Lorentz对称性破坏和甚高能截面
Lorentz Symmetry Violation and Very High-Energy Cross Sections
摘要：
我们讨论了最近提出的洛伦兹对称性破坏模式非常高的能量截面的影响。由于引入基本长度$a$打破了局部洛伦兹不变性，运动学被修改，最终状态的性质在碰撞式（两个入射粒子相对于真空静止系具有相等的相反动量）和固定目标（一个入射粒子相对于真空静止系静止）情况下根本不同。在第一种情况下，允许的最终状态的属性类似于相对论运动学，只要相关的波矢量比临界波矢量尺度$a^{-1}$小得多。但是，如果一个入射粒子接近于在真空静止系中静止，能量守恒会在非常高的能量下减小终态相空间，并可能导致从远低于基本长度倒数的入射粒子波矢量开始的截面急剧下降。然后，弗鲁瓦萨尔界限可能不再相关，因为总的截面似乎变得比局部的、洛伦兹不变的场论所允许的小得多。这个新的假设对宇宙射线天体物理学和到达地球的高能宇宙射线有重要的实验意义。
英文摘要：
We discuss the implications of a recently proposed pattern of Lorentz symmetry violation on very high-energy cross sections. As a consequence of the breaking of local Lorentz invariance by the introduction of a fundamental length, $a$ , the kinematics is modified and the properties of final states are fundamentally different in collider-like (two incoming particles with equal, opposite momenta with respect to the vacuum rest frame) and fixed-target (one of the incoming particles at rest with respect to the vacuum rest frame) situations. In the first case, the properties of the allowed final states are similar to relativistic kinematics, as long as the relevant wave vectors are much smaller than the critical wave vector scale $a^{-1}$ . But, if one of the incoming particles is close to rest in the vacuum rest frame, energy conservation reduces the final-state phase space at very high energy and can lead to a sharp fall of cross sections starting at incoming-particle wave vectors well below the inverse of the fundamental length. Then, the Froissart bound may cease to be relevant, as total cross sections seem to become much smaller than it would be allowed by local, Lorentz-invariant, field theory. Important experimental implications of the new scenario are found for cosmic-ray astrophysics and for very high-energy cosmic rays reaching the earth.
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