Some Inequalities among Hadron Masses

Some rigorous inequalities governing hadron masses in QCD are proved. One states that the electromagnetic mass shift of the pion is positive. The other states that if $m_{A\overline{B}}$ is the mass of the lightest meson made from a quark of type $A$ and an antiquark of type $B$, then—under conditions such that annihilation into gluons can be ignored—$2m_{A\overline{B}}>~m_{A\overline{A}}+m_{B\overline{B}}$. These inequalities agree with experimental data and have analogs for arbitrary vectorlike gauge theories. The first inequality has applications to the vacuum alignment problem in vectorlike technicolor theories.