Self Energy of Massless Quarks in the MIT Bag

Abstract

In this talk 1 would like to tell you about a calculation of the self energy of a massless quark in the MIT bag [1]. The motivation for doing this calculation goes beyond simply finding small corrections to the hadron masses predicted by the bag model. The bag model gives reasonable results for the masses only when an ad hoc “zero-point” energy is added, that is,

$$M = N\omega + N\alpha {\vec \sigma _1} \cdot {\vec \sigma _2}\,{I_{mag}} + \frac{4}{3}p\pi {R^3} - \,{Z_0}/R$$

where N is the number of quarks in the bag, ω the kinetic energy perquark--2.04/R for massless quarks, I_mag the energy of interaction between quarks due to exchange of a transverse gluon--0.12/R for massless quarks, α the fine structure constant--usually taken to be about 2.2, R the bag radius, p the bag pressure, and -Z₀/R the zero-point energy [2]. This negative zero-point energy was introduced in analogy with the attraction of parallel conducting plates; unfortunately all attempts to find a similar negative energy in the bag have failed. There is a good physical reason for this failure: this zero-point energy causes an empty bag to have energy $\frac{4}{3}{\mkern 1mu} \pi p{{R}^{3}}{\mkern 1mu} - {{Z}_{0}}/R$ and hence makes the vacuum unstable.