The HEJ Fixed Order Generator

For high jet multiplicities event generation with standard fixed-order generators becomes increasingly cumbersome. For example, the leading-order production of a Higgs Boson with five or more jets is computationally prohibitively expensive.

To this end, HEJ 2 provides the HEJFOG fixed-order generator that allows to generate events with high jet multiplicities. To facilitate the computation the limit of Multi-Regge Kinematics with large invariant masses between all outgoing particles is assumed in the matrix elements. The typical use of the HEJFOG is to supplement low-multiplicity events from standard generators with high-multiplicity events before using the HEJ 2 program to add high-energy resummation.

Installation

The HEJFOG comes bundled together with HEJ 2 and the installation is very similar. After downloading HEJ 2 and installing the prerequisites as described in Installation the HEJFOG can be installed with:

cmake /path/to/FixedOrderGen -DCMAKE_INSTALL_PREFIX=target/directory
make install

where /path/to/FixedOrderGen refers to the FixedOrderGen subdirectory in the HEJ 2 directory. If HEJ 2 was installed to a non-standard location, it may be necessary to specify the directory containing HEJ-config.cmake. If the base installation directory is /path/to/HEJ, HEJ-config.cmake should be found in /path/to/HEJ/lib/cmake/HEJ and the commands for installing the HEJFOG would read:

cmake /path/to/FixedOrderGen -DHEJ_DIR=/path/to/HEJ/lib/cmake/HEJ -DCMAKE_INSTALL_PREFIX=target/directory
make install

The installation can be tested with:

make test

provided that the CT10nlo PDF sets is installed.

Running the fixed-order generator

After installing the HEJFOG you can modify the provided configuration file configFO.yml and run the generator with:

HEJFOG configFO.yml

When using the HEJ docker image, the corresponding command is:

docker run -v $PWD:$PWD -w $PWD hejdock/hej HEJFOG configFO.yml

The resulting event file, by default named HEJFO.lhe, can then be fed into HEJ 2 like any event file generated from a standard fixed-order generator, see Running HEJ 2.

Settings

Similar to HEJ 2, the HEJFOG uses a YAML configuration file. The settings are

process

The scattering process for which events are being generated. The format is

in1 in2 => out1 out2 ...

The incoming particles, in1, in2 can be

  • quarks: u, d, u_bar, and so on

  • gluons: g

  • protons p or antiprotons p_bar

The outgoing particles out1, out2, etc. can be

  • jets: At least two final state jets j are required. Multiple jets can be grouped together, e.g. 2j.

  • bosons: At most a single Higgs (h), W+, or W- boson, which might further decay. Final states with more than one boson are curently not supported.

  • leptons: If there is no Higgs or W boson the final state may contain a single lepton pair. Flavours have to be chosen such that the leptons can originate from the decay of a single virtual W or Z boson.

    In the case of a Z boson only final states with two charged leptons are supported. The interference between a virtual Z boson and photon is taken into account, but the invariant mass of the leptons will be chosen close to the Z boson mass.

    Valid examples include e+ nu_e and e+ e-.

Instead of the leptons, decays of the bosons can be added through the decays. The latter is required to decay a Higgs boson. So p p => W+ j j is the same as p p => e+ nu_e 2j, if the decay W+ => e+ nu_e is specified in decays.

events

Specifies the number of events to generate.

jets

Defines the properties of the generated jets.

min pt

Minimum jet transverse momentum in GeV.

peak pt

Optional setting to specify the dominant jet transverse momentum in GeV. If the generated events are used as input for HEJ resummation, this should be set to the minimum transverse momentum of the resummation jets. In all cases it has to be larger than min pt. The effect is that only a small fraction of jets will be generated with a transverse momentum below the value of this setting.

algorithm

The algorithm used to define jets. Allowed settings are kt, cambridge, antikt, cambridge for passive. See the FastJet documentation for a description of these algorithms.

