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Prog. Theor. Phys. Supplement No.67 (1979) pp. 115-208

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Dynamical Theory of Hadrons Based upon Extended Particle Picture

Osamu Hara

Atomic Energy Research Institute, Nihon University, Tokyo 101

Abstract:

An extended particle model of hadrons is discussed on the basis of an assumption 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 levels near the ground state, the internal motion of such a body can be described by two kinds of variables ξµ(σ) and ξαr(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 ξµ(σ) corresponds to a string. On the other hand it can be shown that the excitons described by ξαr(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 quark-like excitons described by ξαr(σ), with its higher recurrences due to the excitation of the string-like mode described by ξµ(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 SU6. 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 π0-2γ 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 ΣNK. 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. Here a very satisfactory point is that our model incorporates both the string-like mode and the quark-like mode. So it opens a possibility to write down the Veneziano type amplitude for any realistic process according to the first principle.
The actual calculation has been made with K-N and K-N systems for problems not directly related to pomerons, which are beyond the scope of our calculation based upon the lowest order Born approximation disregarding unitarity. It has been shown that both the high energy K-N and K-N charge exchange scattering and the decay width of the higher resonances can be understood consistently within the framework of this model. On the other hand, the leading term in the K+-p backward scattering is proportional to u and so is strongly suppressed near u \eqsim 0. The remaining terms contain a factor u-1, which diverge at u = 0. If we introduce a small imaginary part for u as a higher order correction, however, this difficulty can be avoided, and it has been shown that the general feature of the empirical data can be reproduced reasonably by adjusting the magnitude of this imaginary part.


URL : http://ptp.ipap.jp/link?PTPS/67/115/
DOI : 10.1143/PTPS.67.115

[ Full Text PDF : FREE ACCESS (6408K) ] Citation:

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  2. Progress of Theoretical Physics Vol. 64 No. 5 (1980) pp. 1710-1722 :
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  3. Progress of Theoretical Physics Vol. 64 No. 5 (1980) pp. 1874-1877 :
    Level Structures of Exotic Baryons in the Joined Spring Model and Statistics of Quarks
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  4. Progress of Theoretical Physics Vol. 64 No. 6 (1980) pp. 2242-2256 :
    A Variant of the Extended Particle Model of Hadrons in Terms of Grassmann Numbers
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  5. Progress of Theoretical Physics Vol. 65 No. 3 (1981) pp. 1105-1109 :
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  6. Progress of Theoretical Physics Vol. 68 No. 3 (1982) pp. 883-897 :
    Multi-Quark Hadrons in the Joined-Spring Quark Model
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  7. Progress of Theoretical Physics Vol. 83 No. 5 (1990) pp. 1025-1053 :
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  8. Progress of Theoretical Physics Supplement No.105 (1991) pp. 287-288 :
    26. Comments on Yukawa's Nonlocal Field Theory
    Osamu Hara

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