Introduction to Event Generators Simon Plätzer Particle Physics, University of Vienna at the Physics Event Generator Computing Workshop CERN | 24 November 2018
Event Generators in Collider Physics Workfmow predict Fundamental theory Experimental predictions observation L Feynman Rules Complex hadronic → → partonic cross section fjnal state. Perturbative expansion: 1 % accuracy in reach , ~ 10 % accurate , sophisticated analysis steadily improving algorithms Coarse details only: Jet structure from Jets from few quarks and tens of hadrons, gluons. leptons and photons. infere
Event Generators in Collider Physics Workfmow predict Fundamental theory Event generator Experimental predictions observation simulation L Feynman Rules Complex hadronic Model evolution → → partonic cross section into observed events. fjnal state. Perturbative expansion: Leading corrections to 1 % accuracy in reach , ~ 10 % accurate , sophisticated analysis all orders, accuracy steadily improving mostly unclear. algorithms Coarse details only: Structure built up from Jet structure from Jets from few quarks and tens of hadrons, multiple emissions and gluons. hadronization models. leptons and photons. infere
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
Structure of Cross Sections Cross section and measurements Cross section structure factorizes due to large energy scale separations exclusive event weight from probabilities cross section hard cross section to resolve more details Huge complexity and probabilistic interpretation calls for Monte Carlo methods. Allows for interpretation as event rate: We are actually simulating the dynamics!
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 Λ QCD .
Hard Cross Sections Hard cross section calculations Matrix element squared Lorentz invariant phase space . 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
A Glimpse at QCD Corrections Strong coupling is small at large momentum transfers: Justifjes perturbation theory. Divergences difgerential in phase space and explicit in regulator. . Subtraction terms required for fmexible calculation of observables: Negative weights unavoidable, though physical cross sections stay positive.
The landscape of infrared sensitive observables logarithmic structure “leading” contribution LO coupling order “accuracy” inclusive cross section exclusivity/resolution difgerential “jet bin” cross section
The landscape of infrared sensitive observables logarithmic structure “leading” contribution LO coupling order “accuracy” inclusive cross section exclusivity/resolution difgerential “jet bin” cross section
The landscape of infrared sensitive observables logarithmic structure “leading” contribution NLO LO coupling order “accuracy” inclusive cross section exclusivity/resolution difgerential “jet bin” cross section
The landscape of infrared sensitive observables logarithmic structure “leading” contribution NLO LO coupling order “accuracy” inclusive cross section exclusivity/resolution difgerential “jet bin” cross section
The landscape of infrared sensitive observables logarithmic structure “leading” contribution NLO LO coupling order “accuracy” inclusive cross section exclusivity/resolution difgerential “jet bin” cross section
The landscape of infrared sensitive observables logarithmic structure “leading” contribution NNLO NLO LO coupling order “accuracy” inclusive cross section exclusivity/resolution difgerential “jet bin” cross section
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. colour dipoles radiate 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:
Resummation and Parton Showers logarithmic structure “leading” contribution LO coupling order “accuracy” inclusive cross section exclusivity/resolution difgerential “jet bin” cross section
Resummation and Parton Showers logarithmic structure “leading” contribution LL LO coupling order “accuracy” inclusive cross section exclusivity/resolution difgerential “jet bin” cross section
Resummation and Parton Showers logarithmic structure “leading” contribution LL LO NLL coupling order “accuracy” inclusive cross section exclusivity/resolution difgerential “jet bin” cross section
Parton Shower Evolution Iterative procedure ofg adding subsequent emissions no-emission probability ordering! emission kernel kinematic mapping 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
NLO Matching logarithmic structure “leading” contribution LL LO NLL coupling order “accuracy” inclusive cross section exclusivity/resolution difgerential “jet bin” cross section
NLO Matching logarithmic structure “leading” contribution NLO LL LO NLL coupling order “accuracy” inclusive cross section exclusivity/resolution difgerential “jet bin” cross section
Matching Expand shower action on NLO cross section: Additional subtraction terms to remove double counting.
Matching Expand shower action on NLO cross section: dσ matched = + – Additional subtraction terms to remove double counting.
Merging multiple emissions logarithmic structure “leading” contribution NLO LL LO NLL coupling order “accuracy” inclusive cross section exclusivity/resolution difgerential “jet bin” cross section
Merging multiple emissions logarithmic structure “leading” contribution NLO LL LO NLL coupling order “accuracy” inclusive cross section exclusivity/resolution difgerential “jet bin” cross section
Merging multiple emissions logarithmic structure “leading” contribution NLO LL LO NLL coupling order “accuracy” inclusive cross section exclusivity/resolution difgerential “jet bin” cross section
Merging multiple emissions logarithmic structure “leading” contribution NLO LL LO NLL coupling order “accuracy” inclusive cross section exclusivity/resolution difgerential “jet bin” cross section
Event Generator Structure Parton Distribution Functions: Loop-level ME calculation: Adaptive MC Integrator: LHAPDF library Dedicated libraries via BLHA Parallelization Tree-level ME calculation: Cross section assembly Recursion algorithms, caching Matching and Merging: Phase space generator Subtractions, negative weights Parton Shower Evolution: Decays Hadronization Veto & Weighting Algorithms Soft Photon Radiation Multi-Parton Interactions Plethora of intermediate interfaces: fjle formats and runtime Analysis interfaces, efgectively only HepMC as fjnal output established as a true standard.
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 out 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.
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