Introduction to Monte Carlo Event Generators Rachid Mazini Academia Sinica, Taiwan 6th School for LHC Physics NCP Islamabad, Pakistan 21-31 August 2017

Outline Hadron-level event generation Parton showering Hadronization and underlying event Examples of results MC Simulation Introduction to MC Event Generators R. Mazini Academia Sinica

A high-mass dijet event Mjj = 5.15 TeV CMS PAS EXO-12-059 Introduction to MC Event Generators R. Mazini Academia Sinica

LHC dijet p Hard process Introduction to MC Event Generators R. Mazini Academia Sinica

LHC dijet p Hard process Parton showers Introduction to MC Event Generators R. Mazini Academia Sinica

LHC dijet p Hard process Parton showers Underlying event Introduction to MC Event Generators R. Mazini Academia Sinica

LHC dijet p Hard process Parton showers Underlying event Confinement Introduction to MC Event Generators R. Mazini Academia Sinica

) LHC dijet quark jet ) p beam jet beam jet p Hard process Parton showers Underlying event Confinement Hadronization quark jet Introduction to MC Event Generators ) R. Mazini Academia Sinica

Theoretical Status p Hard process Exact fixed-order perturbation theory p Hard process Introduction to MC Event Generators R. Mazini Academia Sinica

Theoretical Status p Hard process Parton showers Exact fixed-order perturbation theory Approximate all-order perturbation theory p Hard process Parton showers Introduction to MC Event Generators 10 R. Mazini Academia Sinica

Theoretical Statusquark jet ) Theoretical Statusquark jet Exact fixed-order perturbation theory Approximate all-order perturbation theory Semi-empirical ) local models only p beam jet beam jet p Hard process Parton showers Underlying event Confinement Hadronization quark jet Introduction to MC Event Generators ) R. Mazini Academia Sinica

QCD Factorization momentum fractions parton distributions at scale µ2 hard process cross section Jet formation and underlying event take place over a much longer time scale, with unit probability Hence they cannot affect the cross section Scale dependences of parton distributions and hard process cross section are perturbatively calculable, and cancel order by order Introduction to MC Event Generators R. Mazini Academia Sinica

Parton Shower 0 1 E3 3 hard process Ei+1 z = Ei E0 E1 E2 2 Shower = sequence of emissions with decreasing angles and energies Approximation: keep only contributions  1/ For very small energy and/or angle, emission is “unresolvable” Introduction to MC Event Generators R. Mazini Academia Sinica

Parton Shower Ei+1 hard process E0 E1 E3 ✓0 ✓1 ✓3 ✓2E2 ✓4 E4 z = Ei Introduction to MC Event Generators R. Mazini Academia Sinica

Parton Shower Evolution hard process ✓0 ✓1 Ei+1 z = ✓3 ✓2E2 ✓4 E4 Ei E0 E1 E3 ✓0 4 1 + z2 H A D Pq!q (z) = 3 1 z R O (E1, ✓1) N I Z A T I O N (E2, ✓2) (E3, ✓3) (E4, ✓4) E✓ < Qmin E0 Introduction to MC Event Generators 15 R. Mazini Academia Sinica

Parton Shower Evolution hard process ✓0 ✓1 Ei+1 z = ✓3 ✓2E2 ✓4 E4 Ei E0 E1 E3 ✓0 4 1 + z2 H A D Pq!q (z) = 3 1 Pg!g (z) = z R O (E0 - E1, ✓1) (E1, ✓1) N I Z A T I O N ✓ 1 + z + (1 - z) 3 z(1 - z) 4 4 (E2, ✓2) (E3, ✓3) 1 2 (E4, ✓4) ⇥z 2 2⇤ Pg!q = + (1 - z) E✓ < Qmin E E0 Introduction to MC Event Generators R. Mazini Academia Sinica

