Chiral effective theory of diquarks and the U_A(1) anomaly

TL;DR

This paper develops an effective chiral theory for diquarks, incorporating the U_A(1) anomaly, and explores its implications for diquark masses and heavy baryon spectra, linking theoretical constructs with lattice QCD and experimental data.

Contribution

It introduces a novel linear sigma-model for diquarks with a new chirally symmetric coupling that accounts for the U_A(1) anomaly effects.

Findings

The effective Lagrangian includes a new meson-diquark-diquark coupling.

The U_A(1) anomaly significantly influences diquark masses.

An inverse mass ordering between strange and nonstrange diquarks is found.

Abstract

The diquark is a strongly correlated quark pair that plays an important role in hadrons and hadronic matter. In order to treat the diquak as a building block of hadrons, we formulate an effective theory of diquark fields with $SU(3)_R \times SU(3)_L$ chiral symmetry. We concentrate on the scalar ($0^+$) and pseudoscalar ($0^-$) diquarks and construct a linear-sigma-model Lagrangian. It is found that the effective Lagrangian contains a new type of chirally symmetric meson-diquark-diquark coupling that breaks axial $U_A(1)$ symmetry. We discuss consequences of the $U_A(1)$ anomaly term to the diquark masses as well as to the singly heavy baryon spectrum, which is directly related to the diquark spectrum. We find an inverse mass ordering between strange and nonstrange diquarks. The parameters of the effective theory can be determined by the help of lattice QCD calculations of diquarks and also from the mass spectrum of the singly heavy baryons. We determine the strength of the $U_A(1)$ anomaly term, which is found to give a significant portion of the diquark masses.