R

The R parameter used in the jet algorithm.

max rapidity

Maximum absolute value of the jet rapidity.

beam

Defines various properties of the collider beam.

energy

The beam energy in GeV. For example, the 13 TeV LHC corresponds to a value of 6500.

particles

A list [p1, p2] of two beam particles. The only supported entries are protons p and antiprotons p_bar.

pdf

The LHAPDF number of the PDF set. For example, 230000 corresponds to an NNPDF 2.3 NLO PDF set.

subleading fraction

This setting is related to the fraction of events that are not a FKL configuration. All possible subleading process are listed in subleading channels. This value must be positive and not larger than 1. It should typically be chosen between 0.01 and 0.1. Note that while this parameter influences the chance of generating subleading configurations, it generally does not correspond to the actual fraction of subleading events.

subleading channels

Optional parameters to select a specific subleading process, multiple channels can be selected at once. If multiple subleading configurations are possible one will be selected at random for each event, thus each final state will include at most one subleading process, e.g. either unordered or central qqbar. Only has an effect if subleading fraction is non-zero. Subleading processes requested here also have to be available from HEJ, for a list of implemented processes see event treatment. The following values are allowed:

  • all: All channels allowed. This is the default.

  • none: No subleading contribution, only the leading (FKL) configurations are allowed. This is equivalent to subleading fraction: 0.

  • unordered: Unordered emission allowed. Unordered emission are any rapidity ordering where exactly one gluon is emitted outside the rapidity ordering required in FKL events. More precisely, if at least one of the incoming particles is a quark or antiquark and there are more than two jets in the final state, subleading fraction states the probability that the flavours of the outgoing particles are assigned in such a way that an unordered configuration arises.

  • extremal qqbar: Production of a quark-antiquark pair as extremal partons in rapidity. If the central qqbar channel is allowed, subleading fraction gives the probability of emitting a quark-antiquark pair in place of two gluons adjacent in rapidity at the most forward or backwards quarks.

  • central qqbar: Production of a central quark-antiquark pair. This setting is similar to extremal qqbar, but subleading fraction gives the probability of emitting a quark-antiquark pair in place of two gluons adjacent in rapidity at any point inside the FKL gluon chain.

unweight

This setting defines the parameters for the partial unweighting of events. You can disable unweighting by removing this entry from the configuration file.

sample size

The number of weighted events used to calibrate the unweighting. A good default is to set this to the number of target events. If the number of events is large this can lead to significant memory consumption and a lower value should be chosen. Contrarily, for large multiplicities the unweighting efficiency becomes worse and the sample size should be increased.

max deviation

Controls the range of events to which unweighting is applied. A larger value means that a larger fraction of events are unweighted. Typical values are between -1 and 1.

decays

Optional setting specifying the decays of the particle. Only the decay into two particles is implemented. Each decay has the form

boson: {into: [p1,p2], branching ratio: r}

where boson is the corresponding boson, p1 and p2 are the particle names of the decay product (e.g. photon) and r is the branching ratio. The branching ratio is optional (1 by default).

Decays of a Higgs boson are treated as the production and subsequent decay of an on-shell Higgs boson, so decays into e.g. Z bosons are not supported. In contrast W bosons are decayed off-shell, thus the branching ratio should not be specified or set to 1.

scales

Specifies the renormalisation and factorisation scales for the output events. For details, see the corresponding entry in the HEJ 2 settings. Note that this should usually be a single value, as the weights resulting from additional scale choices will simply be ignored when adding high-energy resummation with HEJ 2.

event output

Specifies the name of a single event output file or a list of such files. See the corresponding entry in the HEJ 2 settings for details.

random generator

Sets parameters for random number generation. See the HEJ 2 settings for details.

analyses

Specifies the name and settings for one or more analyses library. This can be useful to specify cuts at the fixed-order level. See the corresponding entry in the HEJ 2 settings for details.

vev

Higgs vacuum expectation value in GeV. All electro-weak constants are derived from this together with the particle properties.

particle properties

Specifies various properties of the different particles (Higgs, W or Z). These have to be specified for all bosons. See the corresponding entry in the HEJ 2 settings for details.

Higgs coupling

This collects a number of settings concerning the effective coupling of the Higgs boson to gluons. See the corresponding entry in the HEJ 2 settings for details.