HEP Analysis

John Morris

Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties HEP Analysis MC Corrections MC Corrections Re-Weighting Tag & Probe John Morris Smearing Summary Queen Mary University of London Measurements 2012 Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental Modelling Searches Searches Higgs BSM Conclusion 1 / 105 HEP Analysis John Morris HEP Analysis Monte Carlo What is MC? Why use MC? MC Generation Outline Detector Sim Reconstruction • Monte Carlo (MC) Reconstruction • What is MC and why do we use it? Event Properties MC Corrections • MC event generation MC Corrections • MC detector simulation Re-Weighting Tag & Probe • What happens when MC does not agree with data? Smearing Summary • Event re-weighting Measurements • 4-vector smearing Cross section Luminosity • Cross Section measurement Selection Backgrounds Efficiency • Systematic uncertainties Results Uncertainties Statistical • These notes will focus on the ATLAS experiment, but also apply Luminosity Experimental to other experiments Modelling • Searches Borrowing slides, plots and ideas from E. Rizvi, T. Sjostrand Searches and ATLAS public results Higgs BSM Conclusion 2 / 105 HEP Analysis John Morris HEP Analysis Monte Carlo What is MC? This is not an in-depth MC course Why use MC? MC Generation Detector Sim • The subject of MC is vast Reconstruction Reconstruction • There are many different models, generators and techniques Event Properties • Could spend hours, weeks, months on each MC Corrections MC Corrections • These slides are just a brief outline Re-Weighting Tag & Probe • Focus on the generalities Smearing Summary • Explain the steps involved Measurements • Not going to get bogged down in details Cross section Luminosity Selection Aim of this course Backgrounds Efficiency • Aim is to provide a working knowledge of MC basics Results • Steps involved in generation Uncertainties Statistical • Introduction to various systematics Luminosity Experimental • Techniques for correcting MC to describe data Modelling Searches • Overview of a measurement Searches Higgs • Systematics BSM Conclusion 3 / 105 HEP Analysis John Morris Monte Carlo (MC) - What is MC? Monte Carlo What is MC? Why use MC? MC Generation Detector Sim • MC is a simulation of collisions between particles Reconstruction • Reconstruction For these notes, pp collisions in ATLAS at the LHC Event Properties • MC is used in all particle physics experiments MC Corrections MC Corrections • MC generation is broadly split into 2 parts: Re-Weighting 1 Generation of the physics process Tag & Probe Smearing • Matrix element calculation Summary • ...(lots of steps)... Measurements • 4-vectors of final state hadrons Cross section Luminosity 2 Simulation of the detector Selection Backgrounds • Trigger, tracking and calorimeter simulation Efficiency • ...(lots of steps)... Results • Analysis objects like electrons and jets Uncertainties Statistical • End result: Luminosity Experimental • MC Samples in the same format as the actual data Modelling • With additional information from Step 1, the truth record Searches Searches Higgs BSM Conclusion 4 / 105 HEP Analysis John Morris Monte Carlo (MC) - What is MC? Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental Modelling Searches • MC simulates what happens at the LHC and ATLAS Searches Higgs • Many different programmes can be used at each stage BSM Conclusion 5 / 105 HEP Analysis John Morris Monte Carlo (MC) - Why use MC? Monte Carlo What is MC? Why use generators? Why use MC? MC Generation Detector Sim • Allows studies of complex multi-particle physics Reconstruction Reconstruction • Allows studies of theoretical models Event Properties • ⇒ What does a SUSY signal look like? MC Corrections MC Corrections Can be used to Re-Weighting Tag & Probe Smearing • Predict cross sections and topologies of various processes Summary • ⇒ Feasibility study - Can we find the theoretical particle X? Measurements Cross section • Simulate background processes to the signal of interest Luminosity Selection • ⇒ Can devise analysis strategies Backgrounds Efficiency • Study detector response Results Uncertainties • ⇒ Optimise trigger & detector selection cuts Statistical Luminosity • Study detector imperfections Experimental Modelling • ⇒ Can evaluate acceptance corrections Searches • See next week for a discussion of acceptance Searches Higgs • Remove the effect of the apparatus from the measurement BSM • ⇒ Unfold the data. Correcting the data for detector effects Conclusion 6 / 105 HEP Analysis John Morris MC Generation Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Use random numbers for integration Reconstruction Reconstruction • Code uses random number generator to integrate Event Properties x2 MC Corrections Z MC Corrections f (x) .dx = (x2 − x1) hf (x)i Re-Weighting x1 Tag & Probe Smearing N Summary 1 X hf (x)i = f (x ) Measurements N i Cross section i=1 Luminosity Selection Backgrounds Efficiency • Cross section randomly sampled over phase space Results • Want to generate events that simulate nature Uncertainties Statistical • Get average and fluctuations right Luminosity Experimental • Need to make random choices, as in nature Modelling • An event with n particles involves O (10n) random choices Searches • LHC events involve 1000’s of random choices Searches Higgs BSM Conclusion 7 / 105 HEP Analysis John Morris Monte Carlo Generation Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental Modelling Searches Searches Higgs BSM Conclusion 8 / 105 HEP Analysis John Morris Monte Carlo Generation Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental Modelling Searches Searches Higgs BSM Conclusion 9 / 105 HEP Analysis John Morris Monte Carlo Generation Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction Identifying theoretical modelling uncertainties Reconstruction Event Properties MC Corrections • Let’s look at some of these steps in more detail MC Corrections Re-Weighting • There are several ways to perform each step Tag & Probe Smearing • This choice leads to theoretical modelling uncertainties Summary • These uncertainties enter into most LHC results Measurements Cross section • Want to understand where they come from Luminosity Selection • Theoretical modelling uncertainties include: Backgrounds Efficiency • Generator uncertainties Results • PDF uncertainties Uncertainties Statistical • Parton shower uncertainties Luminosity • Hadronisation uncertainties Experimental Modelling Searches Searches Higgs BSM Conclusion 10 / 105 HEP Analysis John Morris Matrix element calculation Monte Carlo What is MC? Why use MC? Normally calculated at LO or NLO MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section • Higher order corrections are important: Luminosity Selection • Normalisation and shape of kinematic distributions Backgrounds Efficiency • Multiplicity of objects like jets Results Uncertainties • Higher order corrections are hard to calculate and CPU intensive Statistical Luminosity • Several programs that will do the calculation Experimental Modelling • Different calculation techniques Searches • Different assumptions Searches • Different results Higgs BSM • ⇒ Theoretical modelling uncertainty Conclusion 11 / 105 HEP Analysis John Morris PDF Monte Carlo What is MC? The ProtonPartonDensityFunction (PDF) Why use MC? MC Generation Detector Sim • Proton is not a point-like particle, it’s full of partons Reconstruction Reconstruction • Need to calculate: Event Properties • Probability of propagator interacting with quarks/gluon MC Corrections 2 MC Corrections • Needed as a function of Q and x Re-Weighting Tag & Probe Smearing HERA I+II inclusive, jets, charm PDF Fit • Various groups provide PDFs Summary 1 xf Q2 = 10 GeV2 Measurements • Parametrised differently Cross section HERAPDF1.7 (prel.) 0.8 Luminosity exp. uncert. • LHC uses: Selection model uncert. Backgrounds parametrization uncert. • xuv CTEQ Efficiency 0.6 Results HERAPDF1.6 (prel.) • MSTW Uncertainties • NNPDF Statistical 0.4 × Luminosity xg ( 0.05) xdv • Get a different result using Experimental Modelling different PDFs Searches 0.2 • ⇒ Theoretical modelling Searches xS (× 0.05) Higgs uncertainty

