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 set 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

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

At most one of the outgoing particles can be a boson, the rest has to be partonic. At the moment only the Higgs boson h is supported. All other outgoing particles are jets. Multiple jets can be grouped together, so p p => h j j is the same as p p => h 2j. There have to be at least two jets. Further decays of the boson can be added through the particle properties.

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. 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 FKL configurations and thus subleading in the high-energy limit. Currently only unordered emissions are implemented, and only for Higgs boson plus multijet processes. 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 parameter to select the production of specific channels that are subleading in the high-energy limit. Only has an effect if subleading fraction is non-zero. Currently three values are supported:

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

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

  • unordered: Unordered emission are allowed.

    Unordered emission are any rapidity ordering where exactly one gluon is emitted outside the FKL rapidity ordering. 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.

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.

particle properties

Specifies various properties of the different particles (Higgs, W or Z). This is only relevant if the chosen process is the production of the corresponding particles with jets. E.g. for the process p p => h 2j the mass, width and (optionally) decays of the Higgs boson are required, while all other particle properties will be ignored.

Higgs, W+, W- or Z

The particle (Higgs, W+, W-, Z) for which the following properties are defined.

mass

The mass of the particle in GeV.

width

The total decay width of the particle in GeV.

decays

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

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

where p1 and p2 are the particle names of the decay product (e.g. photon) and r is the branching ratio.

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.

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.

analysis

Specifies the name and settings for a custom analysis library. This can be useful to specify cuts at the fixed-order level. 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.