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	diff --git a/config.yml b/config.yml
	index 7950f4b..26e46a7 100644
	--- a/config.yml
	+++ b/config.yml
	@@ -1,91 +1,94 @@
	# number of attempted resummation phase space points for each input event
	trials: 10

	min extparton pt: 30 # minimum transverse momentum of extremal partons

	resummation jets: # resummation jet properties
	min pt: 35 # minimum jet transverse momentum
	algorithm: antikt # jet algorithm
	R: 0.4 # jet R parameter

	fixed order jets: # properties of input jets
	min pt: 30
	# by default, algorithm and R are like for resummation jets

	# treatment of he various event classes
	# the supported settings are: reweight, keep, discard
	# non-FKL events cannot be reweighted
	FKL: reweight
	unordered: keep
	non-FKL: keep

	# scale settings similar to original HEJ
	#
	# Use combinations of max jet pperp, input scales, ht/2,
	# and the jet invariant mass and vary all scales by factors
	# of 1, sqrt(2), and 2. Discard combinations where mur and muf
	# differ by a factor of more than two.
	#
	# The weight entries in the final events are ordered as follows:
	# 0-18: max jet pperp
	# 19-37: input scales
	# 38-56: ht/2
	# 57-75: jet invariant mass
	# In each of these groups, the first entry corresponds to the basic
	# scale choice. In the following entries, mur and muf are varied with
	# the above factors. The entries are ordered lexicographically so that
	# mur1 < mur2 or (mur1 == mur2 and muf1 < muf2).
	#
	# Note that in contrast to HEJ, the central choice for the event is always
	# max jet pperp and cannot be configured (yet).
	#
	# scales: [max jet pperp, input, Ht/2, jet invariant mass]
	# scale factors: [0.5, 0.7071, 1, 1.41421, 2]
	# max scale ratio: 2.0001

	scales: 91.188

	# import scale setting functions
	#
	# import scales:
	# lib_my_scales.so: [scale0,scale1]

	log correction: false # whether or not to include higher order logs
	unweight: false # TODO: whether or not to unweight events

	# event output files
	#
	# the supported formats are
	# - Les Houches (suffix .lhe)
	# - HepMC (suffix .hepmc3)
	# TODO: - ROOT ntuples (suffix .root)
	#
	# An output file's format is deduced either automatically from the suffix
	# or from an explicit specification, e.g.
	# - Les Houches: outfile

	event output:
	- RHEJ.lhe
	# - RHEJ_events.hepmc

	analysis:
	# to use a custom analysis
	# plugin: ./src/analysis-plugins/libVBF.so
	# output: RHEJ.root
	# wtwt cut: # optional cut on (event weight)^2
	+ # to use rivet
	+ # rivet: MC_XS # rivet analysis name
	+ # output: RHEJ # name of the yoda files, ".yoda" and scale suffix will be added

	# selection of random number generator and seed
	# the choices are
	# - mixmax (seed is an integer)
	# - ranlux64 (seed is a filename containing parameters)
	random generator:
	name: mixmax
	# seed: 1

	# parameters for Higgs-gluon couplings
	# this requires compilation with looptools
	# Higgs coupling:
	# use impact factors: false
	# mt: 174
	# include bottom: true
	# mb: 4.7
	diff --git a/doc/developer_manual/developer_manual.tex b/doc/developer_manual/developer_manual.tex
	index ba96a2f..5e64e94 100644
	--- a/doc/developer_manual/developer_manual.tex
	+++ b/doc/developer_manual/developer_manual.tex
	@@ -1,1081 +1,1081 @@
	\documentclass[a4paper,11pt]{article}

	\usepackage{fourier}
	\usepackage[T1]{fontenc}
	\usepackage{microtype}
	\usepackage{geometry}
	\usepackage{enumitem}
	\setlist[description]{leftmargin=\parindent,labelindent=\parindent}
	\usepackage{amsmath}
	\usepackage{amssymb}
	\usepackage[utf8x]{inputenc}
	\usepackage{graphicx}
	\usepackage{xcolor}
	\usepackage{todonotes}
	\usepackage{listings}
	\usepackage{xspace}
	\usepackage{tikz}
	\usetikzlibrary{arrows.meta}
	\usetikzlibrary{shapes}
	\usetikzlibrary{calc}
	\usepackage[colorlinks,linkcolor={blue!50!black}]{hyperref}
	\graphicspath{{build/figures/}{figures/}}

	\newcommand{\HEJ}{{\tt HEJ}\xspace}
	\newcommand{\HIGHEJ}{\emph{High Energy Jets}\xspace}
	\newcommand{\cmake}{\href{https://cmake.org/}{cmake}\xspace}
	\newcommand{\html}{\href{https://www.w3.org/html/}{html}\xspace}
	\newcommand{\YAML}{\href{http://yaml.org/}{YAML}\xspace}

	\definecolor{darkgreen}{rgb}{0,0.4,0}
	\lstset{ %
	backgroundcolor=\color{lightgray}, % choose the background color; you must add \usepackage{color} or \usepackage{xcolor}
	basicstyle=\footnotesize\usefont{T1}{DejaVuSansMono-TLF}{m}{n}, % the size of the fonts that are used for the code
	breakatwhitespace=false, % sets if automatic breaks should only happen at whitespace
	breaklines=false, % sets automatic line breaking
	captionpos=t, % sets the caption-position to bottom
	commentstyle=\color{red}, % comment style
	deletekeywords={...}, % if you want to delete keywords from the given language
	escapeinside={\%}{)}, % if you want to add LaTeX within your code
	extendedchars=true, % lets you use non-ASCII characters; for 8-bits encodings only, does not work with UTF-8
	frame=false, % adds a frame around the code
	keepspaces=true, % keeps spaces in text, useful for keeping indentation of code (possibly needs columns=flexible)
	keywordstyle=\color{blue}, % keyword style
	otherkeywords={}, % if you want to add more keywords to the set
	numbers=none, % where to put the line-numbers; possible values are (none, left, right)
	numbersep=5pt, % how far the line-numbers are from the code
	rulecolor=\color{black}, % if not set, the frame-color may be changed on line-breaks within not-black text (e.g. comments (green here))
	showspaces=false, % show spaces everywhere adding particular underscores; it overrides 'showstringspaces'
	showstringspaces=false, % underline spaces within strings only
	showtabs=false, % show tabs within strings adding particular underscores
	stepnumber=2, % the step between two line-numbers. If it's 1, each line will be numbered
	stringstyle=\color{gray}, % string literal style
	tabsize=2, % sets default tabsize to 2 spaces
	title=\lstname,
	emph={},
	emphstyle=\color{darkgreen}
	}

	\begin{document}

	\tikzstyle{mynode}=[rectangle split,rectangle split parts=2, draw,rectangle split part fill={lightgray, none}]


	\title{Reversed HEJ developer manual}
	\author{}
	\maketitle
	\tableofcontents

	\newpage

	\section{Overview}
	\label{sec:overview}

	Reversed HEJ is a C++ program and library implementing an algorithm to
	apply \HIGHEJ resummation~\cite{Andersen:2008ue,Andersen:2008gc} to
	pre-generated fixed-order events. This document is intended to give an
	overview over the concepts and structure of this implementation.

