Multi-Particle Processes at the LHC with HELAC Processes at the LHC with HELAC Malgorzata Worek ITP,...
Transcript of Multi-Particle Processes at the LHC with HELAC Processes at the LHC with HELAC Malgorzata Worek ITP,...
Multi-Particle Processes at Multi-Particle Processes at the LHC with HELACthe LHC with HELAC
Malgorzata Worek
ITP, Karlsruhe University
Dresden 29th May 2008
Outline of the TalkOutline 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 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, m
e = 0.5 MeV, m
Z = 91.187 GeV, m
t = 170.9 GeV
All of this fits into an elegant theory based on the symmetry group →
Not so many parameters ☺ →
SU3C⊗SU2L⊗U 1Y
,s,mW ,mZ ,mH ,mt ,mq,ml ,m ,UCKM ,UPMNS
Yet Something is Lacking !Yet Something is Lacking ! The symmetry actually forbids masses The elegant solution is given by the Higgs mechanism
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
The Mexican hat or champagne bottle ☺
Hunting for the HiggsHunting for the Higgs
Higgs Boson Mass Bounds The LHC can discover Higgs Boson in the whole allowed range
114 GeV < mH < 600 GeV
T. Hambye, K. Riesselmann Phys. Rev. D55 (1997) 7255 LEP Electroweak Working Group March 2008
not allowed
not allowed
allowed
consistency of perturbation theory
vacuum stability
New Hope – Large Hadron ColliderNew Hope – Large Hadron Collider circumference: 27 kmdepth: 50 – 150 mstart: 2008running: 10 years before upgrade
CERNCERN
46º14'00''N6º03'00''E
The Large Hadron ColliderThe Large Hadron Collider
Alice ATLAS CMS LHCb
The Large Hadron ColliderThe Large Hadron Collider
Higgs Boson Discovery Channels Higgs Boson Discovery Channels Decay Width Branching Ratios
Dominant production mechanisms
Clean signals dependingon the mass range
Expected Cross Sections at the LHCExpected Cross Sections at the LHC
August 2008: turn on the machine Low luminosity:
High luminosity
Total inelastic pp cross section
Event rate at low/high luminosity
Interesting events are rare !
We need luminosity to be high to maximise number of events
L=1033cm−2s−1 ⇒ 10fb−1/ year
L=1034cm−2s−1 ⇒ 100 fb−1/ year
tot ≃ 80mb
R =Nevtsec
= ⋅L ≃ 108/s 109/s
ppW ≃ 150nb ≃ 10−5 tot
s = 14TeV
Final States at the LHC Final States at the LHC
Process Events/sec Events/year
JJet ET > 100 GeV 103 1010
Jet ET > 1 TeV 1.5x10-2 1.5x105
W -> lv 20 2x108
bb 5x105 5x1012
tt 1 107
WW -> lv lv 6x10-3 6x104
Provide description of these events, features of new physics processes (rates, distributions, details of the final states, overall multiplicities, etc. )
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Event from the Theory Point of ViewEvent 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 ViewEvent 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 ViewEvent from the Theory Point of View
Event from the Theory Point of ViewEvent from the Theory Point of View
Event from the Theory Point of ViewEvent from the Theory Point of View
Event from the Theory Point of ViewEvent from the Theory Point of View
Event from the Theory Point of ViewEvent from the Theory Point of View
Real EventReal Event
Simulated production of a Higgs event in ATLAS
Monte Carlo GeneratorsMonte 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 MethodTraditional Method Number of Feynman diagrams contributing to at tree level g gn g
Number of sub-processes contributing to (4 & 5 flavours) pp e enj
Number of Feynman diagrams contributing to at tree level q q n g
n 2 3 4 5 6 7 8 9
FD 4 25 220 2,485 34,300 559,405 10,525,900 224,449,225
n 2 3 4 5 6 7 8 9
FD 3 16 123 1,240 15,495 231,280 4,016,775 79,603,720
n 0 1 2 3 4 5 6 SP 4 12 94 158 620 876 2476
Biggest ObstaclesBiggest 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 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
2×3p2×8q
Complete Complete Standard ModelStandard Model
Convolution Convolution withwithPDFsPDFs
Features of a MC generatorFeatures of a MC generator
Summation over Summation over subprocessessubprocesses
Matching to Matching to parton showers parton showers
and hadronisationand hadronisation
ReliabilityReliability
ExtensibilityExtensibility
SpeedSpeed
FlexibilityFlexibility
Complete Complete Standard ModelStandard Model
Convolution Convolution withwithPDFsPDFs Summation over Summation over
subprocessessubprocesses
Matching to Matching to parton showers parton showers
and hadronisationand hadronisation
ReliabilityReliability
ExtensibilityExtensibility
SpeedSpeed
FlexibilityFlexibility
HELAC-PHEGASFortran code Fortran code
Complete Complete Standard ModelStandard Model
Convolution Convolution withwithPDFsPDFs Summation over Summation over
subprocessessubprocesses
Matching to Matching to parton showers parton showers
and hadronisationand hadronisation
ReliabilityReliability
ExtensibilityExtensibility
SpeedSpeed
FlexibilityFlexibility
