Numerical Evaluation of Multi-loop Integrals
|
|
- Rodger Cox
- 5 years ago
- Views:
Transcription
1 Numerical Evaluation of Multi-loop Integrals Sophia Borowka MPI for Physics, Munich In collaboration with: J. Carter and G. Heinrich Based on arxiv: [hep-ph] DESY-HU Theory Seminar, Berlin May 24th, 212 S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 1
2 The LHC Era has begun We are probing energies which have never been reached at colliders before High experimental precision is possible due to high luminosities Precise theoretical predictions become necessary S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 2
3 Searching for the Higgs ATLAS 12 CMS 12 S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 3
4 Higgs Production in gluon fusion Multi-dimensional parameter integrals need to be evaluated which can contain UV, soft and collinear singularities LO (NLO in other processes) NLO NNLO S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 4
5 Higher Order Corrections to the Higgs Production 1 2 σ(pp H+X) [pb] s = 14 TeV 1 LO NLO NNLO M H [GeV] Harlander & Kilgore 2 Anastasiou, Melnikov, Petriello 5 S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 5
6 Making Predictions in the LHC Era A lot of progress has been achieved towards the goal of describing hadron collider processes consistently at NLO Calculations beyond NLO are also progressing well, but automation is difficult, and analytic methods to calculate e.g. two-loop integrals involving massive particles reach their limit Numerical methods are in general easier to automate, problems mainly are Extraction of IR and UV singularities Numerical convergence in the presence of integrable singularities (e.g. thresholds) Speed/accuracy Many people are/have been working on purely numerical methods, e.g. Soper/Nagy et al., Binoth/Heinrich et al., Kurihara et al., Passarino et al., Lazopoulos et al., Anastasiou et al., Denner/Pozzorini, Freitas et al., Weinzierl et al., Czakon/Mitov et al.,... S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 6
7 Making Predictions in the LHC Era A lot of progress has been achieved towards the goal of describing hadron collider processes consistently at NLO Calculations beyond NLO are also progressing well, but automation is difficult, and analytic methods to calculate e.g. two-loop integrals involving massive particles reach their limit Numerical methods are in general easier to automate, problems mainly are Extraction of IR and UV singularities (solved with SecDec 1.) Numerical convergence in the presence of integrable singularities (e.g. thresholds) Speed/accuracy Many people are/have been working on purely numerical methods, e.g. Soper/Nagy et al., Binoth/Heinrich et al., Kurihara et al., Passarino et al., Lazopoulos et al., Anastasiou et al., Denner/Pozzorini, Freitas et al., Weinzierl et al., Czakon/Mitov et al.,... S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 7
8 Making Predictions in the LHC Era A lot of progress has been achieved towards the goal of describing hadron collider processes consistently at NLO Calculations beyond NLO are also progressing well, but automation is difficult, and analytic methods to calculate e.g. two-loop integrals involving massive particles reach their limit Numerical methods are in general easier to automate, problems mainly are Extraction of IR and UV singularities (solved with SecDec 1.) Numerical convergence in the presence of integrable singularities (e.g. thresholds) (solved with SecDec 2.) Speed/accuracy Many people are/have been working on purely numerical methods, e.g. Soper/Nagy et al., Binoth/Heinrich et al., Kurihara et al., Passarino et al., Lazopoulos et al., Anastasiou et al., Denner/Pozzorini, Freitas et al., Weinzierl et al., Czakon/Mitov et al.,... S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 8
9 Public Implementations of the Sector Decomposition Method on the Market sector decomposition (uses GiNaC) C. Bogner & S. Weinzierl 7 FIESTA (uses Mathematica, C) A. Smirnov, V. Smirnov & M. Tentyukov 8 9 SecDec (uses Mathematica, Perl, Fortran/C++) J. Carter & G. Heinrich 1 Limitation until recently: Multi-scale integrals were limited to the Euclidean region (i.e., no thresholds) NOW: Extension of SecDec to general kinematics! SB, J. Carter & G. Heinrich 12 S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 9
10 SecDec 2. Computes... Feynman graphs for arbitrary kinematics, and more general parametric functions with no poles within the integration region Feynman graph or parametric function S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 1
11 Parametric Functions A general parametric function can be a phase space integral where IR divergences are regulated dimensionally polynomial functions, e.g. hypergeometric functions pf p 1 (a 1,..., a p ; b 1,..., b p 1 ; β) S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 11
12 Operational Sequence of the SecDec Program graph info Feynman integral iterated sector decomposition no multiscale? yes 6 expansion in ǫ 5 subtraction of poles 4 contour deformation 7 8 numerical integration result n Cm ǫ m m= 2L S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 12