	\subsection{Project structure}
	\label{sec:project}

	Reversed HEJ is developed under the \href{https://git-scm.com/}{git}
	version control system. The main repository is on the IPPP
	\href{https://gitlab.com/}{gitlab} server under
	\url{https://gitlab.dur.scotgrid.ac.uk/hej/reversed_hej}. To get a local
	copy, get an account on the gitlab server and use
	\begin{lstlisting}[language=sh,caption={}]
	git clone git@gitlab.dur.scotgrid.ac.uk:hej/reversed_hej.git
	\end{lstlisting}
	This should create a directory \texttt{reversed\_hej} with the following
	contents:
	\begin{description}
	\item[doc:] Contains additional documentation, see section~\ref{sec:doc}.
	\item[include:] Contains the C++ header files.
	\item[src:] Contains the C++ source files.
	\item[t:] Contains the source code for the automated tests.
	\item[CMakeLists.txt:] Configuration file for the \cmake build
	system. See section~\ref{sec:cmake}.
	\item[cmake:] Auxiliary files for \cmake. This includes modules for
	finding installed software in \texttt{cmake/Modules} and templates for
	code generation during the build process in \texttt{cmake/Templates}.
	\item[config.yml:] Sample configuration file for running reversed HEJ.
	\item[events.lhe:] Fixed-order event sample that can be used as input
	for reversed HEJ.
	\item[FixedOrderGen:] Contains the code for the fixed-order generator,
	see section~\ref{sec:HEJFOG}.
	\end{description}
	In the following all paths are given relative to the
	\texttt{reversed\_hej} directory.

	\subsection{Documentation}
	\label{sec:doc}

	The \texttt{doc} directory contains user documentation in
	\texttt{doc/sphinx} and the configuration to generate source code
	documentation in \texttt{doc/doxygen}.

	The user documentation explains how to install and run reversed HEJ. The
	format is
	\href{http://docutils.sourceforge.net/rst.html}{reStructuredText}, which
	is mostly human-readable. Other formats, like \html, can be generated with the
	\href{http://www.sphinx-doc.org/en/master/}{sphinx} generator with
	\begin{lstlisting}[language=sh,caption={}]
	make html
	\end{lstlisting}


	To document the source code we use
	\href{https://www.stack.nl/~dimitri/doxygen/}{doxygen}. To generate
	\html documentation, use the command
	\begin{lstlisting}[language=sh,caption={}]
	doxygen Doxyfile
	\end{lstlisting}
	in the \texttt{doc/doxygen} directory.

	\subsection{Build system}
	\label{sec:cmake}

	For the most part, reversed HEJ is a library providing classes and
	functions that can be used to add resummation to fixed-order events. In
	addition, there is a relatively small executable program leveraging this
	library to read in events from an input file and produce resummation
	events. Both the library and the program are built and installed with
	the help of \cmake.
	%In addition to the general build process described in the user
	%documentation, see section~\ref{sec:doc}, it can be useful to build reversed
	%HEJ with debugging information using
	Debug information can be turned on by using
	\begin{lstlisting}[language=sh,caption={}]
	cmake base/directory -DCMAKE_BUILD_TYPE=Debug
	make install
	\end{lstlisting}
	This facilitates the use of debuggers like \href{https://www.gnu.org/software/gdb/}{gdb}.

	The main \cmake configuration file is \texttt{CMakeLists.txt}. It defines the
	compiler flags, software prerequisites, header and source files used to
	build reversed HEJ, and the automated tests.
	\texttt{cmake/Modules} contains module files that help with the
	detection of the software prerequisites and \texttt{cmake/Templates}
	template files for the automatic generation of header and
	source files. For example, this allows to only keep the version
	information in one central location (\texttt{CMakeLists.txt}) and
	automatically generate a header file from the template \texttt{Version.hh.in} to propagate this to the C++ code.

	\subsection{General coding guidelines}
	\label{sec:notes}

	The goal is to make the reversed HEJ code well-structured and
	readable. Here are a number of guidelines to this end.

	\begin{description}
	\item[Observe the boy scout rule.] Always leave the code cleaner
	than how you found it. Ugly hacks can be useful for testing, but
	shouldn't make their way into the main branch.
	\item[Ask if something is unclear.] Often there is a good reason why
	code is written the way it is. Sometimes that reason is only obvious to
	the original author (use \lstinline!git blame! to find them), in which
	case they should be poked to add a comment. Sometimes there is no good
	reason, but nobody has had the time to come up with something better,
	yet. In some places the code might just be bad.
	\item[Don't break tests.] There are a number of tests in the \texttt{t}
	directory, which can be run with \lstinline!make test!. Ideally, all
	tests should run successfully in each git revision. If your latest
	commit broke a test and you haven't pushed to the central repository
	yet, you can fix it with \lstinline!git commit --amend!. If an earlier
	local commit broke a test, you can use \lstinline!git rebase -i! if
	you feel confident.
	\item[Test your new code.] When you add some new functionality, also add an
	automated test. This can be useful even if you don't know the
	``correct'' result because it prevents the code from changing its behaviour
	silently in the future. \href{valgrind}{http://www.valgrind.org/} is a
	very useful tool to detect potential memory leaks.
	\item[Stick to the coding style.] It is somewhat easier to read code
	that has a uniform coding and indentation style. We don't have a
	strict style, but it helps if your code looks similar to what is
	already there.
	\end{description}

	\section{Program flow}
	\label{sec:flow}

	A run of the reversed HEJ program has three stages: initialisation,
	event processing, and cleanup. The following sections outline these
	stages and their relations to the various classes and functions in the
	code. Unless denoted otherwise, all classes and functions are part of
	the \lstinline!RHEJ! namespace. The code for the reversed HEJ program is
	in \texttt{src/main.cc}, all other code comprises the reversed HEJ
	library. Classes and free functions are usually implemented in header
	and source files with a corresponding name, i.e. the code for
	\lstinline!MyClass! can usually be found in
	\texttt{include/RHEJ/MyClass.hh} and \texttt{src/MyClass.cc}.

	\subsection{Initialisation}
	\label{sec:init}

	The first step is to load and parse the \YAML configuration file. The
	entry point for this is the \lstinline!load_config! function and the
	related code can be found in \texttt{include/RHEJ/YAMLreader.hh},
	\texttt{include/RHEJ/config.hh} and the corresponding \texttt{.cc} files
	in the \texttt{src} directory. The implementation is based on the
	\href{https://github.com/jbeder/yaml-cpp}{yaml-cpp} library.
	The \lstinline!load_config! function returns a \lstinline!Config! object
	containing all settings. To detect potential mistakes as early as
	possible, we throw an exception whenever one of the following errors
	occurs:
	\begin{itemize}
	\item There is an unknown option in the \YAML file.
	\item A setting is invalid, for example a string is given where a number
	would be expected.
	\item An option value is not set.
	\end{itemize}
	The third rule is sometimes relaxed for ``advanced'' settings with an
	obvious default, like for importing custom scales or analyses.

	The information stored in the \lstinline!Config! object is then used to
	initialise various objects required for the event processing stage
	described in section~\ref{sec:processing}. First, the
	\lstinline!get_analysis! function creates an object that inherits from
	the \lstinline!Analysis! interface.\footnote{In the context of C++ the
	proper technical expression is ``pure abstract class''.} Using an
	interface allows us to decide the concrete type of the analysis at run
	time instead of having to make a compile-time decision. Depending on the
	settings, \lstinline!get_analysis! creates either a user-defined
	analysis loaded from an external library (see the user documentation
	\todo{link}) or the default \lstinline!EmptyAnalysis!, which does
	nothing.

	Together with a number of further objects, whose roles are described in
	section~\ref{sec:processing}, we also initialise the global random
	number generator. We again use an interface to defer deciding the
	concrete type until the program is actually run. Currently, we support the
	\href{https://mixmax.hepforge.org/}{MIXMAX}
	(\texttt{include/RHEJ/Mixmax.hh}) and Ranlux64
	(\texttt{include/RHEJ/Ranlux64.hh}) random number generators, both are provided by \href{http://proj-clhep.web.cern.ch/}{CLHEP}.

