Multi-Particle Processes at the LHC with HELAC Malgorzata Worek ITP, Karlsruhe University Dresden 29th May 2008
Outline of the Talk Introduction Particle Physics Today The Large Hadron Collider The Higgs Boson Hunt State-of-the-Art for Multi-leg Processes Main Obstacles and Computational Complexity Leading Order level MC Programs HELAC Main Features and Numerical Results Summary & Outlook In collaboration with: Costas G. Papadopoulos Alessandro Cafarella INP, NCSR Δημόκριτος Athens
Particle Physics Today Matter made of three generations of fermions 1 lepton, 1 neutrino and 2 quarks for each generation The interactions are mediated by four vector bosons W, Z, photon γ, gluon g Everything is massive besides the photon and gluon The mass differences are still shocking mν < 1 ev, me = 0.5 MeV, mz = 91.187 GeV, mt = 170.9 GeV All of this fits into an elegant theory based on the symmetry group SU 3 C SU 2 L U 1 Y Not so many parameters, s, m W, m Z, mh, m t, mq, m l,m, UCKM, UPMNS
Yet Something is Lacking! The symmetry actually forbids masses The elegant solution is given by the Higgs mechanism The Mexican hat or champagne bottle Particles get their masses through the interaction with the Higgs boson condenstate in the vacum This theory predicts the existance of a new scalar particle that we could not discover till now
Hunting for the Higgs consistency of perturbation theory not allowed vacuum stability allowed not allowed T. Hambye, K. Riesselmann Phys. Rev. D55 (1997) 7255 LEP Electroweak Working Group March 2008 Higgs Boson Mass Bounds The LHC can discover Higgs Boson in the whole allowed range 114 GeV < mh < 600 GeV
New Hope Large Hadron Collider circumference: 27 km depth: 50 150 m start: 2008 running: 10 years before upgrade CERN 46º14'00''N 6º03'00''E
The Large Hadron Collider Alice ATLAS CMS LHCb
The Large Hadron Collider
Higgs Boson Discovery Channels Decay Width Branching Ratios Clean signals depending on the mass range Dominant production mechanisms
Expected Cross Sections at the LHC s = 14 TeV August 2008: turn on the machine Low luminosity: L=1033 cm 2 s 1 10fb 1 / year High luminosity L=1034 cm 2 s 1 100 fb 1 / year Total inelastic pp cross section tot 80 mb Event rate at low/high luminosity Nevt R = = L 108 / s 10 9 / s sec Interesting events are rare! pp W 150 nb 10 5 tot We need luminosity to be high to maximise number of events
Final States at the LHC Process Jet ET > 100 GeV Jet ET > 1 TeV W -> lv - bb - tt WW -> lv lv Events/sec 103 1.5x10-2 Events/year 1010 1.5x105 20 2x108 5x105 5x1012 1 6x10-3 107 6x104 Provide description of these events, features of new physics processes (rates, distributions, details of the final states, overall multiplicities, etc. )
Event from the Theory Point of View Stolen from the talk of Torbjorn Sjostrand, 'Physics at the Terascale' Kick-off Workshop, December 2007, DESY Hamburg
Event from the Theory Point of View
Event from the Theory Point of View
Event from the Theory Point of View
Event from the Theory Point of View
Event from the Theory Point of View
Event from the Theory Point of View
Event from the Theory Point of View
Event from the Theory Point of View
Event from the Theory Point of View
Event from the Theory Point of View
Real Event Simulated production of a Higgs event in ATLAS
Monte Carlo Generators Physics program of two main LHC experiments ATLAS and CMS: - Discovery of Higgs boson - Search for signal of new physics beyond the SM Signal events dug out from a bulk of background events Due to SM processes Mostly QCD processes, accompanied by additional electroweak bosons Final state - high number of jets or identified particles Reliable predictions for multi-particle final states needed! All this can be described by Monte Carlo generators - General purpose tools are PYTHIA, HERWIG and SHERPA - If you want matrix elements with more states you need LO MC - For example AlpGen, HELAC, MadEvent, Whizard,... Benchmarking against real data turns MC simulation into powerful tool!
