Introduction to Event Generators
Bryan Webber Cavendish Laboratory University of Cambridge
Introduction to Event Generators 1 Bryan Webber, MCnet School, 2014 Introduction to Event Generators
• Lecture 1: Monte Carlo event generation ✤ theoretical foundations and limitations • Lecture 2: Parton showering ✤ parton splitting, dipoles, coherence • Lecture 3: Non-perturbative issues ✤ hadronization and underlying event • Lecture 4: Overview of results ✤ jets, W, Z, top, Higgs, BSM
Introduction to Event Generators 2 Bryan Webber, MCnet School, 2014 MC Event Generators
HERWIG http://projects.hepforge.org/herwig/ Angular-ordered parton shower, cluster hadronization
v6 Fortran; Herwig++
PYTHIA http://www.thep.lu.se/∼torbjorn/Pythia.html
kt-ordered parton shower, string hadronization v6 Fortran; v8 C++
SHERPA http://projects.hepforge.org/sherpa/ Dipole-type parton shower, cluster hadronization
C++ “General-purpose event generators for LHC physics”, A Buckley et al., arXiv:1101.2599, Phys. Rept. 504(2011)145
Introduction to Event Generators 3 Bryan Webber, MCnet School, 2014 OtherOther Relevant Software relevant software
Some examples(with (with apologies apologies for many for omissions): omissions) Other event/shower generators: PhoJet, Ariadne, Dipsy, Cascade, Vincia Matrix-element generators: MadGraph/MadEvent, CompHep, CalcHep, Helac, Whizard, Sherpa, GoSam, aMC@NLO Matrix element libraries: AlpGen, POWHEG BOX, MCFM, NLOjet++, VBFNLO, BlackHat, Rocket Special BSM scenarios: Prospino, Charybdis, TrueNoir Mass spectra and decays: SOFTSUSY, SPHENO, HDecay, SDecay Feynman rule generators: FeynRules PDF libraries: LHAPDF Resummed (p ) spectra: ResBos ? Approximate loops: LoopSim Jet finders: anti-k and FastJet ? Analysis packages: Rivet, Professor, MCPLOTS Detector simulation: GEANT, Delphes Constraints (from cosmology etc): DarkSUSY, MicrOmegas Standards: PDF identity codes, LHA, LHEF, SLHA, Binoth LHA, HepMC Can be meaningfully combined andSjöstrand, used for LHC Nobel physics! Symposium, May 2013
IntroductionTorbj¨orn Sj¨ostrandto Event Generators Challenges for4 QCD TheoryBryan Webber, slide MCnet 21/24 School, 2014 Overview of Results
http://mcplots.cern.ch/
Introduction to Event Generators 5 Bryan Webber, MCnet School, 2014 Jets
Introduction to Event Generators 6 Bryan Webber, MCnet School, 2014 Jet pT
7000 GeV pp Jets 7000 GeV pp Jets 107
6 Jet Transverse Momentum (anti-k (0.4)) Jet Transverse Momentum (anti-k (0.4)) 10 T 6 T 10
ATLAS 3M events ATLAS 3M events [pb/GeV] ≥ [pb/GeV] ≥ T 5 Herwig++ (Def) T Herwig++ (Def) 10 105
/dp Pythia 8 (Def) /dp Pythia 8 (Def)
σ Sherpa (Def) σ Sherpa (Def) d d 104 104 Rivet 1.8.3, Rivet 1.8.3,
3 103 10
2 102 10
10 10
1 1 -1 ATLAS_2011_S9128077 10 ATLAS_2011_S9128077 10-1 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 10-2 mcplots.cern.ch mcplots.cern.ch 200 400 600 800 0 200 400 600 800 p (leading jet) [GeV] p (2nd jet) [GeV] T T Ratio to ATLAS Ratio to ATLAS 1.5 1.5
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0.5 0.5 200 400 600 800 0 200 400 600 800
Leading jet Second jet
Introduction to Event Generators 7 Bryan Webber, MCnet School, 2014 Jet pT
7000 GeV pp Jets 7000 GeV pp Jets 104 6 10 Jet Transverse Momentum (anti-k (0.4)) Jet Transverse Momentum (anti-k (0.4)) T T 5 10 ATLAS 3M events ATLAS 3M events [pb/GeV] ≥ [pb/GeV] 3 ≥ T Herwig++ (Def) T 10 Herwig++ (Def) 4
/dp 10 Pythia 8 (Def) /dp Pythia 8 (Def)
σ Sherpa (Def) σ Sherpa (Def) d d 103 Rivet 1.8.3, 102 Rivet 1.8.3, 102
10 10 1
10-1 1 10-2
-3 10 ATLAS_2011_S9128077 ATLAS_2011_S9128077 10-1 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 10-4 mcplots.cern.ch mcplots.cern.ch 100 200 300 400 500 100 150 200 p (3rd jet) [GeV] p (4th jet) [GeV] T T Ratio to ATLAS Ratio to ATLAS 1.5 1.5
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Introduction to Event Generators 8 Bryan Webber, MCnet School, 2014 1
Event shapes provide information about the properties of hadronic final states from particle collisions. Suitably defined event-shape variables were among the first observables proposed to test the theory of quantum chromodynamics (QCD) [1, 2] and have been important in en- + abling progress in the theory. At e e and ep colliders, event shapes have played a crucial role in the extraction of the strong coupling constant as. They have been essential in tuning the parton shower and non-perturbative components of Monte Carlo (MC) event generators and have provided a laboratory for developing and testing analytical probes of the hadronization process. More recently, a large set of event-shape variables suitable for pp colliders has been proposed [3]. An important aspect of these variables is their normalization to the measured sum of transverse momentum or energy of all the objects in the event. It is thus expected that energy-scale uncertainties should cancel to a large extent. Event-shape variables represent a valuable tool for early measurements of the properties of QCD multijet events at the Large Hadron Collider (LHC) and the tuning of MC models [4]. This Letter presents the first measurement of hadronic event shapes with a data sample of 7 TeV proton-proton collisions collected with the Compact Muon Solenoid (CMS) detector at 1 the LHC. The data sample corresponds to an integrated luminosity of 3.2 pb . A detailed description of the CMS experiment can be found elsewhere [5]. CMS uses a right- handed coordinate system, with the origin located at the nominal collision point, the x-axis pointing towards the center of the LHC ring, the y-axis pointing up (perpendicular to the LHC plane), and the z-axis along the anticlockwise beam direction. The polar angle q is measured from the positive z-axis, the azimuthal angle f is measured in the xy plane, and the pseudora- pidity is defined as h = ln[tan(q/2)]. The central feature of the CMS apparatus is a super- conducting solenoid, of 6 m internal diameter, providing an axial field of 3.8 T. Within the field volume are the silicon pixel and strip tracker,Jet the crystalevent electromagnetic shapes calorimeter (ECAL), and the brass/scintillator hadron calorimeter7000 GeV pp (HCAL). MuonsJets are measured7000 inGeV gas-ionization pp Jets ) ) C m,C detectors embedded in the steel return yoke.Central Transverse In Thrust the (125 < p < region 200) h < 1.74, the HCALCentral Transverse cells Minor have (90 < p < 125) 1
0.2 3M events CMS | | CMS ≥ 4.1M events widths of 0.087 in pseudorapidity andHerwig++ 0.087 (Def) rad in azimuth (f≥ ). In the (h, f) Herwig++plane, (Def) and for Pythia 8 (Def) Pythia 8 (Def) h < 1.48, the HCAL cells map on to 5Sherpa (Def)5 ECAL crystal arrays to form calorimeterSherpa (Def) towers 0.15 1/N dN/d ln(T 1/N dN/d ln(1-T | | ⇥ Rivet 1.8.3, projecting radially outwards from close to the nominal interactionRivet 1.8.3, point. At larger values of h , the size of the towers increases and the matching ECAL arrays contain fewer crystals. A | | 0.1 10-1 preshower detector consisting of two planes of silicon sensors interleaved with lead is located in front of the ECAL at h > 1.479. In addition to the barrel and endcap detectors, CMS has | | 0.05 extensive forward calorimetry covering the region 3.0 < h < 5.0. CMS_2011_S8957746 | | CMS_2011_S8957746 0 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 10-2 mcplots.cern.ch mcplots.cern.ch Two event-shape variables have been studied:-10 the central-5 transverse thrust t-6 , and the-4 central-2 ln(1-T ) ? C ln(T ) thrust minor Tm, . The two variables probe different QCD radiativeC processes and are mostly m,C C Ratio to CMS Ratio to CMS sensitive to the modeling of two-1.5 and three-jet topologies. The term central1.5 ( ) indicates that C the input to the calculation of these quantities are jets in the central region of the detector 2 ( h < 1.3), where sub-leading contributions1 in the calculation of the event-shape1 variables are | | less significant, and systematic uncertainties on the jet reconstruction are smaller.
0.5 0.5 The central transverse thrust is definedmeasure as-10 [3] of the-5 momentum out of this-6 plane and-4 is defined-2 as
Âi ~p ,i nˆ T Âi ~p ,i nˆ T, t , Tc1 max | ? · |,Tm, | ? ⇥ (1) C |. (2) ? C ⌘ ⌘ nˆ T Âi p ,i C ⌘ Âi p ,i ? ? where p ,i is the transverseIntroduction momentum to Event GeneratorsTwo-jet of selected events jet thati. The are axis wellnˆ T9 which balanced maximizes have low the values sum,Bryan Webber, of these MCnet twoSchool, variables, 2014 while isotropic ? and thus minimizes t , , is called the thrustmultijet axis eventsnˆ T, . The have central high transversevalues. thrust is a measure ? C C of the momentum in the plane defined by nˆ T, and the beam axis. The central thrust minor is a The transverseC momenta of jets are used as input to the event-shape calculation. Jets are recon- structed using individual particles that have been identified, and whose energies have been measured, using a particle flow technique [6], which combines information from all subde- tectors: charged tracks in the tracker and energy deposits in the electromagnetic and hadronic calorimeters, as well as signals in the preshower detector and the muon system. The energy cal- ibration is performed separately for each particle type. As a result, the input to the jet clustering is almost fully calibrated and the resulting jets require only a small energy correction (below 10% in the central region). Jet clustering is performed using the anti-kT clustering algorithm [7] with a distance parameter R = 0.5. Five MC generators are used to produce simulated samples for comparison with the data; the specifics of each generator are detailed below. In addition to the generator-level samples, we use “full-simulation” samples, where the events produced at the generator level are processed with a simulation of the CMS detector response based on GEANT4 [8]. As event-shape distri- butions are sensitive to QCD radiation, they are primarily affected by the description of the parton showering and the hadronization process, and, to a lesser extent, by the description of multiparton interactions, which is included in all generators used.
The first generator considered is PYTHIA 6.4.22 (PYTHIA6) [9] with tune D6T [10]. In this ver- sion of PYTHIA, parton showers are ordered by mass. The second generator is PYTHIA 8.145 (PYTHIA8) [11] with tune 2C [12]. In this version of PYTHIA, parton showers are ordered by pT. The underlying event model is based on the multiple-parton interaction model of PYTHIA6, interleaved with initial- and final-state radiation. The third generator is HERWIG++ 2.4.2 [13] used with the tune of older version 2.3. The parton showering in HERWIG++ is based on the coherent-branching algorithm, with angular ordering of the showers. The underlying event is simulated using an eikonal multiple parton-parton scattering model. The fourth is MAD- GRAPH 4.4.24 [14] in conjunction with PYTHIA6, with tune D6T. Events containing from two to four jets matched to partons with pT above 20 GeV/c are produced with MADGRAPH using a matrix element (ME) calculation and subsequently passed to PYTHIA to generate parton show- ers (PS). The MLM matching procedure [15] is used to avoid double counting between the ME and PS calculations. For the matching, the minimum jet pT threshold is set to 30 GeV/c. Finally, the ALPGEN 2.13 [16] generator is used in a similar way to MADGRAPH. ALPGEN samples are produced separately for each jet multiplicity from two to six jets, matched to partons with pT above 20 GeV/c, and are weighted according to their theoretical cross section. Events produced with ALPGEN using the ME calculation are passed to PYTHIA, and the MLM matching proce- dure is used to avoid double counting. For the matching of ME partons to jets, the lower jet pT threshold is set to 20 GeV/c and the maximum distance between partons and jets is kept to its default value of DR = 0.7. The data were collected between April and August 2010. Noncollision background is removed by applying quality cuts that ensure the presence of a well-reconstructed primary vertex [17]. The selected data sample is then divided into three bins defined by pT,1, the pT of the leading jet (the jet reconstructed offline with the highest pT). The low-pT bin contains events with 90 < pT,1 < 125 GeV/c, the medium-pT bin with 125 < pT,1 < 200 GeV/c, and the high-pT bin with 3
used as inputs to the clustering algorithm to form calorimeter jets. Tracks originating from the interaction vertex [28] are associated with these calorimeter jets based on the separation in h-f space between the jet direction and track direction at the interaction vertex. In the case of par- tially overlapping jets, tracks are assigned to the jet with the minimum pT-weighted distance between each track and the jet axis. These tracks are categorized as muon, charged pion, and electron candidates, and the jet momentum is corrected by substituting their expected parti- cle energy deposition in the calorimeter with their momentum. These track-corrected jets are referred to as JPT jets.
The pT of both types of jets are corrected to the particle-level jet pT [29]. In both cases, the ra- tio of the reconstructed jet pT to the particle jet pT is close to unity, and only small additional corrections to the jet energy scale, of the order of 5–10%, are needed. These corrections are derived from GEANT4-based [30] CMS simulations, based on the pT ratio of the particle jet formed from all stable (ct > 1 cm) particles to the reconstructed jet, and also in situ measure- ments using dijet and photon + jet events [29]. The uncertainty on the absolute jet energy scale is studied using both data and MC events and is found to be less than 5% for all values of jet pT and h. In order to remove jets coming from instrumental noise, jet quality requirements are applied [31].
The JPT jets are reconstructed with the anti-kT jet clustering algorithm and distance parameter D = 0.5 [23]. The tracks associated with JPT jets are used to measure the charged-hadron multi- plicity and the transverse size of the jets in the jet pT range 50 GeV/c < pT < 1TeV/c. The PF jets reconstructed with a distance parameter D = 0.7 are used to measure the jet shapes in the jet pT rangeJet 20 GeV/c < pprofileT < 1TeV/c. Owing to the larger jet size, jet shape measurements evaluate a larger fraction of the momentum from the originating parton and are relatively more sensitive 1960 GeV ppbar to momentum depositedJets by multiple-parton7000 GeV pp interactions (MPIs), thusJets providing important in- (r) ρ
(r/R) Differential jet shapeformation ρ(r/R) (186 < p < 208) to tune both the parton showering and MPI models in the event generators. To T Differential jet shape ρ(r/R) ρ
minimizeCDF the contribution from additional pp interactionsATLAS in a triggered event (pileup), events 577k events 5.8M events
10 ≥ Herwig++ (Def) ≥ Herwig++ (Def) with onlyPythia 8 (Def) one reconstructed primary vertex are selectedPythia for 8 (Def) jet shape measurements, as the measurementsSherpa (Def) use both charged10 and neutral particles. ForSherpa charged-hadron (Def) multiplicity and jet Rivet 1.8.3, transverse size studies,Rivet 1.8.3, the events with multiple vertices are also considered as these studies use only those tracks that are associated with the primary vertex. The primary vertex is defined 1 as the vertex with the highest sum1 of transverse momenta of all reconstructed tracks pointing to it.
