Uncertainty of topological charge on the lattice and definition of quark masses

2021 Fiscal Year Final Research Report

• Project/Area Number: 18K03662
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 15010:Theoretical studies related to particle-, nuclear-, cosmic ray and astro-physics
• Research Institution: High Energy Accelerator Research Organization
• Principal Investigator: Yamada Norikazu 大学共同利用機関法人高エネルギー加速器研究機構, 素粒子原子核研究所, 講師 (50399432)
• Project Period (FY): 2018-04-01 – 2022-03-31
• Keywords: 素粒子論 / 数値シミュレーション / 非摂動計算 / CP対称性 / トポロジー

Outline of Final Research Achievements

Focusing on the topological charge, we carried out lattice numerical study. At θ=π, 2d CP$^1$ model becomes gapless without CP violation. Whether the same happens or not has been a long-standing problem. We carefully looked at the response of the topological charge on the lattice against the smearing procedure and developed a new method called "sub-bolume method", which avoids notorious sign problem, to study this problem. It turned out that 4d SU(2) gauge theory shows spontaneous CP violation at θ=π.

Free Research Field

素粒子論

Academic Significance and Societal Importance of the Research Achievements

ゲージ理論にθ項を導入すると作用が複素数になることから生じる符号問題のため通常の計算手法が使えず、これまで理論のθ~O(1)の領域を調べる手段はなかった。今回開発したsub-volume法により複素作用を持つ系の非摂動領域の研究が可能となった。この新手法については今後詳細を詰める必要はあるが、応用として例えば有限密度QCDの非摂動ダイナミクスの研究が挙げられる。