13 General Feynman Integral Graph infos are converted into tensorial Feynman integral G µ 1...µ R in D dimensions at L loops with N propagators to power ν j of rank R After loop momentum integration, a generic scalar Feynman integral G = ( 1)Nν N j=1 Γ(ν j) Γ(N ν LD/2) N j=1 dx j x ν j 1 j δ(1 N l=1 x l ) U Nν (L+1)D/2 ( x) F Nν LD/2 ( x) where N ν = N j=1 ν j and where U and F can be constructed via topological cuts S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 13
14 Construction of the Functions U and F Example: 1-loop box p p 4 x 2 x 4 p p 3 U( x) =x 1 + x 2 + x 3 + x 4 (L-line cut), F ( x) =s 12 x 1 x 3 + s 23 x 2 x 4 + p 2 1x 1 x 2 + p 2 2x 2 x 3 + p 2 3x 3 x 4 + p 2 4x 1 x 4 (L+1-line cut) and F( x) = F ( x) + U( x) N x j mj 2 iδ j=1 S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 14
15 Operational Sequence of the SecDec Program graph info Feynman integral iterated sector decomposition no multiscale? yes 6 expansion in ǫ 5 subtraction of poles 4 contour deformation 7 8 numerical integration result n Cm ǫ m m= 2L S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 15
16 Sector Decomposition Overlapping divergences are factorized 1 dx x 1 dy y 1 (x + y) 2+ɛ = (1) + (2) 1 dx 1 dt 1 x 1+ɛ (1 + t) 2+ɛ + x t dt dy t y 1 y 1+ɛ (1 + t) 2+ɛ Iterated sector decomposition is done, where dimensionally regulated soft, collinear and UV singularities are factored out Hepp 66, Binoth & Heinrich S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 16
17 Operational Sequence of the SecDec Program graph info Feynman integral iterated sector decomposition no multiscale? yes 6 expansion in ǫ 5 subtraction of poles 4 contour deformation 7 8 numerical integration result n Cm ǫ m m= 2L S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 17
18 Contour Deformation I For kinematics in the physical region, F can still vanish F Bubble = m 2 (1 + t 1 ) 2 s t 1 iδ but a deformation of the integration contour Im(z) 1 Re(z) and Cauchy s theorem can help 1 f (t)dt = f (t)dt + c 1 z(t) f (z(t))dt = t S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 18
19 Contour Deformation II Im(z) The integration contour is deformed by 1 Re(z) t z = t + i y, y j ( t)= λt j (1 t j ) F( t) t j Soper 99 Integrand is analytically continued into the complex plane F( t) F( t + i y( t)) = F( t) + i j y j ( t) F( t) t j + O(y( t) 2 ) Soper, Nagy, Binoth; Kurihara et al., Anastasiou et al., Freitas et al., Weinzierl et al. S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 19
20 Find the Optimal Deformation Parameter λ I Robust method: check the maximally allowed λ for F and maximize the modulus at critical points 3 lambda = 1.2 lambda = 1. lambda =.5 Re(F(t 1 )) 2 +Im(F(t 1 )) example is for 1-loop bubble, m 2 = 1., s = 4.5 with Feynman parameter t t 1 S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 2
21 Find the Optimal Deformation Parameter λ II Faster convergence: minimize the complex argument of F.8.7 lambda = 1.2 lambda = 1. lambda =.5 Im(F(t 1 ))/Re(F(t 1 )) example is for 1-loop bubble, m 2 = 1., s = 4.5 with Feynman parameter t t 1 S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 21
22 Operational Sequence of the SecDec Program graph info Feynman integral iterated sector decomposition no multiscale? yes 6 expansion in ǫ 5 subtraction of poles 4 contour deformation 7 8 numerical integration result n Cm ǫ m m= 2L S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 22
23 Subtraction, Expansion, Numerical Integration Subtraction The factorized poles in a subsector integrand I U, F are extracted by subtraction (e.g. logarithmic divergence) 1 Expansion dt j t 1 b j ɛ I(, ɛ) j I(t j, ɛ) = b j ɛ + 1 dt j t 1 b j ɛ j (I(t j, ɛ) I(, ɛ)) After the extraction of poles, an expansion in the regulator ɛ is done Numerical Integration Monte Carlo integrator programs containted in CUBA library or BASES can be used for numerical integration Hahn et al. 4 11, Kawabata 95 S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 23
24 Operational Sequence of the SecDec Program graph info Feynman integral iterated sector decomposition no multiscale? yes 6 expansion in ǫ 5 subtraction of poles 4 contour deformation 7 8 numerical integration result n Cm ǫ m m= 2L S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 24
25 Results Successful application of the public SecDec 1. program to massless multi-loop diagrams up to 5-loop 2-point functions and 4-loop 3-point functions for Euclidean kinematics Successful application of SecDec 2. to various multi-scale examples, e.g., the massive 2-loop vertex graph, planar and non-planar 6- and 7-propagator massive 2-loop box diagrams Timings for the 2-loop vertex diagram and a relative accuracy of 1% using the CUBA 3. library on an Intel(R) Core i7 CPU at 2.67GHz p p1 p2 s/m 2 timing (finite part) secs secs S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 25
26 Results II: Massive Two-loop Vertex Graph G 4 1 p1 4 p p2 2 Finite real and imaginary part of P Real - Analytic -5 Real - SecDec Imag - Analytic Imag - SecDec s Kotikov et al. 97, Davydychev & Kalmykov 4, Ferroglia et al. 4, Bonciani et al. 4 S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 26
27 Results III: Massive Non-planar 6-propagator Graph 5-5 Massive Bnp6, finite part m Real (SecDec) Imag (SecDec) s 12 massless case: Tausk 99 S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 27