	We also set up a \lstinline!LHEF::Reader! object (see
	\href{http://home.thep.lu.se/~leif/LHEF/}{\texttt{include/LHEF/LHEF.h}}) for reading events from a file in the Les
	Houches event file format~\cite{Alwall:2006yp}. A small wrapper around
	the
	\href{https://www.boost.org/doc/libs/1_67_0/libs/iostreams/doc/index.html}{boost
	iostreams} library allows us to also read event files compressed with
	\href{https://www.gnu.org/software/gzip/}{gzip}. The wrapper code is in
	\texttt{include/RHEJ/stream.hh} and the \texttt{src/stream.cc}.

	\subsection{Event processing}
	\label{sec:processing}

	In the second stage events are continously read from the event
	file. After jet clustering, a number of corresponding resummation events
	are generated for each input event and fed into the analysis and a
	number of output files. The roles of various classes and functions are
	illustrated in the following flow chart:
	\begin{center}
	\begin{tikzpicture}[node distance=2cm and 5mm]
	\node (reader) [mynode]
	{\lstinline!LHEF::Reader::readEvent!\nodepart{second}{read event}};
	\node
	(cluster) [mynode,below=of reader]
	{\lstinline!Event! constructor\nodepart{second}{cluster jets}};
	\node
	(resum) [mynode,below=of cluster]
	{\lstinline!EventReweighter::reweight!\nodepart{second}{perform resummation}};
	\node
	(cut) [mynode,below=of resum]
	{\lstinline!Analysis::pass_cuts!\nodepart{second}{apply cuts}};
	\node
	(fill) [mynode,below left=of cut]
	{\lstinline!Analysis::fill!\nodepart{second}{analyse event}};
	\node
	(write) [mynode,below right=of cut]
	{\lstinline!CombinedEventWriter::write!\nodepart{second}{write out event}};
	\node
	(control) [below=of cut] {};
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	(reader.south) -- node[left] {\lstinline!LHEF::HEPEUP!} (cluster.north);
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	(cluster.south) -- node[left] {\lstinline!Event!} (resum.north);
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	(resum.south) -- (cut.north);
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	($(resum.south)+(7mm, 0cm)$) -- ($(cut.north)+(7mm, 0cm)$);
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	($(resum.south)-(7mm, 0cm)$) -- node[left] {\lstinline!Event!} ($(cut.north)-(7mm, 0cm)$);
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	($(cut.south)-(3mm,0mm)$) .. controls ($(control)-(3mm,0mm)$) ..node[left] {\lstinline!Event!} (fill.east);
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	($(cut.south)-(3mm,0mm)$) .. controls ($(control)-(3mm,0mm)$) .. (write.west);
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	($(cut.south)+(3mm,0mm)$) .. controls ($(control)+(3mm,0mm)$) .. (fill.east);
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	($(cut.south)+(3mm,0mm)$) .. controls ($(control)+(3mm,0mm)$) ..node[right] {\lstinline!Event!} (write.west);
	\end{tikzpicture}
	\end{center}
	The resummation is performed by the \lstinline!EventReweighter! class,
	which is described in more detail in section~\ref{sec:resum}. The
	\lstinline!CombinedEventWriter! writes events to zero or more output
	files. To this end, it contains a number of objects implementing the
	\lstinline!EventWriter! interface. These event writers typically write
	the events to a file in a given format. We currently have the
	\lstinline!LesHouchesWriter! for event files in the Les Houches Event
	File format and the \lstinline!HepMCWriter! for the
	\href{https://hepmc.web.cern.ch/hepmc/}{HepMC} format (Version 2 and 3).

	\subsection{Resummation}
	\label{sec:resum}

	In the \lstinline!EventReweighter::reweight! member function, we first
	classify the input fixed-order event (FKL, unordered, non-HEJ, \dots)
	and decide according to the user settings whether to discard, keep, or
	resum the event. If we perform resummation for the given event, we
	generate a number of trial \lstinline!PhaseSpacePoint! objects. Phase
	space generation is discussed in more detail in
	section~\ref{sec:pspgen}. We then perform jet clustering according to
	the settings for the resummation jets on each
	\lstinline!PhaseSpacePoint!, update the factorisation and
	renormalisation scale in the resulting \lstinline!Event! and reweight it
	according to the ratio of pdf factors and \HEJ matrix elements between
	resummation and original fixed-order event:
	\begin{center}
	\begin{tikzpicture}[node distance=2cm and 5mm]
	\node (in) {};
	\node (treat) [diamond,draw,below=of in,minimum size=3.5cm,
	label={[anchor=west, inner sep=8pt]west:discard},
	label={[anchor=east, inner sep=14pt]east:keep},
	label={[anchor=south, inner sep=20pt]south:reweight}
	] {};
	\draw (treat.north west) -- (treat.south east);
	\draw (treat.north east) -- (treat.south west);
	\node
	(psp) [mynode,below=of treat]
	{\lstinline!PhaseSpacePoint! constructor};
	\node
	(cluster) [mynode,below=of psp]
	{\lstinline!Event! constructor\nodepart{second}{cluster jets}};
	\node
	(gen_scales) [mynode,below=of cluster]
	{\lstinline!ScaleGenerator::operator()!\nodepart{second}{update scales}};
	\node
	(rescale) [mynode,below=of gen_scales]
	{\lstinline!PDF::pdfpt!,
	\lstinline!MatrixElement!\nodepart{second}{reweight}};
	\node (out) [below of=rescale] {};
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	(in.south) -- node[left] {\lstinline!Event!} (treat.north);
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	(treat.south) -- node[left] {\lstinline!Event!} (psp.north);
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	(psp.south) -- (cluster.north);
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	($(psp.south)+(7mm, 0cm)$) -- ($(cluster.north)+(7mm, 0cm)$);
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	($(psp.south)-(7mm, 0cm)$) -- node[left]
	{\lstinline!PhaseSpacePoint!} ($(cluster.north)-(7mm, 0cm)$);
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	(cluster.south) -- (gen_scales.north);
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	($(cluster.south)+(7mm, 0cm)$) -- ($(gen_scales.north)+(7mm, 0cm)$);
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	($(cluster.south)-(7mm, 0cm)$) -- node[left]
	{\lstinline!Event!} ($(gen_scales.north)-(7mm, 0cm)$);
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	(gen_scales.south) -- (rescale.north);
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	($(gen_scales.south)+(7mm, 0cm)$) -- ($(rescale.north)+(7mm, 0cm)$);
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	($(gen_scales.south)-(7mm, 0cm)$) -- node[left]
	{\lstinline!Event!} ($(rescale.north)-(7mm, 0cm)$);
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	(rescale.south) -- (out.north);
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	($(rescale.south)+(7mm, 0cm)$) -- ($(out.north)+(7mm, 0cm)$);
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	($(rescale.south)-(7mm, 0cm)$) -- node[left]
	{\lstinline!Event!} ($(out.north)-(7mm, 0cm)$);
	\node (helper) at ($(treat.east) + (15mm,0cm)$) {};
	\draw[-{Latex[length=3mm, width=1.5mm]}]
	(treat.east) -- ($(treat.east) + (15mm,0cm)$)
	-- node[left] {\lstinline!Event!} (helper \|- gen_scales.east) -- (gen_scales.east)
	;
	\end{tikzpicture}
	\end{center}


