contribution to the three-pion exchange nucleon-nucleon potential is calculated in the framework of chiral symmetry. It has pseudoscalar and axial components and is dominated by the former, which has a range of about 1.5 fm and tends to enhance the OPEP. The strength of this force does not depend on the pion mass and hence it survives in the chiral limit.
We study elastic N$α$ scattering and produce a quantitative correlation between the range of the effective potential and the energy of the system. This allows the identification of the waves and energies for which the scattering may be said to be peripheral. We then show that the corresponding phase shifts are sensitive to the tail of the NN potential, which is due to the exchange of two pions. However, the present uncertainties in the experimental phase shifts prevent the use of N$α$ scattering to discriminate the existing models for the NN interaction.
The scalar-isoscalar field of an effective chiral Lagrangian transforms differently in either linear or non-linear frameworks: in the former case it is the counterpart of the pion whereas in the latter it is chiral invariant on its own. We compare the predictions from these two models for nucleon interactions and find results which are identical for two-body and rather different for three-body potentials. Some qualitative features of three-body interactions are discussed.