28 Results IV: Planar Massive Two-loop Box 3e e-12 m=5,m=9,s 23 =-1 Real (SecDec) Imag (SecDec) 2e-12 Finite part of planar 2-loop box 1.5e-12 1e-12 5e-13-5e-13-1e e fs Fujimoto et al. 11 S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 28
29 fs Im Results V: Non-planar Massive Two-loop Box 1.2e-12 1e-12 m=5,m=9,s 23 =-1 Real (SecDec) Imag (SecDec) Finite part of massive non-planar 2-loop box 8e-13 6e-13 4e-13 2e-13-2e I(s,t) Re Im -4e s/m fs I(s,t) Fujimoto et al. 11 S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 29
30 Install SecDec 2. Download: Install: tar xzvf SecDec.tar.gz cd SecDec-2../install Prerequisites: Mathematica (version 6 or above), Perl, Fortran and/or C++ compiler S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 3
31 User Input I param.input: parameters for integrand specification and numerical integration S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 31
32 User Input II template.m: definition of the integrand (Mathematica syntax) p p1 p2 S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 32
33 Program Test Run./launch -p param.input -t template.m S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 33
34 Get the Result resultfile P126 full.res S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 34
35 Summary With SecDec the numerical evaluation of multi-loop integrals is possible for arbitrary kinematics SecDec can also be used for more general parametric functions (e.g. phase space integrals) Useful to check analytic results for multi-loop master integrals, e.g. 2-loop boxes, 3-loop form factors,... Download the public SecDec program: S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 35
36 Outlook Can be used to calculate 2-loop corrections involving several mass scales, e.g. QCD/EW/MSSM corrections Implement contour deformation for more general parametric functions Include option to use Mathematica s numerical integrator Implement further variable transformation to tackle singularities very close to pinch singularities S. Borowka (MPI for Physics) Numerical evaluation of multi-loop integrals 36
Numerical Evaluation of Multi-loop Integrals
Numerical Evaluation of Multi-loop Integrals Sophia Borowka MPI for Physics, Munich In collaboration with G. Heinrich Based on arxiv:124.4152 [hep-ph] HP 8 :Workshop on High Precision for Hard Processes,
More informationNumerical evaluation of multi-scale integrals with SecDec 3
Numerical evaluation of multi-scale integrals with SecDec 3 Sophia Borowka University of Zurich Project in collaboration with G. Heinrich, S. Jones, M. Kerner, J. Schlenk, T. Zirke 152.6595 [hep-ph] (CPC,
More informationNumerical multi-loop calculations with SecDec
Journal of Physics: Conference Series OPEN ACCESS Numerical multi-loop calculations with SecDec To cite this article: Sophia Borowka and Gudrun Heinrich 214 J. Phys.: Conf. Ser. 523 1248 View the article
More informationNumerical multi-loop calculations: tools and applications
Journal of Physics: Conference Series PAPER OPEN ACCESS Numerical multi-loop calculations: tools and applications To cite this article: S. Borowka et al 2016 J. Phys.: Conf. Ser. 762 012073 Related content
More informationNumerical evaluation of multi-loop integrals
Max-Planck-Institut für Physik, München, Germany E-mail: sjahn@mpp.mpg.de We present updates on the development of pyse CDE C, a toolbox to numerically evaluate parameter integrals in the context of dimensional
More informationSector Decomposition
Sector Decomposition J. Carter Institute for Particle Physics Phenomenology University of Durham Student Seminar, 06/05/2009 Outline 1 What is Sector Decomposition? Why is Sector Decomposition Important?
More informationFrom Tensor Integral to IBP
From Tensor Integral to IBP Mohammad Assadsolimani, in collaboration with P. Kant, B. Tausk and P. Uwer 11. Sep. 2012 Mohammad Assadsolimani From Tensor Integral to IBP 1 Contents Motivation NNLO Tensor
More informationFully exclusive NNLO QCD computations
Fully exclusive NNLO QCD computations Kirill Melnikov University of Hawaii Loopfest V, SLAC, June 2006 Fully exclusive NNLO QCD computations p. 1/20 Outline Introduction Technology Higgs boson production
More informationSimplified differential equations approach for the calculation of multi-loop integrals
Simplified differential equations approach for the calculation of multi-loop integrals Chris Wever (N.C.S.R. Demokritos) 1 C. Papadopoulos [arxiv: 1401.6057 [hep-ph]] C. Papadopoulos, D. Tommasini, C.
More informationarxiv: v2 [hep-ph] 21 Sep 2015
FR-PHENO-2015-001, MPP-2015-27, ZU-TH 1/15 SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop arxiv:1502.06595v2 [hep-ph] 21 Sep 2015 S. Borowka a, G. Heinrich b, S. P. Jones b,c,
More informationElectroweak LHC NLO QCD
Electroweak LHC physics @ NLO QCD Dept. of physics University of Hawaii A. Lazopoulos Wed 24 oct. 2007 QCD corrections to tri-boson production Kirill Melnikov (UH), Frank John Petriello (Wisconsin U.),
More informationNumerical Evaluation of Loop Integrals
Numerical Evaluation of Loop Integrals Institut für Theoretische Physik Universität Zürich Tsukuba, April 22 nd 2006 In collaboration with Babis Anastasiou Rationale (Why do we need complicated loop amplitudes?)
