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从π介子核子散射振幅出发,根据Mandelstam表示和么正条件,对于奇异量子数为零、重子数为1的费米子Regge轨迹,求得了下列结果:(1)位置参数α(s)的解析性,只有右方物理割而无左方动力割,但是左方有从s=0到-∞的运动学割。(2)当s2时,α(s)为实数。不同宇称的轨迹对s的依赖不同。(3)讨论了费米子Regge迹在阈能(W0=M+μ)附近的行为。凡是与共振态、束缚态有关的Regge轨迹,α(W0)≠0。求得了在阈附近的表示,定性方面同玻色子轨迹相同。(4)还有一大类Regge轨迹,它们同共振态、束缚态无关,α(W0)=0。这类轨迹在能量趋近阈能时,有无穷多个极点趋于ReJ=0(即我们在费米子情况下得到Gribov-Pomeranchuk极点凝聚现象),这类轨迹当能量由阈下趋于阈时,从J平面左半平面共轭成对趋于ReJ=0;当能量从阈上趋于阈时,成对地从第一和第三象限趋于ReJ=0。所有这些极点实数部分Reα→0比虚数部分Imα→0快一或二个数量级。J平面原点是一个凝聚点,这类“非动力”的Regge轨迹阈行为,无论对玻色子、费米子,以至非相对论势散射,定性都相似(只是凝聚的轴线和点不同)。它们实际上是s矩阵在阈的普遍性质的反映。Starting from π-N scattering amplitude and basing on the Mandelstam's representation and unitary condition, analyticity and threshold properties of fermion Regge trajectories of baryon quantum number 1 and strangeness 0 are investigated. The following preliminary results are obtained: (1) The position parameter of the Regge trajectories a(s) has a right-hand physical cut and no left-hand dynamical cut, but has a kinematical left-hand cut at s=0; (2) a(s) in the region s+(s) and α-(s), being of opposite space parity, are complex conjugate to each other. In the region 02, a±(s) are real but the dependence on s may be different; (3) The energy dependence of a(s) at the threshold is obtained; (4) Two kinds of Regge poles are distinguished. Those with a(W0)≠0 (W0-threshold energy) are responsible for dynamical resonances and bounded states. There are other kinds of the Regge trajectories for which a(W0)=0 and whose threshold behaviours are also investigated. As energy approaches the threshold from energy below the threshold, there are infinite pairs of poles approaching Re J=0 from the left half J-plane, each pair containing a couple of conjugate complex poles. While as energy approaches from above the threshold, there are also infinite pairs of poles approaching Re J=0, each pair containing poles in the first and third quadrant of the J-plane. For all these poles, Re α(s)→0 faster than Im a(s)→0 by one or two orders. The poles condense at the origin of the J-plane. We thus obtain the Gribov-Pomenranchuk condensation of the Regge poles in the case of Fermion trajectories. This kind of poles has a purely kinematical origin. They reflect the general properties of the S-matrix at the threshold.
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