Leading order without approximationsLeading order without approximations
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
Complete Complete Standard ModelStandard Model
Convolution Convolution withwithPDFsPDFs Summation over Summation over
subprocessessubprocesses
Matching to Matching to parton showers parton showers
and hadronisationand hadronisation
ReliabilityReliability
ExtensibilityExtensibility
SpeedSpeed
FlexibilityFlexibility
Standalone version with build-in CTEQ6L1 Interface to the LHAPDF
Complete Complete Standard ModelStandard Model
Convolution Convolution withwithPDFsPDFs Summation over Summation over
subprocessessubprocesses
Matching to Matching to parton showers parton showers
and hadronisationand hadronisation
ReliabilityReliability
ExtensibilityExtensibility
SpeedSpeed
FlexibilityFlexibility
Lepton colliders, TeVatron, LHC Summation over all sub-processes
Complete Complete Standard ModelStandard Model
Convolution Convolution withwithPDFsPDFs Summation over Summation over
subprocessessubprocesses
Matching to Matching to parton showers parton showers
and hadronisationand hadronisation
ReliabilityReliability
ExtensibilityExtensibility
SpeedSpeed
FlexibilityFlexibility
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
Complete Complete Standard ModelStandard Model
Convolution Convolution withwithPDFsPDFs Summation over Summation over
subprocessessubprocesses
Matching to Matching to parton showers parton showers
and hadronisationand hadronisation
ReliabilityReliability
ExtensibilityExtensibility
SpeedSpeed
FlexibilityFlexibility
PHEGAS – phase space generatorPHEGAS – 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 -
Complete Complete Standard ModelStandard Model
Convolution Convolution withwithPDFsPDFs Summation over Summation over
subprocessessubprocesses
Matching to Matching to parton showers parton showers
and hadronisationand hadronisation
ReliabilityReliability
ExtensibilityExtensibility
SpeedSpeed
FlexibilityFlexibility
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)
Complete Complete Standard ModelStandard Model
Convolution Convolution withwithPDFsPDFs Summation over Summation over
subprocessessubprocesses
Matching to Matching to parton showers parton showers
and hadronisationand hadronisation
ReliabilityReliability
ExtensibilityExtensibility
SpeedSpeed
FlexibilityFlexibility
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)
Complete Complete Standard ModelStandard Model
Convolution Convolution withwithPDFsPDFs Summation over Summation over
subprocessessubprocesses
Matching to Matching to parton showers parton showers
and hadronisationand hadronisation
ReliabilityReliability
ExtensibilityExtensibility
SpeedSpeed
FlexibilityFlexibility
Arbitrary cuts, distributions and scale choices Configuration via scripts Compilers: Lahey Fujitsu, Intel Fortran, GNU gfortran/g95 Multiprecision numerics
Dyson-Schwinger RecursionDyson-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
Sub-amplitude with off-shell boson of momentum P Blobs denote sub-amplitude with the same structure
bP = ∑n=1
nP=P i
bP i ∑P=P1P2
ig
P2
P1P1 ,P2
Dyson-Schwinger RecursionDyson-Schwinger Recursion
For fermion with momentum P
For antifermion with momentum P
P = ∑i=1
nP−P i ℘P i ∑P=P1P2
ig℘bP2P1 P1 ,P2
P = ∑i=1
nP−P i P i ℘ ∑P=P1P2
ig P1bP2℘P1 ,P2
Multi-jet final state 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 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 PSMatching 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 Q
cut
- Variations with the number of ME legs
- Dependencies on the internal jet algorithm
Example pp Example pp →→ W + jets W + jets LHCLHC
Cross sections in pb for inclusive jet rates Range of variation normalized to the
average value Inclusive E
T spectra of leading 4 jets
J. Alwall et al. Eur. Phys. J. C53 (2008) 473
Systematic StudiesSystematic Studies
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
Points represents different
matching scale
=0/2 =0⋅2
LHCLHC
J. Alwall et al. Eur. Phys. J. C53 (2008) 473
Systematic StudiesSystematic Studies
SHERPA systematics at the LHC
Line default settings Shaded area range between
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 Differences within each code
are as large as the differences between the codes
=0/2 =0⋅2
s
LHCLHC
J. Alwall et al. Eur. Phys. J. C53 (2008) 473
Performance tt+jet Production Performance tt+jet Production
87 (3) graphs gg, 40 (1) graph qq with Higgs boson contribution 9 subprocesses α
S
2α 4
Time: ‰ ~ 10 (4) min.
558 (16) graphs gg 246 (5) qq, gq, qg with Higgs boson contribution 25 subprocesses α
S
3α 4
Time: ‰ ~ 106 (34) min.
Intel Pentium 1.7 GHzIntel Fortran
pp t t
pp t t1jet
Summary & OutlookSummary & 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
HELAC
http://helac-phegas.web.cern.ch/helac-phegas/
arXiv:0710.2427 [hep-ph]