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arXiv 1706.09484hep-ph
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中微子在非均匀磁场电子背景中的传播

Neutrino propagation in an electron background with an inhomogeneous magnetic field

Jose F. Nieves, Sarira Sahu

摘要:

本文研究了中微子在双流电子背景介质中传播时的电磁耦合。具体来说,我们计算电磁顶点函数的介质,其中包括一个\emph{normal}电子背景加上另一个电子\emph{stream}背景,是移动速度四矢量$v^μ$相对于正常的背景。所得结果可作为研究中微子电磁性质和介质中各种过程的基础。作为应用,我们计算了中微子在外加磁场存在下的色散关系($\vec B$),着重于$B$不均匀的情况,只保留$1/m^2_W$中的最低阶项和$B$及其梯度中的线性项.我们发现,色散关系包含额外的各向异性条款涉及的衍生物的$\vec B$,如梯度的$\hat k\cdot(\vec v\times\vec B)$,其中涉及流背景速度,和一个长期的形式$\hat k\cdot(\nabla\times \vec B)$,可以存在于没有流背景,除了一个长期的形式$\hat k\cdot\vec v$和众所周知的长期$\hat k\cdot\vec B$,出现在恒定的$\vec B$的情况下。导数相关项在$CP$变换下是偶数。因此,与刚才提到的后两个相反,它们取决于粒子和反粒子密度的总和,因此在粒子和反粒子密度相等的$CP$对称介质中可以是非零的。

英文摘要:

We study the electromagnetic coupling of a neutrino that propagates in a two-stream electron background medium. Specifically, we calculate the electromagnetic vertex function for a medium that consists of a \emph{normal} electron background plus another electron \emph{stream} background that is moving with a velocity four-vector $v^μ$ relative to the normal background. The results can be used as the basis for studying the neutrino electromagnetic properties and various processes in such a medium. As an application, we calculate the neutrino dispersion relation in the presence of an external magnetic field ($\vec B$), focused in the case in which $B$ is inhomogeneous, keeping only the terms of the lowest order in $1/m^2_W$ and linear in the $B$ and its gradient. We show that the dispersion relation contains additional anisotropic terms involving the derivatives of $\vec B$, such as the gradient of $\hat k\cdot(\vec v\times\vec B)$, which involve the stream background velocity, and a term of the form $\hat k\cdot(\nabla\times \vec B)$ that can be present in the absence of the stream background, in addition to a term of the form $\hat k\cdot\vec v$ and the well known term $\hat k\cdot\vec B$ that arises in the constant $\vec B$ case. The derivative-dependent terms are even under a $CP$ transformation. As a result, in contrast to the latter two just mentioned, they depend on the sum of the particle and antiparticle densities and therefore can be non-zero in a $CP$-symmetric medium in which the particle and antiparticle densities are equal.

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