SLIDE 1 Introduction to Event Generators
Simon Plätzer Particle Physics, University of Vienna at the Physics Event Generator Computing Workshop CERN | 24 November 2018
SLIDE 2 Event Generators in Collider Physics Workfmow
Fundamental theory predictions L Feynman Rules → → partonic cross section Perturbative expansion: ~ 10 % accurate, steadily improving Coarse details only: Jets from few quarks and gluons. Experimental
Complex hadronic fjnal state. 1 % accuracy in reach, sophisticated analysis algorithms Jet structure from tens of hadrons, leptons and photons. infere predict
SLIDE 3 Event Generators in Collider Physics Workfmow
Fundamental theory predictions L Feynman Rules → → partonic cross section Perturbative expansion: ~ 10 % accurate, steadily improving Coarse details only: Jets from few quarks and gluons. Experimental
Complex hadronic fjnal state. 1 % accuracy in reach, sophisticated analysis algorithms Jet structure from tens of hadrons, leptons and photons. infere predict Event generator simulation Model evolution into observed events. Leading corrections to all orders, accuracy mostly unclear. Structure built up from multiple emissions and hadronization models.
SLIDE 4
Multipurpose Event Generators
Indispensable tools for experiments & phenomenology. Realistic, fully detailed simulation spanning orders of magnitude in relevant energy scales. Factorization dictates work fmow. Hard process calculation Parton shower algorithms Multiple interaction models Hadronization models
SLIDE 5
Structure of Cross Sections
Cross section and measurements Cross section structure factorizes due to large energy scale separations Huge complexity and probabilistic interpretation calls for Monte Carlo methods. Allows for interpretation as event rate: We are actually simulating the dynamics! event weight from hard cross section probabilities to resolve more details exclusive cross section
SLIDE 6
Structure of Event Generators
Hard process calculation Exact calculations in QCD/QED perturbation theory, cross sections from MC integration. PDF from external libraries. Parton shower algorithms Multiple radiation of quarks, gluons and photons, approximate but to all orders in QCD/QED perturbation theory. Multiple interaction models Several difgerent approaches. Inspired by perturbation theory and unitarity. Hadronization models Formation of hadrons, followed by decays and QED radiation. Strong coupling increases from inside to outside, relative energy scales decrease. Gluon self interaction and quark confjnement at scales below ΛQCD.
SLIDE 7
Hard Cross Sections
Hard cross section calculations Phase space generators map unit hypercube to physical momenta Primary purpose: Importance sampling of phase space, then interface to adaptive Monte Carlo integrators (VEGAS, MONACO, FOAM, …) Complicated phase spaces can be factored, 3 n - 4 degrees of freedom for n particles . Matrix element squared Lorentz invariant phase space
SLIDE 8
A Glimpse at QCD Corrections
Strong coupling is small at large momentum transfers: Justifjes perturbation theory. Subtraction terms required for fmexible calculation of observables: Negative weights unavoidable, though physical cross sections stay positive. . Divergences difgerential in phase space and explicit in regulator.
SLIDE 9 The landscape of infrared sensitive observables
coupling order “accuracy” exclusivity/resolution “jet bin” logarithmic structure “leading” contribution inclusive cross section difgerential cross section LO
SLIDE 10 The landscape of infrared sensitive observables
coupling order “accuracy” exclusivity/resolution “jet bin” logarithmic structure “leading” contribution inclusive cross section difgerential cross section LO
SLIDE 11 The landscape of infrared sensitive observables
coupling order “accuracy” exclusivity/resolution “jet bin” logarithmic structure “leading” contribution inclusive cross section difgerential cross section LO NLO
SLIDE 12 The landscape of infrared sensitive observables
coupling order “accuracy” exclusivity/resolution “jet bin” logarithmic structure “leading” contribution inclusive cross section difgerential cross section LO NLO
SLIDE 13 The landscape of infrared sensitive observables
coupling order “accuracy” exclusivity/resolution “jet bin” logarithmic structure “leading” contribution inclusive cross section difgerential cross section LO NLO
SLIDE 14 The landscape of infrared sensitive observables
coupling order “accuracy” exclusivity/resolution “jet bin” logarithmic structure “leading” contribution inclusive cross section difgerential cross section LO NLO NNLO
SLIDE 15
Factorization of Emissions
QCD cross sections factorize into hard cross section and emission probability, for soft and collinear parton emission. For soft emissions colour correlations persist, for collinear emissions spin correlations are present. Factorization is universal and process independent,whenever the ‘scale’ of the splitting is much smaller compared to the scales involved in the hard process: Small momentum components and/or small relative transverse momenta. (Double-)logarithmic divergences when including phase space: colour dipoles radiate