-1 -1 10 10 CDF_2005_S62171844 Jet observables ATLAS_2011_S8924791 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 mcplots.cern.ch mcplots.cern.ch 0 We0.5 have studied several1 observables0 to characterize0.2 the0.4 jet structure.0.6 These observables are complementary andr/R they can provide a more comprehensive picture ofr the composition of jets. Ratio to CDF Ratio to ATLAS 1.5 In order to compare the resulting1.5 measurements with theoretical predictions, all the observ- ables are corrected back to the particle level by taking into account detector effects using MC simulations. 1 1
4.1 Jet shapes4 4 Jet observables
0.5 ( ) 0.5 0 The0.5 differential jet1 shape r r is defined0 as the0.2 average fraction0.4 of the0.6 transverse momentum ρ(r)" Ψ(r)" contained inside an annulus of inner radius ra = r dr/2 and outer radius rb = r + dr/2 as 1-Ψ(r)" rb" r R" " R" illustrated in Fig. 1: ra"  pT,i 1 r Figure 1: Pictorial definition of the differential (top) and integrated (bottom) jet shape quanti- ties. Analytical definitions of these quantities are given in the text. where dr = 0.1. The integrated jet shape Y(r) is defined as the average fraction of the transverse momentum of particles inside a cone of radius r around the jet axis:  pT,i r The sums run over the reconstructed particles, with the distance r = (y y )2 +(f f )2 i i jet i jet relative to the jet axis described by yjet and fjet, and R = 0.7. q The observed detector-level jet shapes and true particle-level jet shapes differ because of jet energy resolution effects, detector response to individual particles, smearing of the jet direc- tions, smearing of the individual particle directions, and inefficiency of particle reconstruction, especially at low pT. The data are unfolded to the particle level using bin-by-bin corrections derived from the CMS simulation based on the PYTHIA 6.4 (PYTHIA6) MC generator [32] tuned to the CMS data (tune Z2). The Z2 tune is identical to the Z1 tune described in [33], except that Z2 uses the CTEQ6L [34] parton distribution function (PDF), while Z1 uses CTEQ5L [35] PDF. The correction factors are determined as functions of r for each jet pT and rapidity bin and vary between 0 and 20%. Since the MC model affects the momentum and angular distributions and flavour composition of particles in a jet, and therefore the simulated detector response to the jet, the unfolding factors depend on the MC model. In order to estimate the systematic un- certainty due to the fragmentation model, the corrections are also derived using PYTHIA8 [36], PYTHIA6 tune D6T [32], and HERWIG++ [37]. The largest difference of these three sets of cor- rection factors from those of PYTHIA6 tune Z2 is assigned as the uncertainty on the correction. This uncertainty is typically 2–3% in the region where the bulk of the jet energy is deposited and increases to as high as 15% at large radii where the momentum of particles is very small. For very high pT jets where the fraction of jet momentum deposited at large radii is extremely small, the uncertainty is less than 1% at r = 0.1 and reaches 25% at high radii. The impact of the calibration uncertainties for particles used to measure the jet shapes is studied separately for charged hadrons, neutral hadrons, and photons. The calibration of each type of particle is varied within its measurement uncertainty, depending on its pT and h. The resulting Jet multiplicity 7000 GeV pp Jets 7000 GeV pp W 108 * [pb] Jet multiplicity (anti-k (0.4)) Jet multiplicity ((E >20,|η_j|<2.8,E >20,|η_e|<2.47 ,p ^ν>25,M_T>40,∆R >0.5)) T Tj Te T µ j σ 7 10 ATLAS jets) [pb] ATLAS 2.9M events 6.8M events jet Herwig++ (Def) ≥ 4 Herwig++ (Def) ≥ N 10 Pythia 8 (Def) ≥ Pythia 8 (Def) 6 10 Sherpa (Def) Sherpa (Def) (W + Rivet 1.8.3, Rivet 1.8.3, 105 σ 103 104 103 102 102 ATLAS_2011_S9128077 ATLAS_2010_S8919674 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 10 mcplots.cern.ch mcplots.cern.ch 2 4 6 0 1 2 3 N jet Njet Ratio to ATLAS Ratio to ATLAS 1.5 1.5 1 1 0.5 0.5 2 4 6 0 1 2 3 Multijets W+jets Introduction to Event Generators 11 Bryan Webber, MCnet School, 2014 π 0.9 ALICE Preliminary K/π in pp s=7 TeV, pch 10-15 GeV/c T, jet 0.8 | ALICE TPC Coherent, uncorr. (ref.) 0.7 ALICE TPC Multi-Template, uncorr. 0.6 PYTHIA Perugia 0 + GEANT3 Uncorrected K/ 0.5 0.4 0.3 anti-k , R=0.4, |η | < 0.5 0.2 T jet p > 0.15 GeV/c 0.1 T, track |η | < 0.9 track 0 1.4 1.2 1 Scaled to ref. 0.8 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ch ALI−PREL−68942 z ch ch Figure 1: Uncorrected K/⇡ ratio as a function of z for pT,jet = 10 15 GeV/c for data and MC (PYTHIA + - anti-k Perugia0). The uncorrectedK +K results for data of the TPC CoherentT Fit (full points) arep+p compared to those 0.6 0.6 jet of the TPC Multi-Templateπ++ Fitπ- (rectangles) and the detectorR=0.4; level |η MC|<0.5 truth (open points).π++π- The error bars p track>0.15 GeV/c Chargedrepresent the statistical uncertainties andparticles the error boxes indicateT the systematic uncertainties. in jets |ηtrack|<0.9 particle ratio 0.4 0.4 -1 ) - + - c π++π K +K p+p 1 1 pp s = 7 TeV 1 0.2 ALICE Preliminary0.2 (GeV/ 10-1 -1 5-10 GeV/c -1 10-15 GeV/c track T -2 -2 -2 p 10 15-20 GeV/c 0 0 -3 -3 -3 pp s = 7 TeV c dN/d 10 0 0.2 0.4anti- 0.6k T 0.8 1 0 0.2 0.4 0.6 0.8 1 ALICE Preliminary2 jet 2 jets R=0.4; |η |<0.5 -4 5-10 GeV/c 1.5 -4 1.5 -4 10 ptrack>0.15 GeV/c 1/N 10-15 GeV/c 1 T 1 -5 -5 track -5 10 15-20 GeV/c 0.5 |η |<0.9 0.5 scaled to 5-10 GeV/ c 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 2 2 2 1 ALI−PREL−68757 1 1 zch 0 0 0 Figure 3: Corrected K/⇡ (left) and p/⇡ (right) ratios as a function of zch in charged jets from pp collisions 2×10-1 1 2 3 4 10 20 2×10-1 1 2 3 4 10 20 2×10-1 1 2 3 4 10 20 scaled to 15-20 GeV/ ch at ps = 7 TeV. The ratios for p =5 10 (diamonds), 10 15 (circles) and 15 20 GeV/ctrack(stars) are ALI−PREL−68745 T,jet p (GeV/c) shown. T Figure 2: Corrected pT spectra of ⇡ (left), K (middle) and p (right) in charged jets from pp collisions at ch pp s = 7 TeV 2.5 p 5-10 GeV/c ch 2.5 + - 2.5 ps = 7 TeV.T,jet The spectra for p π++π- =5 10ALICE (diamonds), Preliminary 10 15K (circles)+K and 15 20 GeV/c (stars)p+p are 2 T,jet 2 2 shown.MC/Data 1.5 1.5 1.5 1 1 1 0.5 0.5 0.5 2.5 pch 10-15 GeV/c 2.5 data 2.5 T,jet ch PYTHIA Perugia0 ch ch Comparing2 the ratios for the three di↵erent2 pT,jetPYTHIAbins, Perugia0NoCR a scaling is observed2 for z > 0.2 in all pT,jet bins PYTHIA6 PYTHIA Perugia2011 1.5 ch 1.5 1.5 for the K/⇡ ratio and for pT,jet = 10 15 and 15 20 GeV/c in case of p/⇡. Data In Fig.1 4, the spectra shown in Fig. 21 are compared to the PYTHIA [9]1 tunes Perugia0, Perugia0NoCR 0.5 0.5 0.5 (noCR2.5stands for no colour reconnection2.5 ) and Perugia2011jet [10] for ⇡,2.5 K and p. The best agreement is anti-k ; R=0.4; |η |<0.5 pch 15-20 GeV/chc T 2 T,jet 2 ptrack>0.15 GeV/c ; |ηtrack|<0.9 2 observed at high pT,jet and high particle pT.T For low particle pT, all considered PYTHIA tunes undershoot (overshoot)1.5 the pions (protons). Typically,1.5 all three tunes describe the data1.5 within 30% except for protons 1 1 1 with pT0.5< 0.5 GeV/c, where the deviation0.5 goes beyond 100%, and with 0.5pT close to the upper bound of the ch 2×10-1 1 2 3 4 5 6 10 20 2×10-1 1 2 3 4 5 6 10 20 2×10-1 1 2 3 4 5 6 10 20 pT,jet bin, where the discrepancy is around 50% for some tunes. The maximum of the proton spectra around p =2GeV/c (cf. Fig. 2) is reproduced very well by all PYTHIA tunes, but they fail to describeptrack the (GeV/ widthc) ALIT −PREL−68777 T and the high-pT slope. Of the tunes considered, Perugia0NoCR gives the best description of the K spectra in all pch bins. FigureT 4:,jet MC/data ratios of the ⇡ (left), K (middle) and p (right) pT spectra in charged jets from pp collisions at ps = 7 TeV. ALICE, arXiv:1408.5723 Introduction to Event 4Generators Conclusions 123 Bryan Webber, MCnet School, 2014 We presented the first measurement of identified jet fragmentation of charged hadrons at hadron colliders ch from ALICE. The particle yields and ratios as functions of pT and z of primary hadrons (⇡,K,p)in ch charged jets from pp collisions at ps =7TeVwithpT,jet =5 20 GeV/c are extracted using advanced PID ch ch ch techniques. We observe that the pT,jet scaling of the z spectra disappears at lowest pT,jet. Furthermore, our measurements show an increase of the strangeness fraction with zch and a suppression of leading baryons at high zch. PYTHIA simulations reproduce the data typically within 30% accuracy. However, we observe ch a tension between data and PYTHIA at low pT,jet and for pions and protons at low particle pT. 4 Multiplicities in Z0 decay + Hadron multiplicities in e e at 91 GeV Nch ⇡± LEP, SLD 10 1 ⇡0 Pythia 8.145 Sherpa 1.2.3 multiplicity Herwig++ 2.5.0 K± K0 1 ⌘ p 0 0, K⇤ D ± ⇤ 0, B ± ⌘0 ⌃± 1 10 1.3 1.2 1.1 1.0 0.9 MC/data 0.8 0.7 Nch 0 1 2 5 mass [GeV] Introduction to Event Generators 13 Bryan Webber, MCnet School, 2014 (a) LEP/SLD identified particle multiplicities [157] Mean p vs particle mass ? 1.4 STAR [GeV] i Pythia 8.145 ? 1.2 p h Sherpa 1.2.3 1 Herwig++ 2.5.0 0.8 0.6 0.4 K0 p¯ ⇤¯ ⌅¯ + 0.2 0 0 ⇡ K ⇢ K⇤ ⇤ ⌅ ⌃ (⌦+⌦¯) 0 1.4 1.2 1 MC/data 0.8 0.6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 mass [GeV] (b) STAR identified particle mean p [354] ? + Figure 27: Identified hadron multiplicities in e e collisions at the Z peak and p vs. particle mass in pp collisions at 200 GeV. These observables are determined primarilyh ?i by the tuning of the hadronization models, both the flavour and kinematic aspects, but the overall multiplicities are also strongly dependent on the tuning of the parton showers (and MPI models, for the hadron collider observables). Up-to-date versions of these plots can be found at http://mcplots.cern.ch/. 167 Min Bias and Underlying Event Introduction to Event Generators 14 Bryan Webber, MCnet School, 2014 + + Min bias pT(p , K ) 200 GeV pp Soft QCD 200 GeV pp Soft QCD ] ] -2 10 -2 0.22 pT(π+) pT(K+) [GeV [GeV STAR 7M events 0.2 STAR 7M events ≥ ≥ dy Herwig++ (Def) dy Herwig++ (Def) T T N N 2 Pythia 8 (Def) 2 0.18 Pythia 8 (Def) d d dp dp T Sherpa (Def) T Sherpa (Def) p 0.16p π π Rivet 1.8.3, Rivet 1.8.3, 1 1 2 0.142 1 0.12 0.1 0.08 0.06 0.04 10-1 STAR_2008_S7869363 STAR_2008_S7869363 0.02 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 mcplots.cern.ch mcplots.cern.ch 0.2 0.4 0.6 0.8 0.2 0.4 0.6 p [unit{GeV} ] p [unit{GeV} ] T T Ratio to STAR Ratio to STAR 1.5 1.5 1 1 0.5 0.5 0.2 0.4 0.6 0.8 0.2 0.4 0.6 Introduction to Event Generators 15 Bryan Webber, MCnet School, 2014 Underlying Event 900 GeV pp Underlying Event 7000 GeV pp Underlying Event 〉 〉 φ φ d d 3 η 0.9 η Average Charged Particle Density (TRNS) (|η| < 2.5, p > 0.1 GeV/c) Average Charged Particle Density (TRNS) T /d N/d chg 2 0.8 CMS ATLAS 7.3M events 6.8M events d 〈 ≥ ≥ Herwig++ (Def) N Herwig++ (Def) 2 2.5 d Pythia 8 (Def) 〈 Pythia 8 (Def) 0.7 Sherpa (Def) Sherpa (Def) 0.6 Rivet 1.8.3, 2 Rivet 1.8.3, 0.5 1.5 0.4 0.3 1 0.2 CMS_2011_S9120041 ATLAS_2010_S8894728 0.5 0.1 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 mcplots.cern.ch mcplots.cern.ch 0 10 20 0 5 10 15 20 p (leading track-jet) [GeV] p (leading track) [GeV] T T Ratio to CMS Ratio to ATLAS 1.5 1.5 1 1 0.5 0.5 0 10 20 0 5 10 15 20 Transverse charged particle density Introduction to Event Generators 16 Bryan Webber, MCnet School, 2014 Underlying Event 900 GeV pp Underlying Event 7000 GeV pp Underlying Event 〉 〉 T T p p 〈 Average p vs p (TRNS) (|η| < 2.5, p > 0.5 GeV/c) 〈 Average p vs p (TRNS) (|η| < 2.5, p > 0.5 GeV/c) T T1 T 1.6 T T1 T 1.4 ATLAS ATLAS 7.3M events 6.8M events Herwig++ (Def) ≥ Herwig++ (Def) ≥ Pythia 8 (Def) 1.4 Pythia 8 (Def) Sherpa (Def) Sherpa (Def) 1.2 Rivet 1.8.3, 1.2 Rivet 1.8.3, 1 1 0.8 0.8 0.6 0.6 ATLAS_2010_S8894728 ATLAS_2010_S8894728 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 0.4 mcplots.cern.ch 0.4 mcplots.cern.ch 2 4 6 8 10 0 5 10 15 20 p (leading track) [GeV] p (leading track) [GeV] T T Ratio to ATLAS Ratio to ATLAS 1.5 1.5 1 1 0.5 0.5 2 4 6 8 10 0 5 10 15 20 Transverse mean pT Introduction to Event Generators 17 Bryan Webber, MCnet School, 2014 Vector Bosons Introduction to Event Generators 18 Bryan Webber, MCnet School, 2014 0 Z pT Absolute normalization Normalized to data 1960 GeV ppbar Z (Drell-Yan) 7000 GeV pp Z (Drell-Yan) ] -1 103 p (Z) (muon channel) p (Z) (electron channel, dressed) T T [GeV 1 T 2 D0 ATLAS 7M events ≥ 10 7.9M events ≥ Herwig++ (Def) /dp Herwig++ (Def) (Z) [pb/GeV] σ T Pythia 8 (Def) Pythia 8 (Def) d 10-1 10 Sherpa (Def) σ Sherpa (Def) /dp 1/ σ d Rivet 1.8.3, Rivet 1.8.3, 1 10-2 10-1 10-3 10-2 10-4 10-3 -5 D0_2010_S8671338 10 ATLAS_2011_S9131140 10-4 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 mcplots.cern.ch mcplots.cern.ch 0 100 200 300 0 100 200 300 p (Z) [GeV] p (ee) [GeV] T T Ratio to D0 Ratio to ATLAS 1.5 1.5 1 1 0.5 0.5 0 100 200 300 0 100 200 300 Introduction to Event Generators 19 Bryan Webber, MCnet School, 2014 Limitations of LO+parton shower 0 Hard subprocess: qq¯ Z /W ± • ! pT(Z) pT(jet 1) pT(jet 2) • Leading-order (LO) normalization need next-to-LO (NLO) • Worse for high pT and/or extra jets need multijet merging Introduction to Event Generators 20 Bryan Webber, MCnet School, 2014 