Kisei Kinoshita

Increase of single-particle spectra and a new form of scaling. inclusive reactions and urbaryon rearrangement diagrams. v

The properties of a formula for single-particle distribution function are investigated in connection with the mechanism of the increase of some spectra with energy. A new form of scaling, which approaches Feynman scaling at asymptotic energies, is proposed. Recent experiments on p+p-7(p,K- and rr-) +anything up to ISR energies are consistent with the new scaling, in which the energy dependence and the longitudinal shape of the spectrum are simultaneously determined by single parameter for. each species of the produced particle. The concave rise of the averaged multiplicity up to ISR energies is obtained as a result of the new scaling: above ISR energies, the logarithmic increase is predicted to set in. The transverse shapes of spectra are shown to reveal their common dependence on longitudinal mass, after factorizing out an energy dependent part on the basis of the new scaling.

Whole-Region Formula for Single-Particle Distributions and Two-Body Reactions at All Angles*)

A formula for inclusive distributions ab-?cX is proposed, which incorporates the large Pr scaling with power fall-off in pr, the limiting behaviour in the fragmentation region and the approach from below to the Feynman scaling in the central region. By taking the exxad clusive limit X =d of the formula, the differential cross section for ab-?cd at all angles is obtained, which exhibits both the fixed-angle scaling at large angles and the Regge-like bexad haviour at small angles. The parameters in the formula are determined by the bond numbers of urbaryon lines connecting a, b, c and X (or d). The formula is closely related to the structure functions of the colliding hadrons. Construction of the formula from certain factors assigned to urbaryon lines is suggested. § 1. Introduction and summary The quantum number dependence of inclusive spectra is one of the proxad minent features at large transverse momenta,2l quite similarly to those at small ones. 8l This fact indicates that the quantum number flow in hadron collisions is. closely related to the energy-momentum flow, reflecting the dynamical structure of hadrons. In previous papers,l we discussed that the longitudinal spectra are characterized by the flow of urbaryon lines from colliding hadrons to produced ones, and proposed the interpolation formula 5l which gives. a unified description of shapes and scaling properties of the spectra in the small PT region. In this paper, we attempt to extend the formula so as to be able to describe singlexad particle distributions in the whole kinematical region, including two-body rexad actions at the exclusive limit. Our starting bases are the following. We define the valence urbaryons as the ones which characterize the internal quantum number of hadrons, and denote the number of valence urbaryons in a hadron i by ni.*l. Assuming the quark model description of the internal quantum numbers of hadrons, we have ni = 2 and 3 for a meson and a baryon, respectively. We take a view that hadron reactions are characterized by the bond number niJ which denotes the number of valence urbaryons connecting i and j. In general, there may be infinite numbers of urbaryon pairs and gluons in a hadron. The above view implies that

Whole-Region Description of Inclusive Spectra and Composite Structure of Hadrons

Properties of the whole-region formula, which is somewhat rectified from the original one by field theoretical arguments in § 4, are summarized in § 2. A manxad ifestly covariant model of the scattering of on-shell hadron and off-shell urbaryon is given in § 3. The model is specified so as to give the hadron structure suggested from the formula. The resulting structure functions exhibit the Regge behaviour and the threshold behaviour which is in accord with the dimensional counting. The hadron-urbaryon amplitudes thus constructed are applied to a few typical reaction mechanisms of ab~cX in § 4. The whole region formula is shown to be understood as the convolution of dominating dynamical mechanism in each kinexad matical region. The dynamical model of ab~cX presented here includes, except for spin dependence disregarded here, both of the fusion mechanism o£ meson productions