Hadronization Models In parton shower, relative transverse momenta evolve from a high scale Q towards lower values At a scale near LQCD~200 MeV, perturbation theory breaks down and hadrons are formed Before that, at scales ~ few x LQCD, there is universal preconfinement of colour Colour, flavour and momentum flows are only locally redistributed by hadronization Introduction to MC Event Generators R. Mazini Academia Sinica

Hadronization Models In parton shower, relative transverse momenta evolve from a high scale Q towards lower values At a scale near LQCD~200 MeV, perturbation theory breaks down and hadrons are formed Before that, at scales ~ few x LQCD, there is universal preconfinement of colour Colour, flavour and momentum flows are only locally redistributed by hadronization Introduction to MC Event Generators R. Mazini Academia Sinica

String Hadronization Model In parton shower, relative transverse momenta evolve from a high scale Q towards lower values At a scale near LQCD~200 MeV, perturbation theory breaks down and hadrons are formed Before that, at scales ~ few x LQCD, there is universal preconfinement of colour Colour flow dictates how to connect hadronic string (width ~ few x LQCD) with shower Introduction to MC Event Generators R. Mazini Academia Sinica

String Hadronization Model In parton shower, relative transverse momenta evolve from a high scale Q towards lower values At a scale near LQCD~200 MeV, perturbation theory breaks down and hadrons are formed Before that, at scales ~ few x LQCD, there is universal preconfinement of colour Colour flow dictates how to connect hadronic string (width ~ few x LQCD) with shower Introduction to MC Event Generators R. Mazini Academia Sinica

String Hadronization Model At short distances (large Q), QCD is like QED: colour field lines spread out (1/r potential) At long distances, gluon self-attraction gives rise to colour string (linear potential, quark confinement) Intense colour field induces quark-antiquark pair creation: hadronization + – Introduction to MC Event Generators R. Mazini Academia Sinica

Cluster Hadronization Model In parton shower, relative transverse momenta evolve from a high scale Q towards lower values At a scale near LQCD~200 MeV, perturbation theory breaks down and hadrons are formed Before that, at scales ~ few x LQCD, there is universal preconfinement of colour Decay of preconfined clusters provides a direct basis for hadronization Introduction to MC Event Generators R. Mazini Academia Sinica

Cluster Hadronization Model In parton shower, relative transverse momenta evolve from a high scale Q towards lower values At a scale near LQCD~200 MeV, perturbation theory breaks down and hadrons are formed Before that, at scales ~ few x LQCD, there is universal preconfinement of colour Decay of preconfined clusters provides a direct basis for hadronization Introduction to MC Event Generators R. Mazini Academia Sinica

Cluster Hadronization Model Mass distribution of preconfined clusters is universal Phase-space decay model for most clusters High-mass tail decays anisotropically (string-like) Introduction to MC Event Generators R. Mazini Academia Sinica

Hadronization Status No fundamental progress since 1980s Available non-perturbative methods (lattice, AdS/ QCD, ...) are not applicable Less important in some respects in LHC era ✤ Jets, leptons and photons are observed objects, not hadrons But still important for detector effects ✤ ✤ Jet response, heavy-flavour tagging, lepton and photon isolation, ... Introduction to MC Event Generators R. Mazini Academia Sinica

Underlying Event (MPI) Multiple parton interactions in same collision ✤ Depends on density profile of proton Assume QCD 2-to-2 secondary collisions ✤ Need cutoff at low pT Need to model colour flow ✤ Colour reconnections are necessary Introduction to MC Event Generators R. Mazini Academia Sinica

Sample of Event Generator Results Introduction to MC Event Generators R. Mazini Academia Sinica

MC Event Generators HERWIG PYTHIA SHERPA http://projects.hepforge.org/herwig/ Angular-ordered parton shower, cluster hadronization v6 Fortran; Herwig++ Herwig 7 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 MC Event Generators R. Mazini Academia Sinica

