微中子震盪與羅倫茲破壞

Abstract

在微中子震盪的理論中，對於只有兩種風味微中子的情況，物質效應可以被精確的解出來。系統中的微中子混合角可以被重新定義之外，微中子震盪機率也可以透過震盪方程式計算。但在標準模型下(Standard Model)有三種風味的微中子，在這種情況下，物質效應無法被我們寫下像是兩種風味微中子一樣的簡潔方程式去重新定義三個混合角與震盪機率。 在粒子物理與廣義相對論裡，羅倫茲對稱是一個基礎的對稱。但有一些弦論(String Theory)的模型中，預測這個對稱可能可以被破壞。若有羅倫茲對稱被破壞，它會在微中子震盪的漢米爾頓函數(Hamiltonian)中加入一些羅倫茲對稱破壞參數。而且微中子震盪被認為是一項強而有力的工具去探索羅倫茲對稱破壞效應。 為了了解物質效應與羅倫茲對稱破壞如何影響本徵值、混合矩陣與震盪機率，我們發展出了一套新的近似理論，當我們考慮到物質效應與羅倫茲對稱破壞時用來計算本徵值、混合矩陣與震盪機率。透過這個方法我們發現到在低能量情況時，加入物質效應與羅倫茲對稱破壞參數將會影響每一個混合角。而在高能量微中子的極限與主導的情況下，我們所得到的第二階震盪機率跟使用複雜費時的公式計算近似結果是一模一樣的。

In the theory of neutrino oscillations, matter effect in two-flavor neutrino situation has been solved exactly. The mixing angle can be redefined and oscillation probability can be calculated by exact formulas. However, there are three flavor neutrinos in Standard Model. Under this circumstance, we can no longer write down elegant formulas to redefine three mixing angles or calculate oscillation probabilities for matter effect solutions. Lorentz symmetry, a fundamental symmetry in particle physics and general theory of relativity, could be broken at or below the Plank scale as predicted by some string models. This Lorentz violation phenomenon would contribute some Lorentz violation parameters to the Hamiltonian of neutrino oscillations. Neutrino oscillation is regarded as a powerful tool to probe the Lorentz violation. To understand how matter effect and Lorentz violation parameters affect the eigenvalues, mixing matrix and oscillation probabilities, we develop a new approximation method to calculate these terms when we consider matter effect and Lorentz violation. Through this new expansion, we find that adding matter effect and Lorentz violation effect would make a change on all three mixing angles at low energy scale. While in the case of ultra-high-energy limit and dominance, the second order approximation of probabilities we obtaining is the same as the equations calculated by solution formulas that are more tedious and time consuming.