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Theory of strong interactions

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  • J.J Sakurai
  • The Enrico Fermi Institute for Nuclear Studies and the Department of Physics, The University of Chicago, Chicago, Illinois, USA

All the symmetry models of strong interactions which have been proposed up to the present are devoid of deep physical foundations. It is suggested that, instead of postulating artificial “higher” symmetries which must be broken anyway within the realm of strong interactions, we take the existing exact symmetries of strong interactions more seriously than before and exploit them to the utmost limit. A new theory of strong interactions is proposed on this basis.Following Yang and Mills we require that the gauge transformations that are associated with the three “internal” conservation laws—baryon conservation, hypercharge conservation, and isospin conservation—be “consistent with the local field concept that underlies the usual physical theories.” In analogy with electromagnetism there emerge three kinds of couplings such that in each case a massive vector field is coupled linearly to the conserved current in question. Each of the three fundamental couplings is characterized by a single universal constant. Since, as Pais has shown, there are no other internal symmetries that are exact, and since any successful theory must be simple, there are no other fundamental strong couplings. Parity conservation in strong interactions follows as the direct consequence of parity conservation of the three fundamental vector couplings. The three vector couplings give rise to corresponding current-current interactions. Yukawa-type couplings of pions and K particles to baryons are “phenomenological,” and may arise, for instance, out of four-baryon current-current interactions along the lines suggested by Fermi and Yang. All the successful features of Chew-Low type meson theories and of relativistic dispersion relations can, in principle, be in accordance with the theory whereas none of the predictions based on relativistic Yukawa-type Lagrangians are meaningful unless ?M is considerably less than unity.Simple and direct experimental tests of the theory should be looked for in those phenomena in which phenomenological Yukawa-type couplings are likely to play unimportant roles. The fundamental isospin current coupling in the static limit gives rise to a short-range repulsion (attraction) between two particles whenever the isospins are parallel (antiparallel). Thus the low-energy s-wave ?N interaction should be repulsive in the T = 32 state and attractive in the T = 12 state in agreement with observation. In ?? s-wave scattering the T = 0 state is strongly attractive, and there definitely exists the possibility of an s-wave resonance at energies of the order of the K?p threshold, while the T = 1 ?? phase shift is likely to remain small; using the K matrix formalism of Dalitz and Tuan, we might be able to compare the “ideal” phase shifts derived in this manner with the “actual” phase shifts deduced from K?p reactions. It is expected that the two-pion system exhibits a resonant behavior in the T = 1 (p-wave) state in agreement with the conjecture of Frazer and Fulco based on the electromagnetic structure of the nucleon. The three pion system is expected to exhibit two T = 0, J = 1 resonances. It is conjectured that the two T = 12 and one T = 32 “higher rsonances” in the ?N interactions may be due to the two T = 0 3? resonances and the one T = 1 2? resonance predicted by the theory. Multiple pion production is expected at all energies to be more frequent than that predicted on the basis of statistical considerations. The fundamental hypercharge current coupling gives rise to a short-range repulsion (attraction) between two charge-doublet particles when their hypercharges are like (opposite). If the isospin current coupling is effectively weaker than the hypercharge current coupling, the KN “potential” should be repulsive and the KN “potential” should be attractive, and the charge exchange scattering of K+ and K? should be relatively rare, at least in s states. All these features seem to be in agreement with current experiments. Conditions for the validity of Pais' doublet approximation are discussed. The theory offers a possible explanation for the long-standing problem as to why associated production cross sections are small and K? cross sections are large. The empirical fact that the ratio of (KK2N) to (K?N) + (K?N) in NN collisions seems to be about twenty to thirty times larger than simple statistical considerations indicate is not surprising. The fundamental baryonic current coupling gives rise to a short-range repulsion for baryon-baryon interactions and an attraction for baryon-antibaryon interactions. There should be effects similar to those expected from “repulsive cores” for all angular momentum and parity states in both the T = 1 and T = 0, NN interactions at short distances though the T = 1 state may be more repulsive. A simple Thomas-type calculation gives rise to a spin-orbit force of the right sign with not unreasonable order of magnitude. The ?N and ?N interactions at short distances should be somewhat less repulsive than the NN interactions. Annihilation cross sections in NN collisions are expected to be large even in Bev regions in contrast to the predictions of Ball and Chew. The observed large pion multiplicity in NN annihilations is not mysterious. It is possible to invent a reasonable mechanism which makes the reaction p + p ? ?+ + ?? very rare, as recently observed. Fermi-Landau-Heisenberg type theories of high energy collisions are not expected to hold in relativistic NN collisions; instead the theory offers a theoretical justification for the “two-fire-ball model“ of high-energy jets previously proposed on purely phenomenological grounds.Because of the strong short-range attraction between a baryon and antibaryon there exists a mechanism for a baryon-antibaryon pair to form a meson. The dynamical basis of the Fermi-Yang-Sakata-Okun model as well as that of the Goldhaber-Christy model follows naturally from the theory; all the ad hoc assumptions that must be made in order that the compound models work at all can be explained from first principles. It is suggested that one should not ask which elementary particles are “more elementary than others,” and which compound model is right, but rather characterize each particle only by its internal properties such as total hypercharge and mean-square baryonic radius. Although the fundamental couplings of the theory are highly symmetric and universal, it is possible for the three couplings alone to account for the observed mass spectrum. The theory can explain, in a trivial manner, why there are no “elementary” particles with baryon number greater than unity provided that the baryonic current coupling is sufficiently strong. The question of whether or not an |S| = 2 meson exists is a dynamical one (not a group-theoretic one) that depends on the strength of the hypercharge current coupling. A possible reason for the nonexistence of a ?0? (charge-singlet, nonstrange boson) is given. The theory realizes Pais' principles of economy of constants and of a hierarchy of interactions in a natural and elegant manner.It is conjectured that there exists a deep connection between the law of conservation of fermions and the universal V-A weak coupling. In the absence of strong and electromagnetic interactions, baryonic charge, hypercharge, and electric charge all disappear, and only the sign of ?5 can distinguish a fermion from an antifermion, the fermionic charge being diagonalized by ?5; hence 1 + ?5 appears naturally in weak interactions. Parity conservation in strong interactions, parity conservation in electromagnetic interactions, parity nonconservation in weak interactions can all be understood from the single common principle of generalized gauge invariance. It appears that in the future ultimate theory of elementary particles all elementary particle interactions will be manifestations of the five fundamental vector-type couplings corresponding to the five conservation laws of “internal attributes”—baryonic charge, hypercharge, isospin, electric charge, and fermionic charge. Gravity and cosmology are briefly discussed; it is estimated that the Compton wavelength of the graviton is of the order of 108 light years.It is suggested that every conceivable experimental attempt be made to detect directly quantum manifestations of the vector fields introduced in the theory, especially by studying Q values of pions in various combinations in NN annihilations and in multiple pion production.

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Annals of Physics

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