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--- Summary --- Peter Uwer Advanced Computing and Analysis Techniques in Physics Research February 22-27, 2010, Jaipur, India Methodology of Computations.

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Presentation on theme: "--- Summary --- Peter Uwer Advanced Computing and Analysis Techniques in Physics Research February 22-27, 2010, Jaipur, India Methodology of Computations."— Presentation transcript:

1 --- Summary --- Peter Uwer Advanced Computing and Analysis Techniques in Physics Research February 22-27, 2010, Jaipur, India Methodology of Computations in Theoretical Physics

2 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 2 Statistics  5 + 4 + 6 = 15 presentations  450 min = 7.5 h  In total 367 transparencies, 1.2 min / slide  Average number of transparencies: 24.4 / talk  Extreme values: min: 10, max: 56

3 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 3 Where the speakers came from Europe: 8, Japan: 2, Russia: 2, US: 2

4 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 4 Main topics  Automation of higher order corrections –Techniques for loop integrals –Computational aspects –Real corrections and subtractions  Computer Algebra  Various topics 3 2 2 2 6

5 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 5 Automation of higher order corrections  What is the basic problem ? [Daniel Le Maitre] arbitrary unphysical scale

6 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 6 Automation of higher order corrections  Born approximation is not reliable, need to go beyond leading-order LHC Born approximation Next-to-leading order (NLO) O(10) diagrams 350 diagrams Example: Top-quark production + 1 Jet

7 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 7 Automation of higher order corrections ∫ 2 ∫ + * x 2Re + 2 ∫ Leading-order, Born approximation Next-to-leading order (NLO) n-legs (n+1)-legs, real corrections Generic one-loop calculation IR divergent virtual corrections

8 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 8 Automation of higher order corrections Bottleneck in one-loop calculation:  Calculation of the virtual corrections  Many diagrams  Each with complicated analytical structure  Numerical stability and speed  Combination of virtual corrections with real ones  Cancellation of IR singularities, conceptually solved, but cumbersome if done by hand Need for new methods and automation Algorithms crucial for automation

9 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 9 Automation of higher order corrections A typical one-loop diagram  complicated function of many variables How do we calculate this efficiently?

10 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 10 Techniques for loop integrals Different approaches:  Refinement of mixed approaches  Improved integration methods  New algorithms

11 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 11 Techniques for loop integrals [Tord Riemann] Basic idea: Make use of the fact that all the scalar one-loop integrals are known analytically  Derive reduction avoiding leading Gram determinants in the denominator Explicit reduction formulae are implemented in Computer code Exceptional configuration with vanishing Gram determinants are handled by special reduction (extrapolation)

12 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 12 Techniques for loop integrals [Tord Riemann] x allows to test numerical stability

13 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 13 Techniques for loop integrals [Giovanni Ossola] General structure of one-loop amplitude:

14 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 14 Automation of higher order corrections [Giovanni Ossola] Reduction at the integrand level  Structures in red vanish after integration and their form is known  finite number of terms  Determine coefficients by solving linear system of equations OPP method (Ossola, Pittau, Papadopoulos)

15 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 15 Automation of higher order corrections [Giovanni Ossola]  OPP method very powerfull  Available as Fortran program CutTools  Can be combined with automated amplitude generation (combination with HELAC already done)  Many new results recently (pp->Wjjj,pp->ttbb, pp->ttjj) One-loop amplitudes solved ?

16 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 16 Techniques for loop integrals Basic idea: Recursive (deterministic) integration over Feynman parameter, combined with extrapolation [Elise de Doncker]  use DQAGE from QUADPACK recursively

17 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 17 Techniques for loop integrals [Elise de Doncker] Six-point scalar integrals are reduced algebraically to 3- and 4-point scalar integrals 3- and 4-point integrals are then evaluated numerically Technique also applicable to tensor integrals Recursive integration might be interesting also for other fields

18 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 18 Techniques for loop-integrals Sector decomposition to isolate singularities [Mikhail Tentyukov] to find the decomposition of a complicated integrand highly non-trivial

19 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 19 Techniques for loop-integrals Feynman Integral Evaluation by a Sector decomposiTion Approach FIESTA [Mikhail Tentyukov] Computer algebra part in Mathematica combined with numerical integration routine Important:  Publicly available  Different Algorithms for sector decomposition  Applicable to multi-loop integrals  Important new 4-loop results  Circumvent memory problem in Mathematica  Own interpreter to process formulae of TeraByte length

20 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 20 Techniques for loop-integrals Alternative algorithm for sector decomposition [Toshiaki Kaneko] Sector decomposition based on computational geometry  implementation underway

21 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 21 Techniques for loop-integrals Methods rely on  Increased computational power  Increased main memory  Parallelization is used frequently