Jets Introduction to MC Event Generators R. Mazini Academia Sinica

Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 Jet pT 7000 GeV pp Jets 7000 GeV pp Jets d/dp [pb/GeV] Rivet 1.8.3,  3M events d/dp [pb/GeV] 107 Rivet 1.8.3,  3M events 106 Jet Transverse Momentum (anti -k (0.4)) Jet Transverse Momentum (anti-k (0.4)) T 106 T ATLAS ATLAS T 105 Herwig++ (Def) Pythia 8 (Def) T 105 Herwig++ (Def) Pythia 8 (Def) Sherpa (Def) Sherpa (Def) 104 104 103 103 102 102 10 10 1 mcplots.cern.ch mcplots.cern.ch 1 10-1 ATLAS_2011_S9128077 ATLAS_2011_S9128077 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 10-1 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 10-2 200 400 600 800 200 400 600 800 p (2nd jet) [GeV] T p (leading jet) [GeV] T Ratio to ATLAS Ratio to ATLAS 1.5 1.5 1 1 0.5 0.5 200 400 600 Leading jet 800 200 400 600 800 Second jet http://mcplots.cern.ch Introduction to MC Event Generators R. Mazini Academia Sinica

Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 Jet pT 7000 GeV pp Jets 7000 GeV pp Jets d/dp [pb/GeV] Rivet 1.8.3,  3M events d/dp [pb/GeV] 104 Rivet 1.8.3,  3M events 106 105 104 103 102 Jet Transverse Momentum (anti-k (0.4)) Jet Transverse Momentum (anti-k (0.4)) T T ATLAS Herwig++ (Def) Pythia 8 (Def) Sherpa (Def) ATLAS Herwig++ (Def) Pythia 8 (Def) Sherpa (Def) 103 T T 102 10 10 1 10-1 10-2 10-3 10-4 1 mcplots.cern.ch mcplots.cern.ch ATLAS_2011_S9128077 10-1 ATLAS_2011_S9128077 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 100 200 300 400 500 p (3rd jet) [GeV] T 100 150 200 p (4th jet) [GeV] T Ratio to ATLAS Ratio to ATLAS 1.5 1.5 1 1 0.5 0.5 100 200 300 400 500 100 150 200 Extra jets from parton showers Introduction to MC Event Generators R. Mazini Academia Sinica

Jet event shapes Tc ⌘ max Âi |~p?,i · nˆ T| Âi |~p?,i ⇥ nˆ T,C | 7000 GeV pp Jets 7000 GeV pp Jets dN/d ln(1-T ) C Rivet 1.8.3,  4.1M events ) m,C Rivet 1.8.3,  3M events Central Transverse Thrust (125 < p < 200) CMS dN/d ln(T Central Transverse Minor (90 < p < 125) 1 0.2 CMS Herwig++ (Def) Pythia 8 (Def) Sherpa (Def) Herwig++ (Def) Pythia 8 (Def) Sherpa (Def) 1/N 1/N 0.15 0.1 10-1 0.05 mcplots.cern.ch mcplots.cern.ch CMS_2011_S8957746 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 -10 -5 CMS_2011_S8957746 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 -4 -2 10-2 -6 ln(1-T ) ln(T ) C m,C Ratio to CMS Ratio to CMS 1.5 1.5 1 1 0.5 0.5 -10 -5 -6 -4 -2 Âi |~p?,i · nˆ T| Âi |~p?,i ⇥ nˆ T,C | Tc ⌘ max Tm,C ⌘ i p?,i nˆ T  i p?,i  Introduction to MC Event Generators R. Mazini Academia Sinica

