TY - JOUR

T1 - Asymptotic planarity

T2 - An S-matrix basis for the Okubo-Zweig-Iizuka rule

AU - Chew, G. F.

AU - Rosenzweig, C.

N1 - Funding Information:
Two sets of striking experimental facts, the exchange degeneracy of high-lying Regge trajectories and the validity of the Okubo-Zweig.Iizuka (OZI) ideal-mixing selection rules for particles on these trajectories, can be combined into the statement that the hadron S-matrix in certain regions is approximately planar. The adjective "planar" describes the leading component of Veneziano's topological expansion \[1\ ] -a component characterized by the combination of exchange degeneracy with * This work was supported in part by the US Energy and Research Development Administra-tion (ERDA) and in part by an NSF contract, number MPS74-08175-A01. ** Present Address: Physics Department, University of 'Pittsburgh, Pittsburgh, PA 15260.

PY - 1976/2/23

Y1 - 1976/2/23

N2 - A mechanism is exhibited that monotonically depresses the cylinder component of the topological expansion with increasing t, and it is conjectured that all non-planar S-matrix components diminish as t increases, exchange degeneracy and the Okubo-Zweig-Iizuka rule becoming more accurately satisfied. Such asymptotic planarity is compared to the field-theoretical concept of asymptotic freedom. The characteristics low-t cylinder "quenching interval" is found to be the inverse of the mean value over a two-reggeon loop, of 1 2π2(α′)2(t1 - t2)2/(-t), where t1 and t2 are the squared masses of the loop reggeons and α′ is the trajectory slope. For leading trajectories the low-t cylinder quenching interval is predicted by this formula to be roughly 0.5 GeV2-consistent with the observed pomeron intercept and slope, with the p-ω and f-A2 mass differences and with the (φ,ω) deviation from ideal mixing. As t grows negatively over a corresponding interval, it is predicted that the pomeron will become nearly a pure SU(3) singlet. If the pion mass helps to set the scale for reggeon loops coupled to unnatural-parity trajectories, the cylinder quenching interval will be larger, explaining the large (η, η′) deviation from ideal mixing as well as the large π-η mass difference. Even when the small-t cylinder quenching is rapid ("precocious planarity") the large-t approach to the planar limit turns out to be gentle. A by-product of this study is an explanation of the approximate reality and linearity of trajectories at large t.

AB - A mechanism is exhibited that monotonically depresses the cylinder component of the topological expansion with increasing t, and it is conjectured that all non-planar S-matrix components diminish as t increases, exchange degeneracy and the Okubo-Zweig-Iizuka rule becoming more accurately satisfied. Such asymptotic planarity is compared to the field-theoretical concept of asymptotic freedom. The characteristics low-t cylinder "quenching interval" is found to be the inverse of the mean value over a two-reggeon loop, of 1 2π2(α′)2(t1 - t2)2/(-t), where t1 and t2 are the squared masses of the loop reggeons and α′ is the trajectory slope. For leading trajectories the low-t cylinder quenching interval is predicted by this formula to be roughly 0.5 GeV2-consistent with the observed pomeron intercept and slope, with the p-ω and f-A2 mass differences and with the (φ,ω) deviation from ideal mixing. As t grows negatively over a corresponding interval, it is predicted that the pomeron will become nearly a pure SU(3) singlet. If the pion mass helps to set the scale for reggeon loops coupled to unnatural-parity trajectories, the cylinder quenching interval will be larger, explaining the large (η, η′) deviation from ideal mixing as well as the large π-η mass difference. Even when the small-t cylinder quenching is rapid ("precocious planarity") the large-t approach to the planar limit turns out to be gentle. A by-product of this study is an explanation of the approximate reality and linearity of trajectories at large t.

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U2 - 10.1016/0550-3213(76)90038-9

DO - 10.1016/0550-3213(76)90038-9

M3 - Article

AN - SCOPUS:0001170735

SN - 0550-3213

VL - 104

SP - 290

EP - 306

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 2

ER -