Traditional Method Number of Feynman diagrams contributing to g g n g at tree level n 2 FD 4 3 4 25 220 5 6 2,485 7 34,300 8 9 559,405 10,525,900 224,449,225 n g at tree level Number of Feynman diagrams contributing to q q n FD 2 3 3 16 4 123 5 1,240 6 15,495 7 231,280 8 4,016,775 9 79,603,720 Number of sub-processes contributing to pp e e nj (4 & 5 flavours) n 0 1 SP 4 12 2 94 3 158 4 620 5 876 6 2476
Biggest Obstacles Complexity of calculation based on Feynman diagrams ~ n! Flavours of partons never detected (b-tagging) For given jet configuration very many contributing sub-processes Neither the colour nor the spin of any parton is observed Amplitude with p quark and q gluons 2 3 p 2 8 q contributions Amplitude peaks in complicated ways inside the momentum phase space Straightforward integration is impractical Search for efficient mappings - importance sampling Automated calculation of the ME based on recursive equations & MC summation over helicity and colour as well as over flavour
Convolution with PDFs Summation over subprocesses Complete Standard Model Matching to parton showers and hadronisation Features of a MC generator Flexibility Reliability Speed Extensibility
Convolution with PDFs Summation over subprocesses Complete Standard Model Matching to parton showers and hadronisation HELAC-PHEGAS Fortran code Flexibility Reliability Speed Extensibility
Convolution with PDFs Summation over subprocesses Complete Standard Model Leading order without approximations Matching to parton showers and hadronisation Electroweak, QCD and mixed contributions Unitary and Feynman gauges Fixed width and complex mass schemes for unstable particles All correlations (colour, spin) taken into account naturally Non-zero fermion masses CKM matrix and Running couplings Flexibility Reliability Speed Extensibility
Convolution with PDFs Summation over subprocesses Complete Standard Model Matching to parton showers and hadronisation Standalone version with build-in CTEQ6L1 Interface to the LHAPDF Flexibility Reliability Speed Extensibility
Convolution with PDFs Summation over subprocesses Complete Standard Model Matching to parton showers and hadronisation Lepton colliders, TeVatron, LHC Summation over all sub-processes Flexibility Reliability Speed Extensibility
Convolution with PDFs Summation over subprocesses Complete Standard Model Matching to parton showers and hadronisation Parton level weighted/unweigted events Parton shower and hadronisation via interface to PYTHIA Merging parton showers and matrix elements via MLM scheme Also possible via CKKW scheme - HERWIG++ LHA files and interfacing routines Flexibility Reliability Speed Extensibility
Convolution with PDFs Summation over subprocesses Complete Standard Model Matching to parton showers and hadronisation PHEGAS phase space generator Automatic multi-channel phase-space mapping Self-adapting procedure to reshape the generated phase space density For example: per mille level tt +- 0,1,2 jets (6,7,8 final states) with full off-shell and finite width effects Flexibility Reliability Speed Extensibility
Convolution with PDFs Summation over subprocesses Complete Standard Model Matching to parton showers and hadronisation Straightforward inclusion of new physics effects New models: for example MSSM (under way) New couplings: for example effective Hγγ and Hgg couplings (completed, available in the next version) Flexibility Reliability Speed Extensibility
Convolution with PDFs Summation over subprocesses Complete Standard Model Matching to parton showers and hadronisation 3n complexity due to the Dyson-Schwinger recursive algorithm Monte Carlo summation over: - helicity configurations - color configurations (completed, available in the next version) - subprocesses (under way) Trivial parallelization over clusters (LSF at CERN) Flexibility Reliability Speed Extensibility