Jet profile pT,i pT,i  1 dr r(r) =  1960 GeV ppbar Jets 7000 GeV pp Jets (r/R) Rivet 1.8.3,  5.8M events (r) Rivet 1.8.3,  577k events Differential jet shape  (r/R) (186 < p < 208) T Differential jet shape (r/R) CDF Herwig++ (Def) Pythia 8 (Def) Sherpa (Def) ATLAS Herwig++ (Def) Pythia 8 (Def) Sherpa (Def) 10 10 1 1 mcplots.cern.ch mcplots.cern.ch 10-1 10-1 CDF_2005_S6217184 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 ATLAS_2011_S8924791 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 0.5 1 0.2 0.4 0.6 r/R r Ratio to CDF Ratio to ATLAS 1.5 1.5 1 1 0.5 0.5 0.5 1 0.2 0.4 0.6  rb ra R  ra <ri<rb pT,i 1 dr r(r) =  ri<R pT,i Introduction to MC Event Generators R. Mazini Academia Sinica

Jet multiplicity Multijets W+jets N jet Njet 7000 GeV pp Jets 7000 GeV pp W  [pb] 108 Rivet 1.8.3,  2.9M events (W +  N jets) [pb] Rivet 1.8.3,  6.8M events Jet multiplicity (anti-k (0.4)) Jet multiplicity ((E >20,|_j|<2.8,E >20,|_e|<2.47 ,p ^>25,M_T>40,R >0.5)) * T Tj Te T  j 107 ATLAS ATLAS jet Herwig++ (Def) Pythia 8 (Def) 104 Herwig++ (Def) Pythia 8 (Def) 106 Sherpa (Def) Sherpa (Def) 105 103 104 103 mcplots.cern.ch 102 mcplots.cern.ch 102 ATLAS_2011_S9128077 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 ATLAS_2010_S8919674 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 1 2 10 2 4 6 3 N jet Njet Ratio to ATLAS Ratio to ATLAS 1.5 1.5 1 1 0.5 0.5 2 4 6 1 2 3 Multijets W+jets Introduction to MC Event Generators R. Mazini Academia Sinica

Hadrons from Z0 decay 10-1 Nch Nch ⇡± ⇡0 K± K0 D0,± B0,± ⌃± ⌘0 Hadron multiplicities in e+e- at 91 GeV multiplicity Nch ⇡± ⇡0 LEP, SLD Pythia 8.145 Sherpa 1.2.3 Herwig++ 2.5.0 10 1 K± K0 ⌘ 1 p K⇤0 ⇤ D0,± B0,± ⌘0 ⌃± 10-1 1.3 1.2 1.1 1.0 0.9 0.8 0.7 MC/data Nch 1 2 5 mass [GeV] Introduction to MC Event Generators R. Mazini Academia Sinica

Underlying Event Introduction to MC Event Generators R. Mazini Academia Sinica

Underlying Event Transverse charged particle density 900 GeV pp Underlying Event 7000 GeV pp Underlying Event d2 N/dd Rivet 1.8.3,  7.3M events d N chg/dd Rivet 1.8.3,  6.8M events 0.9 3 Average Charged Particle Density (TRNS) Average Charged Particle Density (TRNS) (| | < 2.5, p > 0.1 GeV/c) T 0.8 CMS ATLAS Herwig++ (Def) 2.5 Herwig++ (Def) 2 Pythia 8 (Def) Sherpa (Def) Pythia 8 (Def) Sherpa (Def) 0.7 leading jet 0.6 2 0.5 f Df 1.5 0.4 towards |Df| < 600 0.3 1 mcplots.cern.ch mcplots.cern.ch 0.2 transverse 600 < |Df| < 1200 transverse 600 < |Df| < 1200 CMS_2011_S9120041 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 ATLAS_2010_S8894728 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 0.5 0.1 10 20 p (leading track-jet) [GeV] T 5 10 15 20 away |Df| > 1200 p (leading track) [GeV] T Ratio to CMS Ratio to ATLAS 1.5 1.5 1 1 0.5 0.5 10 20 5 10 15 20 Transverse charged particle density Introduction to MC Event Generators R. Mazini Academia Sinica

