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

• 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
• Project Status: Completed (Fiscal Year 2021)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2021: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2018: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
• 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 / ゲージ理論 / 格子シミュレーション / 素粒子 / 非摂動力学 / 格子場の理論 / QCD / CP violation / instanton

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.

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。

Research Products

• [Journal Article] Peeking into the θ vacuum (2021)
  • Author(s): Ryuichiro Kitano, Ryutaro Matsudo, Norikazu Yamada, Masahito Yamazaki
  • Journal Title: Physics Letters B Volume: 822 Pages: 136657-136657
  • DOI: 10.1016/j.physletb.2021.136657
  • Peer Reviewed / Open Access
• [Journal Article] Is N = 2 Large? (2021)
  • Author(s): Kitano Ryuichiro、Yamada Norikazu、Yamazaki Masahito
  • Journal Title: Journal of High Energy Physics Volume: 2021 Issue: 2 Pages: 073-073
  • DOI: 10.1007/jhep02(2021)073
  • Peer Reviewed / Open Access
• [Presentation] Peeking into the θ vacuum of 4d SU(2) Yang-Mills theory (2021)
  • Author(s): Norikazu Yamada
  • Organizer: Cambridge High Energy Workshop 2021 -Axion Physics-
  • Int'l Joint Research / Invited
• [Presentation] Peeking into the θ vacuum (2021)
  • Author(s): Norikazu Yamada
  • Organizer: YITP workshop QCD phase diagram and lattice QCD
  • Int'l Joint Research / Invited
• [Presentation] Peeking into the θ vacuum of 4d Yang-Mills theory (2021)
  • Author(s): Norikazu Yamada
  • Organizer: Lattice 21
  • Int'l Joint Research