2.6 Event Generators
51
evolution reaches a perturbative cut-off scale, hadronisation sets in, resulting in
numerous colourless mesons and baryons. These are subsequently allowed to decay,
sometimes developing decay chains. Finally, the event generation terminates with
stable particles emerging from the interaction.
For jet substructure analyses, results can be obtained at formally (N)LO+LL accuracy for observables either on the level of coloured final state partons or on the level
of stable particles. Often these predictions have better predictive power than their
accuracy suggests, owing to the partial inclusion of formally higher order effects and
tuning of (the many) free parameters to experimental data [291–295]. In general, this
leads to a reliable modelling of the internal structure of jets in many different aspects
(integrated and differential jet shapes, particle multiplicities, angular and energy
correlations,…), which facilitates experimental analyses. This also permits event
generators to be used for the validation of (semi-)analytical calculations, especially
when no experimental data are available. The three general-purpose event generators used extensively at the LHC are Pythia [248–250, 296], Herwig [297–300]
and Sherpa [301, 302], which has been built around the multi-leg matrix element
generators Amegic [303] and Comix [304].
Simulated events obtained from event generators can be passed through detector
simulations, either detailed ones using the GEANT toolkit [305, 306] or simplified
detector simulations like PGS [307] or DELPHES [308]. With these, the effect of
the granularity of detector readout units, finite efficiencies and a realistic detector
response can be studied. Additionally, overlaying simulated events with minimumbias (MB) events can be used for studies of the effects of pileup. At the end of this
long chain of detailed simulation steps, simulated events on the level of the detector
reconstruction are obtained and can be directly compared to recorded collision data.
These simulations can be used to directly test the underlying physical principles,
together with the approximations made in event generators. They can also be used
to derive corrections for data in order to obtain measurements fully corrected for
detector effects.
2.6.1 Parton Distribution Functions
Particle collisions involving hadrons in the initial state are described by colliding
clouds of partons, with the number density of parton flavour i given by the parton
distribution function f i (x, μ
2
f ). The PDFs depend on the longitudinal momentum
fraction x carried by the parton relative to the hadron momentum, and the factorisation
scale μ f , usually taken to be the hard scale probed by the interaction, μ f = Q. The
form of PDFs cannot be predicted in perturbative QCD, but has to be parametrised
at some starting scale Q 0 . The evolution of the PDFs to some scale Q, with Q >
Q 0 , is obtained by the DGLAP equations [309–312]. The free parameters of the
parametrisations have to be obtained from experimental data. It is due to the freedom
of choosing a parametrisation, the theoretical treatment of heavy quark mass effects,
assumptions on the sea quark densities and the wealth of experimental data to choose
51
evolution reaches a perturbative cut-off scale, hadronisation sets in, resulting in
numerous colourless mesons and baryons. These are subsequently allowed to decay,
sometimes developing decay chains. Finally, the event generation terminates with
stable particles emerging from the interaction.
For jet substructure analyses, results can be obtained at formally (N)LO+LL accuracy for observables either on the level of coloured final state partons or on the level
of stable particles. Often these predictions have better predictive power than their
accuracy suggests, owing to the partial inclusion of formally higher order effects and
tuning of (the many) free parameters to experimental data [291–295]. In general, this
leads to a reliable modelling of the internal structure of jets in many different aspects
(integrated and differential jet shapes, particle multiplicities, angular and energy
correlations,…), which facilitates experimental analyses. This also permits event
generators to be used for the validation of (semi-)analytical calculations, especially
when no experimental data are available. The three general-purpose event generators used extensively at the LHC are Pythia [248–250, 296], Herwig [297–300]
and Sherpa [301, 302], which has been built around the multi-leg matrix element
generators Amegic [303] and Comix [304].
Simulated events obtained from event generators can be passed through detector
simulations, either detailed ones using the GEANT toolkit [305, 306] or simplified
detector simulations like PGS [307] or DELPHES [308]. With these, the effect of
the granularity of detector readout units, finite efficiencies and a realistic detector
response can be studied. Additionally, overlaying simulated events with minimumbias (MB) events can be used for studies of the effects of pileup. At the end of this
long chain of detailed simulation steps, simulated events on the level of the detector
reconstruction are obtained and can be directly compared to recorded collision data.
These simulations can be used to directly test the underlying physical principles,
together with the approximations made in event generators. They can also be used
to derive corrections for data in order to obtain measurements fully corrected for
detector effects.
2.6.1 Parton Distribution Functions
Particle collisions involving hadrons in the initial state are described by colliding
clouds of partons, with the number density of parton flavour i given by the parton
distribution function f i (x, μ
2
f ). The PDFs depend on the longitudinal momentum
fraction x carried by the parton relative to the hadron momentum, and the factorisation
scale μ f , usually taken to be the hard scale probed by the interaction, μ f = Q. The
form of PDFs cannot be predicted in perturbative QCD, but has to be parametrised
at some starting scale Q 0 . The evolution of the PDFs to some scale Q, with Q >
Q 0 , is obtained by the DGLAP equations [309–312]. The free parameters of the
parametrisations have to be obtained from experimental data. It is due to the freedom
of choosing a parametrisation, the theoretical treatment of heavy quark mass effects,
assumptions on the sea quark densities and the wealth of experimental data to choose