56
2 Phenomenology of Jet Substructure
but until now no automatisation has been achieved due to the enormous complexity
of these calculations. Due to the difficulty of calculating higher order contributions
with matrix element methods, these can not be used to reliably predict the internal
structures of jets. The parton shower formalism, on the other hand, has been obtained
for the region of soft and collinear emissions, with numerous successive branchings
leading to a high parton multiplicity in the final state. Parton showers are thus well
suited to model jet substructure with perturbative methods, while the description of
well separated jets is not guaranteed. The two approaches complement each other
and much effort has been made to combine them without double-counting of graphs
generated by the matrix elements and the parton shower, or with gaps in the phase
space coverage.
Multileg tree-level calculations provide real corrections to the 2 → n process of
the form 2 → n + 1, 2 → n + 2, …. When merging these individual contributions, a
naive combination would result in double counting, since configurations with higher
parton multiplicities contribute to inclusive 2 → n process with lower multiplicity.
A merging with parton showers exacerbates the issue. Solutions to this problem
are offered by the CKKW [365], CKKW-L [366], MLM [367] and UMEPS [368]
methods. These methods introduce Sudakov form factors approximately accounting
for the effect of virtual corrections, and have been extensively used in older versions
of Pythia, Herwig and Sherpa.
When including full higher-order information, starting with one loop diagrams
leading to predictions at full NLO precision, the first parton shower emission needs
to be corrected to account for changes of the Born-level kinematics. Two successful
approaches used in this context are the MC@NLO [369] and Powheg [370, 371]
methods. These have become standard for the generation of simulated events at the
LHC, leading to NLO predictions with varying parton multiplicities fully matched
to parton showers. The fixed-order matrix element calculations at NLO are either an
integral part of the event generator as in the case of Herwig 7 [300],
15 or obtained
from the external programs MadGraph5_aMC@NLO [372] or Powheg Box [373]
as in the case of Pythia, and BlackHat [350] for Sherpa. Recently, a number of
studies have been performed on multileg NLO merging [374–376], which can also
be extended to full NNLO calculations matched to parton showers [191, 377]. In the
not too distant future, these will become the new standard for event simulation at the
LHC.
2.6.5 Multiple Parton Interactions
Multiple parton interactions (MPIs) are additional 2 → 2 scatterings that occur
within the same pp interaction as the primary hard scattering. To first approximation,
MPIs are scatterings of the spectator partons in the proton. Since the 2 → 2 partonparton cross section diverges for p T → 0 like α S ( p
2
T )/ p
4
T , the divergence needs to be
15 Herwig 7 also offers the possibility to use external matrix element calculations as input.
2 Phenomenology of Jet Substructure
but until now no automatisation has been achieved due to the enormous complexity
of these calculations. Due to the difficulty of calculating higher order contributions
with matrix element methods, these can not be used to reliably predict the internal
structures of jets. The parton shower formalism, on the other hand, has been obtained
for the region of soft and collinear emissions, with numerous successive branchings
leading to a high parton multiplicity in the final state. Parton showers are thus well
suited to model jet substructure with perturbative methods, while the description of
well separated jets is not guaranteed. The two approaches complement each other
and much effort has been made to combine them without double-counting of graphs
generated by the matrix elements and the parton shower, or with gaps in the phase
space coverage.
Multileg tree-level calculations provide real corrections to the 2 → n process of
the form 2 → n + 1, 2 → n + 2, …. When merging these individual contributions, a
naive combination would result in double counting, since configurations with higher
parton multiplicities contribute to inclusive 2 → n process with lower multiplicity.
A merging with parton showers exacerbates the issue. Solutions to this problem
are offered by the CKKW [365], CKKW-L [366], MLM [367] and UMEPS [368]
methods. These methods introduce Sudakov form factors approximately accounting
for the effect of virtual corrections, and have been extensively used in older versions
of Pythia, Herwig and Sherpa.
When including full higher-order information, starting with one loop diagrams
leading to predictions at full NLO precision, the first parton shower emission needs
to be corrected to account for changes of the Born-level kinematics. Two successful
approaches used in this context are the MC@NLO [369] and Powheg [370, 371]
methods. These have become standard for the generation of simulated events at the
LHC, leading to NLO predictions with varying parton multiplicities fully matched
to parton showers. The fixed-order matrix element calculations at NLO are either an
integral part of the event generator as in the case of Herwig 7 [300],
15 or obtained
from the external programs MadGraph5_aMC@NLO [372] or Powheg Box [373]
as in the case of Pythia, and BlackHat [350] for Sherpa. Recently, a number of
studies have been performed on multileg NLO merging [374–376], which can also
be extended to full NNLO calculations matched to parton showers [191, 377]. In the
not too distant future, these will become the new standard for event simulation at the
LHC.
2.6.5 Multiple Parton Interactions
Multiple parton interactions (MPIs) are additional 2 → 2 scatterings that occur
within the same pp interaction as the primary hard scattering. To first approximation,
MPIs are scatterings of the spectator partons in the proton. Since the 2 → 2 partonparton cross section diverges for p T → 0 like α S ( p
2
T )/ p
4
T , the divergence needs to be
15 Herwig 7 also offers the possibility to use external matrix element calculations as input.