On the consistency of effective models of nucleon structure with chiral symmetry (original) (raw)
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Physical Review Letters, 2009
The chiral low-energy constants cD and cE are constrained by means of accurate ab initio calculations of the A = 3 binding energies and, for the first time, of the triton β decay. We demonstrate that these low-energy observables allow a robust determination of the two undetermined constants, a result of the surprising fact that the determination of cD depends weakly on the short range correlations in the wave functions. These two-plus three-nucleon interactions, originating in chiral effective field theory and constrained by properties of the A = 2 system and the present determination of cD and cE, are successful in predicting properties of the A = 3, and 4 systems. 21.45.Ff, The fundamental connection between nuclear forces and the underlying theory of quantum chromodynamics (QCD) remains one of the greatest contemporary theoretical challenges, due to the non-perturbative character of QCD in the low-energy regime relevant to nuclear phenomena. However, the last two decades of theoretical developments provide us with a bridge to overcome this obstacle, in the form of chiral perturbation theory (χPT) [1]. The χPT Lagrangian, constructed by integrating out degrees of freedom of the order of Λ χ ∼ 1 GeV and higher (nucleons and pions are thus the only explicit degrees of freedom), is an effective Lagrangian of QCD at low energies. As such, it retains all conjectured symmetry principles, particularly the approximate chiral symmetry, of the underlying theory. Furthermore, it can be organized in terms of a perturbative expansion in positive powers of Q/Λ χ where Q is the generic momentum in the nuclear process or the pion mass [1]. Though the subject of an ongoing debate about its validity [2, 3], the naive extension of this expansion to non-perturbative phenomena provides a practical interface with existing manybody techniques, and clearly holds a significant value for the study of the properties of QCD at low energy and its chiral symmetry.
The nucleon axial isoscalar coupling in quantum chromodynamics sum rules
Physics Letters B, 1994
The correction arising from the three-gluon condensate to the QCD sum rules of the nucleon coupling constant to the axial isoscalar current, g~t, is calculated. It is found that the contribution of the three-gluon condensate can make the sum rules more stable. The resultant theoretical value, g] = 0.58 + 0.20, agrees with the phenomenological estimate. The first moments of the spin structure functions for proton, neutron and deuteron are found to be consistent with the improved Ellis-Jaffe sum rules.
Scalar response of the nucleon, chiral symmetry and nuclear matter properties
2010
In this talk we present a description of nuclear binding in a chiral approach based on the existence of a chiral invariant scalar field associated with the generation of the masses through spontaneous chiral symmetry breaking. We discuss the emergence of such a field on the example of the NJL model. We also incorporate the effect of confinement at the level of the nucleon substructure to stabilize nuclear matter. In a particular quark-diquark model we illustrate the simutaneous influences of spontaneous chiral symmetry breaking and confinement on the nucleon mass and on the nuclear matter description.
Chiral Symmetry in Nuclei -- Theoretical Expectations and Hard Facts
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It is widely believed that chiral symmetry is restored not only at high temperatures, but also at high nuclear densities. The drop of the order parameter of the chiral phase transition, the chiral condensate, with density has indeed been calculated in various models and is as such a rather robust result. In this talk I point out that the connection of this property with actual observables is far less clear. For this task a good hadronic description of the primary production of hadrons, their propagation inside the nuclear medium, their decay and the propagation of the decay products through the medium to the detector all have to be treated with equal accuracy and weight. In this talk I illustrate with the examples of ω production and π 0 π 0 production how important in particular final state interactions are.
Chiral corrections to the vector and axial couplings of quarks and baryons
Physical Review D, 2008
We calculate chiral corrections to the semileptonic vector and axial quark coupling constants using a manifestly Lorentz covariant chiral quark approach up to order O(p 4) in the two-and tree-flavor picture. These couplings are then used in the evaluation of the corresponding couplings which govern the semileptonic transitions between octet baryon states. In the calculation of baryon matrix elements we use a general ansatz for the spatial form of the quark wave function, without referring to a specific realization of hadronization and confinement of quarks in baryons. Matching the physical amplitudes calculated within our approach to the model-independent predictions of baryon chiral perturbation theory (ChPT) allows to deduce a connection between our parameters and those of baryon ChPT.
