arXiv 2406.005312024-06-01hep-ph

通过波包方法研究具有最小长度不确定关系的中微子振荡

Neutrino oscillation with minimal length uncertainty relation via wave packet approach

M. M. Ettefaghi

备注：: 11 pages, 1 figure, to appear in PLB

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AI总结：

本文基于广义不确定性原理（GUP）并采用波包方法微扰推导中微子振荡概率，发现通过较小的有效位置宽度可对最小长度尺度给出更强限制，并利用MINOS等加速器实验确定了形变参数的上限。

摘要：

量子引力理论和弦理论都表明存在一个最小可测长度以及相关的广义不确定性原理（GUP）。量子引力的普适性意味着 GUP 会影响每一个量子力学过程。中微子振荡作为一种量子现象，在宏观距离上展现出量子特性，可能为量子基础探索提供合适的空间。本文基于 GUP 并将中微子视为波包，微扰地推导了中微子振荡概率。我们发现 GUP 修正依赖于跃迁振幅的有效位置宽度 $σ_x$，使得与标准模型相互作用预期相比，较小的 $σ_x$ 能给出对最小长度尺度的更强限制。更明确地说，利用 MINOS 等加速器中微子实验，可以获得形变参数 $β_0$ 约为 $5\times 10^{25}$ 的上限，前提是 $σ_x\sim 10^{-15}\text{m}$，鉴于这些中微子能量约为几 GeV，该取值是合理的。

英文摘要：

Theories of Quantum Gravity as well as string theory suggest the existence of a minimal measurable length and the related Generalized Uncertainty Principle (GUP). The universality of Quantum Gravity implies that the GUP influences every quantum mechanical process. Neutrino oscillation as a quantum phenomenon exhibits quantumness at macroscopic distances and could provide potentially a suitable room for quantum foundation explorations. In this paper, we perturbatively derive the neutrino oscillation probability based on the GUP and by treating neutrinos as wave packets. We see that the GUP modifications are dependent on the effective position width of the transition amplitude $σ_x$ such that with the smaller $σ_x$ we can obtain a stronger bound on the minimal length scale in comparison to what is expected from standard model interactions. More explicitly, one can obtain an upper bound about $5\times 10^{25}$ for the deformation parameter, $β_0$, with accelerator neutrino experiments such as MINOS, provided that $σ_x\sim 10^{-15}\text{m}$ which is reasonable since the energy of these neutrinos is of the order of a few GeV.

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