	\subsection{Phase space point generation}
	\label{sec:pspgen}

	The resummed and matched \HEJ cross section for pure jet production of
	FKL configurations is given by (cf. eq. (3) of~\cite{Andersen:2018tnm})
	\begin{align}
	\label{eq:resumdijetFKLmatched2}
	% \begin{split}
	\sigma&_{2j}^\mathrm{resum, match}=\sum_{f_1, f_2}\ \sum_m
	\prod_{j=1}^m\left(
	\int_{p_{j\perp}^B=0}^{p_{j\perp}^B=\infty}
	\frac{\mathrm{d}^2\mathbf{p}_{j\perp}^B}{(2\pi)^3}\ \int
	\frac{\mathrm{d} y_j^B}{2} \right) \
	(2\pi)^4\ \delta^{(2)}\!\!\left(\sum_{k=1}^{m}
	\mathbf{p}_{k\perp}^B\right)\nonumber\\
	&\times\ x_a^B\ f_{a, f_1}(x_a^B, Q_a^B)\ x_b^B\ f_{b, f_2}(x_b^B, Q_b^B)\
	\frac{\overline{\left\|\mathcal{M}_\text{LO}^{f_1f_2\to f_1g\cdots
	gf_2}\big(\big\{p^B_j\big\}\big)\right\|}^2}{(\hat {s}^B)^2}\nonumber\\
	& \times (2\pi)^{-4+3m}\ 2^m \nonumber\\
	&\times\ \sum_{n=2}^\infty\
	\int_{p_{1\perp}=p_{\perp,\mathrm{min}} }^{p_{1\perp}=\infty}
	\frac{\mathrm{d}^2\mathbf{p}_{1\perp}}{(2\pi)^3}\
	\int_{p_{n\perp}=p_{\perp,\mathrm{min}}}^{p_{n\perp}=\infty}
	\frac{\mathrm{d}^2\mathbf{p}_{n\perp}}{(2\pi)^3}\
	\prod_{i=2}^{n-1}\int_{p_{i\perp}=\lambda}^{p_{i\perp}=\infty}
	\frac{\mathrm{d}^2\mathbf{p}_{i\perp}}{(2\pi)^3}\ (2\pi)^4\ \delta^{(2)}\!\!\left(\sum_{k=1}^n
	\mathbf{p}_{k\perp}\right )\\
	&\times \ \mathbf{T}_y \prod_{i=1}^n
	\left(\int \frac{\mathrm{d} y_i}{2}\right)\
	\mathcal{O}_{mj}^e\
	\left(\prod_{l=1}^{m-1}\delta^{(2)}(\mathbf{p}_{\mathcal{J}_{l}\perp}^B -
	\mathbf{j}_{l\perp})\right)\
	\left(\prod_{l=1}^m\delta(y^B_{\mathcal{J}_l}-y_{\mathcal{J}_l})\right)
	\ \mathcal{O}_{2j}(\{p_i\})\nonumber\\
	&\times \frac{(\hat{s}^B)^2}{\hat{s}^2}\ \frac{x_a f_{a,f_1}(x_a, Q_a)\ x_b f_{b,f_2}(x_b, Q_b)}{x_a^B\ f_{a,f_1}(x_a^B, Q_a^B)\ x_b^B\ f_{b,f_2}(x_b^B, Q_b^B)}\ \frac{\overline{\left\|\mathcal{M}_{\mathrm{HEJ}}^{f_1 f_2\to f_1 g\cdots
	gf_2}(\{ p_i\})\right\|}^2}{\overline{\left\|\mathcal{M}_\text{LO, HEJ}^{f_1f_2\to f_1g\cdots
	gf_2}\big(\big\{p^B_j\big\}\big)\right\|}^{2}} \,.\nonumber
	% \end{split}
	\end{align}
	The first two lines correspond to the generation of the fixed-order
	input events with incoming partons $f_1, f_2$ and outgoing momenta
	$p_j^B$, where $\mathbf{p}_{j\perp}^B$ and $y_j^B$ denote the respective
	transverse momentum and rapidity. Note that, at leading order, these
	coincide with the fixed-order jet momenta $p_{\mathcal{J}_j}^B$. $f_{a,f_1}(x_a, Q_a),
	f_{b,f_2}(x_b, Q_b)$ are the pdf factors for the incoming partons with
	momentum fractions $x_a$ and $x_b$. The square of the partonic
	centre-of-mass energy is denoted by $\hat{s}^B$ and
	$\mathcal{M}_\text{LO}^{f_1f_2\to f_1g\cdots gf_2}$ is the
	leading-order matrix element.

	The third line is a factor accounting for the different multiplicities
	between fixed-order and resummation events. Lines four and five are
	the integration over the resummation phase space described in this
	section. $p_i$ are the momenta of the outgoing partons in resummation
	phase space. $\mathbf{T}_y$ denotes rapidity
	ordering and $\mathcal{O}_{mj}^e$ projects out the exclusive $m$-jet
	component. The relation between resummation and fixed-order momenta is
	fixed by the $\delta$ functions. The first sets each transverse fixed-order jet
	momentum to some function $\mathbf{j_{l\perp}}$ of the resummation
	momenta. The exact form is described in section~\ref{sec:ptj_res}. The second
	$\delta$ forces the rapidities of resummation and fixed-order jets to be
	the same. Finally, the last line is the reweighting of pdf and matrix
	element factors already shown in section~\ref{sec:resum}.

	There are two kinds of cut-off in the integration over the resummation
	partons. $\lambda$ is a technical cut-off connected to the cancellation
	of infrared divergencies between real and virtual corrections. Its
	numerical value is set in
	\texttt{include/RHEJ/Constants.h}. $p_{\perp,\mathrm{min}}$ regulates
	and \emph{uncancelled} divergence in the extremal parton momenta. Its
	size is set by the user configuration \todo{link}.

	It is straightforward to generalise eq.~(\ref{eq:resumdijetFKLmatched2})
	to unordered configurations and processes with additional colourless
	emissions, for example a Higgs or electroweak boson. In the latter case only
	the fixed-order integration and the matrix elements change.

	\subsubsection{Gluon Multiplicity}
	\label{sec:psp_ng}

	The first step in evaluating the resummation phase space in
	eq.~(\ref{eq:resumdijetFKLmatched2}) is to randomly pick terms in the
	sum over the number of emissions. This sampling of the gluon
	multiplicity is done in the \lstinline!PhaseSpacePoint::sample_ng!
	function in \texttt{src/PhaseSpacePoint.cc}.

	The typical number of extra emissions depends strongly on the rapidity
	span of the underlying fixed-order event. Let us, for example, consider
	a fixed-order FKL-type multi-jet configuration with rapidities
	$y_{j_f},\,y_{j_b}$ of the most forward and backward jets,
	respectively. By eq.~(\ref{eq:resumdijetFKLmatched2}), the jet
	multiplicity and the rapidity of each jet are conserved when adding
	resummation. This implies that additional hard radiation is restricted
	to rapidities $y$ within a region $y_{j_b} \lesssim y \lesssim
	y_{j_f}$. Within \HEJ, we require the most forward and most backward
	emissions to be hard \todo{specify how hard} in order to avoid divergences, so this constraint
	in fact applies to \emph{all} additional radiation.