Convolution with PDFs Summation over subprocesses Complete Standard Model Matching to parton showers and hadronisation Arbitrary cuts, distributions and scale choices Configuration via scripts Compilers: Lahey Fujitsu, Intel Fortran, GNU gfortran/g95 Multiprecision numerics Flexibility Reliability Speed Extensibility
Dyson-Schwinger Recursion Alternative to Feynman Diagrams representation Express n-point Green's functions in terms of 1-, 2-,... (n-1)-point functions Diagrammatic representation, e.g. QED-like theory Interaction of a spinor field to a gauge boson b P = n n=1 P=P i b P i P=P P 1 2 ig P 2 P 1 P 1, P 2 Sub-amplitude with off-shell boson of momentum P Blobs denote sub-amplitude with the same structure
Dyson-Schwinger Recursion For fermion with momentum P P = n i =1 P P i P i P=P P 1 2 ig b P 2 P1 P 1, P 2 For antifermion with momentum P P = n i i =1 P P i P P=P P 1 2 ig P 1 b P 2 P1, P 2
Multi-jet final state How to simulate hard processes with additional hard radiation Matrix element: - Exact at some given order in αs - all interferences are included - High energetic and well separated partons - Soft/Collinear regions are not adequately described luck of multiple unresolved gluon emission - Difficult to match to hadronisation models Parton Showers: - Include logarithmically enhanced soft and collinear contributions of parton emissions - Able to connect both hard and fragmentation scales - Not enough high energetic gluons are emitted that have large angle from the shower initiator Clearly two descriptions complement each other!
Matching ME to PS Goal LL accuracy in the prediction of final state with varying number of extra jets Problem Double Counting - jet can appear both from hard emission during shower evolution and from inclusion of higher order ME Solution Matching algorithm Recipe Cross section for each multiplicity N are calculating using LO ME for N partons Followed by full shower evolution Removal of double counting via inclusion of Sudakov form factors in the LO ME Vetoing shower evolutions leading to multiparton final state already described ME
Matching ME to PS A few algorithms along these lines: CKKW-L, MLM Differ mainly: - Jet definition used for the ME evaluation - Way the ME rejection weights are constructed - Details concerning starting conditions of jet vetoing inside PS Have similar systematics: - Residual dependence on the phase space separation cut Qcut - Variations with the number of ME legs - Dependencies on the internal jet algorithm
Example pp W + jets Cross sections in pb for inclusive jet rates Range of variation normalized to the average value Inclusive ET spectra of leading 4 jets J. Alwall et al. Eur. Phys. J. C53 (2008) 473 LHC
Systematic Studies LHC HELAC systematics at the LHC pt spectrum of W η distribution of leading jet ΔR separation distribution of the clustering scale (di logarithmic spectra) Full line default settings Shaded area range between = 0 /2 = 0 2 Points represents different matching scale J. Alwall et al. Eur. Phys. J. C53 (2008) 473
LHC Systematic Studies SHERPA systematics at the LHC Line default settings Shaded area range between = 0 /2 = 0 2 Points represents different matching scale 20%-40% effects Change in matching scale effects smaller than or of the order of those induced by the variation of s Differences within each code are as large as the differences between the codes J. Alwall et al. Eur. Phys. J. C53 (2008) 473
Performance tt+jet Production pp t t 87 (3) graphs gg, 40 (1) graph qq with Higgs boson contribution 9 subprocesses αs 2α 4 Time: ~ 10 (4) min. pp t t 1jet 558 (16) graphs gg 246 (5) qq, gq, qg with Higgs boson contribution 25 subprocesses αs 3α 4 Time: ~ 106 (34) min. Intel Pentium 1.7 GHz Intel Fortran
Summary & Outlook HELAC PHEGAS - Framework for high energy phenomenology - Standard Model fully included - Tested - Ready to be used for LHC, TeVatron, ILC - High colour charge processes Multijet production Testing phase To be available very soon HELAC MSSM - Development phase http://helac-phegas.web.cern.ch/helac-phegas/ arxiv:0710.2427 [hep-ph] HELAC