Duality for the real part of the πN scattering amplitudescattering amplitude

Abstract

F r o m the f in i te-energy sum rule 0) which correlates the t -channel Regge-pole ampl i tude at high energy to the s-channel resonant ampl i tude at low energy, the concept of the dual i ty s t emmed (2). The pomeron , however , has a special fea ture in the dua l i ty theory. Especial ly in the Hara r i conjec ture (3), the pomeron is dis t inguished f rom other Regge poles; the pomeron is associated wi th a nonresonant background amplitude re la ted to the forward diffraction peak at high energy, while the o ther o rd inary Regge poles are associated wi th the low-energy resonance by duali ty. In this note, we examine the Hara r i conjec ture for the real pa r t of the r : -~ ) scatte r ing ampl i tude , though the conjec ture is, in a narrow sense, val id only for the imag ina ry par t of it. A similar analysis at low energy (up to 2 GeV) has been done, using the phase-shif t da ta of ~-2V scat ter ing 0). Wc examine the conjec ture in a h igh .energy region wi th the aid of the fo rward dispersion re la t ion (FDR). I t is shown tha t the crossing-even ampl i tude Re A'(+)(v) is consis tent w i th the P ' exehange ampl i tude up to ~ 15 GeV and also the crossing-odd ampl i tude Re A'<-)(v) is so, wi th the p-exchange one up to ~ 2 0 GeV. The d isagreement at h igher energy will be discussed. Thc forward T:-2V scat ter ing ampl i tude is defined by