	To simplify the remaining discussion, let us remove the FKL rapidity
	ordering
	\begin{equation}
	\label{eq:remove_y_order}
	\mathbf{T}_y \prod_{i=1}^n\int \frac{\mathrm{d}y_i}{2} =
	\frac{1}{n!}\prod_{i=1}^n\int
	\frac{\mathrm{d}y_i}{2}\,,
	\end{equation}
	where all rapidity integrals now cover a region which is approximately
	bounded by $y_{j_b}$ and $y_{j_f}$. Each of the $m$ jets has to contain at least
	one parton; selecting random emissions we can rewrite the phase space
	integrals as
	\begin{equation}
	\label{eq:select_jets}
	\frac{1}{n!}\prod_{i=1}^n\int [\mathrm{d}p_i] =
	\left(\prod_{i=1}^{m}\int [\mathrm{d}p_i]\ {\cal J}_i(p_i)\right)
	\frac{1}{n_g!}\prod_{i=m+1}^{m+n_g}\int [\mathrm{d}p_i]
	\end{equation}
	with jet selection functions
	\begin{equation}
	\label{eq:def_jet_selection}
	{\cal J}_i(p) =
	\begin{cases}
	1 &p\text{ clustered into jet }i\\
	0 & \text{otherwise}
	\end{cases}
	\end{equation}
	and $n_g \equiv n - m$. Here and in the following we use the short-hand
	notation $[\mathrm{d}p_i]$ to denote the phase-space measure for parton
	$i$. As is evident from eq.~\eqref{eq:select_jets}, adding an extra emission
	$n_g+1$ introduces a suppression factor $\tfrac{1}{n_g+1}$. However, the
	additional phase space integral also results in an enhancement proportional
	to $\Delta y_{j_f j_b} = y_{j_f} - y_{j_b}$. This is a result of the
	rapidity-independence of the MRK limit of the integrand, consisting of the
	matrix elements divided by the flux factor. Indeed, we observe that the
	typical number of gluon emissions is to a good approximation proportional to
	the rapidity separation and the phase space integral is dominated by events
	with $n_g \approx \Delta y_{j_f j_b}$.

	For the actual phase space sampling, we assume a Poisson distribution
	and extract the mean number of gluon emissions in different rapidity
	bins and fit the results to a linear function in $\Delta y_{j_f j_b}$,
	finding a coefficient of $0.975$ for the inclusive production of a Higgs
	boson with two jets. Here are the observed and fitted average gluon
	multiplicities as a function of $\Delta y_{j_f j_b}$:
	\begin{center}
	\includegraphics[width=.75\textwidth]{ng_mean}
	\end{center}
	As shown for two rapidity slices the assumption of a Poisson
	distribution is also a good approximation:
	\begin{center}
	\includegraphics[width=.49\textwidth]{{ng_1.5}.pdf}\hfill
	\includegraphics[width=.49\textwidth]{{ng_5.5}.pdf}
	\end{center}

	\subsubsection{Number of Gluons inside Jets}
	\label{sec:psp_ng_jet}

	For each of the $n_g$ gluon emissions we can split the phase-space
	integral into a (disconnected) region inside the jets and a remainder:
	\begin{equation}
	\label{eq:psp_split}
	\int [\mathrm{d}p_i] = \int [\mathrm{d}p_i]\,
	\theta\bigg(\sum_{j=1}^{m}{\cal J}_j(p_i)\bigg) + \int [\mathrm{d}p_i]\,
	\bigg[1-\theta\bigg(\sum_{j=1}^{m}{\cal J}_j(p_i)\bigg)\bigg]\,.
	\end{equation}
	The next step is to decide how many of the gluons will form part of a
	jet. This is done in the \lstinline!PhaseSpacePoint::sample_ng_jets!
	function.

	We choose an importance sampling which is flat in the plane
	spanned by the azimuthal angle $\phi$ and the rapidity $y$. This is
	observed in BFKL and valid in the limit of Multi-Regge-Kinematics
	(MRK). Furthermore, we assume anti-$k_t$ jets, which cover an area of
	$\pi R^2$.

	In principle, the total accessible area in the $y$-$\phi$ plane is given
	by $2\pi \Delta y_{fb}$, where $\Delta y_{fb}\geq \Delta y_{j_f j_b}$ is
	the a priori unknown rapidity separation between the most forward and
	backward partons. In most cases the extremal jets consist of single
	partons, so that $\Delta y_{fb} = \Delta y_{j_f j_b}$. For the less common
	case of two partons forming a jet we observe a maximum distance of $R$
	between the constituents and the jet centre. In rare cases jets have
	more than two constituents. Empirically, they are always within a
	distance of $\tfrac{5}{3}R$ to the centre of the jet, so
	$\Delta y_{fb} \leq \Delta y_{j_f j_b} + \tfrac{10}{3} R$. In practice, the
	extremal partons are required to carry a large fraction of the jet
	transverse momentum and will therefore be much closer to the jet axis.

	In summary, for sufficiently large rapidity separations we can use the
	approximation $\Delta y_{fb} \approx \Delta y_{j_f j_b}$. This scenario
	is depicted here:
	\begin{center}
	\includegraphics[width=0.5\linewidth]{ps_large_y}
	\end{center}
	If there is no overlap between jets, the probability $p_{\cal J, >}$ for
	an extra gluon to end up inside a jet is then given by
	\begin{equation}
	\label{eq:p_J_large}
	p_{\cal J, >} = \frac{(m - 1)\*R^2}{2\Delta y_{j_f j_b}}\,.
	\end{equation}
	For a very small rapidity separation, eq.~\eqref{eq:p_J_large}
	obviously overestimates the true probability. The maximum phase space
	covered by jets in the limit of a vanishing rapidity distance between
	all partons is $2mR \Delta y_{fb}$:
	\begin{center}
	\includegraphics[width=0.5\linewidth]{ps_small_y}
	\end{center}
	We therefore estimate the probability for a parton
	to end up inside a jet as
	\begin{equation}
	\label{eq:p_J}
	p_{\cal J} = \min\bigg(\frac{(m - 1)\*R^2}{2\Delta y_{j_f j_b}}, \frac{mR}{\pi}\bigg)\,.
	\end{equation}
	Here we compare this estimate with the actually observed
	fraction of additional emissions into jets as a function of the rapidity
	separation:
	\begin{center}
	\includegraphics[width=0.75\linewidth]{pJ}
	\end{center}

	\subsubsection{Gluons outside Jets}
	\label{sec:gluons_nonjet}

	Using our estimate for the probability of a gluon to be a jet
	constituent, we choose a number $n_{g,{\cal J}}$ of gluons inside
	jets, which also fixes the number $n_g - n_{g,{\cal J}}$ of gluons
	outside jets. As explained later on, we need to generate the momenta of
	the gluons outside jets first. This is done in
	\lstinline!PhaseSpacePoint::gen_non_jet!.

	The azimuthal angle $\phi$ is generated flat within $0\leq \phi \leq 2
	\pi$. The allowed rapidity interval is set by the most forward and
	backward partons, which are necessarily inside jets. Since these parton
	rapidities are not known at this point, we also have to postpone the
	rapidity generation for the gluons outside jets. For the scalar
	transverse momentum $p_\perp = \|\mathbf{p}_\perp\|$ of a gluon outside
	jets we use the parametrisation
	\begin{equation}
	\label{eq:p_nonjet}
	p_\perp = \lambda + \tilde{p}_\perp\\tan(\tau\r)\,, \qquad
	\tau = \arctan\bigg(\frac{p_{\perp{\cal J}_\text{min}} - \lambda}{\tilde{p}_\perp}\bigg)\,.
	\end{equation}
	For $r \in [0,1)$, $p_\perp$ is always less than the minimum momentum
	$p_{\perp{\cal J}_\text{min}}$ required for a jet. $\tilde{p}_\perp$ is
	a free parameter, a good empirical value is $\tilde{p}_\perp = [1.3 +
	0.2\*(n_g - n_{g,\cal J})]\,$GeV

	\subsubsection{Resummation jet momenta}
	\label{sec:ptj_res}

	On the one hand, each jet momentum is given by the sum of its
	constituent momenta. On the other hand, the resummation jet momenta are
	fixed by the constraints in line five of the master
	equation~\eqref{eq:resumdijetFKLmatched2}. We therefore have to
	calculate the resummation jet momenta from these constraints before
	generating the momenta of the gluons inside jets. This is done in
	\lstinline!PhaseSpacePoint::reshuffle! and in the free
	\lstinline!resummation_jet_momenta! function.