A Formula Describing Inclusive Reactions in the Whole Kinematical Region Including Two-Body Large Angle Scattering

where S.=2Cnax+ncx)r-1, S-=2(nbx+ ncx)r-1, x 1=u*ls, x2=t*ls, x=1Mx2ls, x=2q11 1/s and mr2 =mc2 +q.l 2 ~ t*u* Is. Here we follow the notations summarized in the Appendix of Ref. 3). The number of valence bond (flow of valence urbaryon lines) connecting i and j in the reaction ab~cX is denoted as niJ• as shown in Fig. 1. Equation (1) has a discontinuity at x=O if nax~nbx· It was suggested to improve the formula (1) by replacing (1x) f!. with (1-x 1) fi• (1-x 2) fi-Y However, this replacement destroys a good property of (1) that p vanishes in the kinematical boundary £=1 for S±>O. In this note I would like to show that the following version of (1) is able to describe not only the inclusive spectra at both large and small transverse momenta, but also differential cross sections of two-body reactions at large angles: p =F(mr2) x 12

Scaling Behaviour of Hadron Interactions and Urbaryon Bond Model

A model is given which treats the exclusive and inclusive reactions unifiedly and is applicable to both the peripheral and large transverse momentum. reactions; inclusive amplitudes Me constructed by assignment of certain factors to urbaryon lines, and the corresponding exclusive amplitudes are obtained by _taking the exclusive limit of specifying the anything state to be a hadron. The model incorporates various types of scaling properties, i.e., the Bjorken scaling, the Feynman scaling, the large transverse momentum scaling and the large angle scaling, and also the Regge-like behaviour of exclusive and inclusive reactions. § 1. Introduction and summary In a series -of papers/>-~> we have investigated inclusive reactions from the viewpoint of the urbaryon line flow. The following points in our work form the bases of the present paper. First, the Mueller amplitude is characterized by - the urbaryon rearrangement diagrams selected by means of the reduction rule of urbaryon lines ;2> the rule is a formulation as to how the simple diagrams represent net contributions of complicated higher order processes. Second, the Mueller amplitude for each diagram is parametrized by an interpolation formula,4> which gives a unified description of shapes and scaling properties of inclusive spectra at small transverse momentum (PT). The formula exibits a new form of scaling,8> which is related to the Feynman scaling and large PT scaling. Furxad thermore, we have extended the formula so as to describe the single-particle spectra in the whole kinematical region, including two-body reactions as the exxad clusive limit ;6>• 7> the large PT scaling8> of the former and the large angle scaling9> of the latter are ui::tifiedly understood. In this paper, we present a model of hadron interactions, which gives a foundation_ and a generalization of the extended formula. The model also gives a new argument on the Bjorken scaling for the virtual photon-hadron interactions. _ We assume that the hadrons are characterized by the valence urbaryons and hadron interactions are specified by the number of valence urbaryon lines nk!> connecting particles k and l. Hereafter we shall call the urbaryon lines connecting hadrons the urbaryon bond on the analogy of chemical bond. The valence urxad baryon may be the key concept to understand the flows of energy-momenta and

Local duality in the invariant amplitudes for πN scattering

Abstract Local duality for π N scattering in the low- and intermediate-energy regions is investigated from comparisons of the invariant amplitudes constructed from phase-shift data with the interpolated Regge ones. The following results are obtained: (i) Local duality is satisfied with the order A ′ (+) , B (−) , A ′ (−) and B (+) . In particular, local duality for the A ′ (+) amplitude is valid even for the c.m. energy down to 1.5 GeV and finite t -region. (ii) The crossing-even amplitudes having excellent local duality are made up constructively by the prominent resonances which lie on the leading trajectories and have the regularity of the Kycia-Riley rule. (iii) The Freund-Harari conjecture is examined for isospin nonflip amplitudes A ′ (+) and B (+) . The conjecture works well for the imaginary part but not for the real part. Moreover, the modified interference model proposed by Coulter, Ma and Shaw is also examined for the B (−) amplitude: The real part of the background term fills up the dip near t = −0.6, in contradiction with the observations.

