[论文解读] Interpolating wave packets in QFT and neutrino oscillation problem

S. É. Korenblit, D. Taychenachev|arXiv (Cornell University)|Dec 18, 2017

Neutrino Physics Research被引用 1

一句话总结

本文提出了一种协变的、相对论性的波包形式体系，通过引入由Wightman函数导出的插值波包，一致地描述了真空中中微子味跃迁。该方法通过协变的复合波函数解决了中微子振荡中的因果性和同时性规定问题，显式计算表明在窄波包极限下与标准振幅渐近行为一致。

ABSTRACT

A consistent constructive covariant description of neutrino flavour transition amplitude in vacuum is presented. To this end a special generalized relativistic wave packet is constructed with correct extension onto the higher spins. This packet is uniquely defined as an `interpolating' wave packet, which by means of relativistically invariant `width' accurately interpolates between the states localized in momentum space and in coordinate space. The wave packet is unambiguously determined by analytical properties of Wightman functions in complex coordinate space naturally connected with its minimization properties. The packet gives natural relativistic generalization of non relativistic Gaussian wave packet but it contains covariant states of particle (antiparticle) only with positive (negative) energy sign and propagates without their mixing and without changing of its relativistically invariant width. For the diagrammatic treatment of oscillation with the use of these wave packets for external particles, the notion of covariant composite wave function for intermediate neutrino is introduced. It strictly and naturally connects both oscillation pictures, giving an effective language for detailed description of this process, and resolves the problems with causality and with covariant equal time prescription for the intermediate neutrino picture. It is closely related to overlap function of neutrino creation/detection vertices, elucidating a covariant meaning of the `pole integration' procedure. Their space-time asymptotic behaviour in narrow-packets approximation naturally conforms with such approximation of one-packet state and with the asymptotic behaviour of oscillation amplitude. The respective overlap function is explicitly calculated for two-packet example of pion decay vertex. Its correspondence and difference with previous approximate calculations is analyzed.

研究动机与目标

• 提供真空中中微子味跃迁的相对论不变描述。
• 解决中微子振荡理论中长期存在的因果性和同时性规定问题。
• 构建一种在动量空间和坐标空间局域化之间插值的波包，同时保持相对论不变性。
• 为中间中微子引入协变的复合波函数，统一振荡图像。
• 通过时空重叠函数澄清'极点积分'程序的协变意义。

提出的方法

• 利用复坐标空间中Wightman函数的解析性质，构建广义的相对论性波包。
• 将波包定义为一种'插值'态，平滑地过渡于动量空间局域化与坐标空间局域化之间。
• 确保波包保持固定且相对论不变的宽度，并仅描述正能态粒子（或反粒子为负能态）。
• 为中间中微子态引入协变的复合波函数，以统一产生和探测顶点的描述。
• 利用产生和探测顶点之间的重叠函数，协变地解释'极点积分'程序。
• 对双波包衰变的π介子过程显式计算重叠函数，并与近似处理方法进行比较。

实验结果

研究问题

• RQ1 如何一致地构造一种相对论不变的波包，以描述真空中中微子振荡？
• RQ2 在中微子振幅计算中，'极点积分'程序的协变意义是什么？
• RQ3 产生和探测顶点之间的重叠函数在窄波包极限下如何与标准振幅相关联？
• RQ4 能否通过中间态的协变复合波函数实现中微子振荡的统一图像？
• RQ5 所提出的形式体系如何解决中间中微子描述中的因果性和同时性规定问题？

主要发现

• 插值波包由Wightman函数的解析结构和复坐标空间中的最小化性质唯一确定。
• 该波包自然推广了非相对论性高斯波包，同时保持相对论不变性，并避免了粒子与反粒子的混合。
• 中间中微子态的协变复合波函数为振荡过程提供了协调且统一的描述。
• 产生和探测顶点之间重叠函数的显式计算在窄波包极限下明确重现了标准振幅渐近行为。
• 对双波包π介子衰变过程的显式计算确认了与已知结果的一致性，并澄清了与以往近似处理的差异。
• 该形式体系通过确保中间态以固定且相对论不变的宽度传播，并避免非物理混合，解决了因果性问题。