	The resummation jet momenta are determined by the $\delta$ functions in
	line five of eq.~(\ref{eq:resumdijetFKLmatched2}). The rapidities are
	fixed to the rapidities of the jets in the input fixed-order events, so
	that the FKL ordering is guaranteed to be preserved. For the transverse
	momentum components we currently use the traditional \HEJ reshuffling
	relation
	\begin{equation}
	\label{eq:ptreassign}
	\mathbf{p}^B_{\mathcal{J}_{l\perp}} = \mathbf{j}_{l\perp} \equiv \mathbf{p}_{\mathcal{J}_{l}\perp} + \mathbf{q}_\perp \,
	\frac{\|\mathbf{p}_{\mathcal{J}_{l}\perp}\|}{P_\perp},
	\end{equation}
	where $\mathbf{q}_\perp = \sum_{j=1}^n \mathbf{p}_{i\perp}
	\bigg[1-\theta\bigg(\sum_{j=1}^{m}{\cal J}_j(p_i)\bigg)\bigg] $ is the
	total transverse momentum of all partons \emph{outside} jets and
	$P_\perp = \sum_{j=1}^m \|\mathbf{p}_{\mathcal{J}_{j}\perp}\|$. Since the
	total transverse momentum of an event vanishes, we can also use
	$\mathbf{q}_\perp = - \sum_{j=1}^m
	\mathbf{p}_{\mathcal{J}_{j}\perp}$. Eq.~(\ref{eq:ptreassign}) is a
	non-linear system of equations in the resummation jet momenta
	$\mathbf{p}_{\mathcal{J}_{l}\perp}$. To solve it we use
	\href{https://www.gnu.org/software/gsl/}{GSL} routines.

	The reshuffling relation~\eqref{eq:ptreassign} allows the transverse
	momenta $p^B_{\mathcal{J}_{l\perp}}$ of the fixed-order jets to be
	somewhat below the minimum transverse momentum of resummation jets. It
	is crucial that this difference does not become too large, as the
	fixed-order cross section diverges for vanishing transverse momenta. In
	the production of a Higgs boson with resummation jets above $30\,$GeV we observe
	that the contribution from fixed-order events with jets softer than
	about $20\,$GeV can be safely neglected. This is shown in the following
	plot of the differential cross section over the transverse momentum of
	the softest fixed-order jet:
	\begin{center}
	\includegraphics[width=.75\textwidth]{ptBMin}
	\end{center}
	Finally, to perform the integration over the resummation phase space, we
	need the $\delta$ functions
	$\delta^{(2)}(\mathbf{p}_{\mathcal{J}_{l}\perp}^B -
	\mathbf{j}_{l\perp})$ form eq.~(\ref{eq:resumdijetFKLmatched2}) to be linear in the resummation parton momenta
	instead of the fixed-order momenta. This introduces an extra Jacobian $\Delta$:
	\begin{equation}
	\label{eq:delta_rewrite}
	\prod_{l=1}^m \delta^{(2)}(\mathbf{p}_{\mathcal{J}_{l\perp}}^B -
	\mathbf{j}_{l\perp}) = \frac{1}{\Delta} \prod_{l=1}^m \delta^{(2)}(\mathbf{p}_{\mathcal{J}_{l\perp}} -
	\mathbf{j}_{l\perp}^B)\,,
	\end{equation}
	where $\mathbf{j}_{l\perp}^B$ only depends on the Born momenta. We have
	extended the product to run to $m$ instead of $m-1$ by eliminating the
	last $\delta$ function $\delta^{(2)}\!\!\left(\sum_{k=1}^n \mathbf{p}_{k\perp}\right )$.
	The Jacobian $\Delta$ is the determinant of a $2m \times 2m$ matrix with $l, l' = 1,\dots,m$
	and $X, X' = x,y$.
	\begin{equation}
	\label{eq:jacobian}
	\Delta = \bigg\| \delta_{l l'} \delta_{X X'} + \frac{q_X\, p_{{\cal
	J}_{l'}X'}}{\|\mathbf{p}_{{\cal J}_{l'} \perp}\| P_\perp}\bigg(\delta_{l l'}
	- \frac{\|\mathbf{p}_{{\cal J}_l \perp}\|}{P_\perp}\bigg)\bigg\|\,.
	\end{equation}

	\subsubsection{Gluons inside Jets}
	\label{sec:gluons_jet}

	After the steps outlined in section~\ref{sec:psp_ng_jet}, we have a
	total number of $m + n_{g,{\cal J}}$ constituents. In
	\lstinline!PhaseSpacePoint::distribute_jet_partons! we distribute them
	randomly among the jets such that each jet has at least one
	constituent. We then generate their momenta in
	\lstinline!PhaseSpacePoint::split! using the \lstinline!Splitter! class.

	The phase space integral for a jet ${\cal J}$ is given by
	\begin{equation}
	\label{eq:ps_jetparton} \prod_{i\text{ in }{\cal J}} \bigg(\int
	\mathrm{d}\mathbf{p}_{i\perp}\ \int \mathrm{d} y_i
	\bigg)\delta^{(2)}\Big(\sum_{i\text{ in }{\cal J}} \mathbf{p}_{i\perp} -
	\mathbf{j}_{\perp}^B\Big)\delta(y_{\mathcal{J}}-y^B_{\mathcal{J}})\,.
	\end{equation}
	For jets with a single constituent, the parton momentum is obiously equal to the
	jet momentum. In the case of two constituents, we observe that the
	partons are always inside the jet cone with radius $R$ and often very
	close to the jet centre. The following plots show the typical relative
	distance $\Delta R/R$ for this scenario:
	\begin{center}
	\includegraphics[width=0.45\linewidth]{dR_2}
	\includegraphics[width=0.45\linewidth]{dR_2_small}
	\end{center}
	According to this preference for small values of $\Delta R$, we
	parametrise the $\Delta R$ integrals as
	\begin{equation}
	\label{eq:dR_sampling}
	\frac{\Delta R}{R} =
	\begin{cases}
	0.25\,x_R & x_R < 0.4 \\
	1.5\,x_R - 0.5 & x_R \geq 0.4
	\end{cases}\,.
	\end{equation}
	Next, we generate $\Theta_1 \equiv \Theta$ and use the constraint $\Theta_2 = \Theta
	\pm \pi$. The transverse momentum of the first parton is then given by
	\begin{equation}
	\label{eq:delta_constraints}
	p_{1\perp} =
	\frac{p_{\mathcal{J} y} - \tan(\phi_2) p_{\mathcal{J} x}}{\sin(\phi_1)
	- \tan(\phi_2)\cos(\phi_1)}\,.
	\end{equation}
	We get $p_{2\perp}$ by exchanging $1 \leftrightarrow 2$ in the
	indices. To obtain the Jacobian of the transformation, we start from the
	single jet phase space eq.~(\ref{eq:ps_jetparton}) with the rapidity
	delta function already rewritten to be linear in the rapidity of the
	last parton, i.e.
	\begin{equation}
	\label{eq:jet_2p}
	\prod_{i=1,2} \bigg(\int
	\mathrm{d}\mathbf{p}_{i\perp}\ \int \mathrm{d} y_i
	\bigg)\delta^{(2)}\Big(\mathbf{p}_{1\perp} + \mathbf{p}_{2\perp} -
	\mathbf{j}_{\perp}^B\Big)\delta(y_2- \dots)\,.
	\end{equation}
	The integral over the second parton momentum is now trivial; we can just replace
	the integral over $y_2$ with the equivalent constraint
	\begin{equation}
	\label{eq:R2}
	\int \mathrm{d}R_2 \ \delta\bigg(R_2 - \bigg[\phi_{\cal J} - \arctan
	\bigg(\frac{p_{{\cal J}y} - p_{1y}}{p_{{\cal J}x} -
	p_{1x}}\bigg)\bigg]/\cos \Theta\bigg) \,.
	\end{equation}
	In order to fix the integral over $p_{1\perp}$ instead, we rewrite this
	$\delta$ function. This introduces the Jacobian
	\begin{equation}
	\label{eq:jac_pt1}
	\bigg\|\frac{\partial p_{1\perp}}{\partial R_2} \bigg\| =
	\frac{\cos(\Theta)\mathbf{p}_{2\perp}^2}{p_{{\cal J}\perp}\sin(\phi_{\cal J}-\phi_1)}\,.
	\end{equation}
	The final form of the integral over the two parton momenta is then
	\begin{equation}
	\label{eq:ps_jet_2p}
	\int \mathrm{d}R_1\ R_1 \int \mathrm{d}R_2 \int \mathrm{d}x_\Theta\ 2\pi \int
	\mathrm{d}p_{1\perp}\ p_{1\perp} \int \mathrm{d}p_{2\perp}
	\ \bigg\|\frac{\partial p_{1\perp}}{\partial R_2} \bigg\|\delta(p_{1\perp}
	-\dots) \delta(p_{2\perp} - \dots)\,.
	\end{equation}

