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arXiv 0902.2348nucl-th
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用相对论耦合道方法计算电磁介子形状因子

Electromagnetic meson form factor from a relativistic coupled-channel approach

Elmar P. Biernat, Kajetan Fuchsberger, William H. Klink, Wolfgang Schweiger

摘要:

利用点形式相对论量子力学导出了赝标介子类空动量转移的电磁形状因子的表达式。本文将电子与受限夸克-反夸克对的弹性散射问题处理为相对论性的双通道问题,分别考虑$q\bar{q}e$和$q\bar{q}eγ$态。近似的$q\bar{q}e$系统的总速度是保守的(电磁)相互作用的顶点,这简化为一个Bakamjian-Thomas型质量算子的本征值问题。在消除$q\bar{q}eγ$通道后,电磁介子电流和形状因子可以直接从单光子交换光学势中读出。通过选择足够大的电子-介子系统的不变质量,集团可分性破坏变得可以忽略不计。与通常的前形表达式,从观众电流的$q^+=0$参考系,建立一个等价。将这种多通道方法推广到任意束缚少体系统的电弱形状因子是非常明显的。通过适当扩展希尔伯特空间,这种方法也能够适应交换电流效应。

英文摘要:

Point-form relativistic quantum mechanics is used to derive an expression for the electromagnetic form factor of a pseudoscalar meson for space-like momentum transfers. The elastic scattering of an electron by a confined quark-antiquark pair is treated as a relativistic two-channel problem for the $q\bar{q}e$ and $q\bar{q}eγ$ states. With the approximation that the total velocity of the $q\bar{q}e$ system is conserved at (electromagnetic) interaction vertices this simplifies to an eigenvalue problem for a Bakamjian-Thomas type mass operator. After elimination of the $q\bar{q}eγ$ channel the electromagnetic meson current and form factor can be directly read off from the one-photon-exchange optical potential. By choosing the invariant mass of the electron-meson system large enough, cluster separability violations become negligible. An equivalence with the usual front-form expression, resulting from a spectator current in the $q^+=0$ reference frame, is established. The generalization of this multichannel approach to electroweak form factors for an arbitrary bound few-body system is quite obvious. By an appropriate extension of the Hilbert space this approach is also able to accommodate exchange-current effects.

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