HEP Computing Tools - lecture and tutorial Graduate lecture Rene Poncelet 9th/11th March 2020 Cavendish Laboratory 1
Disclaimer This course is meant to: • Be a starting point in HEP computing. • Provide a guided first contact with a Monte-Carlo Event Generator. • Introduce various (abstract) concepts which HEP physicists encounter in day-to-day basis. • Provide (hopefully) ”Ah, this is how it looks in practice” moments. This course does not provide: • A complete or general overview over HEP computing. This would be just to wide... • A theoretical background for introduced concepts. This would take a long time... • A complete introduction into the usage of MC-event-generators. They are just too complicated... 2
What it is about? 3
What it is about? → The study of fundamental interactions requires high energies → High energy scattering processes produce many particles, particularly if strongly interacting particles are involved → QCD → Interesting processes (production of massive particles like top-quarks, electroweak bosons (W,Z,H, γ )) are rare, due to large required energies or α EW couplings → How do we learn to distinguish interesting processes from the rest? ⇒ Modelling of such events is essential! Q: How one can understand these complex processes from a theoretical point of view? QFT + Lagrange density L → Events ⇐ Far too complicated! 4
What it is about? → The study of fundamental interactions requires high energies → High energy scattering processes produce many particles, particularly if strongly interacting particles are involved → QCD → Interesting processes (production of massive particles like top-quarks, electroweak bosons (W,Z,H, γ )) are rare, due to large required energies or α EW couplings → How do we learn to distinguish interesting processes from the rest? ⇒ Modelling of such events is essential! Q: How one can understand these complex processes from a theoretical point of view? QFT + Lagrange density L → Something happens → Events 4
The (theory) picture in mind QCD tells how factorize processes at different energy scales Q : • Q ≫ Λ QCD Hard scattering perturbative QCD • Q ≥ O (Λ QCD ) Parton-shower, PDF-evolution • Q ∼ O (Λ QCD ) Hadronization, Multi-parton interactions / Underlying event,. . . non-perturbative QCD ⇓ Monte Carlo Event Generators 5
Monte Carlo Integration in a nut-shell � I = d xf ( x ) Ω • Numerical integration technique relying on random numbers • Hit: ω max · # 1 ≤ f (# 2 ) • Estimator for I : I = # hits ˆ # trials • MC sampling with Hit-and-Miss algorithm: Accepting event # if ω max · # ′ ≤ f (#) ⇓ [source: Rajiv Gupta] Straight-forward translation to cross section: � d Φ |M (Φ) | 2 σ = Ω � [0 , 1] n d n � x )) | 2 = x J ( � x ) |M (Φ( � 6
The hard interaction: The fixed order picture Hadronic cross section in collinear factorization: �� 1 � d x 1 d x 2 f a / h 1 ( x 1 , µ 2 F ) f b / h 2 ( x 2 , µ 2 σ ab ( x 1 P 1 , x 2 P 2 ; α S ( µ 2 R ) , µ 2 R , µ 2 σ h 1 h 2 ( P 1 , P 2 ) = F )ˆ F ) 0 ab • Factorization allows to describe the parton content of hadrons with the help of PDFs • And partonic cross sections independent of the hadrons content or state Partonic cross section as a perturbative series in α S : � � σ (0) σ (1) σ (2) α 3 σ ab = ˆ ˆ + ˆ + ˆ + O S ab ab ab ���� ���� ���� LO NLO NNLO The leading order cross section: � σ (0) d Φ X |M (0) ( ab → X ) | 2 ˆ ab = 7
The hard interaction beyond LO • Higher order in the coupling → additional emissions • It is necessary to sum (incoherently) over processes with a different number of final partons · · · • Exchange or emission of partons lead to divergences virtual - UV/IR real - IR collinear real - IR soft angle between partons arbitrarily virtual momentum arbitrarily gluon energy arbitrarily small large/small small 1 1 1 For example real emission: ( p + k ) 2 | p 2 , k 2 =0 = 2 p · k = p 0 k 0 (1 − cos θ ) → How to deal with these singularities? → Subtraction schemes 8
The general idea of subtraction • Add to the original cross section σ = σ LO + σ NLO � � � � σ LO = d σ NLO = d σ R + d σ B σ NLO ≡ d σ V , m m +1 m an identity involving approximations to the real radiation cross section � � � σ NLO = � d σ R − d σ A � d σ A + d σ V + m +1 m +1 m and regroup the terms as � � � � � σ NLO = �� d σ R � � d σ A � � d σ V + d σ A + ǫ =0 − ǫ =0 m +1 m 1 ǫ =0 • for d σ A it must be possible to 1. obtain the Laurent expansion by integration over the single particle unresolved space (preferably analytically) 2. approximate d σ R (preferably pointwise) • Schemes: Dipole Subt. [Catani,Seymour’98] , FKS [Frixione,Kunst,Signer’95] , Antenna Subtraction [Kosower’97] , Nagy-Soper [Nagy,Soper’07] 9