More informationarxiv: v3 [hep-ph] 20 Apr 2017
MITP/14-76 A quasi-finite basis for multi-loop Feynman integrals arxiv:1411.7392v3 [hep-ph] 2 Apr 217 Andreas von Manteuffel, a Erik Panzer, b, c and Robert M. Schabinger a a PRISMA Cluster of Excellence
More informationTowards Jet Cross Sections at NNLO
Towards Jet Cross Sections at HP.4, September, MPI Munich Expectations at LHC Large production rates for Standard Model processes single jet inclusive and differential di-jet cross section will be measured
More informationLoop-Tree Duality Method
Numerical Implementation of the Loop-Tree Duality Method IFIC Sebastian Buchta in collaboration with G. Rodrigo,! P. Draggiotis, G. Chachamis and I. Malamos 24. July 2015 Outline 1.Introduction! 2.A new
More informationEvaluating multiloop Feynman integrals by Mellin-Barnes representation
April 7, 004 Loops&Legs 04 Evaluating multiloop Feynman integrals by Mellin-Barnes representation V.A. Smirnov Nuclear Physics Institute of Moscow State University Mellin-Barnes representation as a tool
More informationReducing full one-loop amplitudes at the integrand level
Reducing full one-loop amplitudes at the integrand level Costas Papadopoulos, Les Houches 2007 In collaboration with G. Ossola and R. Pittau 27/06/2007 HEP-NCSR DEMOKRITOS 1 The History Passarino-Veltman
More informationThe Higgs pt distribution
The Higgs pt distribution Chris Wever (TUM) In collaboration with: F. Caola, K. Kudashkin, J. Lindert, K. Melnikov, P. Monni, L. Tancredi GGI: Amplitudes in the LHC era, Florence 16 Oktober, 2018 Outline
More informationLOOP-TREE DUALITY AND QUANTUM FIELD THEORY IN 4D
LOOP-TREE DUALITY AND QUANTUM FIELD THEORY IN 4D Germán F. R. Sborlini in collaboration with R. Hernández-Pinto and G. Rodrigo Institut de Física Corpuscular, UV- CSIC (Spain) and Departamento de Física,
More informationPhysics at LHC. lecture seven. Sven-Olaf Moch. DESY, Zeuthen. in collaboration with Martin zur Nedden
Physics at LHC lecture seven Sven-Olaf Moch Sven-Olaf.Moch@desy.de DESY, Zeuthen in collaboration with Martin zur Nedden Humboldt-Universität, December 03, 2007, Berlin Sven-Olaf Moch Physics at LHC p.1
More informationThreshold cross sections for Drell-Yan & Higgs productions in N 3 LO QCD
Narayan Rana 20/10/2016 1/46 Threshold cross sections for Drell-Yan & Higgs productions in N 3 LO QCD Narayan Rana 20/10/2016 in collaboration with T. Ahmed, M. C. Kumar, M. Mahakhud, M. K. Mandal, P.
More informationNNLO antenna subtraction with two hadronic initial states
NNLO antenna subtraction with two hadronic initial states Institut für Theoretische Physik, Universität Zürich, Winterthurerstr. 190, 8057 Zürich, Switzerland E-mail: radja@physik.uzh.ch Aude Gehrmann-De
More informationPhysics at LHC. lecture one. Sven-Olaf Moch. DESY, Zeuthen. in collaboration with Martin zur Nedden
Physics at LHC lecture one Sven-Olaf Moch Sven-Olaf.Moch@desy.de DESY, Zeuthen in collaboration with Martin zur Nedden Humboldt-Universität, October 22, 2007, Berlin Sven-Olaf Moch Physics at LHC p.1 LHC
More informationSchematic Project of PhD Thesis: Two-Loop QCD Corrections with the Differential Equations Method
Schematic Project of PhD Thesis: Two-Loop QCD Corrections with the Differential Equations Method Matteo Becchetti Supervisor Roberto Bonciani University of Rome La Sapienza 24/01/2017 1 The subject of
More informationMultiloop integrals in dimensional regularization made simple
Multiloop integrals in dimensional regularization made simple Johannes M. Henn Institute for Advanced Study based on PRL 110 (2013) [arxiv:1304.1806], JHEP 1307 (2013) 128 [arxiv:1306.2799] with A. V.
More informationSPLITTING FUNCTIONS AND FEYNMAN INTEGRALS
SPLITTING FUNCTIONS AND FEYNMAN INTEGRALS Germán F. R. Sborlini Departamento de Física, FCEyN, UBA (Argentina) 10/12/2012 - IFIC CONTENT Introduction Collinear limits Splitting functions Computing splitting
More informationSM Predictions for Gluon- Fusion Higgs Production
SM Predictions for Gluon- Fusion Higgs Production Massimiliano Grazzini, Frank Petriello, Jianming Qian, Fabian Stoeckli Higgs Workshop, CERN, June 5, 2010 Outline Introduction: status of ggh Three updates:
More informationMaster integrals without subdivergences
Master integrals without subdivergences Joint work with Andreas von Manteuffel and Robert Schabinger Erik Panzer 1 (CNRS, ERC grant 257638) Institute des Hautes Études Scientifiques 35 Route de Chartres
More informationNLO-QCD calculation in GRACE. - GRACE status - Y. Kurihara (KEK) GRACE Group LoopFest IV
NLO-QCD calculation in GRACE - GRACE status - Y. Kurihara (KEK) GRACE Group 19/Aug./2005 @ LoopFest IV GRACE Author list J. Fujimoto, T. Ishikawa, M. Jimbo, T. Kaneko, K. Kato, S. Kawabata, T. Kon, Y.
More informationHigher Order QCD Lecture 2
Higher Order QCD Lecture 2 Lance Dixon, SLAC SLAC Summer Institute The Next Frontier: Exploring with the LHC July 21, 2006 Lecture 2 Outline NLO NNLO L. Dixon, 7/21/06 Higher Order QCD: Lect. 2 2 What
More informationAutomatic calculations of Feynman integrals in the Euclidean region
Automatic calculations of Feynman integrals in the Euclidean region Krzysztof Kajda University of Silesia 9 dec 2008 Krzysztof Kajda (University of Silesia) Automatic calculations of Feynman integrals
More informationA. Mitov 3-loop time-like splitting functions in Mellin space and NNLO fragmentation
Three-loop time-like splitting functions in Mellin space and NNLO fragmentation Alexander Mitov DESY Work in progress with: M. Cacciari; Lance Dixon; S-O. Moch Also based on: hep-ph/0604160 (with Sven
More informationReduction of one-loop amplitudes at the integrand level-nlo QCD calculations
Reduction of one-loop amplitudes at the integrand level-nlo QCD calculations Costas G. Papadopoulos NCSR Demokritos, Athens Epiphany 2008, Krakow, 3-6 January 2008 Costas G. Papadopoulos (Athens) OPP Reduction
More informationgg! hh in the high energy limit
gg! hh in the high energy limit Go Mishima Karlsruhe Institute of Technology (KIT), TTP in collaboration with Matthias Steinhauser, Joshua Davies, David Wellmann work in progress gg! hh : previous works
More informationGoSam: Automated One Loop Calculations within and beyond the SM
GoSam: Automated One Loop Calculations within and beyond the SM Nicolas Greiner Max-Planck Institute for Physics in collaboration with G.Cullen,H.vanDeurzen,G.Heinrich,G.Luisoni,P.Mastrolia,E.Mirabella,G.Ossola,T.Peraro,J.Schlenk,
More informationThe rare decay H Zγ in perturbative QCD
The rare decay H Zγ in perturbative QCD [arxiv: hep-ph/1505.00561] Thomas Gehrmann, Sam Guns & Dominik Kara June 15, 2015 RADCOR 2015 AND LOOPFEST XIV - UNIVERSITY OF CALIFORNIA, LOS ANGELES Z Z H g q
More informationPrecision Higgs physics. at hadron colliders
Precision Higgs physics at hadron colliders Claude Duhr in collaboration with C. Anastasiou, F. Dulat, E. Furlan, T. Gehrmann, F. Herzog, A. Lazopoulos, B. Mistlberger RadCor/LoopFest 2015 UCLA, 16/06/2015
More informationMultiloop scattering amplitudes in the LHC Era
Multiloop scattering amplitudes in the LHC Era Francesco Moriello Based on arxiv:1609.06685 In collaboration with: R. Bonciani, V. Del Duca, H. Frellesvig, J.M. Henn, V. Smirnov October 26, 2016 Outline
More informationHyperInt - exact integration with hyperlogarithms
HyperInt - exact integration with hyperlogarithms Erik Panzer erikpanzer@ihes.fr (CNRS, ERC grant 257638, F. Brown) Institute des Hautes Études Scientifiques 35 Route de Chartres 9144 Bures-sur-Yvette
More informationStructural Aspects of Numerical Loop Calculus
Structural Aspects of Numerical Loop Calculus Do we need it? What is it about? Can we handle it? Giampiero Passarino Dipartimento di Fisica Teorica, Università di Torino, Italy INFN, Sezione di Torino,
More informationHiggs + Jet angular and p T distributions : MSSM versus SM
Higgs + Jet angular and p T distributions : MSSM versus SM Oliver Brein ( Institute for Particle Physics Phenomenology, Durham, UK ) in collaboration with Wolfgang Hollik e-mail: oliver.brein@durham.ac.uk
More informationNumerical Computation of a Non-Planar Two-Loop Vertex Diagram
Numerical Computation of a Non-Planar Two-Loop Vertex Diagram Elise de Doncker, 1 Department of Computer Science, Western Michigan University, Kalamazoo, MI 498 Yoshimitsu Shimizu, 2 Hayama Center for
More informationBound-state effects in ttbar production at the LHC
1 Bound-state effects in ttbar production at the LHC Hiroshi YOKOYA (National Taiwan University) based on works in collaboration with K.Hagiwara(KEK) and Y.Sumino(Tohoku U) GGI workshop, Firenze, 2011.09.28
More informationRecent developments in automated NLO calculations
Recent developments in automated NLO calculations Giuseppe Bevilacqua NCSR Demokritos, Athens Workshop on Standard Model and Beyond and Standard Cosmology Corfu - August 31, 2009 In collaboration with
More informationHighlights of top quark measurements in hadronic final states at ATLAS
Highlights of top quark measurements in hadronic final states at ATLAS Serena Palazzo 1,2,, on behalf of the ATLAS Collaboration 1 Università della Calabria 2 INFN Cosenza Abstract. Measurements of inclusive
More informationarxiv: v1 [hep-ph] 30 Dec 2015
June 3, 8 Derivation of functional equations for Feynman integrals from algebraic relations arxiv:5.94v [hep-ph] 3 Dec 5 O.V. Tarasov II. Institut für Theoretische Physik, Universität Hamburg, Luruper
More informationA semi-numerical approach to one-loop multi-leg amplitudes p.1
A semi-numerical approach to one-loop multi-leg amplitudes Gudrun Heinrich Universität Zürich UNIVERSITAS TURICENSIS MDCCC XXXIII LoopFest V, SLAC, 21.06.06 A semi-numerical approach to one-loop multi-leg
More informationfrom D0 collaboration, hep-ex/
