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自動計算−その歴史と展望−
栗原良将(KEK)
シンポジウム「物質の創生と発展」2004年11月5日@日光霧降高原
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GRACE author list
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散乱断面積の計算
プロセスを決める。(例、e+e–→W+W−)すべてのファイマン図を描く。
散乱振幅の式を書き下す。(γμダンス)
位相空間で積分する。
必要に応じて、高次補正を加える。
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摂動論の自動計算
前史QED n-loopのグラフ生成 佐々木(1976年)
ELWK n-loopのグラフ生成 金子 (1987年)
モンテカルロ積分(BASES)/イベント生成(SPRING)
川端(1986年)
QED treeの自動化(GRAND) 金子(1989年)
graph gen./REDUCE/BASES/SPRING
そして、1990年The second workshop on Japan Linear Collider
→挫折
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The second workshop on Japan Linear Collider(1990年11月6 8日− @KEK)
Some technical Problems in Calculation Feynman AmplitudeY. Shimizu(KEK)
Automatic Calculation of Feynman Amplitude-GRACE and CHANEL-
T. Kaneko(MGU) and H. Tanaka(ICRR)
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Y. Shimizu
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Y. Shimizu
T. Kaneko & H. Tanaka
自動化
数値化
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自動計算とは
0. 与えられたLagrageanからFeynman ruleを生成する。
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幼年期(1990年〜1992年)
e+e–→W+W−γ (18) ,system check, (1991),HP-WSe+e–→W+W−γ, ZZγ (18,8) ,LC physics, (1992),HP-WSe+e–→ννW+W− (60) ,Higgs search, (1993),Intel iPSC/860×8
(自動計算が人力を越えた!)
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3-body processes, (O(10)),GRACE ComHEP comparison,,(1993-1994),HP-WS
e+e–→l+l−γγ, (80), LEP Physics, (1993), Intel iPSC/860×8check for L3 event (l+l−γγ,M
γγ>60GeV)
青年期(1993年〜1994年)
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青年期(1993年〜1994年)
e+e–→e+νetb, (20), Single Top @LEP2, (1994),HP-WS
e+e–→ννbb, (28), Higgs serach@LEP2, (1994),HP-WSe+e–→e+νudγ, (142), Radiative 4f @LEP2, (1994),HP-WSe+e–→e+ν
eud, (20), gauge cancelletion@LEP2,(1995),HP-WS
数値実験による新たな現象の発見
数値計算の安定性の証明
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New epoch (1995) “LEP2 war”
Workshops on LEP2 physics General meeting
Feb. 2-3, Jun. 15-16, Nov. 2-3 WW Cross-Sections and Distributions WW Event Generators WG SM Processes WG
Sveral meetings
Yellow Report CERN 96-01 v1,v2
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Comparison Table
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WW event generators on the market
生き残りGRACE inside
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New epoch (1995) LEP2 war
e+e–→4 fermion (grc4f), 76 processes (144), LEP2, HP-WSe+e–→2,3-body SUSY processes, (SUSY23), 23processes,
LEP2,HP-WS(論文は1997年)
自動計算は市民権を得て、以後次々と新たな自動計算システムが現れる
e+e–衝突におけるTree level計算の一応の目標達成
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発展期(1996年〜2001年)
e+e–, γe,γγ→HH+X,Higgs self-coupling, 1996, HP-WS
Single W Production, TGC, 1996, HP-WS
e+e–→bbudμνμ, (232), top-pair production,1997,Super
e+e–→4 quaks, GRACE-KoralW, 1998, HP-WS
e+e–→chargino-pair and their decay, SUSY@LC,
1999,HP-WS
e+e–→ννγ(γ), event generator or LEP2, 2001,alpha
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周辺機器の開発Improved QEDPS, QED parton shower, 1996
QEDPS for hard photon radiation processes, 1996
QEDPS for non-annihilation processes, 2000
QEDPS for single-W processes, 2000
*
GRACE+PS
GRACE+SF
○ BDK
√s'
e+e–→e+e–μ+μ–
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ep→el+l−X, HERA process, GRAPE, T. Abe, 1999-2001
ハドロン・プロセスへの拡張
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pp→bbbb,O(100), TEVATRON/LHC, GR@PPA, S. Tsuno, 2000-2003,Intel PC
ハドロン・プロセスへの拡張
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W + jets (up to 3 jets) with the subsequent W decay to a fermion pair,Z + jets (up to 2 jets) with the subsequent Z decay to a fermion pair,Four bottom quarks via Z and Higgs-boson mediated processes as well
as those from pure QCD interactions (same as GR@PPA_4b),top-quark pair with the subsequent decay to W and b, and the W decay
to a fermion pair,di-boson (WW, WZ and ZZ) with the subsequent W/Z decay to a
fermion pair.
