Title: The MIT Bag Model: The Dirac Equation for a Quark Confined to a Spherical Region
Abstract: Quarks, like the leptons (electrons, μ and τ mesons) are Dirac s = 1/2 particles. Unlike the leptons, quarks have additional internal degrees of freedom, specified by “flavor” (including isospin that determines their charge) and “color,” They come in three colors and three generations of isospin doublets (u, d; up and down quarks; s, c; strange and charmed quarks; and b, t; bottom and top quarks). They appear in nature only in “colorless” combinations corresponding to the scalar irreducible representations of the color symmetry SU(3) [the analogue of S = 0 multiparticle spin states, corresponding to the scalar irreducible representations of SU(2)]. The “colorless” combinations can arise either from quark—antiquark combinations or combinations of three quarks. Protons, e.g., are made of two up quarks, each with charge of + 2/3e, and one down quark with charge − 1/3e, whereas neutrons are made of one up quark and two down quarks, total charge = (+2/3 − 1/3 − 1/3)e = 0. These three-quark systems have a total spin, S = 1/2, and isospin, I = 1/2, with M 1 = ±1/2. The quark aggregates are confined to finite regions of space, for the three-quark aggregates of the nucleon, to a region of approximately 1.2 fm. The confinement mechanism is not at all understood. One of the most successful phenomenological models for quark confinement is the “MIT bag model,” named after the institution of the inventors of the model. In this model, it is simply assumed the quarks are confined to a spherical region of space, with a radius, r = a, and V(r) = 0 for r < a. The rest mass of the u and d qarks, however, is so small their motion in the region with r < a must be treated by the Dirac equation. In a sense, the MIT bag model is the quark analogue of the nuclear shell model. In one extreme version of the nuclear shell model, the potential is assumed to have the form: V(r) = 0 for r < a, and V = +∞ for r > a. Our discussion of the Klein paradox, however, should convince us an infinite potential is unable to confine a relativistic particle. It may be enough to solve a model in which the quark is in free particle motion inside the region for r < a, but is subject to boundary conditions at r = a that simply dictate the confinement.
Publication Year: 2000
Publication Date: 2000-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
Access and Citation
Cited By Count: 1
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot