Status of OpenLoops and simulation of H WW backgrounds with - PowerPoint PPT Presentation

Status of OpenLoops and simulation of H → WW backgrounds with Sherpa+OpenLoops Philipp Maierhöfer Institute for Theoretical Physics University of Zürich RADCOR 2013 11th International Symposium on Radiative Corrections Lumley Castle, 24 September 2013 Based on F. Cascioli, S. Höche, F. Krauss, P. M., S. Pozzorini, and F. Siegert arXiv:1309.0500

Irreducible background to H → WW ∗ +0,1 jet The OpenLoops Algorithm Sherpa+OpenLoops Outline 1 The OpenLoops Algorithm Loop Amplitudes and Tensor Integrals Open Loops Recursion Performance and Numerical Stability 2 Sherpa+OpenLoops Interfacing Sherpa with OpenLoops Process libraries for ATLAS and CMS 3 Irreducible background to H → WW ∗ +0,1 jet p T Distribution and Jet Veto Effects Squared Loop Contributions ATLAS and CMS Analyses Status of OpenLoops and simulation of H → WW backgrounds • Philipp Maierhöfer RADCOR 2013

Irreducible background to H → WW ∗ +0,1 jet The OpenLoops Algorithm Sherpa+OpenLoops Tensor integral representation of loop amplitudes Decompose Feynman diagrams into p 2 p 3 colour factors , tensor coefficients, and tensor integrals. R � q µ 1 . . . q µ r � p 1 p 4 N µ 1 ...µ r d d q = C · · q r D 0 D 1 . . . D N − 1 r = 0 . . . D i =( q + � i ℓ = 0 p ℓ ) 2 − m 2 i p N p 5 Algebraic colour reduction and summation once per process. Recursive numerical construction of the coefficients [van Hameren ‘09: Dyson-Schwinger recursion for multi-gluon amplitudes] → avoid huge expressions & expensive algebraic simplifications. Tensor integral reduction [Melrose; Passarino, Veltman; Denner, Dittmaier; Binoth et al.; Fleischer, Riemann; . . . ] with Collier [Denner, Dittmaier, Hofer] : Denner-Dittmaier reduction cures numerical instabilities, e. g. by applying expansions in small Gram determinants. Alternatively OPP reduction [Ossola, Papadopoulos, Pittau] with CutTools or Samurai [Mastrolia, Ossola, Reiter, Tramontano] . Status of OpenLoops and simulation of H → WW backgrounds • Philipp Maierhöfer RADCOR 2013

Irreducible background to H → WW ∗ +0,1 jet The OpenLoops Algorithm Sherpa+OpenLoops From Tree Recursion to Open Loops Wave functions w α of “sub-trees” are 4-tuples (for the spinor/Lorentz index) which are built by recursivly connecting lower sub-trees with vertices X β γδ and propagators, starting from external legs. j X β γδ w β ( i ) = w γ ( j ) w δ ( k ) = i p 2 i − m 2 k i A one-loop diagram is an ordered set of sub-trees I n = { i 1 , . . . , i n } i n i n -1 i n i n -1 n − 1 n − 1 β cut D 0 N β N ( I n ; q ) = − − − − − → α ( I n ; q ) = q 0 α 1 1 i 1 i 2 i 1 i 2 Connect sub-trees along the loop to build the numerator N = N α α α ( I n ; q ) = X β N β γδ ( q ) N γ α ( I n − 1 ; q ) w δ ( i n ) Status of OpenLoops and simulation of H → WW backgrounds • Philipp Maierhöfer RADCOR 2013

Irreducible background to H → WW ∗ +0,1 jet The OpenLoops Algorithm Sherpa+OpenLoops Open Loops Recursion α ( I n ; q ) = X β Start from N β γδ ( q ) N γ α ( I n − 1 ; q ) w δ ( i n ) and disentangle the loop momentum q from the coefficients n µ 1 ...µ r ; α ( I n ) q µ 1 . . . q µ r , N β � N β X β γδ = Y β γδ + q ν Z β α ( I n ; q ) = ν ; γδ r = 0 Leads to the recursion formula for “open loops” polynomials N β µ 1 ...µ r ; α : � � N β Y β γδ N γ µ 1 ...µ r ; α ( I n − 1 ) + Z β µ 1 ; γδ N γ w δ ( i n ) µ 1 ...µ r ; α ( I n ) = µ 2 ...µ r ; α ( I n − 1 ) N α µ 1 ...µ r ; α are the coefficients of the tensor integrals. Open loops encode the functional dependence of the numerator of the amplitude on the loop momentum. Numerical implementation requires only universal building blocks , derived from the Feynman rules of the theory. Status of OpenLoops and simulation of H → WW backgrounds • Philipp Maierhöfer RADCOR 2013

Irreducible background to H → WW ∗ +0,1 jet The OpenLoops Algorithm Sherpa+OpenLoops Implementation and performance Input: process definition file FeynArts [Hahn] generates Feynman diagrams. Mathematica organises recursion, reduces colour factors, and generates Fortran 90 code. QCD corrections to Standard Model processes implemented. Rational terms R 2 are restored using tree-level Feynman rules. [Draggiotis, Garzelli, Malamos, Papadopoulos, Pittau ‘09, ‘10; Shao, Zhang, Chao ‘11] 1000 u → W + W − + n g u¯ Time to generate code: u¯ d → W + g + n g 100 u → t¯ seconds to minutes u¯ t + n g gg → t¯ t + n g t TI [ms] 10 Compiled library size: 100 kB to a few MB 1 Runtime per phase space point: 0 . 1 < 1 s for a 2 → 4 process t OPP /t TI 2 (i7-750 single core, ifort 10.1) 1 10 1 10 2 10 3 10 4 number of loop diagrams Status of OpenLoops and simulation of H → WW backgrounds • Philipp Maierhöfer RADCOR 2013

Irreducible background to H → WW ∗ +0,1 jet The OpenLoops Algorithm Sherpa+OpenLoops Numerical Stability √ s = 1 TeV, p T > 50 GeV, ∆ R ij > 0 . 5, 10 6 points/process 10 0 numerical precision, u → W + W − + n g u¯ u¯ d → W + g + n g measured by a scale test 10 − 1 u → t¯ u¯ t + n g gg → t¯ using tensor integrals, t + n g fraction of events 10 − 2 2 → 2 in double precision; 2 → 3 2 → 4 10 − 3 11-15 digits on average, 10 − 4 1 permille with <5 digits 10 − 5 in the worst 2 → 4 case 10 − 6 for well separated particles 10 − 16 10 − 12 10 − 8 10 − 4 10 0 maximal precision ∆ “Suspicious” points are detected on-the-fly and rescued if possible. In practice, e. g. decaying particles can be aligned with the beam: in pp → ℓℓνν j a fraction of O ( 10 − 4 -10 − 5 ) of the points is unstable. In NNLO real emission, MC integration in soft regions is stable down to 10 − 4 Q (double precision). See talk by Dirk Rathlev. Quad precision support is available and can be used on-the-fly for even more challenging applications and reliable stability studies. Status of OpenLoops and simulation of H → WW backgrounds • Philipp Maierhöfer RADCOR 2013

Irreducible background to H → WW ∗ +0,1 jet The OpenLoops Algorithm Sherpa+OpenLoops Sherpa+OpenLoops Loop matrix elements are one building block of NLO simulations. The Sherpa [Gleisberg et al. ‘09] Monte Carlo event generator provides IR subtraction, real emission, phase space integration parton shower and MC@NLO matching [Höche, Krauss, Schönherr, Siegert ‘12] MEPS@NLO multi-jet merging [Höche, Krauss, Schönherr, Siegert ‘13] . . . Sherpa+OpenLoops Seamless integration via dynamic library loader. Steered by standard Sherpa runcards, matrix element generation is completely transparent to the user. Fully automated NLO calculations Status of OpenLoops and simulation of H → WW backgrounds • Philipp Maierhöfer RADCOR 2013

Irreducible background to H → WW ∗ +0,1 jet The OpenLoops Algorithm Sherpa+OpenLoops Process libraries for ATLAS and CMS Libraries for a wide range of processes are available to the ATLAS and CMS Monte Carlo groups. W/Z γ jets HQ pairs single-top Higgs t ¯ V + 3 j γ + 3 j 3 ( 4 ) j t + 1 j tb + 1 j ( H + 2 j ) t ¯ VV + 2 j γγ + 1(2) j tV + 0 ( 1 ) j t + 1 ( 2 ) j VH + 1 j b ¯ t ¯ gg → VV + 1 j V γ + 2 j bV + 0 ( 1 ) j tW + 0 ( 1 ) j tH VVV + 0 ( 1 ) j qq → Hqq + 0 ( 1 ) j (including lower jet multiplicities) Validated process-by-process ( > 100 partonic channels). Automatic regression tests (Python bindings). All contributing 1-loop diagrams, full colour. Off-shell leptonic W/Z decays (complex masses). First step towards a public OpenLoops release. Status of OpenLoops and simulation of H → WW backgrounds • Philipp Maierhöfer RADCOR 2013

Irreducible background to H → WW ∗ +0,1 jet The OpenLoops Algorithm Sherpa+OpenLoops Irreducible background to H → WW ∗ + 0,1 jet Signal: two opposite sign leptons + E miss , binned in jet multiplicities. T 250 Events / 10 GeV Events / 10 GeV ATLAS Preliminary ⊕ ATLAS Preliminary ⊕ Data SM (sys stat) Data SM (sys stat) γ γ WW WZ/ZZ/W 100 WW WZ/ZZ/W ∫ ∫ -1 Single Top -1 Single Top s = 8 TeV, Ldt = 13.0 fb t t s = 8 TeV, Ldt = 13.0 fb t t 200 Z+jets W+jets Z+jets W+jets (*) (*) → → ν µ ν µ ν ν → → ν µ ν H WW e / e (0 jets) H WW e (0 jets) H [125 GeV] H [125 GeV] 80 0-jets 150 60 75% WW 100 40 50 20 0 0 50 100 150 200 250 300 350 400 450 50 100 150 200 250 300 m m [GeV] [GeV] T T Events / 10 GeV Events / 10 GeV 160 ATLAS Preliminary ⊕ ATLAS Preliminary ⊕ Data SM (sys stat) 45 Data SM (sys stat) γ γ WW WZ/ZZ/W WW WZ/ZZ/W ∫ ∫ 140 -1 Single Top 40 -1 Single Top s = 8 TeV, Ldt = 13.0 fb t t s = 8 TeV, Ldt = 13.0 fb t t Z+jets W+jets Z+jets W+jets (*) (*) → → ν µ ν µ ν ν → → ν µ ν H WW e / e (1 jet) 35 H WW e (1 jet) 120 H [125 GeV] H [125 GeV] 30 1-jet 100 25 80 40% WW 20 60 15 40 10 20 5 0 0 50 100 150 200 250 300 350 400 450 50 100 150 200 250 300 m m [GeV] [GeV] T T Data driven analysis: normalise background (from MC simulation) to data in control region (left) and extrapolate to signal region (right). Percent level theory extrapolation uncertainty required . Status of OpenLoops and simulation of H → WW backgrounds • Philipp Maierhöfer RADCOR 2013