Abstract
The $SU(3)$ Yang-Mills matrix model coupled to fundamental fermions is an approximation of quantum chromodynamics (QCD) on a 3-sphere of radius $R$. The spectrum of this matrix model Hamiltonian is estimated using standard variational methods, and is analyzed in the strong coupling limit. By employing a matching prescription to determine the dependence of the Yang-Mills coupling constant $g$ on $R$, we relate the asymptotic values of the energy eigenvalues in the $R \rightarrow \infty$ (flat space) limit to the masses of light hadrons. We find that the matrix model estimates the light hadron spectrum fairly accurately, with the light baryon masses falling within $10\%$, and most light meson masses falling within about $30\%$ of their observed values.
Highlights
The SUð3Þ Yang-Mills matrix model coupled to fundamental fermions is an approximation of quantum chromodynamics (QCD) on a 3-sphere of radius R
We find that the matrix model estimates the light hadron spectrum fairly accurately, with the light baryon masses falling within 10%, and most light meson masses falling within about 30% of their observed values
Hadrons constitute almost all of ordinary matter, and the study of their properties is of fundamental importance to test the predictions of low-energy quantum chromodynamics (QCD)
Summary
Hadrons constitute almost all of ordinary matter, and the study of their properties is of fundamental importance to test the predictions of low-energy quantum chromodynamics (QCD). The matrix model corresponds to a dimensional reduction of Yang-Mills theory on S3 × R, and is a quantum-mechanical model based on 3 × ðN2 − 1Þ-dimensional real matrices as degrees of freedom This model proves to be quite good in describing the mass spectrum of glueballs [28] in the low energy regime of pure Yang-Mills theory. We give estimates for the masses of the light pseudoscalar and vector mesons and spin-12 and spin-32 baryons, which turn out to be surprisingly successful, as can be seen from Fig. 5 and Tables IV and V We consider this model as a new proposal for describing the extreme low energy sector of QCD, i.e., the sector describing light hadrons.
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