SLIDE 16 Resummation and Parton Showers
coupling order “accuracy” exclusivity/resolution “jet bin” logarithmic structure “leading” contribution inclusive cross section difgerential cross section LO
SLIDE 17 Resummation and Parton Showers
coupling order “accuracy” exclusivity/resolution “jet bin” logarithmic structure “leading” contribution inclusive cross section difgerential cross section LO LL
SLIDE 18 Resummation and Parton Showers
coupling order “accuracy” exclusivity/resolution “jet bin” logarithmic structure “leading” contribution inclusive cross section difgerential cross section LO NLL LL
SLIDE 19 Parton Shower Evolution
Iterative procedure ofg adding subsequent emissions No emission probability: Sudakov form factor central to parton showers Sudakov form factor contains the all-order virtual corrections which regularize each individual emission to yield a physical behaviour: Sudakov supression no-emission probability
kinematic mapping emission kernel
SLIDE 20 NLO Matching
NLL coupling order “accuracy” exclusivity/resolution “jet bin” logarithmic structure “leading” contribution inclusive cross section difgerential cross section LO LL
SLIDE 21 NLO Matching
NLL coupling order “accuracy” exclusivity/resolution “jet bin” logarithmic structure “leading” contribution inclusive cross section difgerential cross section LO LL NLO
SLIDE 22
Matching
Expand shower action on NLO cross section: Additional subtraction terms to remove double counting.
SLIDE 23
Matching
Expand shower action on NLO cross section: Additional subtraction terms to remove double counting. dσmatched = + –
SLIDE 24 Merging multiple emissions
NLL coupling order “accuracy” exclusivity/resolution “jet bin” logarithmic structure “leading” contribution inclusive cross section difgerential cross section LO LL NLO
SLIDE 25 Merging multiple emissions
NLL coupling order “accuracy” exclusivity/resolution “jet bin” logarithmic structure “leading” contribution inclusive cross section difgerential cross section LO LL NLO
SLIDE 26 Merging multiple emissions
NLL coupling order “accuracy” exclusivity/resolution “jet bin” logarithmic structure “leading” contribution inclusive cross section difgerential cross section LO LL NLO
SLIDE 27 Merging multiple emissions
NLL coupling order “accuracy” exclusivity/resolution “jet bin” logarithmic structure “leading” contribution inclusive cross section difgerential cross section LO LL NLO
SLIDE 28 Event Generator Structure
Parton Distribution Functions: LHAPDF library Tree-level ME calculation: Recursion algorithms, caching Loop-level ME calculation: Dedicated libraries via BLHA Phase space generator Parton Shower Evolution: Veto & Weighting Algorithms Multi-Parton Interactions Matching and Merging: Subtractions, negative weights Adaptive MC Integrator: Parallelization Hadronization Decays Soft Photon Radiation Analysis Cross section assembly Plethora of intermediate interfaces: fjle formats and runtime interfaces, efgectively only HepMC as fjnal output established as a true standard.
SLIDE 29 Challenges
Virtually all corrections beyond the established approximations spoil the probabilistic interpretation. This already starts with negative weights from NLO and matching subtractions. Weighting algorithms will be crucial to all cutting-edge approaches such as new merging algorithms, showers beyond the leading order and beyond the leading colour approximation, and matching to NNLO. The factorization formulae underlying our software structure do already now turn
- ut to be inappropriate: At the very latest, merging introduces signifjcant and non-
trivial cross talk between hard cross sections ans shower, let alone new shower approaches based on amplitude evolution. More questions raised in discussion tomorrow.
SLIDE 30
Multipurpose Event Generators
Herwig Traditional focus on showers, Qtilde and Dipoles shower, cluster hadronization model, NLO matching and merging. Pythia Sophisticated soft physics, pt-ordered, DIRE and Vincia shower, string hadronization, NLO merging. Sherpa Focus on perturbative improvements, CS and DIRE shower, cluster or string hadronization, NLO matching and merging. + dedicated ME/Matching codes: MadGraph, POWHEG + dedicated “afterburners”: EvtGen, Tauola, Photos
SLIDE 31 Summary
Highly exclusive predictions for collider fjnal states are crucial to high energy physics
- phenomenology. Precision calculations and development of event generators as the
main workhorse is a highly active area of research. In this talk, I could only scratch the surface, highlight structures and current challenges, please see the talks today for much more details. The use of event generator inspired Monte Carlo methods in dedicated resummation approaches should also receive attention within this discussion. I’m happy to collect more questions and queries for the discussion.
SLIDE 32
Thank you!