Parton-shower • How to simulate high multiplicity matrix elements/ phase spaces? • Matrix elements diverge in the IR limits (soft/collinear) → Probabilistic interpretation: most of the emissions are soft and collinear! • Using soft/collinear factorization to describe cross section of additional emission: d σ ( n +1) = d P σ ( n ) 10
Parton-shower • Parton evolution with DGLAP: d P a ( z , Q 2 ) = d Q 2 α S 2 π P a → bc ( z ) d z Q 2 • Initial vs. final state showers: → Initialstate shower → Λ QCD < Q < . . . < Q ′ < Q hard ← Finalstate shower ← • Different orderings of the emissions: • Q 2 ordered (example: old Pythia versions) • p T ordered (example: modern Pythia) • E 2 (1 − cos θ ) (angular) ordered (example: Herwig) • Also important: Kinematics! 11
Hadronization • After showering: Collection of individual partons • Not observed! → Color confinement bounds them into color neutral hadrons • Intrinsically non perturbative effect → phenomenological models (Lund string model, cluster model) • Example cluster model: • Leading N c limit (most parton shower are defined in this limit): gluons are color - anticolor pairs • Color neutral combinations of color charges are close in phase space (collinear emissions!) • Combination of color neutral combinations to hadrons with the aid of fitted probability functions (Fragmentation functions,similar to PDFs) 12
The (theory) picture in mind • Q ≫ Λ QCD Hard scattering perturbative QCD • Q ≥ O (Λ QCD ) Parton-shower, PDF-evolution • Q ∼ O (Λ QCD ) Hadronization, Multi-parton interactions / Underlying event,. . . non-perturbative QCD ⇓ Monte Carlo Event Generators 13
MC-event generators: A try of a classification • Fixed-order programs (the hard interaction) • Provide fixed-order cross section. LO,NLO is the industry standard, and NNLO starts to coming up. • Generation of hard process events of low multiplicity • Provide interfaces to parton-shower programs (LO,NLO events) • examples: MadGraph, Sherps, Herwig, POWHEG, MCFM, . . . and uncounted number of in-house software • Parton-Showers and Hadronization (’Event Generators’) • Dressing up (fixed-order) events with additional radiation, to model soft-collinear emissions • Modelling of hadronization/fragmentation, i.e. the transition between partons and hadrons • Decaying the ’clustered’ hadrons to ’stable’ particles • Modelling of additional radiation activity such as Multi-Parton Interactions (MPI) / Underlying Event (UE), color-reconnection, . . . • Pythia, Herwig, Sherpa, . . . ⇒ frameworks for event simulation 14
MadGraph5 aMC@NLO Website: https://launchpad.net/mg5amcnlo • Automated LO/NLO (QCD and EW) fixed order cross sections for the Standard Model and beyond (UFO model files allow for ’arbitrary’ Lagrangian) • FKS subtraction scheme for NLO cross sections • Interfaces to parton-shower programs: probably most popular MC framework: Madgraph+Pythia • Automated generation of tree-level and one-loop matrix elements (very useful tool: stand-alone mode) • Various modules which allow for additional modelling and event analysis (MadEvent/MadAnalysis/Mad. . . ) 15
Sherpa Website: https://sherpa-team.gitlab.io/ • Automated LO/NLO (QCD and EW) fixed order cross sections (loop-matrix elements from third party tools like MadGraph or OpenLoops) • Catani-Seymour subtraction scheme • Matching to CSS dipole-shower (Catani-Seymour mappings) MC@NLO • Handling of Hadronization/Fragmentation (cluster-hadronization), hadron-decays, MPI/UE, QED bremsstrahlung • Multi-jet merging (CKKW scheme) See tutorial 16
Pythia and Herwig Pythia Website: http://home.thep.lu.se/~torbjorn/pythia81html/Welcome.html • features p T ordered shower which interleaves MPI • Hadronization with Lund fragmentation model • Takes LHE event files as input • Facilities for event-analysis Herwig Website: https://herwig.hepforge.org/ • features angular and p T ordered showers • Spin and color correlations can be incorporated • Does hard scattering and matching (MC@NLO) as well 17
Other tools • Treatment of PDFs: LHAPDF ( https://lhapdf.hepforge.org/ ) • Event analysis: Rivet ( https://rivet.hepforge.org/ ) • One-loop matrix-elements: • OpenLoops ( https://openloops.hepforge.org/ ) • Recola ( https://recola.hepforge.org/ ) • MCFM ( https://mcfm.fnal.gov ) 18
Tutorial 19
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