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Non-perturbative Aspects of Higgs Physics in the Standard Model and Beyond

Hamada, Yu 京都大学 DOI:10.14989/doctor.k23000

2021.03.23

概要

大型ハドロン衝突型加速器の結果を受けて、素粒子物理学の標準模型(SM)の成功が確立された一方で、SMを超えた新しい物理はまだ発見されていない。このような状況下では、SM及びそれを拡張した模型を別の視点から捉え直すことが重要である。特に、本論文では、SMとその拡張模型のヒッグス物理の非摂動的な側面に焦点を当てている。はじめに、ヒッグス場からなるソリトンの研究を行った。まず、2ヒッグス二重項モデル(2HDM)と呼ばれる、SMヒッグスポテンシャルにヒッグス二重項をひとつ追加したモデルにおける、南部モノポールについて考察する。南部モノポールとは、Zボゾンの渦糸を2本付いた磁気単極子状のソリトンである。本論文では2HDMヒッグスポテンシャルが2つの大域的対称性を持つ場合に南部モノポールがトポロジカルに安定であることを示した。さらに、それらの対称性が破れた場合も調べ、宇宙論的な帰結も提示されている。ヒッグス場によって記述されるもう一つの重要なソリトンはスファレロンであり、これは不安定なソリトンである。本論文ではグラディエントフロー法に基づいてスファレロンの解を得る新しい方法を提案している。この方法は、 SMや拡張モデルにも有効であり、宇宙におけるバリオンの非対称性を正確に計算することが可能になると期待される。

第2部では、SMの完全な非摂動的定式化に焦点を当てている。そのような定式化が実現できれば、格子計算を用いてヒッグスセクターの詳細なダイナミクスを計算することができる。本研究では、GrabowskaとKaplanが最近提案したカイラルゲージ理論の定式化の妥当性を検証する。この定式化は、ドメインウォールフェルミオンとグラディエントフローから構成されている。有効作用を計算することで、ドメインウォールフェルミオンから現れるカイラルゼロモードが量子レベルでもカイラルフェルミオンとして振る舞うことを示す。また、QCDにおける軸性U(1)カレントの正しい定義を提案する。

第3部では、いわゆるフラットランドシナリオにおける電弱スケール生成と暗黒物質を説明する現象論的模型の研究である。SMにU(1)ゲージ対称性を追加し、またSMシングレットスカラーと2つのマヨラナフェルミオンをSMに加える。そして、フラットランド条件と呼ばれる、プランクスケールですべてのスカラー場の結合定数が0になるという条件を課す。この条件は、漸近的に安全な量子重力の非摂動揺らぎによって実現されると期待される。この時、Coleman-Weinbergメカニズムにより、シングレットスカラーは真空期待値を得て、U(1)対称性を自発的に破り、電弱対称性の破れを誘発する。この模型はゲージ階層性問題を自然に解決し、また暗黒物質候補を予言する。また、本論文では、この模型がXENON1Tで報告された暗黒物質直接検出実験の制限と無矛盾であり、将来のXENON実験で検証され得ることを示した。

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