Regge Pole Exchange and the Oscillatory Behavior in K+p Scattering

It is shown that the oscillatory behavior of the energy dependence of the total cross secxad tion and the backward cross section at 180o in K+p scattering is explained by the crossed-channel Regge-pole exchange. This behavior is due to the effect that the Regge-pole terms oscillate according to the signature factor since t and/ or u vary as s varies at fixed angle. Here the exchange degeneracy of Regge trajectories is expected to be somewhat violated. These are consistent with the absence of resonances in the K+j.J channel (exotic channel) but the same argument does not hold for the K-j.J channel, where genuine resonances are needed.

DYNAMICAL SEPARATION OF THE RESONANCE TERM FROM THE BACKGROUND TERM.

Abstract The multichannel amplitude containing a resonance is separated into the resonance term and the background term according to the dynamical situation which produces the resonance.

An Approach to Regge Behaviour and Duality Based on an Infinite Sum of One-Particle-Exchange Amplitudes

The implication of Regge asymptotic behaviour is studied on the basis of an infinite sum of one-particle-exchange (lOPE) amplitude, which provides a wide framework including varixad ous versions of dual amplitudes. The imaginary part of Regge-behaved amplitude comes from the s-u crossing term of the convergent lOPE amplitude, accompanied with the diverxad gence of lOPE expression. Duality between t-poles and u- or s-singularities is necessarily contained in Regge behaviour. A general expression for the lOPE amplitude satisfying full Regge behaviour is persued and comments on related models are made in connection with our approach. Phenomenological aspects of various solutions are also discussed. The analysis of hadron scattering using finite energy sum rules has revealed the existence of an intimate connection between Regge pole exchanges and rexad sonant states in direct channel and has developed into Veneziano amplitude. This has created a problem of understanding of the physical implication of Regge pole exchanges. Regge pole exchange originally gave an exchange picture of composite parxad ticles at high energies. Its connection with the one-particle-exchange (OPE) moxad del (which was proposed as an application to hadron reactions of the Sakata model) is quite interesting, especially when we consider its success in describxad ing low energy scattering phenomena, such as nucleon-nucleon scattering. Among the interpretations of Regge behaviour so far proposed, that of an infinite sum of single exchanges of Regge recurrences is the most attractive one for a generxad alization of OPE model. The purpose of the present paper is to give a general expression for the scattering amplitude based on the infinite sum of one-particle-exchange (lOPE) model/), 2 ) in which Regge behaviour is imposed at the asymptotic energy region. As an a posteriori result, the duality concept comes from the requirement of Regge behaviour in all the complex u plane except a positive real axis, where

Particle Exchange, Regge-Pole Exchange and the Veneziano Amplitude for KN Scattering

Based on the observation that the (t, u) -Veneziano terms can be expressed as an infinite sum of one-particle exchange contributions in the physical region, contrary to the (s, t) and (s, u) terms where the particle exchange picture is divergent, the validity of the particle exchange picture and the transcendental mechanism to the Regge pole exchange picture is examined in a KN Veneziano amplitude consisting of (t, u) terms only. At threshold, the contribution of meson exchanges with the lowest mass almost saturates the KN Veneziano amplitude. The hyperon exchange contributions should be discarded there, because of the duality between meson exchange contributions and hyperon exchange contributions. As energy increases, the meson towers with various spin states and degenerate mass begin to contribute one by one. Regge behaviour is obtained as a result of a detailed cancellation among the contributions of meson exchanges with various masses and spins. Here, Regge behaviour in a limited energy region is given by a finite sum of one-meson exchange terms. On the other hand, the hyperon exchange picture with finite terms does not approximate well the amplitude in the low energy region, even at threshold. These situations are understood through the study of the condition for an approximate truncation of infinite series of poles in the (t, u) -terms. The low energy interpolations of Regge asymptotic forms are studied, and the meson Regge pole exchange is also confirmed to give the gross features of the amplitude down to the threshold. The problem of double counting between the t- and u-Regge poles in low energy is noted.