At present at the Tevatron is extracted from the transverse-mass distribution Events / GeV/c 2 2000 1500 1000 500 Fit region 0 50 60 70 80 90 100 110 120 from D0 collaboration, hep-ex/0007044 Transverse
More informationHigher Order Corrections to the Drell-Yan Cross Section in the Mellin Space
Higher Order Corrections to the Drell-Yan Cross Section in the Mellin Space Petra Kovačíková (DESY, Zeuthen) petra.kovacikova@desy.de Corfu Summer School 4 th September 21 Higher Order Corrections to the
More informationBACKGROUND EXPERIENCE AND THEORY INNOVATION FOR LHC
BACKGROUND EXPERIENCE AND THEORY INNOVATION FOR LHC Babis Anastasiou ETH Zurich PADOVA 20-01-2010 A theory revolution Deeper understanding of the structure of gauge theories Sharp theoretical predictions
More informationPrecision Calculations for Collider Physics
SFB Arbeitstreffen März 2005 Precision Calculations for Collider Physics Michael Krämer (RWTH Aachen) Radiative corrections to Higgs and gauge boson production Combining NLO calculations with parton showers
More informationarxiv:hep-ph/ v1 25 Sep 2002
hep-ph/0209302 Direct Higgs production at hadron colliders arxiv:hep-ph/0209302v1 25 Sep 2002 Massimiliano Grazzini (a,b) (a) Dipartimento di Fisica, Università di Firenze, I-50019 Sesto Fiorentino, Florence,
More informationThe forward-backward asymmetry in electron-positron annihilation. Stefan Weinzierl
The forward-backward asymmetry in electron-positron annihilation Stefan Weinzierl Universität Mainz Introduction: I.: II: III: IV.: Electroweak precision physics Higher order corrections Infrared-safe
More informationNext-to-leading order multi-leg processes for the Large Hadron Collider
Next-to-leading order multi-leg processes for the Large Hadron Collider, Thomas Reiter School of Physics, The University of Edinburgh, Edinburgh EH9 3JZ, UK. E-mail: binoth@ph.ed.ac.uk,thomas.reiter@ed.ac.uk
More informationNon-planar two-loop Feynman integrals contributing to Higgs plus jet production
Non-planar two-loop Feynman integrals contributing to Higgs plus jet production Institute for Theoretical Particle Physics (TTP), Karlsruhe Institute of Technology Engesserstraße 7, D-76128 Karlsruhe,
More informationSummary and Outlook. Davison E. Soper University of Oregon. LoopFest V, June 2006
Summary and Outlook Davison E. Soper University of Oregon LoopFest V, June 2006 Parton Showers & jet matching R. Erbacher emphasized how important this issue is for CDF analyses. CDF has been using a somewhat
More informationggf Theory Overview For Highest Precision
ggf Theory Overview For Highest Precision Lumley Castle Franz Herzog Nikhef LHC Higgs Production in the Standard Model 2 LHC Higgs Data 3 Theoretical Formalism To compute cross sections we use the Factorisation
More informationNLM introduction and wishlist
1. NLM introduction and wishlist he LHC will be a very complex environment with most of the interesting physics signals, and their backgrounds, consisting of multi-parton (and lepton/photon) final states.
More informationTwo-loop corrections to t t production in the gluon channel. Matteo Capozi Sapienza University of Rome
Two-loop corrections to t t production in the gluon channel Matteo Capozi Sapienza University of Rome November 7, 2016 Top quark With a mass of m t = 172.44 ± 0.13(stat) ± 0.47(syst)GeV, the top quark
More informationPhysics at the Large Hadron Collider
Herbstschule Maria Laach, September 2005 Physics at the Large Hadron Collider Michael Krämer (RWTH Aachen) Lecture 1: Review of the Standard Model Lecture 2: SM physics at hadron colliders Lecture 3: Higgs
More informationarxiv: v2 [hep-ph] 20 Jul 2014
arxiv:407.67v [hep-ph] 0 Jul 04 Mass-corrections to double-higgs production & TopoID Jonathan Grigo and Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology (KIT) E-mail: jonathan.grigo@kit.edu,
More informationTriangle diagrams in the Standard Model
Triangle diagrams in the Standard Model A. I. Davydychev and M. N. Dubinin Institute for Nuclear Physics, Moscow State University, 119899 Moscow, USSR Abstract Method of massive loop Feynman diagrams evaluation
More informationThreshold Corrections To DY and Higgs at N 3 LO QCD
Threshold Corrections To DY and Higgs at N 3 LO QCD Taushif Ahmed Institute of Mathematical Sciences, India July 2, 2015 Threshold Corrections To DY and Higgs at N 3 LO QCD INFN Sezione Di Torino 1 Prologue
More informationTowards a more accurate prediction of W +b jets with an automatized approach to one-loop calculations
Towards a more accurate prediction of W +b jets with an automatized approach to one-loop calculations Laura Reina Loops and Legs in Quantum Field Theory Wernigerode, April 2012 Outline Motivations: W +b-jet
More informationAsymptotic Expansions of Feynman Integrals on the Mass Shell in Momenta and Masses
Asymptotic Expansions of Feynman Integrals on the Mass Shell in Momenta and Masses arxiv:hep-ph/9708423v 2 Aug 997 V.A. Smirnov Nuclear Physics Institute of Moscow State University Moscow 9899, Russia
More informationarxiv:hep-ph/ v1 18 Nov 1996
TTP96-55 1 MPI/PhT/96-122 hep-ph/9611354 November 1996 arxiv:hep-ph/9611354v1 18 Nov 1996 AUTOMATIC COMPUTATION OF THREE-LOOP TWO-POINT FUNCTIONS IN LARGE MOMENTUM EXPANSION K.G. Chetyrkin a,b, R. Harlander
More informationThe Pentabox Master Integrals with the Simplified Differential Equations approach
The Pentabox Master Integrals with the Simplified Differential Equations approach Costas G. Papadopoulos INPP, NCSR Demokritos Zurich, August 25, 2016 C.G.Papadopoulos (INPP) 5box QCD@LHC 2016 1 / 36 Introduction
More informationSingle Higgs production at LHC as a probe for an anomalous Higgs self coupling
Single Higgs production at LHC as a probe for an anomalous Higgs self coupling Brookhaven National Laboratory E-mail: pgiardino@bnl.gov We explore the possibility of probing the trilinear Higgs self coupling
More informationNLO QCD corrections to Higgs boson pair production via gluon fusion
Wir schaffen Wissen heute für morgen NLO QCD corrections to Higgs boson pair production via gluon fusion Seraina Glaus Theory Group LTP, Paul Scherrer Institute & University Zurich In collaboration with
More informationStudy of H γγ at NLO and NNLO
Study of H γγ at NLO and NNLO G. Dissertori A. Holzner, F. Stöckli ETH Zürich Apr 13, 2005 Introduction Recently obtained : Higgs production (via gluon fusion) at NNLO (QCD), fully differential Anastasiou,
More informationJuly 8, 2015, Pittsburgh. Jets. Zoltan Nagy DESY
July 8, 2015, Pittsburgh Jets Zoltan Nagy DESY What are Jets? A di-jet ATLAS event A multi-jet (6-jet) event What are Jets? What are Jets? The pt is concentrated in a few narrow sprays of particles These
More informationAutomation of NLO computations using the FKS subtraction method
Automation of NLO computations using the FKS subtraction method Institute for Theoretical Physics, Universität Zürich E-mail: frederix@physik.uzh.ch In this talk the FKS subtraction method for next-to-leading
More informationEffects of Beyond Standard Model physics in Effective Field Theory approach on Higgs' pt spectrum
PhD Seminar 2015, PSI Effects of Beyond Standard Model physics in Effective Field Theory approach on Higgs' pt spectrum Agnieszka Ilnicka in collaboration with: M. Grazzini M. Spira M. Wiesemann Motivation
More informationTowards improved predictions for electroweak vector boson pair production at the LHC
Towards improved predictions for electroweak vector boson pair production at the LHC Kirill Melnikov TTP KIT Based on collaboration with M. Dowling, F. Caola, J. Henn, A. Smirnov, V. Smirnov Outline 1)
More informationTheoretical Predictions For Top Quark Pair Production At NLO QCD
Theoretical Predictions For Top Quark Pair Production At NLO QCD Malgorzata Worek Wuppertal Uni. HP2: High Precision for Hard Processes, 4-7 September 2012, MPI, Munich 1 Motivations Successful running
More informatione + e 3j at NNLO: Results for all QED-type Colour Factors p.1
e + e 3j at NNLO: Results for all QED-type Colour Factors Thomas Gehrmann Universität ürich UNIVERSITAS TURICENSIS MDCCC XXXIII in collaboration with A. Gehrmann De Ridder, E.W.N. Glover, G. Heinrich Loopfest
More informationTop mass effects in gluon fusion processes
Top mass effects in gluon fusion processes Thomas Rauh AEC, University of Bern Ramona Gröber, Andreas Maier, TR arxiv:1709.07799 JHEP 1803 (2018) 020 Outline 2 Gluon fusion processes Validity of approximations
More informationScalar One-Loop Integrals using the Negative-Dimension Approach
DTP/99/80 hep-ph/9907494 Scalar One-Loop Integrals using the Negative-Dimension Approach arxiv:hep-ph/9907494v 6 Jul 999 C. Anastasiou, E. W. N. Glover and C. Oleari Department of Physics, University of
More informationThreshold Corrections To DY and Higgs at N 3 LO QCD
Threshold Corrections To DY and Higgs at N 3 LO QCD Taushif Ahmed Institute of Mathematical Sciences, India April 12, 2016 Threshold Corrections To DY and Higgs at N 3 LO QCD Bergische Universitat Wuppertal
More informationThe Two-Loop Five-Point Amplitude in N=4 Super-Yang-Mills Theory and N=8 Supergravity
The Two-Loop Five-Point Amplitude in N=4 Super-Yang-Mills Theory and N=8 Supergravity Lance Dixon (SLAC) S. Abreu, LD, E. Herrmann, B. Page and M. Zeng 1812.08941, 1901.nnnnn DESY Zeuthen, 24 January 2019
More informationMulti-loop calculations: numerical methods and applications
Journal of Physics: Conference Series PAPER OPEN ACCESS Multi-loop calculations: numerical methods and applications To cite this article: S. Borowka et al 217 J. Phys.: Conf. Ser. 92 123 View the article
More informationOutline Motivations for ILC: e + e γ/z q qg LHC: pp l + l + jet (q q l + l g + qg l + l q + qg l + l q) Existing literature The complete EW one-loop c
Complete electroweak corrections to e + e 3 jets C.M. Carloni Calame INFN & University of Southampton Workshop LC08: e + e Physics at TeV scale September 22-25, 2008 in collaboration with S. Moretti, F.
