Baryon-Meson Mass Inequality

Abstract

It is suggested that the inequality $m_B>\frac{3}{2}{m}_M$ is a rigorous result in quantum chromodynamics. The analog for a ($q_1\dots q_N$) baryon in $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ is $m_B>\left(\frac{1}{2}N\right)m_M$. The inequality is proved for weak coupling and a version of the strong-coupling expansion where a separation $H_{q_1{q}_2{q}_3}=H_{12}+H_{23}+H_{31}$ of the problem can be achieved. Implications for quantum chromodynamics and composite models are briefly discussed.