Mirror versus naive assignment in chiral models for the nucleon
International Journal of Modern Physics A, 2014
In the framework of chiral model(s) based on the linear realization of chiral symmetry, we investigate the low-energy phenomenological properties of the nucleon and its chiral partner (identified with either N(1535) or N(1650)) in the naive assignment and compare the results with the ones obtained in the mirror assignment. We find that, within the naive assignment, we are not able to reproduce the experimental value of the isospin-odd scattering length, while the mirror assignment is in good agreement with it for both choices N(1535) and N(1650). The isospin-even scattering length is not yet conclusive in either assignment because it depends crucially on the poorly known scalar mesonic sector. The decay with ΓN(1535)→Nη turns out to be far too small in both the naive and mirror assignments, while ΓN(1650)→Nη is described correctly by both of them. In conclusion, the mirror assignment with N(1650) as the chiral partner of the nucleon is the favored configuration.
Chiral lagrangians and nuclear forces
Physics Letters B, 1992
We obtain the nuclear potential coming from the general chiral invariant effective lagrangian up to third order. It consists of a stronger two-body potential and a weaker three-body force. It accounts for the known spin-isospin dependence in the form of contact terms but also yields novel features of finite range. QCD is the theory of the strong force that binds quarks into baryons and mesons and yet, we do not know how to derive from it the interaction among these bound states. The method of effective lagrangians [ 1 ] allows us to write the most general lagrangian for pions and non-relativistic nucleons which is compatible with the symmetries of QCD. This lagrangian includes all terms with the appropriate transformation properties and undetermined coefficients. It has been argued [ 2 ] that large-No QCD is equivalent to a theory of mesons in which the nucleons arise as solitons; in other words, that the effective lagrangian is that of Skyrme. Without solving QCD, though, we have only dimensional analysis as a guide: for terms with dimension four or higher, additional derivatives are accompanied by extra inverse powers of a characteristic mass M of the underlying theory, of the order of 1 GeV in this case. We can then organize contributions to any given process in powers of Q/M, where Q << M is the highest momentum allowed for any particle involved. The method of effective lagrangians offers a systematic way to describe (and to a given order even predict) the low-energy sector of a theory with a spontaneously broken symmetry. Although the main ideas behind this technique were introduced a while ago [ 3 ], it was only recently that it was applied to nuclear forces [4,5 ]. Weinberg has shown that, when all other particle types are integrated out, the following holds: (i) The lowest order effective potential between nucleons is just a sum over all pairings of the lowest order two-particle effective potential given by the well-known one-pion-exchange term supplemented by a contact interaction, (2gA~ 2~ ~ Vo = (Cs +CT01 "arE)~3(Xl-X2)-\-~-] tl "t2 (art "Vl) (arE' V2) Y([xl-x2 [)-(1'~-~2') , (1) where Y(r)-exp (-mar)/4~r is the usual Yukawa potential. (ii) Corrections come from adding new terms with extra derivatives to the lagrangian, adding loops and (for more than two nucleons) decreasing the number of disconnected pieces in the effective potential. They contribute with factors of the order of Q/M, (Q/M)2 and (Q/M)2 respectively. Consistency of the whole approach seems to require also Q ~ g 2/2mN and so M << mN. The one-pion-exchange term provides the longest range force which accounts for the deuteron quadrupole Research supported in part by the Robert A. Welch Foundation and NSF Grant PHY9009850. 2 World Laboratory Fellow.
Phys Rev C, 2010
Chiral theories with spontaneous symmetry breaking such as the Nambu-Jona-Lasinio (NJL) model lead to the existence of a scalar mode. We present in a detailed manner how the corresponding low momentum effective lagrangian involving the scalar field can be constructed starting from the NJL model. We discuss the relevance of the scalar mode for the problem of the nuclear binding and saturation. We show that it depends on the nucleon mass origin with two extreme cases. If this origin is entirely due to confinement the coupling of this mode to the nucleons vanishes, making it irrelevant for the nuclear binding problem. If instead it is entirely due to spontaneous symmetry breaking it couples to the nucleons but nuclear matter collapses. It is only in the case of a mixed origin with spontaneous breaking that nuclear matter can be stable and reach saturation. We describe models of nucleon structure where this balance is achieved. We also show how chiral constraints and confinement modify the QCD sum rules for the mass evolution in nuclear matter.