Semiclassical meson-baryon dynamics from large-Nc QCD

Manohar, Aneesh V.

doi:10.1016/0370-2693(94)90564-9

Cited by 18 publications

(24 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The pion mass is known to change slightly as density increases, so putting into Eq. (12) the empirical value obtained from π-mesic atoms [17], m ⋆ π (ρ 0 )/m π ≈ 1.05, one obtains (11). Since the coupling g ω related to the hidden gauge coupling g does not scale at mean field [1,5], this result immediately implies that at…”

Section: Linking Chiral and Walecka Mean Fieldsmentioning

confidence: 74%

From chiral mean field to Walecka mean field and kaon condensation

1996

View full text Add to dashboard Cite

A unified treatment of normal nuclear matter described by Walecka's mean field theory and kaon condensed matter described by chiral perturbation theory is proposed in terms of mean fields of an effective chiral Lagrangian. The BR scaling is found to play a key role in making the link between the ground state properties of nuclear matter and the fluctuation into the strangeness-flavor direction. A simple prediction for kaon condensation is presented. * Supported by the Department of Energy under Grant No. Kaon-nuclear physics is probably one of the most exciting new directions in nuclear physics. The issues involved are strangeness productions in heavy-ion collisions and kaon condensation in compact star matter [1]. In discussing kaon-nuclear (or in general pseudoGoldstone boson) interactions appropriate for kaon condensation, chiral Lagrangians are found to be useful in describing the fluctuation in the strangeness direction. While chiral perturbation theory (χPT) is believed to be the most efficient way to implement chiral symmetry of QCD at low energy, there is a subtlety in applying it to nuclear or compact star matter which has not yet been satisfactorily addressed in the literature. This has to do with the consistency in the description of the ground state of the dense matter and of the fluctuation around that background defined by the ground state. In treatments to date, there is no consistency between the two sectors. For instance, the ground state -nuclear matter -is successfully described by Walecka mean-field theory [2] with the parameters of an apparently non-chiral Lagrangian determined from nuclear matter properties while the kaon condensation phenomenon, the physics of which is lodged in an effective action (or potential), is described by low-order chiral perturbation theory with the parameters of a chiral Lagrangian determined mostly by free-space data. Communication between the ground-state sector and the fluctuation sector has been glaringly missing. What would be needed is a formalism that describes both sectors from a given chiral Lagrangian with common parameters operative in both sectors simultaneously. An attractive possibility is that a lump of nuclear matter arises as a nontopological soliton in the form of "chiral liquid" as suggested by Lynn [3] around which fluctuations in various flavor directions could be described. Such a scheme would incorporate chiral symmetry in a self-consistent way in both sectors [1,4]. Unfortunately such a strategy has not been yet formulated into a workable scheme.In this Letter, we supply the missing link at mean field level with the help of the BR scaling introduced by us sometime ago [5]. Linking chiral and Walecka mean fieldsWe begin by restating the result of [5] in a form suitable for making contact with Walecka mean-field theory for nuclear matter. The starting point of Ref.[5] is a chiral Lagrangian for large N c (where N c is the number of colors) implemented with the scale anomaly of QCD, written in terms of pseudo-Goldstone fields U , th...

show abstract

Section: Linking Chiral and Walecka Mean Fieldsmentioning

confidence: 74%

From chiral mean field to Walecka mean field and kaon condensation

1996

View full text Add to dashboard Cite

show abstract

“…One should be able to obtain the leading in 1/N c contributions from classical field theory. For example, it was shown that the N c m 3/2 q oneloop correction to the baryon mass could be obtained from the energy of the pion cloud coupled to a classical baryon source [19]. The term in Eq.…”

Section: Large-nmentioning

confidence: 99%

Structure of largeNccancellations in baryon chiral perturbation theory

et al. 2000

Self Cite

View full text Add to dashboard Cite

We show how to compute loop graphs in heavy baryon chiral perturbation theory including the full functional dependence on the ratio of the Delta-nucleon mass difference to the pion mass, while at the same time automatically incorporating the 1/N c cancellations that follow from the large-N c spin-flavor symmetry of baryons in QCD. The one-loop renormalization of the baryon axial vector current is studied to demonstrate the procedure. A new cancellation is identified in the one-loop contribution to the baryon axial vector current. We show that loop corrections to the axial vector currents are exceptionally sensitive to deviations of the ratios of baryon-pion axial couplings from SU (6) values.

show abstract

“…Nevertheless, the N C counting rules outlined above apply generally, not just in solitonic theories, and one could look into their consequences for theories coupling external baryons to pions . This in fact has been accomplished [28], [29]. The picture that emerges is the following: Suppose one starts with a meson-baryon lagrangian of the form L = L M + L M B where the subscripts denote the purely mesonic part and the meson baryon interactions, and wherein the baryon has been introduced as an external field and provided L M supports a stable soliton, then the leading O(N C ) of this solitonic theory corresponds to the set of all multi loop graphs without a closed meson loop generated from L and evaluated in the limit of a static baryon.…”

Section: The Skyrme Modelmentioning

confidence: 99%

“…The part proportional to the divergent λ may formally be expanded According to (2.27) the divergencies in (2.25) may finally be absorbed into a redefinition of the lagrangians LECs. The total soliton mass (tree + 1-loop) is obtained as 28) where E cas represents the Casimir energy (2.26) and…”

Section: Continuum Contributions: the Phaseshift Formulamentioning

confidence: 99%

Quantum corrections to baryon properties in chiral soliton models

Meier¹,

Walliser²

1997

Physics Reports

View full text Add to dashboard Cite

Chiral lagrangians as effective field theories of QCD are successfully applied to meson physics at low energies in the framework of chiral perturbation theory. Because of their nonlinear structure these lagrangians allow for static soliton solutions which may be interpreted as baryons. Their semiclassical quantization, which provides the leading order in an 1/N C expansion (N C is the number of colors) turned out to be insufficient in many cases to obtain good agreement with empirical baryon observables. However with N C = 3, large corrections are expected in the next-to-leading order which is carried by pionic fluctuations around the soliton background. The calculation of these corrections requires renormalization to 1-loop of the underlying field theory. We present a procedure to calculate the 1-loop contributions for a variety of baryonic observables. In contrast to chiral perturbation theory, terms with an arbitrary number of gradients may in principle contribute and the restriction to low chiral orders can only be justified by the investigation of the scale independence of the results. The results generally give the right sign and magnitude to reduce the discrepancy between theory and experiment with one exception: the axial quantities. These suffer from the fact that the underlying current algebra mixes different N C orders, which suggests a large and positive next-to-next-to-leading order contribution, which is probably sufficient to close the gap to experiment.

show abstract

Semiclassical meson-baryon dynamics from large-Nc QCD

Cited by 18 publications

References 29 publications

From chiral mean field to Walecka mean field and kaon condensation

From chiral mean field to Walecka mean field and kaon condensation

Structure of largeNccancellations in baryon chiral perturbation theory

Quantum corrections to baryon properties in chiral soliton models

Contact Info

Product

Resources

About