Manifestation of Conformal Symmetry in the Light Flavor Baryon Sector

TL;DR

This paper develops a conformal quark-diquark model for light flavor baryons on a conformally compactified AdS_5 cone, explaining mass orderings and predicting missing resonances, with implications for conformal symmetry realization.

Contribution

It introduces a conformal model incorporating gauge potential effects to describe baryon spectra and predicts missing states and gluon propagator behavior.

Findings

Correct mass ordering in N spectrum explained

Predicted 32 missing nucleon and Delta states

Gluon dressing function is finite in infrared

Abstract

On the AdS_5 cone, conformally compactified to R^1xS^3, a quark-diquark model of light flavor baryons is developed. The system on this manifold is decribed in terms of a scalar conformal equation, gauged by the field of a D3 brane whose transversal dimensions have been conformally warpped over R^1xS^3. Such a system does not result exactly conformally invariant because the gauge potential slightly modifies the conformal centrifugal barrier of the free geodesic motion. Thanks to this, the model describes the correct mass ordering in the P11-S11 pairs through the N spectrum as a combined effect of 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. We calculate the number of resonances with masses below 2500 MeV needed for the completeness of the above scheme and find a total of 32 "missing" nucleon and Delta states. Their absence or presence in the respective spectra relates to the degree to which conformal symmetry is realized in the lightest flavor sector. The scheme also allows for the 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.