Matching & Merging • Two rather different objectives: • Matching parton showers to NLO matrix elements, without double counting • MC@NLO Frixione, BW, 2002 • POWHEG Nason, 2004 • Merging parton showers with LO n-jet matrix elements, minimizing jet resolution dependence • CKKW Catani, Krauss, Kühn, BW, 2001 • Dipole Lönnblad, 2001 • MLM merging Mangano, 2002 • See lectures by Stefan Prestel Introduction to Event Generators 21 Bryan Webber, MCnet School, 2014 Z0 at Tevatron http://mcplots.cern.ch/ • Absolute normalization: LO too low • POWHEG agrees with rate and distribution Introduction to Event Generators 22 Bryan Webber, MCnet School, 2014 10 5 Rapidity Distribution14 Results 6 Transverse Momentum Distribution Results Z0 at LHC12 5 Results 0.4 -1 ] ] 10 -1 -1 CMS preliminary CMS CMS 10-2 18.4 pb-1 at s=8 TeV 0.35 [GeV ∫ -1 T 10-2 L dt = 36 pb at s = 7 TeV ∫ /dq 10-3 σ [(GeV) T 0.3 d σ q |η <| 2.1, p > 20 GeV T 1/ -4 /d -3 10 -1 σ 10 0.25 L dt = 36 pb at s = 7 TeV data (e + µ combined) p > 20 GeV |η|< 2.1, T ∫ d /d|y| -5 σ 10 data σ POWHEG + CT10 Pythia/Powheg Z2star 0.2 1/ -4 10 FEWZ CTEQ12NNLO ) d ] -6 -1 0.06 10 σ [GeV 0.05 0.15 T q (1/ -7 -5 /d 10 10 σ 0.04 data (e and combined) d µ σ q [GeV] 1/ T 0.1 0.03 4 POWHEG + CT10 -6 0.02 0.05 10 data / theory 2 0.01 0 5 10 15 20 25 30 q [GeV] T -7 10 0 0 0.5 1 1.5 2 2.5 3 3.5 1 10 102 20 30 40 50 60 70 100 200 300 400 500 q [GeV] |y| q [GeV] T T Figure 6: The normalized differential cross section of transverse momentum of the dimuon Figure 2: The normalized differential cross section for Z bosons as a function of the absolute system from Z boson decay in data (points) compared with the predictions from POWHEG and value of rapidity, combining the muon and electron channels. The error barsFigure correspond 6: The Z-bosonto transverse momentum distribution found from combining the muon the experimental statistical and systematic uncertainties added in quadrature. The shaded area FEWZ for qT > 20 GeV/c. The horizontal lines indicate the bin boundaries and the data points and electron channels, compared to the predictions of the POWHEG generator interfaced with indicates the range of variation predicted by the POWHEG simulation for the uncertainties of are positioned at the average of the entries in the bins. The bands in the upper plot represent CMS, PRD85(2012)032002PYTHIA using the Z2 tune. The error bars correspond to the statistical and systematic uncertain- CMS PAS SMP-12-025 the CT10 PDFs. the uncertainty on the predictions from factorization and renormalization scales and PDFs. ties added in quadrature. The band around the theoretical prediction includes the uncertaintiesThe lower plot shows the ratio between the data and the theory predictions. The bands in the due to scale variations and PDFs. The horizontal error bars indicate the bin boundaries,lower and plot the represent one standard deviation range for combined theoretical and experimental data points are positioned at the center-of-gravity of the bins, based on the POWHEGuncertainties.prediction. The inset figure shows the low qT region on a linear scale. • Normalized to data • POWHEG agrees with distribution (and NNLO) Introduction to Event Generators 23 Bryan Webber, MCnet School, 2014 POWHEG matrix elements [K. Hamilton, J. Tully, P. Richardson – JHEP 0810 (2008) 015] + Drell-Yan pp Z l l at Tevatron Run II, pp W l ¯ at LHC 7 TeV W asymmetry at LHC Electron channel ( y < 1) Muon charge asymmetry in W decays | Z| ⇥ ⇥ µ A 0.3 10 1 ATLAS+CMS+LHCb /d DØ data ATLAS data 0.3 s=7 TeV ⇤ d Herwig++ LO Herwig++ LO 0.25 ⇤ Herwig++ Powheg Herwig++ Powheg Preliminary 1/ 0.2 1 0.2 0.15 0.1 pl > 20 GeV 1 10 T 0.1 0 0.05 -1 2 ATLAS (extrapolated data, W → lν) 35 pb 10 -1 0 Lepton charge asymmetry -0.1 CMS (W→ µν) 36 pb 1.4 1.4 LHCb (W→ µν) 36 pb-1 1.2 1.2 MSTW08 prediction (MC@NLO, 90% C.L.) 1 1 -0.2 CTEQ66 prediction (MC@NLO, 90% C.L.) MC/data 0.8 MC/data 0.8 HERA1.0 prediction (MC@NLO, 90% C.L.) 0.6 0.6 -0.3 2 1 10 10 1 0 0.5 1 1.5 2 0 0.5 1 1.5 2 2.5 3 3.5 4 ⇥ µ N(µ+) N(µ ) | | ⏐ η ⏐ ⌘ = log tan(✓ /2) Aµ = + µ µ (a) N(µ )+N(µ ) ATLAS-CONF-1211-129 Figure 2: The lepton charge asymmetry from W-boson decays in bins of absolute pseudorapidity for the three di erent experiments ATLAS, CMS and LHCb. The asymmetry results of the LHCb and CMS Asymmetry probesCollaborations parton are obtained distributions from the muon channel only and have been communicated within the LHC Simon Pl¨atzer (DESY Theory Group) Herwig++ @ higher orders• Electroweak5/21 Working Group by representatives of the respective collaborations. ¯ + + ud W µ 4⌫ Acknowledgmentsvs du¯ W µ ⌫¯µ ! ! µ ! ! We wish to thank the LHC Electroweak Working Group, in particular M. Mangano, T. Shears, R. Mc- Nulty, M. Pioppi, P. Tan and G. H. de Monchenault for fruitful discussions on the definition of a common Introduction to Event Generators fiducial phase24 space and for the communication of theBryan LHCb andWebber, CMS results.MCnet School, 2014 3 16 W+jets at LHC10 Results CMS, JHEP01(2012)010 CMS ATLAS, PRD85(2012)092002 104 36 pb-1 at s = 7 TeV W→lν + jets -1 Data 2010, s=7 TeV 10 ALPGEN n-jets) W → eν CMS ≥ SHERPA (W) jet jets) [pb] 3 σ 10 PYTHIA(PS only) ET > 30 GeV jet BLACKHAT-SHERPA jet N -1 ≥ ET > 30 GeV (W + ATLAS 36 pb at s = 7 TeV σ 0.4 10-2 2 W → eν (W + 10 data σ energy scale unfolding -1 Ldt=36 pb -3 ∫ 0.3 10 MadGraph Z2 10 anti-k jets, R=0.4 MadGraph D6T { merged T pjet>30 GeV, | yjet|<4.4 Pythia Z2(PS only) T Charge asymmetry 1 0.2 0.2 data n-jets) ≥ MadGraph Z2 (n-1)-jets) 1 ≥ 0.1 0.1 Pythia Z2 Theory/Data (W + σ (W + 0 0 σ ! 1 2 3 4 ≥0 ≥1 ≥2 ≥3 ≥4 0123 inclusive jet multiplicity, n Inclusive Jet Multiplicity, N jet inclusive jet multiplicity, n Figure 10: The ratios (W+ n jets)/ (W) (top) and (W+ n jets)/ (W+ (n 1) jets) ⇥Very good agreement with⇥ predictions⇥ from merged simulations, (bottom) in the electron channel• compared with the expectations from twoFigure MAD 1:G Left:RAPH ThetunesW + n-jets cross section, in inclusive jet multiplicity bins, measured by ATLAS 11.Right: and PYTHIA. Points with errorwhile bars correspond parton toshower the data. alone The uncertainties starts to due fail tothe for the lepton energy njet charge≥ 2 asymmetry in jet multiplicity bins for W events, as measured by CMS 13. scale and unfolding procedure are shown as yellow and hatched bands, respectively. The error bars represent the totalIntroduction uncertainty. to Event Generators 25 Bryan Webber, MCnet School, 2014 miss (typically ET > 25 GeV). Both experiments use the anti-kt algorithm to reconstruct jets, CMS albeit with different radius parameter settings (R =0.4atATLAS,0.5atCMS).Crosssections -1 are generally presented within a fiducial volume, and corrected to the level of particles entering 36 pb at s = 7 TeV 10-1 the detector, to minimise dependence on theoretical corrections. n-jets) W → µν ≥ (W) jet σ The first benchmark is to measure the inclusive jet rates produced in association with the ET > 30 GeV 11 12 13 (W + W or Z (see Fig. 1) .BothexperimentsfindthepredictionsofALPGENandSHERPA, σ -2 10 and the latest NLO predictions from BLACKHAT, provide a good description of the data, data energy scale within uncertainties. The data uncertainties are dominatedbytheuncertaintyonthejetenergy unfolding -3 scale. This, along with some other uncertainties, can be partially cancelled by taking ratios, 10 MadGraph Z2 13 MadGraph D6T such as W + n-jets/W +(n − 1)-jets, as measured at CMS .ATLASmeasurealsotheratio Pythia Z2 of W +jet/Z+jet as a function of the jet pT threshold (see Fig. 2) 14,whichbenefitsfromthis cancellation while also testing the evolution of the predictions with increasing scale, and being 0.2 sensitive to any new physics appearing preferentially in oneoftheW or Z channels. CMS also + − n-jets) σ(W )−σ(W ) ≥ 13 (n-1)-jets) measure the W charge asymmetry (AW = + − )inbinsofinclusivejetmultiplicity ≥ 0.1 σ(W )+σ(W ) (W + (see Fig. 1). The data show a trend for reduced charge asymmetry at higher jet multiplicity, σ (W + 0 σ 1 2 3 4 possibly due to the increased importance of gluon instead of valence quark initial states. This inclusive jet multiplicity, n trend is reproduced in event generators which include explicit matrix elements for multiple Figure 11: The ratio (W+ n jets)/ (W) (top) and (W+ n jets)/ jet(W production,+ (n 1) jets but) not in PYTHIA which relies on the parton shower to produce multiple jets. ⇥ ⇥ ⇥ (bottom) in the muon channel compared with the expectations from twoATLAS MADG alsoRAPH measuretunes a number of differential distributions in V+jet production, from individual and PYTHIA. Points with error bars correspond to the data. The uncertaintiesjet momenta due to the energy and rapidity (y)distributions,tocorrelationsbetweenjetsandtheboson,suchas scale and unfolding procedure are shown as yellow and hatched bands, respectively.∆y(lepton, The jet), error∆y(jet, jet), dijet mass distributions in different jet bins. These distributions bars represent the total uncertainty. pick out many different aspects of the underlying physics. For example, the azimuthal angular separation, ∆φ(jet, jet), (see Fig. 2) highlighting the failure of the parton shower only approach in PYTHIA to produce well separated jets, and is also sensitive to multiple hard parton interactions producing a separate balanced (back-to-back) jet system in association with the Z. 3 V + Heavy Flavour Jets Further information on the underlying physics can be obtained by identifying the flavour of hadrons produced within jets. Measuring the production of W +charm, for example, gives a Top Quark Introduction to Event Generators 26 Bryan Webber, MCnet School, 2014 5 600 700 ATLAS ATLAS 600 -1 500 -1 ∫ L dt = 2.05 fb ∫ L dt = 2.05 fb 500 400 Entries / 10 GeV Data 2011 Entries / 10 GeV Data 2011 400 MC@NLO 300 MC@NLO 300 200 200 100 100 0 0 20 40 60 80 100 120 140 160 180 200 40 60 80 100 120 140 160 180 Lepton p [GeV] b-tagged jet p [GeV] T T (a) (b) Fig. 1 The distribution of (a) lepton pT and (b) b-tagged jet pT for the selected events compared to the MC@NLO simulation of tt¯ events. The data is shown as closed (black) circles with the statistical uncertainty. The MC@NLO prediction is normalised Top quarkto the data and is shown as a solid pairs (red) line. The overflow events5 at highatpT are added LHC into the final bin of each histogram. 350 600 600 700 ATLAS ATLAS 300 ATLAS -1 ATLAS L dt = 2.05 fb 600 -1 500 -1-1 dN / d|y| 500 L dt = 2.05 fb L L dt dt = = 2.05 2.05 fb fb ∫ ∫ 250 ∫∫ 500 400 400 Events / 20 GeV Data 2011 Entries / 10 GeV Data 2011 Entries / 10 GeV 200 Data 2011 400 MC@NLO 300 MC@NLOMC@NLO 300 150 300 200 200 200 100 Data 2011 100 100 MC@NLO 100 50 0 00 0 20 40 60 80 100 120 140 160 180 200 4050 60 100 80 100 150 120 200 140 160 250 180 300 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Lepton p [GeV] Leading additionalb-tagged jet jet p p [GeV] [GeV] T TT Leading additional jet |y| -1 -1 CMS Preliminary,(a) 12.1 fb at s = 8 TeV (b)(a) -1 CMS Preliminary,(b) 12.1 fb at s = 8 TeV ×10-3 CMS Preliminary, 12.1 fb at s = 8 TeV 25 -1 -1 t 0.8 Data t e/µ + Jets Combined Data e/µ + Jets Combined σ DataMC@NLOT Fig. 1 The distribution of (a) lepton pT and (b) b-tagged jetFig.pTd for 2 theDistribution selectede/µ + eventsJets of (a) Combined compared leading additional to the jet p andsimulation (b) leading additional jet rapidity in the selected events compared dy MadGraph -2 MadGraph GeV ¯ GeV [email protected] MC@NLO¯ to the1 simulation of tt events.MadGraph The data is shown as closed (black) circles with the statistical uncertainty. The of tt events. The data is shown as closed (black) circles with the statisticalσ uncertainty. The prediction is normalised 10 20 MC@NLO MC@NLO t t MC@NLO t T to the datat T and is shown as a solid (red) line. The overflow events at highpredictionpT are is added normalised into the to final the databinMC@NLO of and each is histogram. shown as a solid (red) line. In the p distribution, the overflow events σ POWHEG σ POWHEG d T at high p 0.6are added into the final bin of the histogram. In the rapidityd distribution, variable bin sizes are used such that the dp dm POWHEG 1 σ bin edges match the rapidity intervals used to construct the gap fractions. 1 -3 35015 σ 10 6000.5 ATLAS 300 ATLAS 0.4 -1 L dt = 2.05 fb -4 -1 dN / d|y| 500 10 10 L dt = 2.05 fb ∫ 250 ∫ 0.3 400 0.2 -5 Events / 20 GeV 2005 Data 2011 10 MC@NLO 3000.1 150 0 10-6 0 50 100 150 200 250 300 0 400 600 800 1000 1200 1400 1600 200-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 100 ptt GeV Data 2011 tt T ytt m GeV MC@NLO 50ATLAS, arXiv:1203.5015 100 Frixione, Nason, BW, JHEP 08(2003)007 0 0 CMS50 PAS 100 TOP-12-027 150 200 250 300 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2Alioli, Nason, Oleari, Re, JHEP 06(2010)043 Leading additional jet p [GeV] Introduction to Event GeneratorsT Leading 27additional jet |y| Bryan Webber, MCnet School, 2014 (a) (b) Fig. 2 Distribution of (a) leading additional jet pT and (b) leading additional jet rapidity in the selected events compared to the MC@NLO simulation of tt¯ events. The data is shown as closed (black) circles with the statistical uncertainty. The MC@NLO prediction is normalised to the data and is shown as a solid (red) line. In the pT distribution, the overflow events at high pT are added into the final bin of the histogram. In the rapidity distribution, variable bin sizes are used such that the bin edges match the rapidity intervals used to construct the gap fractions. 