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arXiv 1105.6013hep-thhep-ph
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规范/引力对偶的Reggeon交换

Reggeon exchange from gauge/gravity duality

M. Giordano, R. Peschanski

摘要:

在封闭背景下的规范/引力对应框架下,我们对介子-介子散射中的夸克-反夸克Reggeon交换进行了分析。在规范理论方面,Reggeon交换被描述为快速射弹之间的t通道中的夸克-反夸克交换。相应的振幅用沿组成夸克和反夸克轨道的威尔逊圈表示。交换费米子的路径被积分,而“旁观者”费米子被处理在程函近似。在重力方面,我们遵循以前提出的方法,我们评估威尔逊回路的期望值,利用规范/重力对偶的一个通用的限制规范理论。振幅是在鞍点近似下通过确定欧几里得“浮动边界极小曲面”的限制视界附近获得的,即,通过最小化过程固定交换夸克和反夸克的轨迹,这涉及面积和长度项。在讨论了平面上一个简单的问题(包括具有浮动边界的肥皂膜)后,作为热身练习,我们解决了与Reggeon交换相关的变分问题,其中基本几何形状是螺旋面。一个紧凑的表达式的Reggeon交换振幅,包括一个小的费米子质量的影响,然后通过解析延拓从欧几里得闵可夫斯基时空。我们发现,特别是一个线性雷吉轨迹,相应的雷吉极点奇异性补充的对数削减引起的非零夸克质量。解析延拓也导致同伴的贡献,对应于卷积的碰撞介子之间的多重弹性再散射相互作用的相同Reggeon交换振幅。

英文摘要:

We perform the analysis of quark-antiquark Reggeon exchange in meson-meson scattering, in the framework of the gauge/gravity correspondence in a confining background. On the gauge theory side, Reggeon exchange is described as quark-antiquark exchange in the t channel between fast projectiles. The corresponding amplitude is represented in terms of Wilson loops running along the trajectories of the constituent quarks and antiquarks. The paths of the exchanged fermions are integrated over, while the "spectator" fermions are dealt with in an eikonal approximation. On the gravity side, we follow a previously proposed approach, and we evaluate the Wilson-loop expectation value by making use of gauge/gravity duality for a generic confining gauge theory. The amplitude is obtained in a saddle-point approximation through the determination near the confining horizon of a Euclidean "minimal surface with floating boundaries", i.e., by fixing the trajectories of the exchanged quark and antiquark by means of a minimisation procedure, which involves both area and length terms. After discussing, as a warm-up exercise, a simpler problem on a plane involving a soap film with floating boundaries, we solve the variational problem relevant to Reggeon exchange, in which the basic geometry is that of a helicoid. A compact expression for the Reggeon-exchange amplitude, including the effects of a small fermion mass, is then obtained through analytic continuation from Euclidean to Minkowski space-time. We find in particular a linear Regge trajectory, corresponding to a Regge-pole singularity supplemented by a logarithmic cut induced by the non-zero quark mass. The analytic continuation leads also to companion contributions, corresponding to the convolution of the same Reggeon-exchange amplitude with multiple elastic rescattering interactions between the colliding mesons.

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