Unnatural Parity Mesons in the Dual Unitarization Scheme

Abstract

The spectrum of parity mesons is studied in the dual unitarization scheme extended to a two-channel problem. It is shown that the pion trajectory lies higher than the B meson trajectory at t=O and that the cylinder coupling of parity has the negative sign, i.e., the unnatural parity pomeron has odd charge conjugation parity. It is also shown that there are consistent solutions satisfying the bootstrap eq nations for both un­ natural and natural parity reggeons. )~?) In this paper we discuss parity reggeons in the dual unitarization scheme extended to a multi-channel problem. Our as­ sumptions are as follows: (1) Three-meson (reggeon) vertices are types of NNN and of UUN, where N denotes vector ( V) and tensor (T) mesons (reggeons), while U denotes pseudoscalar (P) and axial vector (B, JPc = 1 +-) mesons (reg­ geons). The coupling constant of the NNN(UUN) vertex is gN(gu). (2) 1>aN -au> 1/2, where the exchange degenerate input trajectories of N and U are denoted by aN and au. (3) The ratio of the produced N line with twist to that without twist is given by eN and that of the U case by eu. The mass spectrum of the pseudoscalar mesons is strongly deviated from that of the ideal nonet owing to too light pion and probably kaon masses. On the other hand, the mass of the B meson is close to those of the A 2 and f mesons, that is, the difference between the B trajectory and the A 2 is approximately unity for t>l.5 GeV 2 • This means that the SU(6) mass spectrum of the 3P 2 and 1P 1 states holds in the first approximation, though the masses of other SU(3) partners of the B meson are not yet known. Therefore it is intriguing to consider some dynamical mechanism that can shift the pseudoscalar meson trajectories upwards from the expected SU(6) spectrum and then break the exchange degeneracy be­ tween P and B. Here we mean by the SU(6) spectrum aN-au=l. In this paper we shall search such a mechanism in the dual unitarization scheme. We shall often use the SU(6) spectrum to get explicit expressions, because the use