More informationN-jettiness as a subtraction scheme for NNLO
N-jettiness as a subtraction scheme for NNLO! Xiaohui Liu based on:! arxiv:1504.02131, Boughezal, Focke, XL and Petriello arxiv:1505.03893, Boughezal, Focke, Giele, XL and Petriello arxiv:1504.02540, Boughezal,
More informationOn-Shell Recursion Relations for Multi-Parton One-Loop Amplitudes
for Multi-Parton One-Loop Amplitudes Carola F. Berger Stanford Linear Accelerator Center with Zvi Bern, Lance Dixon, Darren Forde, David Kosower SUSY06 June 13th, 2006 [1] Z. Bern, L. J. Dixon, D. A. Kosower,
More informationMaximal Unitarity at Two Loops
Maximal Unitarity at Two Loops David A. Kosower Institut de Physique Théorique, CEA Saclay work with Kasper Larsen & Henrik Johansson; & work of Simon Caron- Huot & Kasper Larsen 1108.1180, 1205.0801,
More informationHiggs production at the Tevatron and LHC
at the Tevatron and LHC Dipartimento di Fisica Teorica, Università di Torino, Italy INFN, Sezione di Torino, Italy E-mail: giampiero@to.infn.it Status of the art in the calculation of Higgs cross sections
More informationHiggs Production at LHC
Higgs Production at LHC Vittorio Del Duca INFN Torino Havana 3 April 2006 1 In proton collisions at 14 TeV, and for the Higgs is produced mostly via M H > 100 GeV gluon fusion gg H largest rate for all
More informationAN INTRODUCTION TO QCD
AN INTRODUCTION TO QCD Frank Petriello Northwestern U. & ANL TASI 2013: The Higgs Boson and Beyond June 3-7, 2013 1 Outline We ll begin with motivation for the continued study of QCD, especially in the
More informationarxiv: v1 [hep-ph] 4 Jul 2016
Attacking One-loop Multi-leg Feynman Integrals with the Loop-Tree Duality arxiv:1607.00875v1 [hep-ph] 4 Jul 2016 Instituto de Física Teórica UAM/CSIC, Nicolás Cabrera 15 & Universidad Autónoma de Madrid,
More informationStatus of Higgs plus one jet at NNLO
Status of Higgs plus one jet at NNLO Matthieu Jaquier Physics Institute University of Zürich Radcor-Loopfest UCLA 7 th June 205 Based on work with X. Chen, T. Gehrmann and E.W.N. Glover Matthieu Jaquier
More informationJoão Pires Universita di Milano-Bicocca and Universita di Genova, INFN sezione di Genova. HP September 2014 Florence, Italy
Jets in pp at NNLO João Pires Universita di Milano-Bicocca and Universita di Genova, INFN sezione di Genova HP.5-5 September 014 Florence, Italy based on: Second order QCD corrections to gluonic jet production
More informationPrecision Phenomenology and Collider Physics p.1
Precision Phenomenology and Collider Physics Nigel Glover IPPP, University of Durham Computer algebra and particle physics, DESY Zeuthen, April 4, 2005 Precision Phenomenology and Collider Physics p.1
More informationOne-Mass Two-Loop Master Integrals for Mixed
One-Mass Two-Loop Master Integrals for Mixed α s -Electroweak Drell-Yan Production work ongoing with Andreas von Manteuffel The PRISMA Cluster of Excellence and Institute of Physics Johannes Gutenberg
More informationBootstrapping One-Loop 2 n Amplitudes
Bootstrapping One-Loop 2 n Amplitudes Carola F. Berger Stanford Linear Accelerator Center with Zvi Bern, Lance Dixon, Darren Forde, David Kosower Loopfest V June 19th, 2006 [1] Z. Bern, L. J. Dixon, D.
More informationPrecision calculations for collider processes Gudrun Heinrich Max Planck Institute for Physics, Munich
Precision calculations for collider processes Gudrun Heinrich Max Planck Institute for Physics, Munich Scientific Board Meeting July 27, 2016 Overview tools FeynArts/FormCalc, Cuba GoSam SecDec NLO phenomenology
More informationCTEQ6.6 pdf s etc. J. Huston Michigan State University
CTEQ6.6 pdf s etc J. Huston Michigan State University 1 Parton distribution functions and global fits Calculation of production cross sections at the LHC relies upon knowledge of pdf s in the relevant
More informationP-ADIC STRINGS AT FINITE TEMPERATURE
P-ADIC STRINGS AT FINITE TEMPERATURE Jose A. R. Cembranos Work in collaboration with Joseph I. Kapusta and Thirthabir Biswas T. Biswas, J. Cembranos, J. Kapusta, PRL104:021601 (2010) T. Biswas, J. Cembranos,
More informationPrecision Calculations for the LHC
Precision Calculations for the LHC LHC Olympics 2006 Zvi Bern, UCLA with Carola Berger, Lance Dixon, Darren Forde and David Kosower hep-ph/0501240 hep-ph/0505055 hep-ph/0507005 hep-ph/0604195 hep-ph/0607014
More informationEvaluating double and triple (?) boxes
Evaluating double and triple (?) boxes V.A. Smirnov a hep-ph/0209295 September 2002 a Nuclear Physics Institute of Moscow State University, Moscow 9992, Russia A brief review of recent results on analytical
More informationThe Pentabox Master Integrals with the Simplified Differential Equations approach
Prepared for submission to JHEP TTP15-042 The Pentabox Master Integrals with the Simplified Differential Equations approach Costas G. Papadopoulos ab Damiano Tommasini a and Christopher Wever ac a Institute
More information