17 Top quark mass measurements • Tevatron combined top mass measurement19 17 still the worlds best But LHC is making progress…Top quark mass Top measurements Mass • Tevatron combined top mass measurement ATLAS best ATLAS still the worlds best best CMS best D0 best CDF Now includes 2 new CDF result on full run-II data PRL 109 152003Now & CDF includes note 10810 2 new CDF result on full run-II data PRL 109 152003 & CDF note 10810 • Work towardsm(t) LHC = massm(t)173.20 = combination173.20 ± 0.51 ± 0.51 ± 0.71 on± 0.71 going GeV GeV – Common treatment = 173.20of modeling = 173.20 ± uncertainties0.87 ± 0.87 GeV GeV (e.g. hadronisation) will be important Systematics dominant! • Also: CMS Measurement• of m(t) – m(t) Wouter Verkerke, NIKHEF Wouter Verkerke, NIKHEF ! test of CPT theorem Introduction to Event Generators 28 Bryan Webber, MCnet School, 2014 CMS-PAS-TOP-12-031 !mt = "272 ±196 ±122 MeV Wouter Verkerke, NIKHEF 12 4 Results 8 4 Results 4.3 b-quark observables 4.2 Initial and final state radiation 9 The b-quarks carry the colour charge of their parent top quark and are thus colour-connected 4.2 Initial and final state radiation to either initial state radiation or the beam remnants. To test the sensitivity to the b-quark We observe a small dependence on the pToT of look the for tt systemeffects due and to in initial the HT andand finalmtkinematicst statedistributions radiation we have (ISR/FSR), studied we transverse investigate momentum the jet mul- (p ) and pseudo-rapidity ( ⇥ ) of the b- T,b | b| that is well described by all of the simulations.tiplicity, Below transverseHT of hadronic 200 GeV energy and mt (tHofTquark, 400 defined GeV from asthere the the hadronic scalar sum top of quark the pT decayof the and four the leading spatial correlations between the b’s from the is a strong turn-on effect. For the jet multiplicity we observe indications of a small sensitivity jets), invariant mass and transverse momentumtwo top of quarks the tt ( system. Rbb and We note bb). that These the are jet p shownT thresh- in Figs. 9, 10, 11 and 12, respectively. The as a function of increasing jet multiplicity. However, the limited statistics of the current dataset old cut of 30 GeV used in theTop analysis willlimited excludemass sample any effects sizes allow from& softer no clearkinematics radiation. separation The of results different models in events with high b-jet pT preclude any firm conclusions. are shown in Figs. 5, 6, 7, and 8, respectively.(Fig. 9c). CMS preliminary, s = 7 TeV, lepton+jets CMSCMS preliminary, preliminary, s = 7s TeV, = 7 TeV,lepton+jets lepton+jets CMSCMS preliminary, preliminary, s = 7s TeV, = 7 TeV,lepton+jets lepton+jets CMS preliminary, s = 7 TeV, lepton+jets 15 -1 -1 20 -1 -1 Data (5.0 fb ) Data (5.0Data fb (5.0-1) fb ) Data (5.0Data fb (5.0) fb-1) Data (5.0 fb ) MG, Pythia Z2 45 MG, Pythia Z2 MG, Pythia Z2 MG, Pythia Z2 MG, Pythia Z2 15 MG, PythiaMG, Pythia P11 Z2 MG, Pythia P11 > [GeV] 10 > [GeV] 25 Powheg, Pythia Z2 Powheg,Powheg, Pythia Pythia Z2 Z2 100> [GeV] MG, PythiaPowheg, P11noCR Pythia Z2 MG, Pythia P11noCR 1D t Powheg, Pythia Z2 10 Powheg, Pythia Z2 1D t MC@NLO, Herwig 40 MC@NLO, Herwig 1D t MC@NLO, Herwig 10 MC@NLO,MC@NLO, Herwig Herwig MC@NLO, Herwig 5 - 35 - m [GeV] data - MG Z2 m [GeV] data - MG Z2 data - MG Z2 p [GeV] p [GeV] tt HT [GeV]tt T,b,had HT [GeV] T,b,had (a) (a) (b) (a) (b) CMS PAS(b) TOP-12-029 CMS preliminary, s = 7 TeV, lepton+jets CMSCMS preliminary, preliminary, s = 7s TeV, = 7 TeV,lepton+jets lepton+jets CMSCMS preliminary, preliminary, s = 7s TeV, = 7 TeV,lepton+jets lepton+jets CMS preliminary, s = 7 TeV, lepton+jets 0.1 -1 -1 15 -1 15 -1 Data (5.0 fb ) Data (5.0Data fb (5.0-1) fb ) Data (5.0Data fb (5.0) fb-1) Data (5.0 fb ) 10 MG, Pythia Z2 MG, Pythia Z2 MG, Pythia Z2 0.14 MG, Pythia Z2 MG, Pythia Z2 MG, PythiaMG, Pythia P11 Z2 MG, Pythia P11 0.08 > [GeV] > [GeV] > [GeV] 10 Powheg, Pythia Z2 0.12 Powheg,Powheg, Pythia Pythia Z2 Z2 0.03 MG, PythiaPowheg, P11noCR Pythia Z2 MG, Pythia P11noCR 2D t Reconstructed top mass depends on kinematics Powheg, Pythia Z2 Powheg, Pythia Z2 2D t MC@NLO, Herwig MC@NLO, Herwig 2D t 10 • MC@NLO, Herwig MC@NLO,MC@NLO, Herwig Herwig MC@NLO, Herwig 5 JES - 0.082D t 2D t 2D t 5 m 0.04 m m 0 0.06 0 But different generators track data well with same input mass • 0.01 0.02 0.04 -5 0 0.02 -5 0 0 -10 0 -5 -0.02 -15 -0.02[GeV] -0.01 -10 [GeV] [GeV] 0.02200 300 400 500 600 700 800 900 1000 Introduction0.051002005 150 200 300to 250Event 400 300 500Generators 350 600 400 450 700 500 800 550 900 600 1000 0.02 1010050 150 200 100 250 30029 150 350 400 200 450 500 550 250 600 5 50Bryan 100 Webber, 150 MCnet 200 School, 250 2014 0 0 0 0 0 0 -0.02 -0.05 -5 -0.02 -10 -5 200 300 400 500 600 700 800 900 1000 100200 150 200 300 250 400 300 500 350 600 400 450 700 500 800 550 900 600 1000 10050 150 200 100 250 300 150 350 400 200 450 500 550 250 600 50 100 150 200 250 data - MG Z2 m [GeV] data - MG Z2 m [GeV] data - MG Z2 data - MG Z2 data - MG Z2 data - MG Z2 p [GeV] p [GeV] tt HT [GeV]tt T,b,had HT [GeV] T,b,had (c) (c) (d) (c) (d) (d) Figure 6: Differential measurements asFigure a function 5: Differential of the invariant measurements mass of as the aFigure t functiont system: 9: Differential of (a)HT, defined measurements as the scalar as sum a function of the ofpT theof pT of the b-jet assigned to the hadronic Number of permutations per mtt bin; (b)themt fourfrom leading the 1D jets: analysis; (a) Number (c) JES of and permutations (d)decaymt from branch: per the H (a)T bin; Number (b) m oft from permutations the 1D analysis; per pT,b,had (c) bin; (b) mt from the 1D analysis; (c) 2D analysis, respectively. The systematicJES uncertainties and (d) mt from are added the 2D in analysis, quadrature respectively.JES to and the (d)statis- Themt from systematic the 2D uncertainties analysis, respectively. are added The in systematic uncertainties are added in tical uncertainties of the data. The hatchedquadrature areas indicate to the statistical the statistical uncertainties uncertaintiesquadrature of the on data. the to The the statistical hatched areas uncertainties indicate the of the statistical data. The hatched areas indicate the statistical simulated samples. uncertainties on the simulated samples.uncertainties on the simulated samples. Top mass & hadronization 1. Hard Process M. Mangano, Top LHC WG, July 2012 2. Shower evolution h h h 3. Gluon splitting – B h q h h h h h q _ g h h q b q _ q q _ g q q g _ q q g 4. Formation of g b “even” clusters e and cluster decay t W to hadrons _q nu q _ 5. Formation of t “odd” cluster 6. Decay of “odd” clusters, if large cluster mass, and decays to hadrons • Study dependence of reconstructed mass on “odd” clusters Introduction to Event Generators 30 Bryan Webber, MCnet School, 2014 Top mass & hadronization Mangano, Top LHC WG, July 2012 Controlled by perturbative shower evolution, mostly insensitive to hadronization modeling Partly shower evolution, partly color reconnection, ambiguous paternity e t Out-of-cone radiation, W _q nu controlled by perturbative q shower evolution, minimally _ sensitive to hadronization t modeling Introduction to Event Generators 31 Bryan Webber, MCnet School, 2014 Top mass & hadronization mtop vs pt(top) mtop(E+O) – 172.5 pt<100 GeV <>=–3.5 GeV 100 mtop(E+O) – mtop(E) pt<100 GeV <>= 1.08 GeV 100 • Dependence of reconstructed mass on “odd” clusters ~ 1 GeV Introduction to Event Generators 32 Bryan Webber, MCnet School, 2014 Top+Top+jets jet production • Matched NLO not adequate for >2 extra jets • Merged multijets better there (for ds/s) Introduction to Event Generators 33 Bryan Webber, MCnet School, 2014 LHC Cross SectionThe Standard Model Summary in one slide 11 Natural SUSY with ATLAS - 26th March 2013 - CERN Tuesday, March 26, 2013 • Surprisingly good agreement • No sign of non-Standard-Model phenomena (yet) Introduction to Event Generators 34 Bryan Webber, MCnet School, 2014 But all is not perfect ... Dijet flavours versus jet pT ATLAS, arXiv:1210.0441 •16 2 4.5 1.1 Data stat. uncert. only Data stat. uncert. only Data stat. uncert. only Pythia 6.423 1.8 Pythia 6.423 4 Pythia 6.423 1 Herwig++ 2.4.2 Herwig++ 2.4.2 Herwig++ 2.4.2 Powheg + Pythia 6.423 1.6 Powheg + Pythia 6.423 Powheg + Pythia 6.423 0.9 3.5 fraction [%] Total error fraction [%] Total error fraction [%] Total error 1.4 BB BC 3 0.8 ATLAS CC ATLAS 1.2 Data 2010, s= 7 TeV Data 2010, s= 7 TeV, Ldt=39 pb-1 0.7 2.5 ∫ 1 Ldt=39 pb-1 0.6 ∫ 2 0.8 0.5 1.5 0.6 0.4 0.4 1 0.3 ATLAS -1 0.2 0.5 0.2 Data 2010, s= 7 TeV, Ldt=39 pb ∫ 0 0 50 100 200 300 50 100 200 300 50 100 200 300 Jet p [GeV] Jet p [GeV] Jet p [GeV] T T T (a) (b) (c) 18 94 9 Data stat. uncert. only Data stat. uncert. only Data stat. uncert. only Pythia 6.423 Pythia 6.423 92 Pythia 6.423 Herwig++ 2.4.2 Herwig++ 2.4.2 90 Herwig++ 2.4.2 8 Powheg + Pythia 6.423 16 Powheg + Pythia 6.423 Powheg + Pythia 6.423 fraction [%] Total error fraction [%] Total error fraction [%] 88 Total error BU 7 CU 14 UU 86 84 6 12 82 5 80 4 10 78 76 ATLAS ATLAS ATLAS 3 Data 2010, s= 7 TeV, Ldt=39 pb-1 8 Data 2010, s= 7 TeV, Ldt=39 pb-1 74 Data 2010, s= 7 TeV, Ldt=39 pb-1 ∫ ∫ 72 ∫ 50 100 200 300 50 100 200 300 50 100 200 300 Jet p [GeV] Jet p [GeV] Jet p [GeV] T T T (d) (e) (f) Fig. 10InterestingThe unfolded dijet flavour fractions forexcess each leading jet pT bin of (black points)(single) with PYTHIA 6.423 (squares),b quark Herwig++ 2.4.2 (circles)jets and •POWHEG+PYTHIA 6.423 (filled triangles) predictions overlaid. The error bars on the data points show statistical uncertainties only, whereas the full uncertainties appear as shaded bands. Introduction to Event Generators 35 Bryan Webber, MCnet School, 2014 KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 8. CMS Collaboration, Measurement of the Cross Section for Pro- (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and duction of bbX¯ Decaying to Muons in pp Collisions at √s = 7TeV,J.HighEnergyPhys.1206,110(2012) BNL (USA) and in the Tier-2 facilities worldwide. 9. CMS Collaboration, Inclusive b-Hadron Production Cross Section with Muons in pp Collisions at √s = 7TeV,J.HighEnergyPhys. 1103,090(2011) References 10. CMS Collaboration, Measurement of BB¯ Angular Correlations Based on Secondary Vertex Reconstruction at √s = 7TeV,J.High 1. D0 Collaboration, B. Abbott, et al., The bb¯ Production Cross Sec- Energy Phys. 1103,136(2011) tion and Angular Correlations in pp¯ Collisions at √s = 1.8TeV, 11. LHCb Collaboration, Measurement of σ(pp bbX¯ ) at √s = Phys. Lett. B 487,264(2000) 7TeVintheForwardRegion,Phys.Lett.B694,209(2010)→ 2. D0 Collaboration, B. Abbott, et al., Cross Section for b Jet Produc- 12. ATLAS Collaboration, Measurement of the Inclusive and Dijet tion in pp¯ Collisions at √s = 1.8TeV,Phys.Rev.Lett.85,5068 Cross Sections of b-Jets in pp Collisions at √s = 7TeVwiththe (2000) ATLAS Detector, Eur. Phys. J. C 71,1846(2011) 3. CDF Collaboration, T. Aaltonen, et al., Measurement of Corre- 13. ATLAS Collaboration, The ATLAS experiment at the CERN lated bb¯ Production in pp¯ Collisions at √s = 1960 GeV, Phys. Large Hadron Collider, JINST 3,S08003(2008) Rev. D 77,072004(2008) 14. M. Cacciari, G.P. Salam, G. Soyez, The Anti-kt Jet Clustering Al- 4. S. Seidel, Heavy Quark Production at the Tevatron, gorithm, J. High Energy Phys. 0804,063(2008) arXiv:0808.3347 [hep-ex], (2008) 15. ATLAS, Data-Quality Requirements and Event Cleaning forJets 5. I. Kenyon, The Measurement of the Cross Section for Beauty Pro- and Missing Transverse Energy Reconstruction with the ATLAS duction at the CERN Anti-ppCollider, J. Phys. G 15,1087(1989) Detector in Proton-Proton Collisions at a Center-of-Mass Energy 6. C. Lourenco, H. Wohri, Heavy Flavour Hadroproduction from of √s = 7TeV,ATLAS-CONF-2010-038 Fixed-Target to Collider Energies, Phys. Rept. 433,127(2006) 16. ATLAS Collaboration, Expected Performance of the ATLAS Ex- 7. CMS Collaboration, Inclusive b-Jet Production in pp Collisions at periment - Detector, Trigger and Physics, arXiv:0901.0512 [hep- √s = 7TeV,J.HighEnergyPhys.1204,084(2012) ph], (2009) Higgs Boson Introduction to Event Generators 36 Bryan Webber, MCnet School, 2014 The cross sections for the ttH¯ process are estimated up The following parton distribution function (PDF) sets to NLO QCD [47–51]. are used: CT10 [78] for the POWHEG, MC@NLO, The total cross sections for SM Higgs boson produc- SHERPA, gg2WW and gg2ZZ samples; CTEQ6L1 [79] tion at the LHC with mH = 125 GeV are predicted to for the ALPGEN, MadGraph and HERWIG samples; be 17.5 pb for √s = 7TeV and 22.3pb for √s = and MRSTMCal [80] for the PYTHIA6, PYTHIA8 and 8TeV[52,53]. AcerMC samples. The branching ratios of the SM Higgs boson as a Acceptances and efficiencies are obtained mostly function of mH,aswellastheiruncertainties,arecalcu- from full simulations of the ATLAS detector [81] us- lated using the