Method of Loop Integration for QCD Analysis

• Project/Area Number: 21540286
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Particle/Nuclear/Cosmic ray/Astro physics
• Research Institution: High Energy Accelerator Research Organization
• Principal Investigator: KANEKO Toshiaki 大学共同利用機関法人高エネルギー加速器研究機構, 計算科学センター, 教授 (40177522)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 素粒子(理論) / QCD / ループ積分 / 超幾何関数 / 次元正規化法

Research Abstract

One loop two and three point functions are expressed in terms of Lauricella FD hypergeometric function in d-dimensional space-time with any combinations of particle masses. Four point functions are expressed by Aomoto-Gelfand Hypergeometric functions. An efficient algorithm has been developed in sector decomposition method for general loop integrations.

Research Products

• [Journal Article] Sector Decomposition Via Computational Geometry (2011)
  • Author(s): T. Kaneko and T. Ueda
  • Journal Title: Proceedings of Science ACAT2010 Pages: 82-82
• [Journal Article] A geometric approach to sector decomposition (2011)
  • Author(s): T.Ueda, T.Kaneko
  • Journal Title: Proceedings of Science Volume: CPP2010 Pages: 15-15
• [Journal Article] Numerical calculation of one-loop integration with hypergeometric functions (2011)
  • Author(s): T.Kaneko
  • Journal Title: Proceedings of Science Volume: CPP2010 Pages: 10-10
• [Journal Article] Broken S3 Symmetry in Flavor Physics (2011)
  • Author(s): T.Kaneko, H.Sugawara
  • Journal Title: Physics Letters Volume: B697 Pages: 329-339
  • Peer Reviewed
• [Journal Article] A Geometric method of sector decomposition (2010)
  • Author(s): T. Kaneko and T. Ueda
  • Journal Title: Computer Physics Communications Volume: 181 Pages: 1352-1361
  • Peer Reviewed
• [Journal Article] A geometric approach to sector decomposition (2010)
  • Author(s): T. Ueda and T. Kaneko
  • Journal Title: Proceedings of Science, CPP2010 Pages: 15-15
• [Journal Article] Numerical calculation of one-loop integration with hypergeometric functions (2010)
  • Author(s): T. Kaneko
  • Journal Title: Proceedings of Science, CPP2010 Pages: 10-10
• [Journal Article] Sector Decomposition Via Computational Geometry (2010)
  • Author(s): T.Kaneko, T.Ueda
  • Journal Title: Proceedings of Science Volume: ACAT2010 Pages: 82-82
• [Presentation] One-loop Integrations with Hypergeometric Functions (2011)
  • Author(s): T. Kaneko
  • Organizer: Mini-workshop on method and automatic tool in perturbative calculation of Quantum Field Theory
  • Place of Presentation: IHEP,北京,中国
  • Year and Date: 2011-11-04
• [Presentation] One-loop Integrations with Hypergeometric Functions (2011)
  • Author(s): T.Kaneko
  • Organizer: Mini-workshop on method and automatica tool in perturbative calculation of Quantum Field Theory
  • Place of Presentation: IHEP,北京,中国
  • Year and Date: 2011-11-04
• [Presentation] One-loop integrations with Hypergeometric functions (2011)
  • Author(s): T. Kaneko
  • Organizer: ACAT 2011
  • Place of Presentation: Brunel Univ., London, UK
  • Year and Date: 2011-09-08
• [Presentation] Numerical calculation of one-loop integration with Hypergeometric functions (2010)
  • Author(s): T. Kaneko
  • Organizer: 3rd CPP Workshop
  • Place of Presentation: KEK,茨城県つくば市
  • Year and Date: 2010-09-24
• [Presentation] Sector decomposition via computational geometry (2010)
  • Author(s): T. Kaneko
  • Organizer: 13th International Workshop on Advanced Computing and Analysis Techniques in Physics Research(ACAT 2010)
  • Place of Presentation: インド・ジャイプール
  • Year and Date: 2010-02-26
• [Presentation] Sector decomposition via computational geometry (2010)
  • Author(s): 金子敏明
  • Organizer: 13^<th> International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2010)
  • Place of Presentation: インド・ジャイプール
  • Year and Date: 2010-02-26