Baryons in QCD_{AS} at Large N_c: A Roundabout Approach

TL;DR

This paper introduces a diagrammatic technique using a 'roundabout' vertex to analyze baryon masses in QCD_{AS} at large N_c, confirming they scale as N_c^2, thus supporting previous plausibility arguments.

Contribution

The paper develops a novel diagrammatic method with a multi-gluon 'roundabout' vertex to demonstrate baryon mass scaling in QCD_{AS} at large N_c.

Findings

Baryon mass in QCD_{AS} scales as N_c^2.

The 'roundabout' diagram simplifies complex calculations.

Method confirms previous theoretical scaling predictions.

Abstract

QCD_{AS}, a variant of large N_c QCD in which quarks transform under the color two-index antisymmetric representation, reduces to standard QCD at N_c = 3 and provides an alternative to the usual large N_c extrapolation that uses fundamental representation quarks. Previous strong plausibility arguments assert that the QCD_{AS} baryon mass scales as N_c^2; however, the complicated combinatoric problem associated with quarks carrying two color indices impeded a complete demonstration. We develop a diagrammatic technique to solve this problem. The key ingredient is the introduction of an effective multi-gluon vertex: a "traffic circle" or "roundabout" diagram. We show that arbitrarily complicated diagrams can be reduced to simple ones with the same leading N_c scaling using this device, and that the leading contribution to baryon mass does, in fact, scale as N_c^2.