HDECAY [54] and PROPHECY4F [55, ing Geant4[82].Thesesimulationsincludearealistic 56] programs and are taken from Refs. [52, 53]. The modelling of the pile-up conditions observed in the data. ( ) interference in the H ZZ ∗ 4ℓ final states with iden- Corrections obtained from measurements in data are ap- tical leptons is taken→ into account→ [53, 55, 56]. plied to account for small differences between data and simulation (e.g. large samples of W, Z and J/ψ decays Higgs Signal and are used to compare lepton reconstruction and identifi- Table 1: Event generators used to model the signal and background cation efficiencies). processes. “PYTHIA” indicates that PYTHIA6 and PYTHIA8 are used for simulations of √s = 7TeVand √s = 8TeVdata,respec- Backgroundtively. Simulation 4. H → ZZ(∗) → 4ℓ channel Process Generator The search for the SM Higgs boson through the ggF, VBF POWHEG [57, 58]+PYTHIA decay H ZZ( ) 4ℓ,whereℓ = e or µ,pro- WH, ZH, ttH¯ PYTHIA ∗ vides good→ sensitivity→ over a wide mass range (110- W+jets, Z/γ +jets ALPGEN [59]+HERWIG ∗ 600 GeV), largely due to the excellent momentum reso- tt, tW, tb MC@NLO [60]+HERWIG tqb AcerMC [61]+PYTHIA lution of the ATLAS detector. This analysis searches qq¯ WW MC@NLO+HERWIG for Higgs boson candidates by selecting two pairs of gg → WW gg2WW [62]+HERWIG isolated leptons, each of which is comprised of two lep- → qq¯ ZZ POWHEG [63]+PYTHIA tons with the same flavour and opposite charge. The → gg ZZ gg2ZZ [64]+HERWIG expected cross section times branching ratio for the pro- → ( ) WZ MadGraph+PYTHIA, HERWIG cess H ZZ ∗ 4ℓ with mH = 125 GeV is 2.2 fb for → → Wγ+jets ALPGEN+HERWIG √s = 7TeVand2.8fbfor√s = 8TeV. Wγ∗ [65] MadGraph+PYTHIA The largest background comes from continuum ( ) ( ) qq¯/gg γγ SHERPA (Z ∗ /γ∗)(Z ∗ /γ∗)production,referredtohereafteras → ( ) ZZ ∗ .Forlowmassestherearealsoimportantback- ATLAS, Phys.Lett.B716(2012)1ground contributions from Z + jets and tt¯ production, where charged lepton candidates arise either from de- Introduction to Event GeneratorsThe event generators used37 to model signal and back-Bryan Webber, MCnet School, 2014 cays of hadrons with b-orc-quark content or from mis- ground processes in samples of Monte Carlo (MC) sim- identification of jets. ulated events are listed in Table 1. The normalisations The 7 TeV data have been re-analysed and combined of the generated samples are obtained from the state of with the 8 TeV data. The analysis is improved in several the art calculations described above. Several different aspects with respect to Ref. [83] to enhance the sensitiv- programs are used to generate the hard-scattering pro- ity to a low-mass Higgs boson. In particular, the kine- cesses. To generate parton showers and their hadroni- matic selections are revised, and the 8 TeV data anal- sation, and to simulate the underlying event [66–68], ysis benefits from improvements in the electron recon- PYTHIA6 [69] (for 7TeV samples and 8TeV sam- struction and identification. The expected signal sig- ples produced with MadGraph [70, 71] or AcerMC) or nificances for a Higgs boson with m = 125 GeV are PYTHIA8 [72] (for other 8TeV samples) are used. Al- H 1.6 σ for the 7 TeV data (to be compared with 1.25 σ ternatively, HERWIG [73] or SHERPA [74] are used in Ref. [83]) and 2.1 σ for the 8 TeV data. to generate and hadronise parton showers, with the HERWIG underlying event simulation performed using JIMMY [75]. When PYTHIA6 or HERWIG are used, 4.1. Event selection TAUOLA [76] and PHOTOS [77] are employed to de- The data are selected using single-lepton or dilepton scribe tau lepton decays and additional photon radiation triggers. For the single-muon trigger, the pT threshold from charged leptons, respectively. is 18 GeV for the 7 TeV data and 24 GeV for the 8 TeV 3 Born term in POWHEG (i.e. by setting the bornonly flag to 1), and by downgrading the Sudakov form factor to pure NLL accuracy, i.e. we set B2 to zero. In the MiNLO case, the central value is chosen according to the procedure discussed earlier, with more than one renormalization scale for each phase space point. In the H fixed ordergg calculation, we chooseHiggs(+jet) as central renormalization and factorization scales the boson mass. From the table, it is clear that the standard NLO result and the integrated Higgs boson production total cross sections in pb at the LHC, 8 TeV + Z e e production total cross sections1 in nb at1 the 14 TeV LHC1 1 KR,KF 1, 1 1, 2 2, 1 1, 2 2 , 1 2 , 2 2, 2 K ,K 1, 1 1, 2 2, 1 1, 1 1 , 1 1 , 1 2, 2 HJ-MiNLOR NLOF 13.33(3) 13.49(3) 11.70(2) 13.03(3)2 16.532(7) 16.45(8)2 2 11.86(2) ZJ-MiNLO NLO 1.916(5) 2.065(6) 1.776(2) 1.662(3) 2.18(1) 2.022(6) 1.987(3) H NLOZ NLO 132.23(1).039(3) 132.28(1).100(3) 112.17.015(2)(1) 131.14(1).938(2) 15.912.068(3)(2) 15.83(2)1.984(2) 11.22(1)2.092(3) HJ-MiNLOZJ-MiNLOLOLO 8.1282(7).3827(5) 8.400(7)1.7322(6) 5.8801.1806(4)(5) 7.1864(6).0348(3) 182.28.1280(2)(7)17.111(2).5677(5)5.982(5)1.4831(5) H LOZ LO 5.741(5)1.793(2) 5.758(5)2.014(2) 4.7341.793(2)(4) 5.644(5)1.555(2) 7.1171.793(2)(6) 6.996(6)1.555(2)4.748(4)2.014(2) + TableTable 1: 6:TotalTotal cross cross section section for for HiggsZ bosone productione production, at the obtained 8 TeV LHC, with obtained the ZJ-MiNLO with theand the HJZ-MiNLOprograms,and boththe H atprograms, full NLO both level at and full at NLO leading level order, and at for leading di erent order, scales for di combinations. erent scales The combinations.maximum and The minimum maximum are and highlighted. minimum are highlighted. 100 100 101 101 H+Pythia HJ-MiNLO one are fairly consistent,HJ+Pythia both at the NLO and at the LO level. At the NLO 1 1 0 0 10 HJ+Pythia level,10 the renormalization-scaleH+Pythia variation dominates the uncertainty band, and it turns out [pb] 10 [pb] 10 to beH very similar for the HJ-MiNLO and H results,H with the first one being slightly shifted [pb/GeV] 2 [pb/GeV] 2 1 1 10 10 dy 10 dy 10 H T H T upwards./ The central values are even closer. Notice/ that the factorization scale variation dp dp 3 d 3 d / / 2 2 10 is10 wider 10 for the HJ-MiNLO result, a fact that we will10 comment on later. H+Pythia HJ+Pythia d d At leading orderHJ+Pythia the HJ-MiNLO central result exceeds the fixedH+Pythia order one by almost 1.5 50%.1.5 1.5 We again see that the renormalization scale variation1.5 dominates the uncertainties. 1.0 1.0 1.0 1.0 ratio ratio 0.5 The0.5ratio scale0.5 variation, however, is quite larger than thatratio 0.5 of the fixed order result. 050100150200250300350400 050100150200250300350400-4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 H For W productionH we have considered both the LHC at 8 TeV configuration (tab. 2) pT [GeV] pT [GeV]y y and the Tevatron at 1.96 TeVH (tab. 3). Here we notice that the WJ-MiNLOH NLO result Match/mergeW e ¯ production MiNLO+Pythia6 total cross sections in nb at the LHC, 8 TeV Figure 2: Comparison between the H+PYTHIA result• and the HJ-MiNLO +PYTHIA result for theH HiggsPYTHIA HJ MiNLOHamilton,PYTHIA Nason, Oleari & Figure 1: Comparison between the + result and the - + result for the K ,K 1, 1 1, 2 2, 1 1, 1 1 , 1 1 , 1 2, 2 boson transverse-momentum distribution. The bandsHiggs-boson are obtainedR F rapidity as in fig. distribution 1. at the LHC at 8 TeV.2 The left2 plotZanderighi, shows2 2 the 7-point arXiv:1212.4504 scale- WJ-MiNLO NLO 4.35(1) 4.65(1) 4.031(7) 3.818(8) 4.84(2) 4.62(2) 4.462(8) variation band for the H generator, while the right plot shows the HJ-MiNLO 7-point band. 0 0W NLO 4.612(8) 4.738(8) 4.552(8) 4.425(7) 4.687(8) 4.530(8) 4.703(8) 10 Introduction to Event Generators10 38 Bryan Webber, MCnet School, 2014 H+Pythia WJ-MiNLO LO 3.182(1) HJ+Pythia3.862(1) 2.713(1) 2.4531(1) 5.006(2) 3.792(2) 3.305(1) HJ+Pythia H+Pythia alsoW theLO rapidity4.002(6) distributions4.379(7) are in3.999(6) good agreement.3.566(6) We3.999(6) thus show3.566 in( fig.6) 14. the379 rapidity(7) [pb/GeV] 1 [pb/GeV] distribution1 of the Higgs boson at the 8 TeV LHC, computed with the H and with the HJ- H T 10 H T 10 Table 2: Total cross section for W e ¯ production at the 8 TeV LHC, obtained with the dp dp MiNLO generators, both interfaced to PYTHIA 6 [37] for shower. We have used the Perugia-0 / / WJ-MiNLO and the W programs, both at full NLO level and at leading order, for di erent scales d d PYTHIA PYTUNE(320) combinations.tune of The(that maximum is to and say, minimum are highlighted.). Hadronization, underlying event and multi- 1.5 parton1.5 collisions were turned o . The two plots show the scale-variation band for each 1.0 hasgenerator.1.0 a much wider The band scale-variation is obtained band as the than upper the fixed-order and lower one. envelope In both of the cases, results the band obtained ratio 0.5 ratio 0.5 1 1 1 1 020406080100isby larger setting020406080100 by aboutthe scale a factor factor of parameters 3. The central (KR,K valueF)to(1 is lower, 1), in (1 both, 2), (2 cases, 1), by (1, about2 ), ( 2 4-5%., 1), ( 2 , 2 ) H H pT [GeV] Inand the (2 leading, 2). We order seep case,T considerable[GeV] the WJ-MiNLO agreementscale band between is more the than two twice approaches, as large as with the the fixed scale- ordervariation one at band the of LHC. the AtHJ- theMiNLO Tevatron,result being the scale slightly variation larger. for the W LO result is clearly too small,In figs. theH 2 NLO and result 3 we being show incompatible the Higgs transverse with it. On momentum the other distributions. hand, for both We LHC begin Figure 3: Same as fig. 2 for a di erent pT range. andby Tevatron noticing that predictions, the central if only values symmetric of the scaleH and variationsHJ-MiNLO aregenerators considered are (i.e. in the very last good agreement. This is not a surprise, since in the H generator, the parameter hfact, that in that direction, we approach the strong couplingseparates regime. the Observe real cross also section that the contributionH result into the sum of a singular and a finite one, H does not show a realistic scale uncertainty in the p We now turn to the case of W production. Motivated by the discussion given for– 21 – the total cross section case, we consider only a 3-point scale variation, i.e. KR = KF = 1/2, 1, 2 for the WJ-MiNLO generator. In fig. 4 we show the l rapidity distribution at { } the Tevatron computed with the W and WJ+MiNLO generators. We essentially see no shape di erence in this distribution, therefore, as for the inclusive cross section, we find that the WJ+MiNLO central value is about 5% below the W one. The WJ band is slightly larger than – 22 – gg Higgs+jets (8 TeV) Figure 6: As in fig. 3, with N =2. cut to disappear, and the merging-parameter dependence reduced, when pT becomes large. We finally turn to discussing the case of the N =2,sharp-D function, Sudakov- reweighted merging; that is, we increase the largest multiplicity by one unit w.r.t. what was done before. The settings are the same as in the N =1case,andfigs.6,7,and8are the analogues of figs. 3, 4, and 5 respectively (with the exception of one panel in fig. 8). The numerators of the ratios that appear in the upper insets are the same as before for the H +0j and H +1j cases; that for H +2j is obviously specific to N =2.Inthelower insets, together with the ratios that allow one to assess the merging systematics, we have plotted (as histograms overlaid with open circles) the ratios of the N =1resultsoverthe N =2ones,bothforµQ =50GeV.WehavealsorecomputedtheAlpgen predictions, by adding the H +3partonsample,forconsistencywithN =2.Thecorrespondingresults will not be shown in the plots, since these are already quite busy, and there is no difference Figure 6: As in fig. 3, with N =2. Figure 7: As in fig. 4, with N =2. cut to disappear, and the merging-parameter dependence reduced, when pT becomes large. at all in the patterns discussed above, except–26– in a very few cases which we shall comment We finallyFxFx: turn to discussing Match/merge the case of the N =2,sharp-D MC@NLO+Herwig6function, Sudakov- upon when appropriate. reweighted• merging; that is, we increase the largest multiplicity by one unit w.r.t. what The common feature of all but one of the observables presentedinfigs.6–8isthat was done before. The settings are the same as in the N =1case,andfigs.6,7,and8are they are extremely close, in both shape and normalization, totheirN =1counterparts the analogues of figs. 3, 4, and 5 respectively (with the exception of oneFrederix panel in fig. 8). of& figs. Frixione, 3–5. This is highly arXiv:1209.6215 non-trivial, since the individual i-parton contributions are The numerators of the ratios that appear in the upper insets are the same as before for different in the two cases. The exception is the pseudorapidityofthesecond-hardestjet the H +0j and H +1j cases; that for H +2j is obviously specific to N =2.Inthelower (upper right panel of fig. 7), which the inclusion of the 2-parton sample turns into a more insets, together with the ratios that allow one to assess the merging systematics, we have central distribution, as anticipated in the discussion relevant to fig. 4, and brings it very Introduction to Event Generatorsplotted (as histograms overlaid with open circles) the ratios of the39N =1resultsoverthe Bryan Webber, MCnet School, 2014 close to the Alpgen result obtained with the same µQ. N =2ones,bothforµ =50GeV.WehavealsorecomputedtheAlpgen predictions, by Q The small impact of the increase of the largest multiplicity is also generally in agree- adding the H +3partonsample,forconsistencywithN =2.Thecorrespondingresults ment with what is found in Alpgen,wheretheinclusionoftheH +3 partoncontribution will not be shown in the plots, since these are already quite busy, and there is no difference changes the fully-inclusive rate by +0.3%. The effects on differential observables are also Figure 7: As in fig. 4, with N =2. at all in the patterns discussed above, except–26– in a very few cases which we shall comment upon when appropriate. –27– The common feature of all but one of the observables presentedinfigs.6–8isthat they are extremely close, in both shape and normalization, totheirN =1counterparts of figs. 3–5. This is highly non-trivial, since the individual i-parton contributions are different in the two cases. The exception is the pseudorapidityofthesecond-hardestjet (upper right panel of fig. 7), which the inclusion of the 2-parton sample turns into a more central distribution, as anticipated in the discussion relevant to fig. 4, and brings it very close to the Alpgen result obtained with the same µQ. The small impact of the increase of the largest multiplicity is also generally in agree- ment with what is found in Alpgen,wheretheinclusionoftheH +3 partoncontribution changes the fully-inclusive rate by +0.3%. The effects on differential observables are also –27– gg Higgs+jets (13 TeV) plots by R. Frederix Introduction to Event Generators 40 Bryan Webber, MCnet School, 2014 Beyond Standard Model Simulation Introduction to Event Generators 41 Bryan Webber, MCnet School, 2014 BSM Simulation • Main generators have some BSM models built in ✤ Pythia 6 has the most models ✤ Herwig++ has careful treatment of SUSY spin correlations and off-shell effects • Trend is now towards external matrix element generators: FeynRules + MadGraph, ... • QCD corrections and matching/merging still needed Introduction to Event Generators 42 Bryan Webber, MCnet School, 2014 1/2 ATLAS Preliminary 1/2 ATLAS Preliminary 106 Data, s=8 TeV 106 Data, s=8 TeV ∫L dt = 20.3 fb -1 Background prediction ∫L dt = 20.3 fb -1 Background prediction 5 ≥8 jets, p ≥ 50 GeV Multi-jets (inc. tt→ qq) 5 ≥8 jets, p ≥ 50 GeV Multi-jets (inc. tt→ qq) 10 T 10 T Σ Sherpa tt → ql,ll Σ Sherpa tt → ql,ll MJ ≥ 340 GeV MJ ≥ 420 GeV 4 Single top 4 Single top 10 MadGraph tt + V 10 MadGraph tt + V Sherpa W+b Sherpa W+b 3 3 Events / 4 GeV 10 Sherpa W→ (e,µ,τ)ν Events / 4 GeV 10 Sherpa W→ (e,µ,τ)ν Sherpa Z Sherpa Z 2 0 2 0 [~,g ∼χ ]:[900,150] [GeV] [~,g ∼χ ]:[900,150] [GeV] 10 1 10 1 10 10 1 1 10-1 10-1 111 Introduction Introduction Introduction10-2 10-2 2 2 1.5 1.5 1 1 0.5 0.5 ManyManyMany extensions extensions extensions0 of of the ofthe Standard the Standard Standard Model Model Model of of particle particle0 of particle physics physics physics predict predict predict the the presence the presence presence of of TeV-scale TeV-scale of TeV-scale strongly strongly strongly 1011 0 2 4 6 810 1010 12 14 16 0 2 4 6 8 10 12 14 16 Data/Prediction Data/Prediction 10 ATLAS Preliminary missATLAS Preliminary1/2 miss 1/2 10 Data 2012, s=8 TeV E9T / HT [GeV ] Data 2012, s=8 TeV ET / HT [GeV ] -1 10 -1 Events interactinginteractinginteracting particles particlesBackground particles prediction that that that decay decayEvents decay to to lighter, lighter, to lighter, weaklyBackground weakly weakly prediction interacting interacting interacting descendants. descendants. descendants. Any Any suchAny such such weakly weakly weakly interacting interacting interacting 9 L dt = 20.3 fb 8 L dt = 20.3 fb 10 ∫ Sherpa tt → ql,ll 10 ∫ Sherpa tt → ql,ll 8 1/2 Sherpa W+b Sherpa1/2 W+b 10 6 ATLAS Preliminary Data,7 s=8 TeV 6 ATLAS Preliminary Data, s=8 TeV 1 lepton CR 10Sherpa W (e, , ) -1 10 1 lepton CR Sherpa10 W (e, , ) -1 particles7particlesparticles that that that are areL dt massive→ are= 20.3 massiveµ τ νfb massive and andBackground and stable stable prediction stable can can contribute can contribute→ contributeL dtµ τ=ν 20.3 fb to to the the to darkBackground the dark prediction dark matter matter matter content content content of of the the of universe. the universe. universe. The The The 10 Sherpa∫ Z 6 Sherpa Z ∫ No b-jets 5 ≥9 jets, p ≥ 50 GeV 10Multi-jets1 (inc.b-jet tt→ qq) 5 ≥9 jets, p ≥ 50 GeV Multi-jets (inc. tt→ qq) 6 10Single top T Single10 top T 10 Σ Sherpa5 tt → ql,ll Σ Sherpa tt → ql,ll MadGraphMJ ≥ t340t+V GeV 10 MadGraph ttM+VJ ≥ 420 GeV strongly5stronglystrongly interacting interacting interacting~ ∼0 parents parents parents wouldSingle would top would be be produced be produced~ produced∼0 in in the the in proton-proton the proton-proton proton-protonSingle top interactions interactions interactions at at the the at Large the Large Large Hadron Hadron Hadron 10 [4 ,g χ ]:[900,150] [GeV] 4 [ ,g χ ]:[900,150]4 [GeV] 10 1 10MadGraph tt + V 101 MadGraph tt + V 104 Sherpa3 W+b Sherpa W+b Collider3ColliderCollider (LHC) (LHC) (LHC)3 [1], [1], and [1], and such and such such10 events events events would would would be be characterized3 characterized be characterized by by significant significant by significant missing missing missing transverse transverse transverse momentum momentum momentum 10 Events / 4 GeV 10 Sherpa W→ (e,µ,τ)ν Events / 4 GeV 10 Sherpa W→ (e,µ,τ)ν 2 2 10Sherpa Z Sherpa Z 10 2 0 2 0 10 [~,g ∼χ ]:[900,150] [GeV] 10 [~,g ∼χ ]:[900,150] [GeV] / from10fromfrom the the unobserved the unobserved unobserved weakly weakly weakly interacting10 interacting1 interacting daughters, daughters, daughters, and and jets and jets from jets from1 from emissions emissions emissions of of quarks quarks of quarks and and/or/ andor gluons. gluons.or gluons. 1 10 1 10 10-1 InIn theIn the context the context context of of R-parity of R-parity R-parity10-1 conserving conserving conserving supersymmetry supersymmetry supersymmetry (SUSY) (SUSY) (SUSY) [2], [2], the [2], the strongly the strongly strongly interacting interacting interacting parent parent parent 1 1 10-2 10-2 22 3 4 5 6 7 8 9 10 11 12 13 14 22 3 4 5 6 7 8 9 10 11 12 13 14 particlesparticlesparticles are are the are-1 the partners the partners partners of of the the of quarks the quarks quarks (squarks, (squarks, (squarks,-1 q ˜)q ˜) and andq ˜) the and the partners the partners partners of of the the of gluons the gluons gluons (gluinos, (gluinos, (gluinos,g ˜),g ˜), and andg ˜), are and are are 1.5 10 1.5 10 1 1 -2 -2 produced0.5producedproduced in in10 pairs. pairs.in pairs. The The The lightest lightest lightest0.5 supersymmetric supersymmetric supersymmetric10 particle particle particle (LSP) (LSP) (LSP) is is stable, stable, is stable, providing providing providing a a candidate candidate a candidate that that can that can can 0 2 0 2 2 3 4 5 6 71.5 8 9 10 11 12 13 2 3 4 5 6 7 8 91.5 10 11 12 13 Data/Prediction contributecontributecontribute to toNumber the1 the to of relic jets the relic p >50 relic darkGeV dark dark matterData/Prediction matter matter density density densityNumber in in the of the 1jets in universep the>50 universe GeV universe [3]. [3]. [3]. 0.5 T 0.5 T Searching0 for 0new signals (a) No b-jets0 2 4 6 8 10 12(b) 14 Exactly 16 one b-jet 0 2 4 6 8 10 12 14 16 IfIf kinematically kinematicallyIf kinematicallyData/Prediction accessible, accessible, accessible, the the squarks the squarks squarksData/Prediction and and gluinos and gluinos gluinos are are produced are produced produced in in the the inpp theppcollisionscollisionspp collisions at at the the at LHC. theLHC. LHC. Emiss/ H [GeV1/2] Emiss/ H [GeV1/2] T T ATLAS CONF-2013-054T T TheyTheyThey can can can be be1/2 expected be expected expected to to decay decay to decay in in cascades, cascades, in cascades,1/2 the the nature the nature nature of of which which of which depends depends depends on on the the on mass the mass mass hierarchy hierarchy hierarchy within within within 9 ATLAS Preliminary ATLAS Preliminary 10610 ATLAS Preliminary Data, s=8 TeV 106 Data, s=8 TeV -1 DataBackground 2012, s prediction=8 TeV -1 Background prediction 8 L dt = 20.3 fb L dt = 20.3 fb ∫ -1 ∫ Events Background prediction thethe model.the model. model. Individual Individual510 Individual≥10L jets, dt = p 20.3 ≥ cascade 50 fb cascadeGeV cascadeMulti-jets decays decays (inc. tt decays→ qq) may may may include include5 include≥10 jets, gluino p gluino ≥ 50 GeV gluino decays decaysMulti-jets decays (inc. to tt→ to qq) top top to squarks top squarks squarks (stop), (stop), (stop),t˜,t˜, t˜, 10 ∫ T Sherpa tt → ql,ll 10 T 107 Σ Sherpa tt → ql,ll Σ Sherpa tt → ql,ll MJ ≥ 340 GeV Sherpa W+b MJ ≥ 420 GeV 4 1 lepton CR Single top 4 Single top 10106 Sherpa W → (e,µ,τ)ν 10 2 b-jets SherpaMadGraph Z tt + V MadGraph tt + V ≥ Sherpa W+b Sherpa W+b 3105 Single top 3 Events / 4 GeV 10 MadGraphSherpa W →tt+V (e,µ,τ)ν Events / 4 GeV 10 g˜ g˜ g˜ t˜+t˜+t¯tt˜¯+ Sherpat¯ W→ (e,µ,τ)ν (1a)(1a)(1a) 4 ~ 0 10 [ Sherpa,g ∼χ ]:[900,150] Z [GeV] Sherpa Z 2 ~ 1∼0 2 ⇥⇥ ⇥ ~ ∼0 10 3 [ ,g χ ]:[900,150] [GeV] 10 [ ,g χ ]:[900,150] [GeV] 10 1 1 10 2 10 0 0 0 followedfollowedfollowed by by the by the10 top the top squark top squark squark decay decay decay to to a a top to top a quark top quark quark and and a and a neutralino, neutralino, a neutralino, ˜1 ˜,1, ˜1, 110 1 1 -1 -1 10 -1 10 10 ˜0 ˜0 ˜0 10-210-2 10-2t˜ t˜ tt˜+t + t1.+1. 1. (1b)(1b)(1b) 2 22 3 4 5 6 7 8 9 10 11 12 13 14 2 1.51.5 1.5 ⇥⇥ ⇥ 1 1 1 0.50.5 0.5 Alternatively,Alternatively,Alternatively, if0 0 if the the if top the top squark top squark squark is is heavier heavier is heavier than than than0 the the gluino, the gluino, gluino, the the three the three three body body body decay, decay, decay, 02 2 3 4 4 5 6 6 7 8 8 10 9 10 12 11 14 12 13 16 0 2 4 6 8 10 12 14 16 Data/Prediction Data/Prediction Number missof jets p >50 GeV1/2 Data/Prediction miss 1/2 ET / HTT [GeV ] ET / HT [GeV ] miss (c) 2 b-jets 0 0 0 Figure 7: E / HT distributions for the multi-jet + M stream with¯ the¯ signal ˜ ¯˜ region ˜ selection, other T • Dashed = Herwig++ g˜ J g ˜ , g˜ t +t +t t+t ++ t1 +1 1 (2)(2) (2) than the final Emiss/ H requirement. The figures on the left are for events with M > 340 GeV, while Figure 3: Jet multiplicity distributionsT for pminT=50 GeV jets in the one-lepton tt¯ and⇥⇥W +⇥jets control J those on the right areT for M > 420 GeV. The minimum multiplicity requirement for pmin = 50 GeV, regions (CR) for di erent b-jet multiplicities.• MonteBackground:J Carlo predictions mostly are beforeSherpa fitting LO to data.multijet Other mergingT details as formay Fig.maymay 1. result. result.R The= result.0 teal.4 jets band Other Other increases in Other the possibilities possibilitiesratio from possibilities plot eight indicates (top) toinclude include nine the experimentalinclude (middle) decays decays and decays uncertainties finally involving involving to ten involving on jets the (bottom). intermediate intermediate intermediate Other details charginos, charginos, as charginos, neutralinos, neutralinos, neutralinos, and and/or/ andor /or 20 Monte Carlosquarks predictionsquarkssquarksforIntroduction and including Fig. including also 1. including includesto Event bottomGenerators the bottom Monte bottom squarks. Carlo squarks. statistical squarks. A uncertainty. A pair pair A43 pair of of Additional cascade cascade of cascade theoretical decays decays decaysBryan will willWebber, produce will produceMCnet produce School, a 2014 a large large a large number number number of of Standard Standard of Standard uncertainties are not shown. ModelModelModel particles, particles, particles, together together together with with with a a pair pair a pairof of LSPs, LSPs, of LSPs, one one from one from from the the end the end of end of each each of each cascade. cascade. cascade. The The LSPs The LSPs LSPs are are assumed assumed are assumed toto be beto stable be stable stable and and andweakly weakly weakly interacting, interacting, interacting, and and so and so result result so result in in missing missing in missing transverse transverse transverse momentum. momentum. momentum. InIn this thisIn notethis note note we we consider we consider consider final final final states states states with with with large large large numbers numbers numbers of of jets jets of together jets together together with with significantwith significant significant missing missing missing trans- trans- trans- verseverseverse momentum momentum momentum in in the the in absence the absence absence of of isolated isolated of isolated electrons electrons electrons or or muons, muons, or muons, using using using the thepp theppcollisioncollisionpp collision data data recorded data recorded recorded by by by 11 thethe ATLASthe ATLAS ATLAS experiment experiment experiment during during during 2012 2012 2012 at at a a centre-of-mass at centre-of-mass a centre-of-mass energy energy energy of of⇤⇤ ofs s=⇤=8s8 TeV.= TeV.8 TeV. The The corresponding The corresponding corresponding inte- inte- inte- 1 1 1 gratedgratedgrated luminosity luminosity luminosity is is 20 20 is.3. 