pp→many, O(1000),TEVATRON/LHC, GR@PPA_ALL, S. Tsuno, 2004
ハドロン・プロセスへの拡張
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数値解析手法の発展
実験解析の質的変化
実験データ 理論計算
LEP2,HERA,TEVATRON以前
Line shape, K-factoracceptance補正
fitting 2体反応
実験データ 理論計算
LEP2,HERA,TEVATRON以降
数値解析もはやLine shapeは存在しない
多体反応
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数値解析手法の発展本質的に多体生成反応
→生成 崩壊の分離不可能−
→信号 バックグランドが一体−
→ スピン相関の重要性
従来の方法では計算出来ない
→ 市場に品物がない
→ 理論屋にも計算出来ない
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計算機能力の歴史
計算速度 1年で1.6倍 5年で10 倍
http://www.kt.rim.or.jp/~abemo/pc/M.Abeより
CPU power
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計算機能力の歴史
メインメモリ
メインメモリ 1年で1.5倍 5年で 7.倍
http://www.kt.rim.or.jp/~abemo/pc/M.Abeより
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ディスク容量 1年で1.8倍 5年で19倍
計算機能力の歴史
ハードディスク容量・転送速度
http://www.kt.rim.or.jp/~abemo/pc/M.Abeより
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拡張期(2002年〜)
LOOP(標準模型)
LOOP(QCD)Tree-SUSYLOOP-SUSY
GRACE/SUSY, MSSM tree, 2003年NLO/QCD w/ parton shower, 2003年
Event generator w/ NLO ME
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ET of µ-pair system
:[µµg-LL]⊗PS
:[µµ(t+v+c)]/PS
:[µµg]⊗PDF (w/Double Counting)
* :[µµg(NLO)]⊗PS
Drell-Yan Process @ NLO LOOP(QCD)
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Single Higgs production
e+e-→ ZH (full number of graphs = 341)
e+e-→ ν ν H (1350) Phys.Lett. B559 (2003) 252-262 (A.Denner et.al. PLB 560(2003)196, NPB 660(2003)289)
e+e-→ e+e- H (4470) hep-ph/0407065 (PLB in press)
top Yukawa
e+e-→ t t H (2327) Phys.Lett. B571 (2003) 163-172 Y.You et.al.PLB 571(2003)85 A.Denner et.al. PLB 575(2003)290, NPB 680 (2004)85
Multi Higgs production
e+e-→ ZHH (5417) Phys.Lett. B576 (2003) 152-164 R.Zhang et.al.PLB(2004)349
e+e-→ ν eν
e HH (19638) in preparation
LOOP(標準模型)
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Internal consistency check
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• GRACE/SM Tree diagrams/Standard ModelT. Ishikawa, et al., GRACE manual (v1.0), KEK Report 92-19F. Yuasa, et al., Prog. Theor. Phys. (Suppl.) 138 (2000) 18
• GRACE/SUSY (v2.2.0)Tree diagrams/MSSMM. Kuroda, hep-ph/9902349 J. Fujimoto, et al., Compt. Phys. Commun. 153 (2003) 106
Programs are avairable from http://minami-home.kek.jp
まとめ
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• GRACE-loop1-loop diagrams/Standard Model (w/ NLG)
e+e−→ννh:G. Belanger, et al., Phys. Lett. B 559 (2003) 252 NLG :G. Belanger, et al., hep-ph/9907406
e+e−→tth, Zhh (G. Belanger’s talk)
• GRACE/SUSY-loop1-loop diagrams/MSSM(w/ NLG)Under development
e+e−→χ1+χ1
−: T. Kon, et al., LoopFest II, 15/May/2003 @ BNL
• GRACE/NLO-QCD1-loop diagrams/QCDUnder developmentY. Kurihara, et al., Nucl. Phys. B 654 (2003) 301
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志ある実験家よ、来たれ!
最後に・・・
古きもの達よ、目覚めよ!