22 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 22 Automation of higher order corrections [Theodoros Diakonidis] Apply reduction scheme presented by Tord Riemann to gg  ttgg @ 1-loop O(1000) Feynman diagrams with complex structure  Automation needed

23 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 23 Automation of higher order corrections DIANA Diagram construction Output (form) hex_m.frm : bub_m.frm 50 different Structures color.F Color2fortran.frm SUn.prc MAPLE INPUT cRank0.m(1…4) : cRank5.m(1…4) OPTIMIZATION ggttgg.m FORTRAN OPT cFi_rtSum3(1…4) : cS_rtSum23(1…4) hex_mf.frm : bub_mf.frm Passrt_hex.F : Passrt_bub.F Hex(Sum_6(4)) : Bubble(Sum_2(4)) Main fortran program gm(line,n1,…,n9) Spinor structures MADGRAPH momenta.dat [Theodoros Diakonidis] (Qgraf  Form  Maple  Fortran) Steering with shell scripts, process specific

24 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 24 Automation of higher order corrections [Thomas Hahn] Process independent automation based on Feynman diagrams and tensor reduction

25 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 25 Automation of higher order corrections [Thomas Hahn] Many new features in the Feynarts-System  Tweaking model files  Diagram selection  Linear combination of fields (mass vs gauge states)  Efficient Fortran code generation, abbreviations to remove common subexpressions  Parallelization of parameter scans Computational aspects  very powerful tool but:

26 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 26 Real corrections and subtractions ∫ 2 ∫ + * x 2Re + 2 ∫ Leading-order, Born approximation Next-to-leading order (NLO) n-legs (n+1)-legs, real corrections  Generic one-loop calculation IR divergent

27 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 27 Real corrections and subtractions Problem: Phase space integration cannot be done in d dim.  Add and subtract a counterterm which is easy enough to be integrated analytically: Construction of subtraction for real corrections more involved, Fortunately a general solution exists:  Dipole subtraction formalism Can be done numerically

28 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 28 Real corrections and subtractions Generic form of individual dipol: Leading-order amplitudes Vector in color space Color charge operators, induce color correlation Spin dependent part, induces spin correlation universal Example gg  ttgg: 36 (singular) dipoles ! ! Color charge operators, induce color correlation Spin dependent part, induces spin correlation Color charge operators, induce color correlation  Automation required

29 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 29 Real corrections and subtractions [Rikkert Frederix] Automation of NLO subtraction terms Two different methods:  Catani-Seymour subtraction  Frixione-Kunszt-Signer subtraction  Fully automated based on Madgraph: MadFKS  useful to interface with MC@NLO

30 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 30 Real corrections and subtractions [Paolo Bolzoni] Extension of subtraction method to NNLO Much more involved due to double unresolved configuration Analytic integration of subtraction terms highly non trivial  Solution using:  Mellin-Barnes representation  Special summation algorithms for nested sums (XSummer in Form)

31 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 31 Computer Algebra -- Form Standard Tool in Theoretical Particle Physics if large expressions are encountered: Form by Jos Vermaseren et al. Important features:  Expression size only limited by disk space (TB)  Only local operations i.e. no factorization  Many ongoing developments Talks by Irina Pushkina and Mikhail Tentyukov

32 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 32 Computer Algebra -- Form [Irina Pushkina, Mikhail Tentyukov] New features:  Architecture independent file storage (32bit vs 64bit)  Checkpoints to save intermediate states  Steps towards open source (summer 2010?)  Two approaches to parallelisation:  Parform based on MPI for cluster  Tform based on threads for multi-core machines  Improved load balancing  Link to Grace system

33 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 33 Computer Algebra -- Form Speed up in Form: [Mikhail Tentyukov]

34 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 34 Techniques for Event generator tuning [James Monk] Tuning framework Professor Change Generator Parameters on the fly through interpolation in parameter space Multi-dimensional interpolation

35 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 35 Remarks  Powerful mixed approach:  Main programming language in Theoretical Particle Physics Fortran Analytic part is combined with numerical part, a chain of different tools is connected using scripts  Very active field, many new and important developments recently  Numerical instabilities Switch to quadrupel and higher accuracy

36 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 36 Remarks Important progress concerning the automation of one-loop amplitudes  OPP Method

37 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 37 Final Remarks  Many thanks to all the speakers  Apologies that not everybody could be mentioned  Many thanks to the audience of track 3 for their contribution in many lively discussions All talks are uploaded, if you want to see the details check Indico

38 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 38 Thank You

39 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 39

40 Peter Uwer | Summary Track 3 | ACAT 2010, 22. Feb. – 27. Feb., Jaipur, India | page 40 Automation of higher order corrections Major problem: (spurious) numerical instabilities for exceptional momentum configurations vanishing Gram determinants in the example above: (integral bases degenerates “0/0”) Traditional approach to tensor reduction [Passarino, Veltman 78]

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