论文标题
长度不确定性对中微子振荡的影响
Effect of minimal length uncertainty on neutrino oscillation
论文作者
论文摘要
在本文中，我们研究了最小长度对静态磁场中中微子振荡的影响。在普遍的不确定性原理的框架内，我们重新制定了哈密顿量的相对论中微子在沿笛卡尔坐标的Z方向以磁场为导向的相对论中微子。使用改良的能谱，我们获得了不同中微子风味的振荡概率。此外，我们获得了中微子质量特征状态的能量差异。我们发现能量和能量差取决于最小长度参数α，当不存在磁场时，能量差异与α无关。此外，我们发现，如果存在磁场，振荡的修饰概率与通常的振荡概率不同。使用当前的实验结果，我们估计上限在变形参数和最小长度上，并发现最小长度尺度上的上限小于Electroweak量表。如果最小长度在普朗克尺度上，则最小长度形式主义会导致与$ su（2）_ {l} \ times u（1）$有效不变尺寸-5 lagrangian，包括neutrino和Higgs领域的量子相同的结果。
In this paper, we study the effect of the minimal length on neutrino oscillation in a static magnetic field. In the framework of the generalized uncertainty principle, we reformulate the Hamiltonian for a relativistic neutrino moving in a magnetic field oriented along the z-direction of Cartesian coordinates. Using the modified energy spectrum, we obtain the oscillation probability for different neutrino flavors. In addition, we obtain the energy differences for the neutrino-mass eigenstates. We find that the energy and energy difference depend on the minimal length parameter α, and the energy difference becomes independent of α when the magnetic field is not present. In addition, we find that the modified probability of oscillation differs from the usual probability of oscillation if a magnetic field is present. Using the current experimental result, we estimate the upper bound on the deformation parameter and the minimal length, and find that the upper bound on the minimal length scale is less than the electroweak scale. If the minimal length is at Planck scale, the minimal length formalism leads to the same result as a quantum theory of gravity with an $SU(2)_{L} \times U(1)$ effective invariant dimension-5 Lagrangian including neutrino and Higgs fields.