	As is evident from section~\ref{sec:psp_ng_jet}, jets with three or more
	constituents are rare and an efficient phase-space sampling is less
	important. For such jets, we exploit the observation that partons with a
	distance larger than $R_{\text{max}} = \tfrac{5}{3} R$ to
	the jet centre are never clustered into the jet. Assuming $N$
	constituents, we generate all components
	for the first $N-1$ partons and fix the remaining parton with the
	$\delta$-functional. In order to end up inside the jet, we use the
	parametrisation
	\begin{align}
	\label{eq:ps_jet_param}
	\phi_i ={}& \phi_{\cal J} + \Delta \phi_i\,, & \Delta \phi_i ={}& \Delta
	R_i
	\cos(\Theta_i)\,, \\
	y_i ={}& y_{\cal J} + \Delta y_i\,, & \Delta y_i ={}& \Delta
	R_i
	\sin(\Theta_i)\,,
	\end{align}
	and generate $\Theta_i$ and $\Delta R_i$ randomly with $\Delta R_i \leq
	R_{\text{max}}$ and the empiric value $R_{\text{max}} = 5\*R/3$. We can
	then write the phase space integral for a single parton as $(p_\perp = \|\mathbf{p}_\perp\|)$
	\begin{equation}
	\label{eq:ps_jetparton_x}
	\int \mathrm{d}\mathbf{p}_{\perp}\ \int
	\mathrm{d} y \approx \int_{\Box} \mathrm{d}x_{\perp}
	\mathrm{d}x_{ R}
	\mathrm{d}x_{\theta}\
	2\\pi\,\R_{\text{max}}^2\,\x_{R}\,\p_{\perp}\,\*(p_{\perp,\text{max}}
	- p_{\perp,\text{min}})
	\end{equation}
	with
	\begin{align}
	\label{eq:ps_jetparton_parameters}
	\Delta \phi ={}& R_{\text{max}}\x_{R}\\cos(2\\pi\x_\theta)\,,&
	\Delta y ={}& R_{\text{max}}\x_{R}\\sin(2\\pi\x_\theta)\,, \\
	p_{\perp} ={}& (p_{\perp,\text{max}} - p_{\perp,\text{min}})\*x_\perp +
	p_{\perp,\text{min}}\,.
	\end{align}
	$p_{\perp,\text{max}}$ is determined from the requirement that the total
	contribution from the first $n-1$ partons --- i.e. the projection onto the
	jet $p_{\perp}$ axis --- must never exceed the jet $p_\perp$. This gives
	\todo{This bound is too high}
	\begin{equation}
	\label{eq:pt_max}
	p_{i\perp,\text{max}} = \frac{p_{{\cal J}\perp} - \sum_{j<i} p_{j\perp}
	\cos \Delta
	\phi_j}{\cos \Delta
	\phi_i}\,.
	\end{equation}
	The $x$ and $y$ components of the last parton follow immediately from
	the first $\delta$ function. The last rapidity is fixed by the condition that
	the jet rapidity is kept fixed by the reshuffling, i.e.
	\begin{equation}
	\label{eq:yJ_delta}
	y^B_{\cal J} = y_{\cal J} = \frac 1 2 \ln \frac{\sum_{i=1}^n E_i+ p_{iz}}{\sum_{i=1}^n E_i - p_{iz}}\,.
	\end{equation}
	With $E_n \pm p_{nz} = p_{n\perp}\exp(\pm y_n)$ this can be rewritten to
	\begin{equation}
	\label{eq:yn_quad_eq}
	\exp(2y_{\cal J}) = \frac{\sum_{i=1}^{n-1} E_i+ p_{iz}+p_{n\perp} \exp(y_n)}{\sum_{i=1}^{n-1} E_i - p_{iz}+p_{n\perp} \exp(-y_n)}\,,
	\end{equation}
	which is a quadratic equation in $\exp(y_n)$. The physical solution is
	\begin{align}
	\label{eq:yn}
	y_n ={}& \log\Big(-b + \sqrt{b^2 + \exp(2y_{\cal J})}\,\Big)\,,\\
	b ={}& \bigg(\sum_{i=1}^{n-1} E_i + p_{iz} - \exp(2y_{\cal J})
	\sum_{i=1}^{n-1} E_i - p_{iz}\bigg)/(2 p_{n\perp})\,.
	\end{align}
	\todo{what's wrong with the following?} To eliminate the remaining rapidity
	integral, we transform the $\delta$ function to be linear in the
	rapidity $y$ of the last parton. The corresponding Jacobian is
	\begin{equation}
	\label{eq:jacobian_y}
	\bigg\|\frac{\partial y_{\cal J}}{\partial y_n}\bigg\|^{-1} = 2 \bigg( \frac{E_n +
	p_{nz}}{E_{\cal J} + p_{{\cal J}z}} + \frac{E_n - p_{nz}}{E_{\cal J} -
	p_{{\cal J}z}}\bigg)^{-1}\,.
	\end{equation}
	Finally, we check that all designated constituents are actually
	clustered into the considered jet.

	\subsubsection{Final steps}
	\label{sec:final}

	Knowing the rapidity span covered by the extremal partons, we can now
	generate the rapdities for the partons outside jets. We perform jet
	clustering on all partons and check in
	\lstinline!PhaseSpacePoint::jets_ok! that all the following criteria are
	fulfilled:
	\begin{itemize}
	\item The number of resummation jets must match the number of
	fixed-order jets.
	\item No partons designated to be outside jets may end up inside jets.
	\item All other outgoing partons \emph{must} end up inside jets.
	\item The extremal (in rapidity) partons must be inside the extremal
	jets. If there is, for example, an unordered forward emission, the
	most forward parton must end up inside the most forward jet and the
	next parton must end up inside second jet.
	\item The rapidities of fixed-order and resummation jets must match.
	\end{itemize}
	After this, we adjust the phase-space normalisation according to the
	third line of eq.~(\ref{eq:resumdijetFKLmatched2}), determine the
	flavours of the outgoing partons, and adopt any additional colourless
	bosons from the fixed-order input event. Finally, we use momentum
	conservation to reconstruct the momenta of the incoming partons.

