Conformal symmetry and light flavor baryon spectra

M. Kirchbach and C. B. Compean
Phys. Rev. D 82, 034008 – Published 10 August 2010

Abstract

The degeneracy among parity pairs systematically observed in the N and Δ spectra is interpreted to hint on a possible conformal symmetry realization in the light flavor baryon sector in line with AdS5/CFT4. The case is made by showing that all the observed N and Δ resonances with masses below 2500 MeV distribute fairly well each over the first levels of a unitary representation of the conformal group, a representation that covers the spectrum of a quark-diquark system, placed directly on a conformally compactified Minkowski spacetime, R1S3, as approached from the AdS5 cone. The free geodesic motion on the S3 manifold is described by means of the scalar conformal equation there, which is of the Klein-Gordon–type. The equation is then gauged by the curved Coulomb potential that has the form of a cotangent function. Conformal symmetry is not exact, this because the gauge potential slightly modifies the conformal centrifugal barrier of the free geodesic motion. Thanks to this, the degeneracy between P11S11 pairs from same level is relaxed, while the remaining states belonging to same level remain practically degenerate. The model describes the correct mass ordering in the P11S11 pairs through the spectra as a combined effect of the above conformal symmetry breaking, on the one side, and a parity change of the diquark from a scalar at low masses, to a pseudoscalar at higher masses, on the other. The quality of the wave functions is illustrated by calculations of realistic mean square charge radii and electric charge form factors on the examples of the proton, and the protonic P11(1440), and S11(1535) resonances. The scheme also allows for a prediction of the dressing function of an effective instantaneous gluon propagator from the Fourier transform of the gauge potential. We find a dressing function that is finite in the infrared and tends to zero at infinity.

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  • Received 8 March 2010

DOI:https://doi.org/10.1103/PhysRevD.82.034008

© 2010 The American Physical Society

Authors & Affiliations

M. Kirchbach and C. B. Compean

  • Instituto de Física, Universidad Autónoma de San Luis Potosí, Avenida Manuel Nava 6, San Luis Potosí, S.L.P. 78290, México

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Issue

Vol. 82, Iss. 3 — 1 August 2010

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