203 fb fb. 3 . fb. Searches Searches. Searches for for new for new new phenomena phenomena phenomena in in final final in final states states states with with withlarge large large jet jet multiplicities multiplicities jet multiplicities – – – requiringrequiringrequiring from from from at at least least at least six six to six to at at to least least at least nine nine nine jets jets – jets – and and – missing and missing missing transverse transverse transverse momentum momentum momentum have have have previously previously previously been been been 1 1 1 reportedreportedreported by by the by the ATLAS the ATLAS ATLAS collaboration collaboration collaboration using using using LHC LHC LHCppppcollisionppcollisioncollision data data corresponding data corresponding corresponding to to 1. 134 to.34 fb 1 fb. 34 [4] fb[4] and and[4] to and to to 1 1 1 4.47.7 fb4 fb. 7 fb[5] [5] at[5] at⇤⇤ ats s=⇤=7s7= TeV. TeV.7 TeV. Searches Searches Searches with with with explicit explicit explicit tagging tagging tagging of of jets jets of from jets from from bottom bottom bottom quarks quarks quarks (b (-jets)b-jets) (b-jets) in in multi-jet multi-jet in multi-jet eventseventsevents were were were also also also performed performed performed by by ATLAS byATLAS ATLAS [6] [6] and [6] and CMS and CMS CMS [7, [7, 8, 8,[7, 9]. 9]. 8, These 9]. These These searches searches searches found found found no no significant significant no significant excess excess excess overoverover the the Standard the Standard Standard Model Model Model expectation expectation expectation and and provided and provided provided stringent stringent stringent limits limits limits on on various various on various supersymmetric supersymmetric supersymmetric models, models, models, includingincludingincluding decays decays decays such such such as as (2) (2) as and (2) and a and a mSUGRA mSUGRA a mSUGRA/CMSSM/CMSSM/CMSSM [10] [10] [10]model model model that that includes that includes includes strong strong strong production production production pro- pro- pro- cesses.cesses.cesses. The The The analysis analysis analysis presented presented presented in in this this in note this note note extends extends extends previous previous previous analyses analyses analyses by by reaching reaching by reaching higher higher higher jet jet multiplicities multiplicities jet multiplicities andandand utilizing utilizing utilizing new new new sensitive sensitive sensitive variables. variables. variables. EventsEventsEvents are are first are first first selected selected selected with with with large large large jet jet multiplicities, jet multiplicities, multiplicities, with with with requirements requirements requirements ranging ranging ranging from from from at at least least at least seven seven seven toto at atto least least at least ten ten jets, ten jets, jets, reconstructed reconstructed reconstructed using using using the the anti- the anti-k anti-tkclusteringt clusteringkt clustering algorithm algorithm algorithm [11] [11] and [11] and jet and jet distance distance jet distance parameter parameter parameter of of of RR==R0.0=4..4.0 Significant. Significant4. Significant missing missing missing transverse transverse transverse momentum momentum momentum is is also also is required also required required in in the the in event. the event. event. An An additional Anadditional additional selection selection selection basedbasedbased on on the on the number the number number of ofb-jetsb of-jetsb-jets gives gives gives enhanced enhanced enhanced sensitivity sensitivity sensitivity to to models models to models which which which predict predict predict either either either more more more or or fewer fewer or fewer b-jetsb-jetsb-jets than than than the the Standard the Standard Standard Model Model Model background. background. background. In In a a complementary In complementary a complementary stream stream stream of of the the of analysis, the analysis, analysis, the theRR the==0R.04.=4 jets jets0.4 jets areare re-clusteredare re-clustered re-clustered into into into large large large (R (R= (=R1.10)=.0)1 composite. composite0) composite jets jets to jets to form form to form an an event event an event variable, variable, variable, the the sum the sum of sum of the the of masses themasses masses of of of thethe compositethe composite composite jets, jets, jets, which which which gives gives gives additional additional additional discrimination discrimination discrimination in in models models in models with with with a a large large a large number number number of of objects objects of objects in in in thethe finalthe final final state state state [12]. [12]. [12]. Events Events Events containing containing containing isolated, isolated, isolated, high- high- high-pTpTelectronselectronspT electrons or or muons muons or muons are are vetoed are vetoed vetoed in in order order in order to to reduce reduce to reduce 11 1 NLO Squark Production g g qi q˜i qi q˜i 10-6 g˜ g˜ [pb/GeV] [pb/GeV] j1 T j2 T -6 qj q˜ -7 10 (a) j qj q˜j 10 NLO /dp max Pythia (p = pPWG) /dp σ T T σ d q q Herwig++ d i q¯ q˜i i q˜i j 10-8 Dipole g g˜ q˜j g˜ qj g˜ q˜j qj q˜j -9 10 Pythia/NLO 1.4 (b) g g 1.4 Herwig++/NLO 1.3 qi q˜ (a) i Dipole/NLO 1.2 q¯j 1.2 qi q˜i 1.1 g q˜j g q˜j 1 1 0.9 g˜ g 0.8 g˜ q¯ 0 500 1000 1500 2000 0 200 400 600 800 1000 j pj1 [GeV] pj2 [GeV] qj q˜ T T q (c) j (a) i q˜i (b) qi q˜i g q¯ -5 -6 q˜j Figure 4: Feynman diagramsj contributing to real emission matrix elementsq¯j with qq initial10 states and an emittedq¯j 10 gluon.g Diagramsg which lead toq˜i q soft˜j and collinearg divergencies are depicted ing (a) and (b), the diagram in (c) is q¯j IR finite. q˜j [pb/GeV] q˜j [pb/GeV] g˜ j3 T q miss T (b) i q˜i q¯j /dp σ -6 /dE (a) qi qi q˜i qi q˜i qi d 10 q˜i file of the SM, in the MSSM model file no counterterms are specified. These have been added σ q¯j q¯j d (c)according to the renormalizationq˜j procedure described above. It has been checked explicitly that g q˜ gg q˜ g -7 i this procedure renders the calculationj UV finite. After canceling all UV divergencies by renor- 10 Figure 5: Feynman diagrams contributingq˜j to real emission matrix elementsq˜j with qg initial states. The diagram malization the IR divergenciesq¯j remain. These will cancel against the IR divergencies of the real inq¯ (a) gives rise to collinear singularities. The diagrams in (b) and (c) are IR finite. The diagrams1.4 in (c) can 1.2 emissionj diagrams by applying the Catani-Seymour subtraction formalism [64,1.3 65]. contribute to the production of a squark and a resonant gluino. 1.1 qi (b) qiqi q˜iq˜i qi q˜i 1.2 1.1 1 (c) q˜j The matrix elements of the real emission can be classified in two di erent topologies.1 The q¯j 0.9 q¯j 0.9 itselffirst provides topology an contains interface diagrams with the with program two quarksMadGraph in the initial 4.4.30 state[68, and 69], an which additionally0.8 automatically emitted Figure 5: Feynman diagrams contributing tog real emission matrix elementsq˜i withg qg initial states. The diagram g 0.7 0.8 produces a code for the squared matrix elements of the real emission diagrams by0 calling100 the 200 300 400 500 0 500 1000 1500 2000 in (a) gives rise to collinear singularities.gluon: The diagrams in (b) and (c) are IR finite. The diagrams in (c)q˜j can q˜j j3 miss p [GeV] ET [GeV] HELAS subroutines based on the helicity+loops amplitude formalism [70]. POWHEG/NLO T contribute to the production of a squark and a resonant gluino. qi qj q˜i q˜j g. (4) The dipoles needed to render theq¯j real emission matrix elements finite are organized in pairs of potentiallyThe t-channelqi collinear diagrams partons contributing with an additionalqi to this process reference are to shownq˜i a spectator in Fig.qi particle. 4.Figure The second For 19: diagramsq˜i topology Same as Fig. 18, but modified Pythia such that the starting scale for the shower is always set to q˜ itself provides an interface withwithis(c) the comprised two program quarks ofMadGraph diagramsin the initial with 4.4.30 state aj quark[68, this and 69], gives a which gluon rise automaticallyto in twelve the initial individual state and dipoles:p anPWG emitted,,seetext. The emitted massless produces a code for the squaredantiquark. matrix elements These diagrams of the real are emission depicted diagramsin Fig. 5. by Apart calling from the implementingT the process gluonFigure can 5: beFeynman collinear diagrams or soft contributing and in each to real case emission any of matrix the other elements three with particlesqg initial instates. the The initial diagram or HELAS subroutines based on the helicity amplitude formalism [70]. finalin (a) state gives can rise serve to collinear as spectator singularities. particle. Thegq Fordiagrams diagramsq˜ inq˜ (b)q¯ with and (c) aquark are IR finite.and a The gluon diagrams in the in initial (c)(5) can The dipoles needed to render the real emission matrix elements finite arei organizedi j j in pairs of statecontribute only three to the dipoles production are of necessary: a squark and The a resonant emitted gluino. antiquark can only become collinear to the j3 potentially collinear partonsinitial withit is an important state additional gluon to while reference include the for othertoi a= spectator threej also particles particle. can For act diagrams as the spectator particle.both Herwig++ Hence, the showers predict higher rates than the NLO calculation up to p 400 GeV NLO⇥ with POWHEG matching to different generators T with two quarks in the initialcounterterms state this givesd⇥A which rise to are twelve subtracted individual from dipoles: the squared The realemitted emission matrix elements read: itself provides an• interface with the programgqj MadGraphq˜i q˜j q¯i 4.4.30 [68, 69],and which agree automatically quite(6) well with each other, the Pythia result ranges slightly below the NLO curve gluon can be collinear or soft and in each case any of the other three particles in the initial or j3 final state can serve as spectatorproduces particle. a Forcode diagrams for the squared with a12 quark matrix and elements a gluon of in the the real initial3 emission diagrams by calling the in order to account for all possible initialqq state configurations. Bothqg topologiesfor leadpT to IR/collinear& 100 GeV and deviates up to 30% from the Herwig++ shower results. HELAS subroutines basedd⇥A on= the helicity amplitudeand d⇥ formalismA = [70].. (7) state only three dipoles are necessary:divergencies. The emitted Diagrams antiquark withqq qq caninitialD onlyi states, become which collinear containqg to soft theDi and collinear divergencies, are The dipoles needed to render thei=1 real emission matrix elementsi=1 finite are organized in pairs of initial state gluon while the othercollected three in particles Figs. 4 can (a) act and as (b). the spectator The diagrams particle. with Hence,qg initial the states which emit a massless counterterms d⇥A which are subtractedpotentially from collinear the squared partons real with emission an additional matrix elements reference read: to a spectator particle.Considering For diagrams the rapidity distributions of the second and the third hardest jet depicted in anti-quark,withThe two real quarks emission result in in diagrams thecollinear initial indivergencies state Fig. 5 this (c) gives haveonly. torise The be to corresponding handled twelve withindividual care diagram in dipoles: parameter is shown The inregions emitted Fig. 5 Gavin et al., arXiv:1305.4061 where(a).gluon12 the can gluino be collinear is heavier or soft than and3 one in or each both case squarks any of in the the other final state. three particles InFig. this case in 20 the these we initial dia- observe or that all showers essentially reproduce the NLO result for the second jet d⇥Agrams= giveqq riseand to anotherd⇥A kind= of singularityqg . since the intermediate(7) gluino can be produced qq final statei can serve as spectatorqg particle.i For diagrams with a quark and(this a gluon also in the holds initial for the hardest jet). The results of the third jet show, however, rather large Introductionon-shell.TheD The soft subtraction and to collinear Event procedure divergencies GeneratorsD for these are divergencies subtracted by is described the Catani-Seymour in detail in dipolesSec. 2.2. which 44 Bryan Webber, MCnet School, 2014 state i=1 only three dipoles are necessary: i=1 The emitted antiquark can only become collinear to the haveinitial been state generated gluon while using the the otherSuperAutoDipole three particles can 1.0 actpackage as the spectator[66, 67].diSuperAutoDipole particle. erences Hence, between the the showers, again as in the case of undecayedq ˜ in the central region of The real emission diagrams in Fig. 5 (c) have to be handled with careA in parameter regions countertermsHaving subtractedd⇥A which the are counterterm subtractedd⇥ fromfrom the squared the real real emission emission matrix matrixthe elements detector.elements the read: IR While Pythia ranges only slightly above the NLO prediction, the Herwig++ where the gluino is heavier thandivergencies one or both in the squarks virtual in corrections the final state. are still In this left. case With these the dia- choice of dipoles as published in 7 j3 grams give rise to another kind[64,of 65] singularity the counterterms since the in intermediate Eq. (7)12 can begluino integrated can be analytically produced3 over theshowers one-parton (in phase particular the default shower) predict higher rates around y = 0. on-shell. The subtraction procedure for these divergenciesd⇥ isA described= qq in detailand in Sec.d⇥A 2.2.