BSM HERAPDF Structure Function Working Group June 2011 10-4 10-3 10-2 10-1 1 Conclusion x 12 / 105 HEP Analysis John Morris Parton Showering Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds • Efficiency Need to go from 2→2 scattering to 100’s of particles Results • A particle can decay into more particles Uncertainties • A particle can emit another particle Statistical Luminosity • All controlled by random numbers Experimental Modelling • Parton shower evolution is a probabilistic process Searches • Searches Occurs with unit total probability Higgs BSM Conclusion 13 / 105 HEP Analysis John Morris Parton Showering Monte Carlo What is MC? 2 Common approaches to parton showering Why use MC? MC Generation Detector Sim • Need to avoid divergences and infinities in calculations Reconstruction • See your QCD course for why these occur Reconstruction Event Properties • Solution requires the final state partons to be ordered MC Corrections MC Corrections • There are 2 common approaches to do this Re-Weighting 2 2 Tag & Probe • Pythia : Q = m Smearing Summary • The parton with the highest pT is calculated first Measurements • Herwig : Q2 ≈ E 2 (1 − cos (θ)) Cross section Luminosity • The parton with the largest angle is calculated first Selection Backgrounds Efficiency This represents a theoretical modelling uncertainty Results Uncertainties • Both provide a good description of data but which is correct? Statistical • Luminosity Neither is correct, but nature is unknown, we only have models Experimental Modelling • All physics measurements need to take this into account Searches • Expect to see a parton shower systematic for every result Searches Higgs • Use both methods for calculation of physics result BSM • Difference between results is a theoretical modelling systematic Conclusion 14 / 105 HEP Analysis John Morris Hadronisation Monte Carlo What is MC? Why use MC? Going from partons to hadrons MC Generation Detector Sim Reconstruction • Partons are not observed directly in nature, only hadrons Reconstruction Event Properties • Hadronisation occurs at low energy scales MC Corrections • Perturbation theory is not valid MC Corrections Re-Weighting • Cannot calculate this process from first principals Tag & Probe Smearing • Require models to simulate what happens Summary • Measurements 2 common approaches are used Cross section • Pythia : Lund string model Luminosity Selection • Herwig : Cluster model Backgrounds Efficiency Results This is another theoretical modelling uncertainty Uncertainties Statistical • Similar type of uncertainty as for parton showering Luminosity Experimental • We don’t know exactly how nature works Modelling • We have 2 reasonable models Searches • Calculate physics result using each method Searches Higgs • Difference is a theoretical modelling systematic BSM Conclusion 15 / 105 HEP Analysis John Morris Hadronisation Monte Carlo What is MC? The Lund string model Why use MC? MC Generation Detector Sim • In WED, field lines go all the way to infinity Reconstruction Reconstruction • Photons do not interact with each other Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity • In QCD, for large charge separation, field lines seem to be Selection Backgrounds compressed into tube-like regions ⇒ string(s) Efficiency Results • Self-interaction among soft gluons in the vacuum Uncertainties Statistical Luminosity Experimental Modelling Searches Searches Higgs BSM Conclusion 16 / 105 HEP Analysis John Morris Hadronisation Monte Carlo What is MC? Why use MC? MC Generation The Lund string model Detector Sim Reconstruction • The strings connecting the 2 partons breaks as they move apart Reconstruction Event Properties • Fragmentation starts in the middle and spreads out MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental • The breakup vertices become causally disconnected Modelling • This is governed by many internal parameters Searches Searches • Higgs Implemented by the Pythia MC program BSM Conclusion 17 / 105 HEP Analysis John Morris Hadronisation Monte Carlo What is MC? The Cluster model Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency • Pre-confinement colour flow is local Results Uncertainties • Forced g → qq¯ branchings Statistical Luminosity • Colour singlet clusters are formed Experimental Modelling • Clusters decay isotropically to hadrons Searches Searches • Relatively few internal parameters Higgs BSM • Implemented by the Herwig MC program Conclusion 18 / 105 HEP Analysis John Morris MC Generation Monte Carlo What is MC? Summary Why use MC? MC Generation Detector Sim • There are many steps involved in generating MC Reconstruction • There are competing models for each step Reconstruction Event Properties • ⇒ Leads to theoretical modelling uncertainties MC Corrections • MC Corrections General practice for a physics measurement Re-Weighting • Decide on a “Nominal” choice for all options Tag & Probe Smearing • Vary the generator, PDF, parton shower and hadronisation Summary • Use the difference in your result as a systematic Measurements Cross section Luminosity Why only a few models? Selection Backgrounds Efficiency • Don’t really know what is happening, only have models Results • Uncertainties Choice a few different models and take the difference Statistical • If model is very poor, doesn’t this inflate the uncertainty? Luminosity Experimental • Why not use my “back-of-an-envelope” model? Modelling Searches • Feel free to come up with a new model! Searches • Need to describe the data accurately Higgs BSM • Need to convince physics community Conclusion 19 / 105 HEP Analysis John Morris MC Generation Monte Carlo What is MC? Why use MC? MC Generation Detector Sim • Reconstruction MC Generator stops with set of Reconstruction “stable” final state particles Event Properties MC Corrections • Complete 4-vector info is known MC Corrections Re-Weighting about every particle Tag & Probe Smearing • All parent-daughter relations are Summary known and stored Measurements Cross section • High energy parton state known Luminosity Selection as parton level Backgrounds Efficiency • Stable particle state known as Results Uncertainties hadron level Statistical Luminosity • This level of information is often called the truth record Experimental Modelling • This is the pure event before it interacts with any apparatus Searches Searches Higgs BSM Conclusion 20 / 105 HEP Analysis John Morris Detector Simulation Monte Carlo What is MC? Why use MC? MC Generation Now need to simulate the detector Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental Modelling Searches Searches Higgs BSM Conclusion 21 / 105 HEP Analysis John Morris Detector Simulation Monte Carlo What is MC? Why use MC? Detector simulation is complex and detailed MC Generation Detector Sim • Simulation of all major components and materials Reconstruction Reconstruction • Tracking, calorimetry, magnets, muon chambers Event Properties • Support structure, cooling pipes, cables MC Corrections • Faulty components leading to missing readout MC Corrections Re-Weighting Tag & Probe • Geant4 program uses generator output 4-vectors Smearing Summary • Simulates interaction of particles within the detector volume Measurements • Particle ionisation in trackers Cross section Luminosity • Energy deposition in calorimeters Selection • Intermediate particle decays, radiation and scattering Backgrounds Efficiency • Full Simulation can take 10 minutes per event! Results Uncertainties • Possible to do a fast simulation - AtlFastII Statistical • Smears 4-vectors instead of doing calorimeter simulation Luminosity Experimental • Modelling Final output is raw data Searches • Charges measured on each tracker wire Searches • Electronic pulses in each calorimeter photomultiplier Higgs BSM • Same format as raw data Conclusion 22 / 105 HEP Analysis John Morris Example of ATLAS material Monte Carlo What is MC? Inner detector material in ATLAS Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental Modelling Searches • Radiation length of various material in ATLAS ID Vs η Searches Higgs • This is what is in the current simulation BSM • Does it match reality? Probably not 100% Conclusion 23 / 105 HEP Analysis John Morris MC Warning Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction MC is not the truth Reconstruction Event Properties • What happened in the MC generator didn’t happen at the LHC MC Corrections MC Corrections • The MC is our best guess Re-Weighting Tag & Probe • The MC only simulates specific physics processes Smearing Summary • The cross section calculation may be: Measurements • Cross section Wrong, Incomplete, Inaccurate Luminosity • Have a false kinematic dependence Selection Backgrounds • The MC code may have unknown bugs in it Efficiency Results • Some processes require higher order corrections which have not Uncertainties been calculated Statistical Luminosity • Experimental Simulation cannot account for all detector effects Modelling Searches Searches Higgs BSM Conclusion 24 / 105 HEP Analysis John Morris Reconstruction Monte Carlo What is MC? Going from electronic pulses to analysis objects Why use MC? MC Generation • Data and MC pass through the same reconstruction algorithms Detector Sim Reconstruction • Raw electronic pulses reconstructed into: Reconstruction Event Properties • Tracks MC Corrections • Calorimeter deposits MC Corrections Re-Weighting • Which are then reconstructed into: Tag & Probe Smearing • Jets, electron, muons, taus, Summary • Photons, tracks, missing ET Measurements Cross section Real life issues need to be reflected in the MC Luminosity • Selection Some parts of the detector become faulty over time Backgrounds Efficiency • e.g. - A section of the calorimeter readout dies and cannot be Results repaired until the detector is opened up in a shutdown Uncertainties Statistical • Lets say that this affects x% of the data luminosity Luminosity Experimental • Need to generate MC with this problem in x% of the MC Modelling Searches • Cannot know x until end of year Searches • ⇒ Need to reprocess the MC at the end of the year Higgs BSM • Some MC bugs do not become apparent for some time Conclusion 25 / 105 HEP Analysis John Morris Event Properties Monte Carlo What is MC? • Final state particles from the Standard Model: Why use MC? • MC Generation Electrons, Muons, Taus, Neutrinos, Photons, (un)charged Hadrons Detector Sim • Each interacts with detector in different ways Reconstruction Reconstruction • e, µ and τ are very similar in theory, however: Event Properties • e leaves a track and doesn’t penetrate further than EM Calo MC Corrections MC Corrections • µ leaves a track and passes through Calo into Muon chambers Re-Weighting • τ looks very much like a jet Tag & Probe Smearing • Decays within the inner detector Summary • ⇒ Lots of tracks, EM and Hadronic Calo deposits Measurements Cross section EM energy without a track Photon Luminosity Selection EM energy with a track Electron Backgrounds Efficiency Hadronic energy