Underlying Event Transverse mean pT 900 GeV pp Underlying Event 7000 GeV pp Underlying Event  p  Rivet 1.8.3,  7.3M events  p  Rivet 1.8.3,  6.8M events T T Average p vs p (TRNS) (|| < 2.5, p > 0.5 GeV/c) T T1 T 1.6 Average p vs p (TRNS) (|| < 2.5, p > 0.5 GeV/c) T T1 T 1.4 ATLAS ATLAS Herwig++ (Def) Pythia 8 (Def) Sherpa (Def) Herwig++ (Def) 1.4 Pythia 8 (Def) Sherpa (Def) leading jet 1.2 1.2 1 1 f Df 0.8 towards |Df| < 600 0.8 mcplots.cern.ch mcplots.cern.ch 0.6 transverse 600 < |Df| < 1200 transverse 600 < |Df| < 1200 0.6 ATLAS_2010_S8894728 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 ATLAS_2010_S8894728 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 0.4 0.4 2 4 6 8 10 5 10 15 20 away |Df| > 1200 p (leading track) [GeV] T p (leading track) [GeV] T Ratio to ATLAS Ratio to ATLAS 1.5 1.5 1 1 0.5 0.5 2 4 6 8 10 5 10 15 20 Transverse mean pT Introduction to MC Event Generators R. Mazini Academia Sinica

Vector Bosons Introduction to MC Event Generators R. Mazini Academia Sinica

Z0 pT Absolute normalization Normalized to data 1960 GeV ppbar Z (Drell-Yan) 7000 GeV pp Z (Drell-Yan) d/dp (Z) [pb/GeV] Rivet 1.8.3,  7.9M events 1/d/dp [GeV-1] Rivet 1.8.3,  7M events 103 p (Z) (muon channel) p (Z) (electron channel, dressed) T T 1 102 D0 Herwig++ (Def) Pythia 8 (Def) Sherpa (Def) T ATLAS Herwig++ (Def) Pythia 8 (Def) Sherpa (Def) T 10-1 10 1 10-2 10-1 10-3 10-2 10-4 10-3 mcplots.cern.ch mcplots.cern.ch 10-5 10-4 D0_2010_S8671338 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 100 200 ATLAS_2011_S9131140 Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3 300 100 200 300 p (Z) [GeV] T p (ee) [GeV] T Ratio to D0 Ratio to ATLAS 1.5 1.5 1 1 0.5 0.5 100 200 300 100 200 300 Introduction to MC Event Generators R. Mazini Academia Sinica

Limitations of LO+parton shower • Hard process: qq¯  Z0/W± pT(Z) pT(jet 1) pT(jet 2) need next-to-LO (NLO) need multijet merging Leading-order (LO) normalization Worse for high pT and/or extra jets • Introduction to MC Event Generators R. Mazini Academia Sinica

Latest Z0+jets (13 TeV) MG5_aMC+Py8 … = NLO+multijet merged event generators ATLAS, EPJC77(2017)361 Introduction to MC Event Generators R. Mazini Academia Sinica

Monte Carlo Simulation in HEP analysis Physics process and detector simulation . . . . data storage . . . . Simulation of many (billions) of events simulate physics process e.g. p p -> Z or p p -> H plus the detector response to the produced particles understand detector response and analysis parameters (lost particles, resolution, efficiencies, backgrounds ) and compare to real data Note : simulations present from beginning to end of experiment, needed to make design choices Exactly the same steps as for the data

Monte Carlo Simulation

Monte Carlo Simulation: The Dream!

Monte Carlo Simulation: The reality

Summary Parton shower keeps large small-angle contributions Shower gives preconfinement of colour This allows local model of hadronization String and cluster models both still viable Underlying event due to multiple interactions LO+PS event generators underestimate multijets Further improvements (NLO+merging) now used Introduction to MC Event Generators R. Mazini Academia Sinica