「瑪約拉納」暗物質的探討

A Study of Majorana Fermionic Dark Matter

葉懿慶(Yi-Chin Yeh)

指導教授 ： 蔡俊謙

中原大學/理學院/物理研究所/碩士(2015年)

https://doi.org/10.6840/CYCU.2015.00134

摘要

對於暗物質的探索，吾人視WIMPs為主要暗物質可能選項，也在文中考慮「瑪約拉納」費米子暗物質。 本文中的模型提出八個擁有二結構的旋量多重態 (ηi)，但本文只使用前四個（量子數分別為I = 1/2, 1/2, 0, 1）來與MSSM作比擬。這些粒子會在希格斯場的自發對稱破缺後混和。而其中本徵質量最輕的粒子就是模型中的WIMPs（χ）。由於瑪約拉納場能夠在費曼圖計算上提供額外的機率振幅，因此也強調本文中在運算機率振幅（S）的過程。本文中使用三個質量參數範圍（μ1,2,3）以及四個耦合參數(g3,4,5,6)。並採取g3=g5=(√2mZsinθcosβ)/v, g4=g6=(√2mZsinθsinβ)/v做為模擬MSSM例子來演練。吾人從不同的μi與Rg ≡tanβ（耦合參數的比例）參數範圍上探討八種不同的情況下來討論模型的可行性，並計算出其對應的截面機率。吾人使用ΩDMh2=0.1187±0.0031來限制我們的參數範圍。在暗物質的直接測量上，吾人以Xenon100和LUX實驗室的實驗結果作為最主要的對比。吾人亦在不同參數情況下的σSS（暗物質標量密度和夸克標量密度的交互作用下的截面機率）和σAV（暗物質軸矢量流和夸克矢量流的交互作用下的截面機率）討論其對於暗物質作用的貢獻。暗物質的直接測量通常忽略了σAV的交互作用，然而吾人發現其在暗物質測量中並非無關緊要的。吾人發現0≤μ1,μ2,μ3≤10TeV, Rg=2的是最沒有被限制的類別，而0≤μ1,μ2,μ3≤1TeV, Rg=2是最多被限制的類別。從不同的交互作用的數值模擬結果來看，粒子η3（I=0）是最為顯著的WIMPs成份，而本模型中提出的WIMPs質量密集落在500GeV至幾個TeV之間。

關鍵字

暗物質 ； 瑪約拉納

並列摘要

In searching dark matter, weakly interacting massive particles (WIMPs) are our major dark matter candidate, and we consider Majorana fermionic dark matter in the content. The model is with eight two-component spinor multiplets (ηi) and we activate only the first four of them with I = 1/2, 1/2, 0, 1, respectively, to mimic the MSSM case as an exercise. These particles will mix after SSB of the Higgs field. The lightest Majorana dark matter particle (χ) is the WIMP in our model. Because Majorana fermionic fields can provide another extra amplitude in Feynmann diagram calculations, there are some details that we have focused on field contraction during proressing $S$ matrix. There are three mass parameters (μ1,2,3) and four couplings (g3,4,5,6). We takeg3=g5=(√2mZsinθcosβ)/v, g4=g6=(√2mZsinθsinβ)/v to mimic the MSSM case as an exercise. We study the dark matter relic density and dark matter nucleus elastic cross sections in 8 different cases of μi and Rg ≡tanβ (coupling ratios). We use ΩDMh2=0.1187±0.0031 to constrain the parameter spaces. In the direct detection, spin-independent and dependent interaction are mainly compared with Xenon100 and LUX experiments. We also point out the various contributions from σSS and σAV, which are cross sections with χ-scalar density x quark-scalar density interaction and χ-axial vector current x quark-vector current interaction, respectively, in different parameter spaces. The σAV interaction between dark matter and nucleon in direct detection are usually ignored, instead we find that the contribution is not negligible. We find that 0≤μ1,μ2,μ3≤10TeV and Rg=2 is the least constrained case, while 0≤μ1,μ2,μ3≤1TeV and Rg=2 is the most constrained case. With comparison of different numerical results of interactions, particle η3（I=0） is the most dominated component of WIMPs in our model, and the mass of WIMPs in our model is concentrated within five hundred GeV/c2 to few TeV/c2.

並列關鍵字

Majorana ； dark matter

參考文獻

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