Conformal symmetry and light flavor baryon spectra

Journal Article · Sun Aug 01 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.034008· OSTI ID:21432848

Kirchbach, M; Compean, C B ^[1]

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1. Instituto de Fisica, Universidad Autonoma de San Luis Potosi, Avenida Manuel Nava 6, San Luis Potosi, S.L.P. 78290 (Mexico)

The degeneracy among parity pairs systematically observed in the N and {Delta} spectra is interpreted to hint on a possible conformal symmetry realization in the light flavor baryon sector in line with AdS{sub 5}/CFT{sub 4}. The case is made by showing that all the observed N and {Delta} 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, R{sup 1} x S{sup 3}, as approached from the AdS{sub 5} cone. The free geodesic motion on the S{sup 3} 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 P{sub 11}-S{sub 11} 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 P{sub 11}-S{sub 11} 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 P{sub 11}(1440), and S{sub 11}(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.

• OSTI ID: 21432848
• Journal Information: Physical Review. D, Particles Fields, Vol. 82, Issue 3; Other Information: DOI: 10.1103/PhysRevD.82.034008; (c) 2010 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANTI DE SITTER SPACE
CONFORMAL GROUPS
CONFORMAL INVARIANCE
DELTA BARYONS
FLAVOR MODEL
FORM FACTORS
GEV RANGE 01-10
GLUONS
KLEIN-GORDON EQUATION
MASS
MINKOWSKI SPACE
N BARYONS
PROTONS
QUANTUM FIELD THEORY
QUARK MODEL
QUARKS
RESONANCE
SPACE-TIME
WAVE FUNCTIONS
BARYONS
BOSONS
COMPOSITE MODELS
DIFFERENTIAL EQUATIONS
DIMENSIONLESS NUMBERS
ELEMENTARY PARTICLES
ENERGY RANGE
EQUATIONS
FERMIONS
FIELD EQUATIONS
FIELD THEORIES
FUNCTIONS
GEV RANGE
HADRONS
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICAL SPACE
N*BARYONS
NUCLEONS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MODELS
PARTICLE PROPERTIES
SPACE
SYMMETRY GROUPS
WAVE EQUATIONS