Hypothesis of Isotopic Spin Independence, Peripheral and Central Interactions in the High Energy Limit

Abstract

In the first part of this paper some consequences of the following three assumptions in the high energy limit are given: Assumption I. If the tital cross section of strongly interacting particles is expressed by the sum of cross sections corresponding to the total isotopic spins I = Imax, Imax - 1, …, Imin, these cross sections tend to a constant independent of I. Assumption II. If the S-matrix of a reaction is given by the sum of the S-matrices corresponding to Imax, Imax - 1, …, Imin, these S-matrices are independent of I. Assumption III. In addition to Assumption II, the S-matrices are independent of strangeness, sign of nucleon numbers of participating particles, hypercharge and so forth. Next, the process π± + p →N + 2nπ, N being a nucleon, is discussed under Assumption II. This process is also investigated in simple models of one pion exchange peripheral collision and in a model of central collision, comparing with the result of Assumption II. A consequences of Assumption II is σ(π− + p →N + 2nπ) = σ(π+ + p →N + 2nπ), where σ(π± + p →N + 2nπ) means the sum of the cross sections over possible charge combinations in the final state. For the peripheral and central collisions we get σ(π− + p →N + 2nπ) > σ(π+ + p →N + 2nπ). One of the differences of the peripheral, central and isotopic spin independent collisions is seen in the charge ratios of the cross sections for small n. Consequently, it is suggested that a possible model of high energy collision, which satisfies the inequality of the total cross sections σ(π− + p) > σ(π+ + p), is the peripheral interaction due to pion-pion interactions. The difference σ(π− + p) - σ(π+ + p) in this theory is expected to vanish in the high energy limit, so that this model is approximately isotopic spin independent. The central collisions should, however, be considered equally important as the peripheral collisions so long as the present discussion is concerned.