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arXiv 0803.1967hep-ph
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用Magnus展开描述物质中的中微子振荡

Describing neutrino oscillations in matter with Magnus expansion

A. N. Ioannisian, A. Yu. Smirnov

备注：
Discussions expanded, two figures and references added, the version will appear in Nucl. Phys. B
发表信息：
Nucl.Phys.B816:94-116,2009
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摘要：

本文提出了描述变密度物质中中微子振荡的新形式。该形式基于Magnus展开，并具有在微扰论的每一阶中保持S-矩阵的么正性的优点。我们发现，马格努斯展开提供了更好的收敛性的系列：恢复的么正性导致更小的偏差，特别是在大的过渡概率的区域的确切结果。根据中微子态的基础和将哈密顿量分成自对易和非对易两部分的方法，得到了各种展开式。特别是，我们开发的绝热微扰理论，它给出了最佳近似的马格努斯展开。我们将该方法应用于地球物质中的中微子振荡，并表明对于太阳振荡参数，二阶Magnus绝热膨胀对所有能量和轨道的精度优于1%.对于大气$Δm^2$和小的1-3混合，近似在共振区（2.7 - 8）GeV之外工作得很好（对于$\sin^2 θ_{13} = 0.01$，$< 3 %$精度）。

英文摘要：

We present new formalism for description of the neutrino oscillations in matter with varying density. The formalism is based on the Magnus expansion and has a virtue that the unitarity of the S-matrix is maintained in each order of perturbation theory. We show that the Magnus expansion provides better convergence of series: the restoration of unitarity leads to smaller deviations from the exact results especially in the regions of large transition probabilities. Various expansions are obtained depending on a basis of neutrino states and a way one splits the Hamiltonian into the self-commuting and non-commuting parts. In particular, we develop the Magnus expansion for the adiabatic perturbation theory which gives the best approximation. We apply the formalism to the neutrino oscillations in matter of the Earth and show that for the solar oscillation parameters the second order Magnus adiabatic expansion has better than 1% accuracy for all energies and trajectories. For the atmospheric $Δm^2$ and small 1-3 mixing the approximation works well ($< 3 %$ accuracy for $\sin^2 θ_{13} = 0.01$) outside the resonance region (2.7 - 8) GeV.

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