without a track Neutral Hadron (eg Neutron) Results Hadronic energy with a track Charged Hadron (eg Proton) Uncertainties Statistical Hadronic energy with many tracks Jet, Tau Luminosity ID and Muon chamber track Muon Experimental Modelling Missing transverse energy Neutrino Searches Missing longitudinal energy Beam remnants Searches Higgs Displaced secondary vertex in-flight decay BSM Conclusion 26 / 105 HEP Analysis John Morris Event Properties Monte Carlo What is MC? • Reconstructing an event requires recognising event properties Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental Modelling Searches Searches Higgs BSM Conclusion 27 / 105 HEP Analysis John Morris Event Display : W → eν Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental Modelling • Searches Electron (yellow) leaves track and EM Calo deposit Searches • Higgs Missing ET (red) identified with a neutrino BSM • W → eν Candidate event Conclusion 28 / 105 HEP Analysis John Morris Event Display : WZ → eνµµ Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental Modelling • Searches Electron (green) and Missing ET (orange) are reconstructed as Searches W → eν, like in the previous slide Higgs BSM • 2 additional Muons (red) reconstructed as Z → µµ Conclusion 29 / 105 HEP Analysis John Morris Event Display : H → 4e Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental Modelling Searches Searches Higgs BSM • 4 electrons reconstructed to candidate Higgs Boson Conclusion 30 / 105 HEP Analysis John Morris Event Display : H → eeµµ Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental Modelling Searches • Searches 2 electrons (green) and 2 muons (red) reconstructed to Higgs candidate Higgs Boson BSM Conclusion 31 / 105 HEP Analysis John Morris When MC gets it wrong Monte Carlo What is MC? Why use MC? Simulating the LHC and ATLAS is difficult MC Generation Detector Sim • As you can see, this is a very complex task Reconstruction • Far more involved that my brief overview Reconstruction Event Properties • MC description of data often not good enough MC Corrections MC Corrections • ⇒ Re-generate MC ⇒ time consuming and difficult to get right Re-Weighting • ⇒ Apply corrections to the MC ⇒ pragmatic and usable Tag & Probe Smearing Summary How to deal with inaccurate descriptions Measurements Cross section • This is broadly split into 3 different methodologies Luminosity Selection • Re-weight the MC: Backgrounds Efficiency • A data event contributes 1 entry to a histogram Results • A MC event may contribute 0.9 or 1.13 entries Uncertainties Statistical • Commonly used for trigger and reconstruction efficiencies Luminosity Experimental • Smear the MC: Modelling • Use random numbers (yet more!) to alter 4-vectors Searches Searches • Commonly used for jet, electron and muon pT Higgs BSM • Tune the MC - Regenerate the MC with tuned input parameters Conclusion 32 / 105 HEP Analysis John Morris Re-Weighting basics Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction Histograms in ROOT Reconstruction Event Properties • You use histograms to plot data and MC MC Corrections MC Corrections • An entry in a histogram contains a weight Re-Weighting Tag & Probe • histogram→ Fill(x, weight); Smearing Summary • For MC we will often want to give weight to an event Measurements √ Cross section • The default in ROOT is to do simple errors σ = N Luminosity Selection • This will get the errors wrong in a weighted distribution Backgrounds p Efficiency • Need to use the sum of squares of weights σ = P w 2 Results Uncertainties • In your code, please ensure than when you book a histogram Statistical • Luminosity TH1D* histo = new TH1D(“name”,“title”,nBins,MinX,MaxX); Experimental • histo→sumw2(); Modelling Searches Searches Higgs BSM Conclusion 33 / 105 HEP Analysis John Morris Re-Weighting MC Monte Carlo What is MC? Number of tracks in ATLAS events Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity • Experimental The MC clearly does not describe the data Modelling • What has gone so wrong? Searches Searches • Is it parton showering, hadronisation or something else? Higgs BSM • Need to understand the root cause of this disagreement Conclusion 34 / 105 HEP Analysis John Morris Pileup Re-Weighting Monte Carlo What is MC? Why use MC? N vertices Vs average N interactions per bunch crossing MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties • Statistical Classic ATLAS example of MC not describing data accurately Luminosity Experimental • This shows that the MC gets the number of vertices wrong Modelling • Problem simulating proton bunches with 1011 protons Searches Searches • Understandably a very difficult task! Higgs BSM • Unfortunately this has big effects for many distributions Conclusion 35 / 105 HEP Analysis John Morris Pileup Re-Weighting Monte Carlo What is MC? Need to determine re-weighting factors Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental • Divide Data by MC to determine correction Modelling Searches • In this case, fit the ratio and determine a weight Searches Higgs • Use this weight for each MC event BSM • histogram → Fill(x, weight); Conclusion 36 / 105 HEP Analysis John Morris Pileup Re-Weighting Monte Carlo What is MC? Why use MC? MC Generation Cartoon illustrating re-weighting procedure Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental Modelling Searches Searches Higgs BSM Conclusion 37 / 105 HEP Analysis John Morris Pileup Re-Weighting Monte Carlo What is MC? Why use MC? Effect of re-weighting on N Tracks MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical • (a) Before re-weighting MC describes the data poorly Luminosity Experimental • (b) After re-weighting the MC description is much better Modelling Searches • We have identified the underlying problem - N vertices Searches • Higgs We have re-weighted the N vertices distribution BSM • Can see effect in the number of tracks distribution Conclusion 38 / 105 HEP Analysis John Morris Re-Weighting Monte Carlo What is MC? Why use MC? We require many different weights MC Generation Detector Sim • Reconstruction Pileup is just 1 example where we need weights Reconstruction • Electrons, muons, taus, photons all require weights for: Event Properties MC Corrections • Trigger, reconstruction, identification MC Corrections Re-Weighting • Jets require weights for: Tag & Probe Smearing • Reconstruction, resolution, jet vertex fraction Summary • Measurements All of these weights provide a correction to specific aspects of Cross section data/MC disagreement Luminosity Selection • Combined all (via multiplication) to provide an overall weight Backgrounds Efficiency Results WEvent = We x Wµ x Wτ x Wjets x WPileup x Wother Uncertainties Statistical where We = WTrigger x WReco x WID Luminosity Experimental Modelling • The vast majority of weights are determined via dedicated Searches Searches studies using the Tag & probe methodology Higgs • BSM ⇒Ideal service task for ATLAS authorship Conclusion 39 / 105 HEP Analysis John Morris Tag & Probe Methods Monte Carlo What is MC? Why use MC? MC Generation A very common methodology for ATLAS Detector Sim Reconstruction Reconstruction • Tag & Probe is a method to study analysis objects (jets, µ, etc) Event Properties • Study trigger, reconstruction efficiencies MC Corrections MC Corrections • Data and MC often disagree in many places Re-Weighting Tag & Probe • Determine many different weights, often binned in pT and η Smearing Summary • Use Standard Model candles like Z → ee, W → µν Measurements Cross section • What to use decay products from well known particles Luminosity • Know that Z → ee has 2 electrons Selection Backgrounds • Know the invariant mass of a Z very well Efficiency Results • “Tag” one electron and study the other, “Probe” electron Uncertainties • Use data-driven methods to determine the detector response Statistical Luminosity • No need for MC in determining trigger, reco efficiencies Experimental Modelling • MC generally only used to determine weights Searches • In ATLAS weights are often called Scale Factors Searches Higgs BSM Conclusion 40 / 105 HEP Analysis John Morris Tag & Probe Methods Monte Carlo What is MC? Why use MC? MC Generation Tag & Probe : Z → ee example Detector Sim Reconstruction e Tag Reconstruction • Tag electron: Event Properties • Matched to Trigger MC Corrections MC Corrections • Tight reconstruction Re-Weighting • Satisfies all conditions for Tag & Probe Z Smearing being an excellent electron Summary • Measurements e Probe Probe electron: Cross section • Minimal selection Luminosity Selection Backgrounds Use probe to determine efficiencies Efficiency Results Uncertainties Probe Passes Selection Statistical Some Efficiency = Luminosity All probes Experimental Modelling Probe Fires Trigger Searches For Example :: Trigger Efficiency = Searches All probes Higgs BSM Conclusion 41 / 105 HEP Analysis John Morris Tag & Probe Methods Monte Carlo What is MC? Why use MC? Tag & Probe : Electron trigger efficiency MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency • Z → ee event selection applied Results Uncertainties • Tag electron used to select events Statistical Luminosity • No requirement on probe to pass trigger Experimental Modelling • Probe electron asked “Did you fire the trigger?” Searches Searches • Trigger efficiency determined for L1, L2 and EF Higgs BSM • Shown as a function of electron ET and η Conclusion 42 / 105 HEP Analysis John Morris Tag & Probe Methods Monte Carlo What is MC? Why use MC? Tag & Probe : Electron Identification efficiency MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency • J/Ψ → ee and Z → ee event selection applied Results Uncertainties • Tag electron used to select events Statistical • No requirement on probe to pass identification cuts Luminosity Experimental Modelling • Probe electron asked “Did you pass ID selection?” Searches • Shown as a function of electron ET and number of vertices Searches Higgs • BSM Note how MC does not match data ⇒ weights are required Conclusion 43 / 105 HEP Analysis John Morris Z → µµ Mass Monte Carlo What is MC? Why use MC? MC Generation What’s wrong with this plot? Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental Modelling • Reconstructed Z mass using invariant mass of 2 muons Searches Searches • Is this a scale or resolution effect? Higgs BSM Conclusion 44 / 105 HEP Analysis John Morris Smearing the MC Monte Carlo What is MC? Why use MC? MC Generation Muons in ATLAS Detector Sim Reconstruction • Muons are reconstructed using 2 detectors in ATLAS Reconstruction Event Properties • Inner detector : Pixel + SCT + TRT MC Corrections • Muon Spectrometer MC Corrections Re-Weighting • Each detector has it’s own momentum resolution Tag & Probe Smearing σ (p) pMS Summary 0 MS MS = ⊕ p1 ⊕ p2 . pT Measurements p pT Cross section Luminosity σ (p) Selection ID ID = p1 ⊕ p2 . pT Backgrounds p Efficiency Results Uncertainties Statistical • These equations quantify the how well we can measure the Luminosity momentum of any given muon Experimental Modelling • A MC muon should be subject to the same uncertainties Searches Searches • ⇒ Smear the MC muon momentum using random numbers Higgs BSM Conclusion 45 / 105 HEP Analysis John Morris Smearing the MC Monte Carlo What is MC? Muons in ATLAS Why use MC? MC Generation   Detector Sim 0 ID,MS ID,MS pT = pT 1 + g∆p1 + g∆p2 pT Reconstruction Reconstruction Event Properties 0 ID,MS • pT : MC muon pT after applying the corrections ∆pi MC Corrections MC Corrections • g : normally distributed random number, mean 0 and width 1 Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental Modelling Searches Searches Higgs BSM • Z mass before(left) and after(right) MC muon smearing Conclusion 46 / 105 HEP Analysis John Morris Smearing the MC Monte Carlo What is MC? Why use MC? Smear depending on detector region MC Generation Detector Sim • Detector resolution varies with region Reconstruction Reconstruction • Resolution in Barrel is different from that in End-Cap Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental Modelling Searches Searches • This is just for muons Higgs BSM • All sub-detectors have similar resolution tables Conclusion 47 / 105 HEP Analysis John Morris Summary so far Monte Carlo What is MC? Monte Carlo (MC) Why use MC? MC Generation Detector Sim • MC generation: Reconstruction • Random numbers used extensively Reconstruction Event Properties • Simulate matrix element MC Corrections • Simulate decays and hadronisation MC Corrections Re-Weighting • Detector simulation: Tag & Probe Smearing • Output 4-vectors put through a complex detector description Summary • MC and data are reconstructed using the same algorithms Measurements Cross section Luminosity MC often doesn’t describe the data Selection Backgrounds • Scale Factors used to provide MC event weights Efficiency Results • Physics objects have their momentum smeared Uncertainties Statistical • “Tag” and “Probe” methodology is widely used in ATLAS Luminosity Experimental Modelling Hopefully the MC now describes the data Searches Searches • After simulation, extensive study and many corrections Higgs BSM • ⇒ Can now use the MC in physics measurements Conclusion 48 / 105 HEP Analysis

John Morris

Monte Carlo What is MC? Why use MC? MC Generation Day 2 Detector Sim Reconstruction • Review of Day 1 Reconstruction Event Properties • MC Generation MC Corrections • Detector simulation MC Corrections Re-Weighting • Correcting MC with re-weighting and smearing Tag & Probe Smearing • Making a measurement Summary • Measurements Cross section Cross section • Acceptance & Purity Luminosity Selection • Luminosity Backgrounds • Systematics Efficiency Results • Searches and exclusions Uncertainties Statistical Luminosity Experimental Modelling Searches Searches Higgs BSM Conclusion 49 / 105 HEP Analysis John Morris MC Generation Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental Modelling Searches Searches Higgs BSM Conclusion 50 / 105 HEP Analysis John Morris MC Generation Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental Modelling Searches Searches Higgs BSM Conclusion 51 / 105 HEP Analysis John Morris Detector Simulation Monte Carlo What is MC? Detector simulation is complex and detailed Why use MC? MC Generation Detector Sim • Simulation of all major components and materials Reconstruction • Tracking, calorimetry, magnets, muon chambers Reconstruction Event Properties • Support structure, cooling pipes, cables MC Corrections • Faulty components leading to missing readout MC Corrections Re-Weighting • Geant4 program uses generator output 4-vectors Tag & Probe Smearing • Simulates interaction of particles within the detector volume Summary Measurements • Particle ionisation in trackers Cross section • Energy deposition in calorimeters Luminosity Selection • Intermediate particle decays, radiation and scattering Backgrounds Efficiency • Final output is raw data Results • Uncertainties Charges measured on each tracker wire Statistical • Electronic pulses in each calorimeter photomultiplier Luminosity Experimental • Same format as raw data Modelling • This represents out best guess of the detector Searches Searches • Detector simulation is very complex Higgs BSM • Difficult to model detector imperfections Conclusion • Difficult to model bits of detector that break during running 52 / 105 HEP Analysis John Morris Correcting MC Monte Carlo What is MC? Use event weighting and 4-vector smearing Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity • Re-weight MC events to achieve same efficiency in MC as in data Selection Backgrounds • Smear MC 4-vectors to achieve same resolution in MC as in data Efficiency Results Uncertainties Statistical Luminosity Experimental Modelling Searches Searches Higgs BSM Conclusion 53 / 105 HEP Analysis John Morris Cross section Monte Carlo What is MC? Why use MC? MC Generation Detector Sim • A cross section is defined by Reconstruction Reconstruction N Event Properties σ = MC Corrections L MC Corrections Re-Weighting Tag & Probe • Smearing Where: Summary • N is the number of events Measurements • L is the total integrated luminosity Cross section Luminosity Selection • Represents a probability that an event will occur Backgrounds Efficiency • Given a fixed luminosity, you expect Results • X number of Z-boson events Uncertainties Statistical • Y number of t¯t events Luminosity • Z number of Higgs events Experimental Modelling • All have different cross sections Searches Searches Higgs BSM Conclusion 54 / 105 HEP Analysis John Morris Cross section Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental √ Modelling • Shows cross section of many different processes at s = 7 TeV Searches • Represents a probability that a process will occur Searches Higgs • For a fixed luminosity, you can expect X events BSM Conclusion 55 / 105 HEP Analysis John Morris Purity & efficiency Monte Carlo What is MC? Why use MC? MC Generation What happens at the LHC Detector Sim Reconstruction • 2 protons interact and a physics process occurs Reconstruction Event Properties • All processes that can occur, do occur MC Corrections MC Corrections • The process you are interesting in is in there somewhere Re-Weighting Tag & Probe Smearing Summary Purity - reduced by background Measurements Cross section Luminosity • You will not only get the events you want Selection Backgrounds • You will get other events as well, ones you don’t want Efficiency Results • Purity is percentage of your events that are signal Uncertainties Statistical Signal events in sample Luminosity Purity = Experimental All events in sample Modelling Searches Searches • Need MC to properly estimate purity Higgs BSM Conclusion 56 / 105 HEP Analysis John Morris Purity & efficiency Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Efficiency - reduced by detector Reconstruction Reconstruction Event Properties • Efficiency is percentage of all signal events that you reconstruct MC Corrections All events in sample MC Corrections Efficiency = Re-Weighting All generated signal events Tag & Probe Smearing Summary Measurements • Your process will have final states objects at all pT Cross section • Luminosity The pT of pretty much all objects obeys an exponential Selection • You will not be able to trigger objetcs at low pT Backgrounds Efficiency • You will not be able to reconstruct objects at low pT Results • ⇒ Reduction in efficiency Uncertainties Statistical • Your process will have final states objects at all η Luminosity Experimental • Your detector will only cover a fixed range in η Modelling • ⇒ Reduction in efficiency Searches Searches Higgs BSM Conclusion 57 / 105 HEP Analysis John Morris Cross section Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Not so simple Reconstruction Reconstruction • Naively a cross section is simply counting events Event Properties MC Corrections • It’s not that easy! MC Corrections Re-Weighting • Assumes that we only measure the process of interest Tag & Probe Smearing • All processes occur ⇒ will will get some background Summary Measurements • Assumes that we have a perfect description of our detector Cross section • Luminosity No holes / cracks Selection • Perfect efficiency for measuring particles Backgrounds Efficiency • Perfect resolution Results • No background events Uncertainties • No dependence on MC models Statistical Luminosity Experimental • We already know that we need to correct for these issues Modelling • Searches ⇒ Cross section calculation needs modification Searches Higgs BSM Conclusion 58 / 105 HEP Analysis John Morris Cross section Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Modified Cross section formula Event Properties MC Corrections MC Corrections Nobs − Nbkg Re-Weighting σ = Tag & Probe L .  . BR Smearing Summary Measurements • Where: Cross section Luminosity • Nobs is the number of observed events Selection • N is the number of expected background events Backgrounds bkg Efficiency • L is the total integrated luminosity Results •  is the acceptance efficiency Uncertainties Statistical • BR is the branching ratio Luminosity Experimental Modelling Searches Searches Higgs BSM Conclusion 59 / 105 HEP Analysis John Morris Luminosity Monte Carlo What is MC? Why use MC? MC Generation Need to know the LHC luminosity Detector Sim Reconstruction N − N Reconstruction σ = obs bkg Event Properties L .  . BR MC Corrections MC Corrections meas meas Re-Weighting µnbfr µ nbfr µ nbfr Tag & Probe L = = = Smearing σinel σinel σvis Summary Measurements Cross section • µ is the average number of interactions per bunch crossing Luminosity Selection • n is the number of bunches colliding at the interaction point Backgrounds b Efficiency Results • fr is the machine revolution frequency Uncertainties • σinel is the total inelastic cross section Statistical Luminosity • meas Experimental µ = µ is the measured µ Modelling •  is the detector luminosity reconstruction efficiency Searches Searches • σ is the visible cross section Higgs vis BSM Conclusion 60 / 105 HEP Analysis John Morris Luminosity Monte Carlo What is MC? Luminosity determination Why use MC? MC Generation Nobs − Nbkg Detector Sim σ = Reconstruction L .  . BR Reconstruction Event Properties • Several methods used to determine the luminosity MC Corrections MC Corrections • LUCID used for primary result, others are cross-checks Re-Weighting Tag & Probe • Instantaneous luminosity decreases over time Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental Modelling Searches Searches Higgs BSM Conclusion 61 / 105 HEP Analysis John Morris Cross section Monte Carlo What is MC? ATLAS Luminosity Why use MC? MC Generation Detector Sim Nobs − Nbkg Reconstruction σ = Reconstruction L .  . BR Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental • ATLAS only records a percentage of what the LHC delivers Modelling Searches • Sub-detectors not all working Searches • Transition time from “Stable Beams” to recording Higgs BSM • Absolute luminosity known to ≈ 4% Conclusion 62 / 105 HEP Analysis John Morris Cross section Example Monte Carlo What is MC? Why use MC? Let’s work through a t¯t cross section measurement MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency • Top quark decays t → bW Results Uncertainties • W decays either W → qq¯ or W → lν Statistical Luminosity • 3 classifications of event: Experimental Modelling • W → qq¯ and W → qq¯ - Fully hadronic Searches • W → qq¯ and W → lν - Semileptonic Searches Higgs • W → lν and W → lν - Dilepton BSM Conclusion 63 / 105 HEP Analysis John Morris Cross section Example Monte Carlo What is MC? Why use MC? MC Generation Focus on the semileptonic classification Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results • Final state: Uncertainties • 1 lepton - e or µ. Don’t use τ as it looks like a jet Statistical Luminosity • Missing ET - from the neutrino Experimental • 4 jets Modelling • Searches 2 of these jets are from b-quarks Searches • Require that we have 1 jet tagged with a b-tagging algorithm Higgs BSM Conclusion 64 / 105 HEP Analysis John Morris Event selection Monte Carlo What is MC? Why use MC? Need to apply an event selection MC Generation Detector Sim • LHC experiments record millions of events Reconstruction Reconstruction • We are looking for a specific process Event Properties • We want to select only the events of our process MC Corrections MC Corrections Re-Weighting • Use only good data Tag & Probe Smearing • Only use data where all components have given a green light Summary • Red light if a sub-detector isn’t working properly Measurements Cross section • Trigger : Require that event passes a electron or muon trigger Luminosity Selection • Backgrounds Place pT and η requirements on the lepton and jets Efficiency • Results Only look at areas of the detector we can measure well Uncertainties • Place quality cuts on the lepton and jets Statistical Luminosity • Reconstruction algorithms usually class object quality Experimental • Modelling Only use “good” objects - reject “bad” objects

Searches • Require missing ET for the neutrino Searches Higgs • Require at least 1 jet is b-tagged BSM Conclusion 65 / 105 HEP Analysis John Morris Observed events Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections Number of observed events MC Corrections Re-Weighting Nobs − Nbkg Tag & Probe σ = Smearing L .  . BR Summary Measurements Cross section Luminosity • Nobs is relatively simple Selection Backgrounds • Apply event selection to the data Efficiency Results • Count how many events we observe Uncertainties Statistical Luminosity Experimental Modelling Searches Searches Higgs BSM Conclusion 66 / 105 HEP Analysis John Morris Background events Monte Carlo What is MC? Why use MC? MC Generation Number of background events Detector Sim Reconstruction Reconstruction Nobs − Nbkg Event Properties σ = MC Corrections L .  . BR MC Corrections Re-Weighting Tag & Probe • Nbkg is not so simple Smearing Summary • How many background events have passed our selection? Measurements Cross section • For the t¯t process, backgrounds are: Luminosity Selection • Single Top - Contains a t quark, W -boson and b-jet Backgrounds • Efficiency W +Jets - Contains a W -boson and sometimes a b-jet Results • Z+Jets - Sometimes a lepton is reconstructed as a jet Uncertainties • DiBoson events WW , WZ, ZZ - can pass the selection Statistical Luminosity • QCD Multijets Experimental Modelling • b-tagging algorithms have “fake-rates” and often tag light jets Searches Searches • Backgrounds are estimated using MC and data-driven methods Higgs BSM Conclusion 67 / 105 HEP Analysis John Morris Background events Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Number of background events Reconstruction Reconstruction N − N Event Properties σ = obs bkg MC Corrections L .  . BR MC Corrections Re-Weighting Tag & Probe Smearing MC estimation of the background Summary Measurements • MC is used to estimate the number of background events Cross section Luminosity • Selection Have to trust MC cross section calculation Backgrounds Efficiency • Have to trust MC generation process and detector simulation Results • Simply count number of MC events expected: Uncertainties Statistical • Normalised MC events to data Luminosity Luminosity Experimental • Put MC samples through event selection Modelling Searches • Done for single top, Z+Jets and DiBoson processes Searches Higgs BSM Conclusion 68 / 105 HEP Analysis John Morris Background events Monte Carlo What is MC? Why use MC? MC Generation Number of background events Detector Sim

Reconstruction Nobs − Nbkg Reconstruction σ = Event Properties L .  . BR MC Corrections MC Corrections Re-Weighting Tag & Probe Data-driven estimation of the background Smearing Summary • There are processes where we don’t trust the MC Measurements Cross section • W +Jets process: Luminosity Selection • Very difficult to calculate Backgrounds Efficiency • Large theoretical uncertainties in normalisation Results • Large theoretical uncertainties in heavy flavour composition Uncertainties • What proportion of jets are light, c, b ? Statistical Luminosity • QCD Multijet processes: Experimental Modelling • Standard Model processes involving light quarks and gluons Searches • Dominates all events at the LHC Searches Higgs • We do not trust the MC BSM Conclusion 69 / 105 HEP Analysis John Morris Background events Monte Carlo What is MC? Why use MC? Data-driven background estimation example MC Generation Detector Sim Reconstruction • Split phase space into 4 regions Reconstruction Event Properties • Use 2 variables MC Corrections • MC Corrections Muon isolation variable Re-Weighting Tag & Probe • Missing ET of event Smearing Summary Measurements Cross section Luminosity Selection • Assume that QCD background is the same in all 4 regions Backgrounds Efficiency • Big assumption ⇒ large uncertainties Results Uncertainties • Count events in regions A,B & C Statistical Luminosity • Extrapolate to number of events expected in signal region D Experimental Modelling • This is just 1 method used Searches Searches • Typically use several methods, all with different assumptions Higgs • Use difference of methods as a systematic BSM Conclusion 70 / 105 HEP Analysis John Morris Acceptance Efficiency Monte Carlo What is MC? Why use MC? Acceptance Efficiency MC Generation Detector Sim Reconstruction Nobs − Nbkg Reconstruction σ = Event Properties L .. BR MC Corrections MC Corrections Re-Weighting • If X number of signal events were generated Tag & Probe Smearing Summary • How many make it into our final selection? Measurements • Events fail to make the selection cuts because: Cross section Luminosity • Events fails to fire a trigger Selection Backgrounds • Inefficient reconstruction algorithms Efficiency • Final state objects: Results • Have too low pT to pass cuts Uncertainties Statistical • Are outside of detector volume - η Luminosity • Go into cracks or broken bits of detector Experimental Modelling • The acceptance efficiency is calculated on the signal t¯t MC Searches • We rely on the MC for our measurement Searches Higgs • We must have high level of trust in MC BSM Conclusion 71 / 105 HEP Analysis John Morris Branching Ratio Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction Branching Ratio Reconstruction Event Properties MC Corrections Nobs − Nbkg MC Corrections σ = Re-Weighting L .  . BR Tag & Probe Smearing Summary • Branching ratio is process dependant Measurements Cross section • Determined by theoretical calculation Luminosity Selection • In the case of t¯t, there are 3 decay types: Backgrounds Efficiency • W → qq¯ and W → qq¯ - Fully hadronic Results • W → qq¯ and W → lν - Semileptonic Uncertainties Statistical • W → lν and W → lν - Dilepton Luminosity Experimental • For the semileptonic case BR = 0.543 Modelling Searches Searches Higgs BSM Conclusion 72 / 105 HEP Analysis John Morris Control plots Monte Carlo What is MC? Does the MC describe the data? Why use MC? MC Generation ATLAS tagged e + ≥ 3 jets 30000 ATLAS tagged µ + ≥ 3 jets Detector Sim 14000 For Approval Data For Approval Data Events Events -1 -1 Reconstruction 12000 ∫ L = 4.66 fb tt 25000 ∫ L = 4.66 fb tt Reconstruction W+jets W+jets Multijet Multijet Event Properties 10000 20000 Z+jets Z+jets 8000 Single Top Single Top MC Corrections 15000 MC Corrections DiBoson DiBoson 6000 uncertainty uncertainty Re-Weighting 10000 Tag & Probe 4000 Smearing 5000 2000 Summary Measurements 0 0 1.8 1.8 Cross section 1.6 1.6 1.4 1.4 Luminosity 1.2 1.2 Selection 1 1 0.8 0.8 Backgrounds 0.6 0.6

Data / Prediction 0.4 Data / Prediction 0.4 Efficiency 0.2 0.2 Results 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 Number Of Jets / Event Number Of Jets / Event Uncertainties Statistical Luminosity • Shows the number of jets after all event selection Experimental Modelling • Simulation histograms are stacked on top of each other Searches Searches • Uncertainty is shown with hatched area Higgs BSM • MC does a good job of describing data Conclusion 73 / 105 HEP Analysis John Morris Control plots Monte Carlo What is MC? Does the MC describe the data? Why use MC? MC Generation 1200 µ ≥ µ ≥ Detector Sim ATLAS tagged + 3 jets 1400 ATLAS tagged + 3 jets For Approval Data For Approval Data Reconstruction 1000 ∫ L = 4.66 fb-1 tt 1200 ∫ L = 4.66 fb-1 tt Reconstruction W+jets W+jets Multijet Events / 0.10 1000 Multijet

Event Properties Events / 5 GeV 800 Z+jets Z+jets MC Corrections Single Top 800 Single Top 600 MC Corrections DiBoson DiBoson uncertainty 600 uncertainty Re-Weighting 400 Tag & Probe 400 Smearing 200 200 Summary Measurements 0 0 1.8 1.8 Cross section 1.6 1.6 1.4 1.4 Luminosity 1.2 1.2 Selection 1 1 0.8 0.8 Backgrounds 0.6 0.6

Data / Prediction 0.4 Data / Prediction 0.4 Efficiency 0.2 0.2 Results 40 60 80 100 120 140 160 180 200 -2 -1 0 1 2 leading jet p [GeV] η T leading jet Uncertainties Statistical Luminosity • Shows the leading (highest pT) jet pT and η Experimental Modelling • Data / Prediction plot shown underneath Searches Searches • Ideally this would be at unity, not always the case Higgs BSM • Keep in mind the uncertainty band and statistical uncertainties Conclusion 74 / 105 HEP Analysis John Morris Control plots Monte Carlo What is MC? Does the MC describe the data? Why use MC? MC Generation µ ≥ µ ≥ Detector Sim ATLAS tagged + 3 jets 1400 ATLAS tagged + 3 jets 3000 For Approval Data For Approval Data Reconstruction ∫ L = 4.66 fb-1 tt 1200 ∫ L = 4.66 fb-1 tt Reconstruction 2500 W+jets W+jets Multijet Events / 0.10 1000 Multijet Event Properties Events / 5 GeV 2000 Z+jets Z+jets MC Corrections Single Top 800 Single Top MC Corrections 1500 DiBoson DiBoson uncertainty 600 uncertainty Re-Weighting 1000 Tag & Probe 400 Smearing 500 Summary 200 Measurements 0 0 1.8 1.8 Cross section 1.6 1.6 1.4 1.4 Luminosity 1.2 1.2 Selection 1 1 0.8 0.8 Backgrounds 0.6 0.6

Data / Prediction 0.4 Data / Prediction 0.4 Efficiency 0.2 0.2 Results 20 30 40 50 60 70 80 90 100 -2 -1 0 1 2 lepton p [GeV] η T lepton Uncertainties Statistical Luminosity • Shows the muon from the W -boson pT and η Experimental Modelling • Data / Prediction plot shown underneath Searches Searches • Statistical fluctuations mean that a few points will be away Higgs BSM • from unity and outside the uncertainty band Conclusion 75 / 105 HEP Analysis John Morris Control plots Monte Carlo What is MC? Does the MC describe the data? Why use MC? MC Generation 1800 ATLAS tagged µ + ≥ 3 jets ATLAS tagged µ + ≥ 3 jets Detector Sim 1600 1600 For Approval Data For Approval Data Reconstruction -1 1400 -1 1400 ∫ L = 4.66 fb tt ∫ L = 4.66 fb tt Reconstruction W+jets W+jets 1200 Multijet 1200 Multijet Event Properties Events / 5 GeV Events / 5 GeV Z+jets Z+jets 1000 1000 MC Corrections Single Top Single Top 800 MC Corrections 800 DiBoson DiBoson uncertainty uncertainty Re-Weighting 600 600 Tag & Probe 400 400 Smearing Summary 200 200 Measurements 0 0 1.8 1.8 Cross section 1.6 1.6 1.4 1.4 Luminosity 1.2 1.2 Selection 1 1 0.8 0.8 Backgrounds 0.6 0.6

Data / Prediction 0.4 Data / Prediction 0.4 Efficiency 0.2 0.2 Results 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 miss ET [GeV] MT(W) [GeV] Uncertainties Statistical Luminosity • Shows the Missing ET and W -boson transverse mass Experimental Modelling • MC needs to describe data across a broad range of distributions Searches Searches • A good analysis should have many control plots Higgs BSM • A good rule is to plot every variable you cut on Conclusion 76 / 105 HEP Analysis John Morris Cross section Monte Carlo What is MC? Pulling it all together Why use MC? MC Generation Detector Sim • Count events for each process and make a yield table Reconstruction Reconstruction Muon Channel Event Properties Data 14940 MC Corrections MC Corrections t¯t (MC) 9084 Re-Weighting Tag & Probe Single top (MC) 980 Smearing Z+Jets (MC) 780 Summary Measurements Diboson (MC) 59 Cross section Multijet (DD) 1310 Luminosity Selection W +Jets (DD) 2880 Backgrounds Efficiency Backgrounds 6009 Results t¯t + Backgrounds 15093 Uncertainties Statistical t¯t acceptance  0.0215 Luminosity Experimental Modelling Searches • Nobs = 14940, Nbkg = 6009 Searches −1 Higgs •  = 0.0215, BR = 0.543, L = 4.66fb BSM σt¯t = 164.2pb Conclusion 77 / 105 HEP Analysis John Morris We have a result! Monte Carlo What is MC? Why use MC? Can we publish yet? MC Generation Detector Sim Reconstruction Nobs − Nbkg Reconstruction σt¯t = = 164.2pb Event Properties L .  . BR MC Corrections MC Corrections Re-Weighting • This result is currently unusable - not even close to publication Tag & Probe Smearing • What is the uncertainty? Summary Measurements • σt¯t = 164.2 ± 1.0pb - fantastic result! World leading Cross section • σt¯t = 164.2 ± 150.0pb - Never mind, will struggle to publish Luminosity Selection Backgrounds Efficiency Now the real work begins Results Uncertainties • The uncertainty on your measurement is critical Statistical Luminosity • More important than central value Experimental Modelling • Crudely speaking Searches • Searches Small uncertainty = Good measurement Higgs • Large uncertainty = Bad measurement BSM Conclusion 78 / 105 HEP Analysis John Morris Evaluating uncertainties Monte Carlo What is MC? Why use MC? MC Generation Determining your measurements’ uncertainty Detector Sim Reconstruction Reconstruction • There are, broadly speaking, 4 main categories of uncertainty Event Properties • Let’s go through them individually MC Corrections MC Corrections • Statistical Re-Weighting Tag & Probe • Determined entirely by how many signal events you have Smearing Summary • Luminosity Measurements Cross section • We only know it to ≈ 4% Luminosity Selection • Experimental Backgrounds Efficiency • Background estimation Results • Uncertainties from re-weighting MC Uncertainties • Uncertainties from smearing MC Statistical Luminosity • Experimental Theoretical modelling uncertainties Modelling • Generator, PDF, parton shower, ISR/FSR Searches • st Searches Introduced in 1 lecture Higgs BSM Conclusion 79 / 105 HEP Analysis John Morris Offset Method Monte Carlo What is MC? Adding uncertainties in quadrature Why use MC? MC Generation Detector Sim • Imagine we have 3 uncertainties, αA, αB and αC Reconstruction • Add uncertainties in quadrature Reconstruction Event Properties • Systematics tend to be asymmetrical MC Corrections MC Corrections • ⇒ Calculate ↑ and ↓ contributions separately Re-Weighting v Tag & Probe u N Smearing q uX Summary 2 2 2 2 αtot = αA + αB + αC = t αi Measurements i Cross section Luminosity Selection Backgrounds Offset method of combining uncertainties Efficiency Results • We are going to want to combine many different uncertainties Uncertainties Statistical • We normally use the offset method to do this Luminosity Experimental • Change something and recalculate the final result Modelling Searches • Difference in results is the uncertainty Searches Higgs α = σSyst A − σNominal BSM A t¯t t¯t Conclusion 80 / 105 HEP Analysis John Morris Statistical uncertainty Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Statistical uncertainty Reconstruction Reconstruction • Determined by number of data events you have Event Properties √ MC Corrections • α = Nevents MC Corrections Re-Weighting • In our t¯t cross section Tag & Probe √ Smearing • Nobs = 14940 ⇒ αNobs = 14940 = 122.2 Summary • Recalculate cross section using Nobs ± αN Measurements obs Cross section • Stat↑ Stat↓ Luminosity σt¯t = 166.4pb σt¯t = 162.0pb Selection Backgrounds • The statistical uncertainty is Efficiency Results • αStat↑ = 166.4 − 164.2 = 2.2pb Uncertainties • αStat↓ = 162.0 − 164.2 = −2.2pb Statistical Luminosity • Our updated measurement is now: Experimental Modelling σt¯t = 164.2 ± 2.2 (Stat.) Searches Searches Higgs BSM Conclusion 81 / 105 HEP Analysis John Morris Luminosity uncertainty Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Luminosity uncertainty Reconstruction Reconstruction Nobs − Nbkg Event Properties σ = MC Corrections L .  . BR MC Corrections Re-Weighting Tag & Probe • Smearing The Luminosity at ATLAS is only known to ≈ 4% Summary • Has a direct impact on the cross section Measurements Cross section • Vary the luminosity and recalculate the cross section Luminosity Lumi↑ Lumi↓ Selection • σ ¯ = 152.7pb σ ¯ = 175.7pb Backgrounds tt tt Efficiency • Our updated measurement is now: Results Uncertainties σt¯t = 164.2 ± 2.2 (Stat.) ± 7.0 (Lumi.) Statistical Luminosity √ Experimental • As 2.22 + 7.02 = 7.3, adding in quadrature gives Modelling Searches σt¯t = 164.2 ± 7.3 (Stat. ⊕ Lumi.) Searches Higgs BSM Conclusion 82 / 105 HEP Analysis John Morris Experiment uncertainties Monte Carlo What is MC? Why use MC? MC Generation Mis-modelling of the detector Detector Sim Reconstruction • Background estimations can have significant uncertainties Reconstruction Event Properties • We know that data and MC do not agree out-of-the-box MC Corrections MC Corrections • Event re-weighting: Re-Weighting Tag & Probe • Correct MC efficiencies to match data efficiencies Smearing • Applied to most (if not all) reconstructed objects Summary Measurements • Applied to Pile-up and missing ET Cross section Luminosity • 4-vector smearing: Selection • Backgrounds Correct MC resolutions to match data resolutions Efficiency • Applied to most (if not all) reconstructed objects Results Uncertainties • Each and every re-weighting/smearing has an uncertainty Statistical Luminosity • Each uncertainty needs to be accounted for in final result Experimental Modelling • Varies between measurements according to event selection Searches Searches • Clearly, different experiments will apply different re-weightings Higgs BSM Conclusion 83 / 105 HEP Analysis John Morris Background uncertainties Monte Carlo What is MC? Why use MC? MC Generation Background estimation uncertainties Detector Sim Reconstruction Nobs − Nbkg Reconstruction σ = Event Properties L .  . BR MC Corrections MC Corrections Re-Weighting • Data-driven methods tend to have large uncertainties Tag & Probe Smearing • Don’t trust the MC for these processes Summary • Use several different data-driven techniques Measurements Cross section • Uncertainty often taken as difference of methods Luminosity Selection • In the case of the t¯t cross section Backgrounds Efficiency • QCD Multijet estimation = 1310 ± 130 events Results • W +Jets estimation = 2880 ± 350 events Uncertainties Statistical • Recalculate cross section for ↑ and ↓ cases Luminosity Experimental • That’s 4 more calculations from this page Modelling Searches • Calculate difference from the nominal result Searches Higgs • Add differences together in quadrature BSM Conclusion 84 / 105 HEP Analysis John Morris Experiment uncertainties Monte Carlo What is MC? Why use MC? MC Generation Detector Sim • All further uncertainties effect  Reconstruction Nobs − Nbkg Reconstruction σ = Event Properties L .. BR MC Corrections MC Corrections Re-Weighting Tag & Probe Re-weighting and smearing Smearing Summary • All re-weighting routines should also provide uncertainties Measurements Cross section • If not, bug the author Luminosity • If you are the author - make sure you provide uncertainties Selection Backgrounds • Efficiency Simply a case of re-running over your MC N times Results • Where N is the total number of possible variations ↑ and ↓ Uncertainties • Use different weights each time to reflect different uncertainties Statistical Luminosity • Recalculate cross section Experimental Modelling • Calculate difference from the nominal result Searches • Add differences together in quadrature Searches Higgs BSM Conclusion 85 / 105 HEP Analysis John Morris Theoretical uncertainties Monte Carlo What is MC? Why use MC? MC Generation Theoretical modelling uncertainties Detector Sim Reconstruction • Theoretical understanding (or lack of it) of what is happening Reconstruction Event Properties • See 1st lecture for introduction to MC Corrections MC Corrections • Calculation of matrix element Re-Weighting • Tag & Probe PartonDensityFunction (PDF) of the proton Smearing • Parton showing and hadronisation Summary • Initial and final state radiation (ISR/FSR) Measurements Cross section • Typically evaluated by using different signal MC samples Luminosity Selection • αTheo. is often not simply the difference from the nominal Backgrounds Efficiency • For some prescriptions you take half the difference Results • Let’s look at the PDF for a complicated case Uncertainties Statistical • Should be common across experiments Luminosity Experimental • Reality is that ATLAS and CMS do things differently Modelling • Working group set up Searches • Searches Expect convergance in 20XY Higgs BSM Conclusion 86 / 105 HEP Analysis John Morris PDF uncertainties Monte Carlo What is MC? Why use MC? MC Generation The PDF4LHC prescription Detector Sim Reconstruction • Test 3 different PDF sets Reconstruction • Event Properties CTEQ (Nominal), MSTW and NNPDF MC Corrections • Each PDF set gives an event weight, based on EventNumber MC Corrections Re-Weighting • The first weight is the PDF nominal value, followed by n Tag & Probe Smearing different tests varying a PDF eigenvector ±1σ Summary Measurements • Uncertainties are calculated differently for each PDF set Cross section 1 Luminosity • Total uncertainty is the envelope Selection 2 Backgrounds • Nominal cross section does not enter systematic Efficiency Results Uncertainties PDF Set Statistical CTEQ MSTW NNPDF Luminosity Experimental N Weights 53 41 101 Modelling N PDF eigenvectors varied ±1σ 26 20 50 Searches Uncertainty method Symmetric Asymmetric Standard Searches Hessian Hessian Deviation Higgs BSM Conclusion 87 / 105 HEP Analysis John Morris PDF uncertainties Monte Carlo What is MC? Why use MC? MC Generation Detector Sim The PDF4LHC prescription Reconstruction Reconstruction • If: Event Properties • X0 = Nominal PDF cross section (first weight, not our σt¯t ) MC Corrections • ± MC Corrections Xi = PDF eigenvector test i, varying the eigenvector by ±1σ Re-Weighting • X¯ = Mean of all PDF eigenvectors (Used for NNPDF) Tag & Probe Smearing • N = All PDF eigenvectors. This does not include the first value Summary • Measurements Then : q 2 Cross section • 1 PN/2 + −
Luminosity CT10 α = 2 i=1 Xi − Xi Selection Backgrounds q Efficiency ↑ PN 2 Results • MSTW α = i=1 (Xi − X0) : if (Xi − X0) > 0 Uncertainties q ↓ PN 2 Statistical • MSTW α = i=1 (Xi − X0) : if (Xi − X0) < 0 Luminosity Experimental Modelling q 2 • 1 PN ¯
Searches NNPDF α = N−1 i=1 X − Xi Searches Higgs BSM Conclusion 88 / 105 HEP Analysis John Morris PDF uncertainties Monte Carlo What is MC? • • Why use MC? CTEQ = 170.5 ± 5.0 pb Envelope Up = 175.5 pb MC Generation +2.6 Detector Sim • MSTW = 168.0−2.2 pb • Envelope Down = 165.1 pb Reconstruction • NNPDF = 166.8 ± 1.7 pb • 1 Envelope = 5.2 pb (3.07%) Reconstruction 2 Event Properties MC Corrections MC Corrections 210 PDF Uncertainty Re-Weighting Measured Cross Section Tag & Probe CTEQ (Symmetric Hessian) Smearing 200 MSTW (Asymmetric Hessian) Summary NNPDF (Standard Deviation) Measurements 190 Envelope Cross section Luminosity Cross Section [pb]

t 180 Selection t Backgrounds Efficiency 170 Results Uncertainties 160 Statistical Luminosity Experimental 150 Modelling 0 20 40 60 80 100 120 Searches Searches MuonChannel >= 3 Jets :: PDF Set (Offset for clarity) Higgs BSM Conclusion 89 / 105 HEP Analysis John Morris Combining channels Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections Combining electron and muon channels MC Corrections Re-Weighting • Do not want a electron results and a muon result Tag & Probe Smearing • Summary Want to combine the channels together Measurements • Relatively simple to do: Cross section Luminosity • Add event yields from electron and muon channels Selection Backgrounds • Must do this for each systematic Efficiency Results • Takes into account correlations Uncertainties Statistical Luminosity Experimental Modelling Searches Searches Higgs BSM Conclusion 90 / 105 HEP Analysis John Morris Full systematic table Monte Carlo What is MC? Relative cross section uncertainty [%] Why use MC? Source e+jets µ+jets Combined MC Generation Detector Sim Statistical Uncertainty ±1.5 ±1.3 ±1.0 Object selection Reconstruction Reconstruction Lepton energy resolution +0.4 /-0.3 +0.2 /-0.1 +0.2 /-0.1 Event Properties Lepton reco, ID, trigger +2.4 /-2.5 +1.5 /-1.5 +1.7 /-1.8 Jet energy scale +3.8 /-4.3 +3.2 /-3.6 +3.5 /-3.8 MC Corrections Jet energy resolution ±0.2 ±0.5 ±0.2 MC Corrections Re-Weighting Jet reconstruction efficiency ±0.06 ±0.06 ±0.06 Tag & Probe Jet vertex fraction +1.2 /-1.4 +1.2 /-1.4 +1.2 /-1.4 Smearing miss ET uncertainty ±0.06 ±0.08 ±0.07 Summary SMT muon reco, ID ±1.3 ± 1.3 ±1.3 Measurements 2 SMT muon χmatchefficiency ±0.6 ±0.6 ±0.6 Cross section Background estimates Luminosity Selection Multijet normalisation ± 5.2 ± 3.9 ± 4.4 Backgrounds W +jet normalisation ± 5.2 ± 5.7 ± 5.5 Efficiency Other bkg normalisation ± 0.2 ± 