= qg . (7) space. This integration yieldsqq the so-calledDi I-terms and PKqg -termsDi which can be evaluated in the 2-particle phase space used for the i=1 Born matrix elements and i=1 virtual corrections. The former Having subtracted the counterterm d⇥A from the real emission matrix elements the IR These di erences can again be attributed to a large extent to di erences in the IS shower. containThe all real the emission 1/ poles diagrams that are necessary in Fig. 5 (c) to cancel have to the be poles handled in the with virtual care contributions.in parameter regions The divergencies in the virtual corrections are still left. With the choice of dipoles as published in j3 where the gluino is heavier than one or both squarks in the final state. InTurning this case these o ISR, dia- the Dipole shower and Pythia predict (within (10%)) identical y distri- [64, 65] the counterterms in Eq. (7) can be integrated analytically over the one-parton phase O space. This integration yields thegrams so-called give riseI-terms to another and PK kind-terms of singularity which can8 since be evaluated the intermediate in gluinobutions. can be produced The Herwig++ default shower, however, still deviates by more than 20% from this on-shell. The subtraction procedure for these divergencies is described in detail in Sec. 2.2. the 2-particle phase space used for the Born matrix elements and virtual corrections. The former result. The pj3 curves for the Herwig++ showers are still nearly identical for pj3 > 100 GeV, contain all the 1/ poles that are necessary to cancel the poles in the virtual contributions. The T T Having subtracted the counterterm d⇥A from the real emission matrixwhile elements the di the erence IR to Pythia is reduced to < 10%. However, for soft jets the default shower divergencies in the virtual corrections are still left. With the choice of dipoles as published in [64, 65] the counterterms8 in Eq. (7) can be integrated analytically overdeviates the one-parton by phase up to +15% from the other two shower MCs. To clarify if these e ects are caused space. This integration yields the so-called I-terms and PK-terms whichsolely can be by evaluated the in missing truncated shower in Herwig++ or if the di erences in the shower al- the 2-particle phase space used for the Born matrix elements and virtual corrections. The former contain all the 1/ poles that are necessary to cancel the poles in the virtualgorithms contributions. (especially The the size of the available phase space for radiation) are responsible for the observed discrepancies would require more detailed studies. 8 A further interesting observable for the comparison of the jet structure of an event with a 33 Conclusions and Prospects • Standard Model has (so far) been spectacularly confirmed at the LHC • Monte Carlo event generation of (SM and BSM) signals and backgrounds plays a big part • Matched NLO and merged multi-jet + parton shower generators have proved essential ✤ Automation and NLO merging in progress ✤ NNLO much more challenging • Best possible SM precision is essential for BSM searches Introduction to Event Generators 45 Bryan Webber, MCnet School, 2014 Thanks for listening! Introduction to Event Generators 46 Bryan Webber, MCnet School, 2014 Backup Introduction to Event Generators 47 Bryan Webber, MCnet School, 2014 ATLAS SUSY Search Introduction to Event Generators 48 Bryan Webber, MCnet School, 2014 ATLAS Exotica Search Introduction to Event Generators 49 Bryan Webber, MCnet School, 2014 CMS Exotica Search LQ1, β=0.5 LQ1, β=1.0 XCLUSION IMITS E CMS EXOTICA 95% CL E L (T V) LQ2, β=0.5 q* (qg), dijet LQ2, β=1.0 q* (qW) LQ3 (bν), Q=±1/3, β=0.0 LeptoQuarks q* (qZ) LQ3 (bτ), Q=±2/3 or ±4/3, β=1.0 q* , dijet pair stop (bτ) q* , boosted Z 0 1 2 3 4 5 6 e*, Λ = 2 TeV Compositeness μ*, Λ = 2 TeV b’ → tW, (3l, 2l) + b-jet q’, b’/t’ degenerate, Vtb=1 0 1 2 3 4 5 6 Z’SSM (ee, µµ) b’ → tW, l+jets 4th Z’SSM (ττ) B’ → bZ (100%) Generation Z’ (tt hadronic) width=1.2% T’ → tZ (100%) Z’ (dijet) t’ → bW (100%), l+jets Z’ (tt lep+jet) width=1.2% t’ → bW (100%), l+l Z’SSM (ll) fbb=0.2 G (dijet) Heavy 0 1 2 3 4 5 6 G (ttbar hadronic) Resonances C.I. Λ , Χ analysis, Λ+ LL/RR G (jet+MET) k/M = 0.2 C.I. Λ , Χ analysis, Λ- LL/RR G (γγ) k/M = 0.1 C.I., µµ, destructve LLIM G (Z(ll)Z(qq)) k/M = 0.1 C.I., µµ, constructive LLIM Contact W’ (lν) C.I., single e (HnCM) W’ (dijet) C.I., single µ (HnCM) Interactions C.I., incl. jet, destructive W’ (td) W’→ WZ(leptonic) C.I., incl. jet, constructive WR’ (tb) 0 5 10 15 WR, MNR=MWR/2 Ms, γγ, HLZ, nED = 3 WKK μ = 10 TeV Ms, γγ, HLZ, nED = 6 ρTC, πTC > 700 GeV Ms, ll, HLZ, nED = 3 String Resonances (qg) Ms, ll, HLZ, nED = 6 s8 Resonance (gg) E6 diquarks (qq) MD, monojet, nED = 3 Axigluon/Coloron (qqbar) MD, monojet, nED = 6 gluino, 3jet, RPV MD, mono-γ, nED = 3 0 1 2 3 4 5 6 MD, mono-γ, nED = 6 gluino, Stopped Gluino MBH, rotating, MD=3TeV, nED = 2 stop, HSCP MBH, non-rot, MD=3TeV, nED = 2 Extra Dimensions stop, Stopped Gluino Long MBH, boil. remn., MD=3TeV, nED = 2 stau, HSCP, GMSB hyper-K, hyper-ρ=1.2 TeV Lived MBH, stable remn., MD=3TeV, nED = 2 & Black Holes neutralino, cτ<50cm MBH, Quantum BH, MD=3TeV, nED = 2 Sh. Rahatlou0 1 2 3 4 5 6 0 1 2 3 4 5 1 6 Introduction to Event Generators 50 Bryan Webber, MCnet School, 2014 Drell-Yan vectorW boson & productionZ0 atDrell-Yan Tevatron vector boson production W boson pT spectrum compared to D0 run I data Z boson pT spectrum compared to D0 run II data D0 Run I: W D0 Run II: Z0 (with MEC) (with MEC) Solid line: NLO Herwig++ POWHEG Blue dashes: MC@NLOSolid line: NLO Herwig++ POWHEG Blue dashes: MC@NLO Red dashes: Herwig++• Herwig++ with ME corrections includes W/Z+jetRed dashes: (MEC) Herwig++ with ME corrections • All agree (tuned) at Tevatron Normalized to data • Hamilton, Richardson, Tully JHEP10(2008)015 Introduction to Event Generators 51 Bryan Webber, MCnet School, 2014 POWHEG matrix elements [L. D’Errico, P. Richardson – JHEP 1202 (2012) 130] pp at Tevatron Run II gg at Tevatron (a) 50 GeV< M <80 GeV (a) 50 GeV< M⇥⇥ <80 GeV 2 ] 10 2 DØ data DØ data [pb/GeV 1 Hw++ POWHEG 10 Hw++ POWHEG [pb/rad/GeV] M Hw++ LO Hw++ LO 10 3 ⇥⇥ /d M ⇥ p /d ⇥⇥ /d ⇥ 2 d 10 /d 4 ⇤ 10 d 3 ⇥ 3 ⇤ 2 ⇥ 2 ⇤ 1 ⇥ 1 ⇤ 0 ⇥ 0 ⇤ (MC - data) -1 ⇥ (MC - data) -1 ⇤ -2 ⇥ -2 ⇤ -3 ⇥ -3 ⇤ 10 20 30 40 50 60 70 80 1.6 1.8 2 2.2 2.4 2.6 2.8 3 p [GeV] ⇥⇥ [rad] ⇥ • Absolute normalization LO too low POWHEG agrees with rate and distribution Simon Pl¨atzer (DESY• Theory Group) Herwig++ @ higher orders 6/21 • At LHC, important background for Higgs search D’Errico & Richardson, JHEP02(2012)130 Introduction to Event Generators 52 Bryan Webber, MCnet School, 2014 panel of Fig. 1 we show the full NLO result normalized to the result obtained neglecting the bottom quark. We see that, when only the top contribution is considered, the cross section at low pT is larger than the corresponding cross section in the large-mt limit. In this region the recoiling parton is soft and/or collinear, and the differential cross section factorizes into a universal factor times the Born level contribution. The limit of the solid and dashed histograms in the left panel of Fig. 1 thus correspond to the ratios σLO(mt,mb)/σLO(mt )=0.949 and σLO(mt)/σLO(mt )=1.066, respectively. →∞ →∞ The results in Fig. 1 show that the impact of the bottom quark is important, especially in the low-pT region, since it substantially deforms the shape of the spectrum. At large pT values, the impact of the bottom quark becomes small and the differential cross section quickly departs from its value in the large-mt limit. This is a well known feature of the large-mt approximation: at large pT the parton recoiling against the Higgs boson is sensitive to the heavy-quark loop, and the large-mt approximation breaks down. Another feature that is evident from Fig. 1 is that the qualitative behaviour of the results is rather different. When considering the NLO result with only the top quark included, in a wide region of transverse momenta the shape of the spectrum is rather stable and in rough agreement with what is obtained in the large-mt approximation. This is not the case when the bottom contribution is included: the shape of the spectrum quickly changes in the small- and intermediate- pT regiont,b and the spectrummass becomes harder. Weeffects will come back to this point inon Sec. 3.1. Higgs pT ) HRes MC@NLO ) !1 Fixed order t Q1 = mh/2,Q2 = mb m ( Q1 = Q2 = mh/2 !1 t /d ) top-quark mass. b m ( ,m When the bottom-quark mass is included, the behaviour of the spectrum is rather different. t When pT < mb the behaviour is still driven by the singularities of the H +3 parton matrix element, m /d ( but in the∼ region mb < pT b ∼ d In order to better understand what happens, in the following we examine the analytic behaviour ,m of the QCD matrix elements [33]. To make the discussion simpler let us consider the amplitude t of the Higgs production in the qg Hq channel. In this channel only one Feynman diagram → m contributes, which is shown in Fig. 2: it consists in a triangular loop in which one of the gluons is ( off shell and radiated from the incoming quark line. In the small-pT region the singular behaviour Figure 1: Transverse momentum distribution for a SM Higgs with mH =125GeVcomputed d ) is due to the collinear region, in which the gluon with momentum p p goes on shell. 1 − 3 at NLO. Left: result normalized toResummed the large-mt approximation. Right: normalized to the mt- dependent result. In Fig. 3 we plot the pT spectrum in this channel normalized to the corresponding result in !1 the large-mt limit. We see that the qualitative behaviour is the same observed in Fig. 1: the t behaviour of the spectrum is distorted in the small and intermediate pT region by the presence of m ( the bottom mass. The mass effects in differential NLO distributions were previously discussed in Ref. [13]. We p3 /d pTh (GeV) have) compared our results with those of Ref. [13] and found agreement. p1 b ,m H t m b mass affects pT<50 GeV ( • p2 d Motivates lower scaleFigure Q 2:2 Typicalfor b*b Feynman & diagrams b*t forterms the qg Hq process. 5 • → Figure 5: Transverse momentumGrazzini spectra & atSargsyan, NLL+NLO for arXiv:1306.4581Q2 = mb and Q2 = mH /2 normalized to the result in the large-mt limit. • Implemented as shower veto in [email protected] both the shape and the normalization of the pT cross section, the choice of the resummation scale Q affects only the shape of the spectrum. In particular, as discussed above, increasing (decreas- ing) Q makes the spectrum harder (softer). In Fig. 6 (left) we present our resummed spectrum at NLL+NLOIntroduction with inclusion to Event of theheavy-quark Generators masses as in Fig. 5, and compare it with the 53 Bryan Webber, MCnet School, 2014 spectrum computed in the large-mt limit for Q = mH /4,mH with the numerical program HqT. We see that, as anticipated, the effect of resummation scale variations is large, well beyond the effect of heavy-quark masses for pT > 20 GeV. In the region pT < 20 GeV instead, the effect of the bottom-quark mass and of resummation∼ scale variation are com∼ parable. In Fig. 6 (right) we present our resummed spectrum computed with Q2 = mb/2,mb, 2mb.Weseethattheeffects of Q2 variations around mb is relatively small, and leaves the shape of the distribution rather stable. § We now move to consider the NNLL+NNLO results. Since for mH =125GeVwehave Figure 3: Transverse momentum distribution for a SM Higgs with m =125GeVcomputed σ (m ,m )/σ (m ) 1.007, the inclusion of heavy quark masses, as happens at H NNLO t b NNLO t →∞ ∼ at NLO in the qg + gq channel. Left: result normalized to the large-m approximation. Right: NLL+NLO, affects the shape of the spectrum, but leaves the normalization of the transverse t momentum cross section essentially unchanged. In Fig. 7 (left) the NNLL+NNLO spectrum normalized to the mt-dependent result. normalized to the NNLL+NNLO result in the large-mt limit is presented, and compared to the large-mt limit results for Q = mH /4andQ = mH . Comparing with Fig. 6 (left) we see that the impact of heavy-quark mass effects in the NNLL+NNLO result is similar to what observed This behaviour is somewhat against intuition: in the region pT mH we could expect the ≪ at NLL+NLO. This should somewhat be expected, since the NNLL+NNLO terms we are adding are evaluated in the large-mt limit. We notice that, as is known [23], the effect of resummation 9 scale variations at this order is much smaller and we conclude that masseffects in the low-pT § 4 We remind the reader (see Sec. 2) that the (αS) terms in our calculation are rescaled with the exact mt dependent Born cross section. O 14