Dynamical Theory of Hadrons Based upon Extended Particle Picture

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An extended particle model of hadrons is discussed on the basis of an assumprion that the hadrons correspond to the respective eigenstates of the internal motion of an extended body, which is taken to be a deformable sphere for simplicity. Such a three-dimensionally extended body has several remarkable features. The first point is that it allows half-integer spin. Because of this, it can be shown that if the discussion is restricted to low lying levels near the ground state, the internal motion of such a body can be described by two kinds of variables ξ^μ(σ) and ξ_α^r(σ) (r=1,2,3), where μ and α denote respectively vector and spinor indices for a four-vector and a two-component spinor, and σ is a Lorentz-invariant Lagrange coordinate labeling each material point of the body. Obviously, the mode described by ξ^μ(σ) corresponds to a string. On the other hand it can be shown that the excitons described by ξ_α^r(σ) can be identified with the quark as far as their spin and unitary spin quantum numbers are concerned. The internal motion of the body can be described in terms of these quarklike excitons described by ξ_α^r(σ), with its higher recurrences due to the excitation of the string-like mode described by ξ^μ(σ). So it inherits many of the attractive features of the quark model. But a great difference is that these quark-like excitons obey Bose-statistics, which is an inevitable consequence of the canonical quantization rule applied to the internal motion. (Another possibility is to introduce Grassmann number to describe the internal motion. But in this paper we shall not discuss this possibility further.) Thus, for example, the ground state of the baryon given by the excitation of three quark-like excitons belonging to the lowest eigenstate of the orbital motion is restricted to the irreducible representation 56 of SU_6. So in this model there is no positive reason to introduce the degree of freedom of colour at least from the symmetry reason. Because of this colour is not introduced in this paper. (Some comments are made on the R-ratio and the π^0-2γ life time too, which are usually taken as additional reasons to introduce colour.) The second point is that it leads to the condition that the triality must be restricted to zero. So in our model particles with fractional charge do not appear and the confinement is automatic. since it is obvious from its nature that the excitons never exist outside the extension of the body. We assume that the interaction between hadrons takes place due to the coupling between currents carried by the quark-like excitons excited in the body, which is mediated by some intermediate field. (In this paper the discussion is restricted to the strong interaction, although we believe that other interactions can be treated analogously.) It can be shown that the form of these currents are determined almost uniquely from the requirement that the theory must be invariant under an arbitrary transformation of σ. So such a scheme leads to a unified description of all hadron interactions in terms of a single coupling constant characterizing the coupling between the current and the intermediate field, which is much more stringent than the conventional ones given from group theoretical approaches. A characteristic feature of the interactions thus constructed is that they are in general not invariant under P and C, although PC holds exactly. Thus in our model the non-conservation of P and C is a general feature, not restricted to the weak interactions. It can be shown, however, that due to the specific form of our primary interaction such P- and C-violating terms vanish in the low energy region except for a part of Σ^^-NK^^-. In higher excitations, however, this is no longer the case and it is expected that, for example, the decay of some of the higher resonances violates P and C. Once the interaction Hamiltonian is thus given, it is straight forward to calculate the scattering amplitude. Her
理論物理学刊行会の論文
1980-04-25

Dynamical Theory of Hadrons Based upon Extended Particle Picture

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