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403An aspect of the multiple production process is discussed from a viewpoint that reactions of hadrons are caused by rearrangement of the sakatons, the constituents of hadrons. It is shown that the energy dependence of experimental cross sections for multiple production processes as well as two-body reactions are approximately given by cr I (phase space volume) cc s-2rnn with r"'-'0.5, where s is the square of total energy in c.m.s. and nR is the least possible number of rearranged sakatons.On the basis of the analyses of the two-body reactions, we make a conjecture that a sakaton rearrangement brings a factor [(pi +pJ)2] -r to the rearrangement amplitude where Pi and p 1 are the four-momenta of hadrons. § I. IntroductionFrom analyses 1 ) of the two-body and quasi-two-body processes in terms of rearrangement of sakatons (fundamental entities of the triplet models), it was found that the energy dependence of the cross sections are closely related to the number of rearranged sakatons nR as (1) where s is the square of total energy in the center of mass frame. The experimental energy dependence of various two-body processes can be reproduced with rIt has also been shown that the characteristic features of the inelastic twobody and quasi-two-body processes (appearance of forw~rd and/or backward peaks, dips, etc.) can be related with the type of rearrangement of sakatons. 2 ) In this paper, we examine the multiple production processes from the same viewpoint of the rearrangement of sakatons; It is shown in § 2 that Eq. (1) is well satisfied by the experimental data on the multiple production processes. In § 3, we make a conjecture on the energy dependent factors of sakaton rearrangement amplitude. Some remarks are given in § 4. In the Appendix the type of sakaton rearrangement for multiple production processes are summarized. at State Univ NY at Stony Brook on March 13, 2015 http://ptp.oxfordjournals.org/ Downloaded from

We find explicit paths of collapse of the Skyrmion, the solutons in the simplest chiral model of pions (without the Skyrme term), even when the quantum effects of breathing and rotational modes are taken into account. The paths are represented by a parameter of a family of trial profile functions of the hedgehog ansatz which has the asymptotic falloff 1/r2 for r -03. I. INTRODUCI'IONStarting from the simplest chiral Lagrangian Jain, Schechter, and Sorkin' investigated the quantum stabilization of the nucleonlike field configuration. At the classical level there is no stable soliton in the system described by (1). Just like the well-known example of the s-wave state of the hydrogen atom, if dynamically stable chiral solitons are obtained by quantum effects, they are very attractive since the Lagrangian (1) has only one parameter, the pion decay constant f,=93 MeV, which is determined by experiment in the meson sector.In this paper we show explicitly that the chiral solitons in (1 ) are not dynamically stable even when the quantum effects of the breathing mode and rotations in ordinary space and isospin space are taken into account. The paths of collapse of the Skyrmion-like configurations are represented explicitly by a family of trial profile functions introduced in Sec. 111. The family of trial functions has the asymptotic falloff l l r for r--. m. When stabilizers exist the asymptotic falloff l / r 2 is obtained from the EulerLagrange equation for the profile function in the chiral limit regardless of the stabilizer. The asymptotic falloff l l r 2 also agrees with that of static meson theory with a massless pion. The family has a positive parameter C and the collapse occurs for both C-m and C+ 0. QUANTIZATION OF THE BREATHING MODEOn the basis of the collective-coordinate method Jain et al. take the rotating and breathing hedgehog ansatz expressed by where A(t E SU(2) is a matrix-valued dynamical variable of the spin-isospin "rotations." The dynamical variable R ( t ) representing the breathing mode is introduced by taking a trial function for the profile function F(r; R (t ) 1. They use the linear and exponential forms given as follows.(i) Linear form:(ii) Exponential form:where p = r / R ( t ) is dimensionless radial argument. The dynamical variable R ( t ) represents the radial extension of profile function. Substitution of (2) into the Lagrangian leads to L -a ( 2 -b < 2 / 3 +~~2~r (~~t ) ,where {(t = [R(t )I 3/2 and the coefficients in ( 5 ) are given by By use of the linear form and exponential form the mass of the I -J -ground state is obtained as 1.701 and 1.145 GeV, respectively, by solving the Schrodinger equation corresponding to the Lagrangian ( 5 ) :Recently, we have shown that if we use more appropriate trial functions for the profile functions the masses of the solitons are much r e d~c e d .~ The trial functions we have used are the following. 42 1868

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