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The relationships between neutrino Majorana mass and other physics

Ohata, Takahiro 京都大学 DOI:10.14989/doctor.k22993

2021.03.23

概要

自然界をミクロなスケールで記述する理論として、素粒子標準模型と呼ばれる確立した理論が知られている。素粒子標準模型は、クォークやレプトンと呼ばれる物質をあらわす粒子、およびヒッグス粒子やゲージ粒子という素粒子を含んでおり、現在までに行われてきた加速器などにおけるほとんどの高エネルギー実験の結果を非常に精度よく再現する。しかしながら、この標準模型によっても未だに説明のつかない問題もまた複数知られている。その例として、ニュートリノ振動などニュートリノの質量や相互作用によるもの、宇宙の暗黒物質や暗黒エネルギーの存在、強いCPの問題等が挙げられる。これまで多種多様な取り組みがなされているが、本論文では、ニュートリノ振動と関わりのある素粒子標準模型の拡張について調べられ、3種のアプローチが提唱されている。

第2章では、ニュートリノのマヨラナ質量とミューオン異常磁気能率アノマリーの関わりが考察されている。このアノマリーは、ミューオン磁気双極子モーメントについて実験値と標準模型理論値の間に大きな差異があるという問題である。ここではタイプIIシーソー模型と呼ばれる素粒子模型を用いて、アノマリーが説明される。タイプIIシーソー模型においては、SU(2)3重項の重い複素スカラー場の効果によりニュートリノマヨラナ質量が現れる。このシーソー模型には左巻きレプトンと重いスカラー場との湯川結合のみが含まれているため、従来の研究では双極子モーメントのずれに正しい方向を得ることは困難であることが知られていた。本論文では、タイプIIシーソー模型にSU(2)1重項の弱荷電スカラー粒子を新たに取り入れ、右巻きレプトンと重いスカラー場との湯川結合によりアノマリーの解決を図っている。この手法でアノマリーを解消するためには、大きな湯川結合と数百GeV相当の荷電スカラー場が必要であるが、そのためにレプトンフレーバーを破る崩壊過程の制限が厳しくなる。よって本論文においては、レプトンの離散対称性を導入することにより問題の解決がなされている。上記を踏まえ、ミューオン異常磁気能率アノマリーとニュートリノマヨラナ質量を同時に解決可能な素粒子模型として、2種の模型が具体的に構成されている。モデル1ではZee−Babu型とタイプIIシーソー型のニュートリノ質量が、モデル2ではタイプIIシーソー型のニュートリノ質量がそれぞれ与えられている。これらの模型の実験的検証可能性として、弱荷電スカラー場がミューオンとタウオンに崩壊する過程について定量的な考察がなされた。

第3章では、ニュートリノマヨラナ質量と暗黒物質の存在の関係について調べられている。ニュートリノマヨラナ質量におけるレプトン数の破れの起源を与えるものとしてマヨロン模型が知られている。マヨロンはレプトン数対称性の破れに伴う南部‐ゴールドストン粒子であり、TeVオーダーの質量をもつ場合に暗黒物質となる可能性を考察している。このような重いマヨロン暗黒物質は、陽電子宇宙線束の近年の観測結果から存在が示唆されるものである。反陽子宇宙線やニュートリノ宇宙線の観測から、レプトン数の破れの真空期待値が統一スケール程度と大きく、また右巻きニュートリノとマヨロンとの湯川結合が非常に小さいと予測される。本論文ではそのような観測制限の元で、宇宙の熱史の中で暗黒物質がどのように生成されるかを考察し、具体的な生成機構として3通りの提案をおこなっている。1つ目は、レプトン数をソフトに破る右巻きニュートリノ質量項によるものである。この寄与により、右巻きニュートリノが世代を変えながらマヨロンへ崩壊する過程が発生し、暗黒物質が生成される。2つ目は、ヒッグス場とマヨロンの散乱過程を用いるものである。南部‐ゴールドストン粒子のもつ性質により通常のFreeze‐out生成は不可能であり、UV Freeze−inにより暗黒物質が生成される。3つ目は、右巻きニュートリノとマヨロンの散乱過程における共鳴によるものである。この生成効果は、マヨロン場の実部ゆらぎの質量程度の温度で顕著になる。生成元となる右巻きニュートリノは2つの起源を持ち、宇宙のインフレーションに伴い生成されるか、もしくはニュートリノの湯川結合により標準模型熱浴から生成される。これらの3つの提案において、具体的な数値計算手法により暗黒物質の残存量を評価し、現在の観測と矛盾しないパラメータ領域を明らかにした。

第4章では、強いCP問題とニュートリノマヨラナ質量との関係について議論されている。強いCP問題に対してはアクシオン模型が有力な候補である。ここではアクシオン模型におけるPeccei−Quinn(PQ)対称性とシーソー模型におけるレプトン数対称性を同一視する新しい手法が提案されている。すなわちアクシオン模型におけるSU(3)カラー荷を持つ重いフェルミオンを、ニュートリノ質量を生成するフェルミオンと同一視する。具体的にはカラー8重項のマヨラナフェルミオンによる輻射シーソー模型を用いる。そのためPQ数とレプトン数が同一視された簡潔なアクシオン模型が構築される。ただしカラー8重項のフェルミオンを用いるため、ドメインウォール数が常に3以上になる問題があり、PQ対称性がインフレーション中に破れる必要が生じる。

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