0.2 ± 0.1 Results Other bkg systematics +1.6 /-1.5 +2.5 /-2.0 +2.2 /-1.8 Uncertainties Signal simulation Statistical b → µX Branching ratio +2.9 /-3.0 +2.9 /-3.1 +2.9 /-3.1 Luminosity ISR/FSR ± 2.4 ± 0.9 ± 1.5 Experimental PDF ± 3.2 ± 3.0 ± 3.1 Modelling NLO generator ± 3.2 ± 3.2 ± 3.2 Searches Parton shower ± 2.2 ± 2.2 ± 2.2 Searches Total systematics ±11.2 ±10.2 ±10.5 Higgs BSM Integrated luminosity ± 3.8 ± 3.8 ± 3.8 Conclusion 91 / 105 HEP Analysis John Morris Final result Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction The final result Reconstruction Event Properties • Combining the electron and muon channels MC Corrections √ MC Corrections • The final cross section for t¯t at s = 7 TeV is Re-Weighting Tag & Probe σ ¯ = 165 ± 2(Stat.) ± 17(Syst.) ± 7(Lumi.) pb Smearing tt Summary Measurements Cross section Luminosity • The theoretical calculation is Selection Theo. +17 Backgrounds σt¯t = 167−18 Efficiency Results Uncertainties Statistical • Majority of measurement is evaluating systematics Luminosity Experimental • Uncertainty tells you the precision of a measurement Modelling Searches Searches Higgs BSM Conclusion 92 / 105 HEP Analysis John Morris Searches & Exclusions Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Searches & Exclusions Reconstruction Reconstruction • Cross sections are a basic measurement Event Properties MC Corrections • They are still very involved and complex MC Corrections • Must be measured Re-Weighting Tag & Probe • We have to understand the Standard Model before Smearing we search for physics beyond the Standard Model Summary Measurements • The LHC is a discovery machine Cross section Luminosity • Designed to search for the Higgs and BSM physics Selection Backgrounds • Exciting PhD topics with plenty of work that needs doing Efficiency Results • We search for new physics and there are 2 options: Uncertainties 1 Discovery!! Statistical Luminosity 2 No discovery - exclude a theory within certain limits Experimental Modelling • Option 2 is by far the most common Searches Searches Higgs BSM Conclusion 93 / 105 HEP Analysis John Morris Searches & Exclusions Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Methods for searching for new physics Reconstruction Reconstruction • Bump hunting Event Properties • MC Corrections Plot invariant mass distributions MC Corrections • Understand the backgrounds Re-Weighting Tag & Probe • Look for a localised excess of events - a bump Smearing • Statistical analysis Summary • Measurements ⇒ New particle ⇒ Higgs candidate Cross section • Gradient searches Luminosity Selection • Plot mass or pT distributions Backgrounds Efficiency • Understand the backgrounds Results • Study gradient of distribution Uncertainties • Statistical Deviation from SM prediction could indicate Luminosity • Quark compositness - quark sub-structure Experimental Modelling • Extra dimensions • Searches TeV gravity Searches Higgs BSM Conclusion 94 / 105 HEP Analysis John Morris Higgs Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Search for the Higgs boson Reconstruction Reconstruction • This is not a definitive Higgs analysis Event Properties • Only a quick overview MC Corrections MC Corrections • ATLAS Higgs search combines results from 5 channels Re-Weighting Tag & Probe • H → ZZ → 4` Smearing Summary • H → γγ Measurements • H → WW → eνµν Cross section Luminosity • H → bb Selection • H → ττ Backgrounds Efficiency • Combined with advanced statistical techniques Results Uncertainties • More complex than cross section e + µ combination Statistical Luminosity • Combined result provides greater significance to the result Experimental Modelling • No individual channel provides a σ = 5.0 discovery Searches • But the combination..... Searches Higgs BSM Conclusion 95 / 105 HEP Analysis John Morris Higgs Monte Carlo What is MC? Why use MC? Search for the Higgs boson H → γγ MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity • Weighted data from 2011 and 2012 shown with background Experimental Modelling • Invariant mass of 2 photons Searches Searches • Clear bump observed around 125 GeV Higgs BSM • Is is statistically significant? Not by itself Conclusion 96 / 105 HEP Analysis John Morris Higgs Monte Carlo What is MC? Why use MC? Search for the Higgs boson H → 4` MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity • Data from 2011 and 2012 shown with background Experimental Modelling • Invariant mass of 4 leptons Searches Searches • Bump observed around 125 GeV Higgs BSM • Only a few events, but are they significant? Not by themselves Conclusion 97 / 105 HEP Analysis John Morris Higgs Monte Carlo What is MC? Why use MC? Higgs boson - Combining results MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results • Global signal strength Uncertainties Statistical • µ = 0 corresponds to background-only hypothesis Luminosity • µ = 1 corresponds to SM Higgs + background hypothesis Experimental Modelling • Combined result appears to be in excess of SM Higgs Searches Searches • Uncertainties are still to large Higgs • BSM Result is consistent with SM Higgs hypothesis Conclusion 98 / 105 HEP Analysis John Morris Higgs Monte Carlo What is MC? Why use MC? Higgs boson - Combined p result MC Generation 0 Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties • p0 is the probability that the background can produce a Statistical fluctuation greater or equal to the excess observed in data Luminosity Experimental • Modelling Dotted line shows SM Higgs + background hypothesis −9 Searches • In range 122-131 GeV, p0 = 1.7x10 corresponding to σ = 5.9 Searches Higgs • σ = 5.0 is the de-facto standard for discovery in physics BSM Conclusion 99 / 105 HEP Analysis John Morris Higgs Monte Carlo What is MC? Excluding the Higgs boson via CLs Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties • CLs is a method used to exclude theories Statistical Luminosity • “It is our duty to be sceptical i.e. to try to falsify or exclude and Experimental Modelling this is not the same as, but rather complementary to, the Searches determination of confidence intervals” - A.L. Read (2000) Searches Higgs • All Higgs masses below the blue dotted line are excluded at 95% BSM Conclusion 100 / 105 HEP Analysis John Morris Recent Higgs results Monte Carlo What is MC? Why use MC? ATLAS Higgs results MC Generation Detector Sim • Mass of new particle MH = 126 ± 0.4 (Stat.) ± 0.4 (Syst.) GeV Reconstruction Reconstruction • Signal strength parameter µ = 1.4 ± 0.3 is consistent with SM Event Properties Higgs hypothesis MC Corrections MC Corrections • p = 1.7x10−9 corresponding to σ = 5.9 Re-Weighting 0 Tag & Probe Smearing • New particle decays to pairs of vector bosons whose net electric Summary charge is zero ⇒ It’s a neutral boson Measurements Cross section • Observation in diphoton (H → γγ) disfavours spin-1 hypothesis Luminosity Selection • More data needed Backgrounds Efficiency Results Uncertainties CMS Higgs results Statistical Luminosity • Mass of new particle MH = 125.3 ± 0.4 (Stat.) ± 0.5 (Syst.) GeV Experimental Modelling • Local excess observed with σ = 5.0 Searches Searches • Observation in diphoton (H → γγ) disfavours spin-1 hypothesis Higgs BSM • More data needed Conclusion 101 / 105 HEP Analysis John Morris Beyond the standard model Monte Carlo What is MC? Why use MC? MC Generation Higgs isn’t the only game in town Detector Sim Reconstruction • Reconstruction ATLAS and CMS are involved in many searches Event Properties • Super Symmetry (SUSY) MC Corrections MC Corrections • Many many different models Re-Weighting Tag & Probe • ≈ 1.3 models per SUSY theorist (some have more than 1) Smearing Summary • Extra dimensions Measurements • How many extra dimensions? Cross section Luminosity • What are their scale? Selection • How strong is gravity in these dimensions? Backgrounds Efficiency 0 0 Results • Additional Bosons - Z and W Uncertainties • Additional Quarks - b0 and t0 Statistical Luminosity • Quark compositness Experimental Modelling Searches • All analysis are producing exclusion plots Searches Higgs BSM Conclusion 102 / 105 HEP Analysis John Morris SUSY Exclusions Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental Modelling Searches Searches Higgs BSM Conclusion 103 / 105 HEP Analysis John Morris Other Exclusions Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction Reconstruction Event Properties MC Corrections MC Corrections Re-Weighting Tag & Probe Smearing Summary Measurements Cross section Luminosity Selection Backgrounds Efficiency Results Uncertainties Statistical Luminosity Experimental Modelling Searches Searches Higgs BSM Conclusion 104 / 105 HEP Analysis John Morris Conclusion Monte Carlo What is MC? Why use MC? MC Generation Detector Sim Reconstruction Summary of what I hope you have learnt Reconstruction Event Properties • Simulating physics collisions is complex, difficult but necessary MC Corrections MC Corrections • Simulating detectors is complex, difficult but necessary Re-Weighting Tag & Probe • We do a very good job Smearing Summary • We can’t get the simulation 100% accurate Measurements • We can correct MC performance to match data performance Cross section Luminosity • Re-weight MC to match MC efficiencies to data Selection Backgrounds • Smear MC 4-vectors to match MC resolutions to data Efficiency Results • Cross section analysis is actually quite involved Uncertainties Statistical • Systematic uncertainties are most of a measurement Luminosity Experimental • Higgs (probably) exists and SUSY (probably) doesn’t Modelling Searches Searches Higgs BSM Conclusion 105 / 105