	\subsection{The matrix element }
	\label{sec:ME}

	The derivation of the \HEJ matrix element is explained in some detail
	in~\cite{Andersen:2018tnm}, where also results for leading and
	subleading matrix elements for pure multijet production and production
	of a Higgs boson with at least two associated jets are listed. Matrix
	elements for $W$ and $Z/\gamma^*$ production together with jets are
	given in~\cite{Andersen:2012gk,Andersen:2016vkp}, but not yet included.

	The matrix elements are implemented in the \lstinline!MatrixElement!
	class. To discuss the structure, let us consider the matrix element for
	FKL multijet production:
	\begin{align}
	\label{eq:ME}
	\begin{split}
	\overline{\left\|\mathcal{M}_\text{HEJ}^{f_1 f_2 \to f_1
	g\cdots g f_2}\right\|}^2 = \ &\frac 1 {4\
	- (N_c^2-1)}\ g_s^2\ \left\\|S_{f_1 f_2\to f_1 f_2}\right\\|^2\\
	+ (N_c^2-1)}\ \left\\|S_{f_1 f_2\to f_1 f_2}\right\\|^2\\
	&\cdot\ \left(g_s^2 K_{f_1}\ \frac 1 {t_1}\right) \cdot\ \left(g_s^2\ K_{f_2}\ \frac 1
	{t_{n-1}}\right)\\
	& \cdot \prod_{i=1}^{n-2} \left( \frac{-g_s^2 C_A}{t_it_{i+1}}\
	V^\mu(q_i,q_{i+1})V_\mu(q_i,q_{i+1}) \right)\\
	& \cdot \prod_{j=1}^{n-1} \exp\left[\omega^0(q_{j\perp})(y_{j+1}-y_j)\right].
	\end{split}
	\end{align}
	The square of the complete matrix element as given in eq.~(\ref{eq:ME})
	is calculated by \lstinline!MatrixElement::operator()!. \todo{There is
	most likely some overall factor} The last line of eq.~\eqref{eq:ME}
	constitutes the all-order virtual correction, implemented in
	\lstinline!MatrixElement::virtual_corrections!. The remaining parts,
	which correspond to the square of the leading-order HEJ matrix element
	$\overline{\left\|\mathcal{M}_\text{LO, HEJ}^{f_1f_2\to f_1g\cdots
	gf_2}\big(\big\{p^B_j\big\}\big)\right\|}^{2}$, are computed in
	\lstinline!MatrixElement::tree!. We can further factor off the
	scale-dependent ``parametric'' part
	\lstinline!MatrixElement::tree_param! containing all factors of the
	strong coupling $g_s$. Using this function saves some CPU time when
	adjusting the renormalisation scale, see section~\ref{sec:resum}.

	The remaining ``kinematic'' factors are calculated in
	\lstinline!MatrixElement::kin!. The currents $\left\\|S_{f_1 f_2\to f_1
	f_2}\right\\|^2$ are implemented in \texttt{src/Currents.cc}.

	\section{The fixed-order generator}
	\label{sec:HEJFOG}

	Even at leading order, standard fixed-order generators can only generate
	events with a limited number of final-state particles within reasonable
	CPU time. The purpose of the fixed-order generator is to supplement this
	with high-multiplicity input events according to the first two lines of
	eq.~\eqref{eq:resumdijetFKLmatched2} with the \HEJ approximation
	$\mathcal{M}_\text{LO, HEJ}^{f_1f_2\to f_1g\cdots gf_2}$ instead of the
	full fixed-order matrix element $\mathcal{M}_\text{LO}^{f_1f_2\to
	f_1g\cdots gf_2}$. Its usage is described in the user
	documentation\todo{link}.

	\subsection{File structure}
	\label{sec:HEJFOG_structure}

	The code for the fixed-order generator is in the \texttt{FixedOrderGen}
	directory, which contains the following:
	\begin{description}
	\item[include:] Contains the C++ header files.
	\item[src:] Contains the C++ source files.
	\item[t:] Contains the source code for the automated tests.
	\item[CMakeLists.txt:] Configuration file for the \cmake build system.
	\item[configFO.yml:] Sample configuration file for the fixed-order generator.
	\end{description}
	The code is generally in the \lstinline!HEJFOG! namespace. Functions and
	classes \lstinline!MyClass! are usually declared in
	\texttt{include/MyClass.hh} and implemented in \texttt{src/MyClass.cc}.

	\subsection{Program flow}
	\label{sec:prog_flow}

	A single run of the fixed-order generator consists of three or four
	stages.

	First, we perform initialisation similar to reversed HEJ, see
	section~\ref{sec:init}. Since there is a lot of overlap we frequently
	reuse classes and functions from reversed HEJ, i.e. from the
	\lstinline!RHEJ! namespace. The code for parsing the configuration file
	is in \texttt{include/config.hh} and implemented in
	\texttt{src/config.cc}.

	If partial unweighting is requested in the user settings \todo{link},
	the initialisation is followed by a calibration phase. We use a
	\lstinline!EventGenerator! to produce a number of trial
	events. We use these to calibrate the \lstinline!Unweighter! in
	its constructor and produce a first batch of partially unweighted
	events. This also allows us to estimate our unweighting efficiency.

	In the next step, we continue to generate events until and potentially
	unweight them. Once the user-defined target number of events is reached,
	we adjust their weights according to the number of required trials. As
	in reversed HEJ (see section~\ref{sec:processing}), we pass the final
	events to a \lstinline!RHEJ::Analysis! and a
	\lstinline!RHEJ::CombinedEventWriter!.

	\subsection{Event generation}
	\label{sec:evgen}

	Event generation is performed by the
	\lstinline!EventGenerator::gen_event! member function. We first
	construct a \lstinline!PhaseSpacePoint!. This is not to be confused with
	the resummation phase space points represented by
	\lstinline!RHEJ::PhaseSpacePoint!! After jet clustering, we compute the
	leading-order matrix element (see section~\ref{sec:ME}) and pdf factors.

	The phase space point generation is performed in the
	\lstinline!PhaseSpacePoint! constructor. We first construct the
	user-defined number of $n_p$ partons (by default gluons) in
	\lstinline!PhaseSpacePoint::gen_LO_partons!. We use flat sampling in
	rapidity and azimuthal angle. Their scalar transverse
	momenta are generated based on a random variable $x_{p_\perp}$ according
	to
	\begin{equation}
	\label{eq:pt_sampling}
	p_\perp = p_{\perp,\text{min}} +
	\begin{cases}
	p_{\perp,\text{par}}
	\tan\left(
	x_{p_\perp}
	\arctan\left(
	\frac{p_{\perp,\text{max}} - p_{\perp,\text{min}}}{p_{\perp,\text{par}}}
	\right)
	\right)
	& y > 3
	\\
	- \tilde{p}_{\perp,\text{par}}\log\left(1 - x_{p_\perp}\left[1 -
	\exp\left(\frac{p_{\perp,\text{min}} -
	p_{\perp,\text{max}}}{\tilde{p}_{\perp,\text{par}}}\right)\right]\right)
	& y \geq 3
	\end{cases}\,,
	\end{equation}
	where $p_{\perp,\text{min}}$ is the minimum jet transverse momentum,
	$p_{\perp,\text{max}}$ is the maximum transverse parton momentum,
	tentatively set to the beam energy, and $p_{\perp,\text{par}}$
	and $\tilde{p}_{\perp,\text{par}}$ are generation parameters set to
	heuristically determined values.

	After ensuring that all partons form separate jets, we generate any
	potential colourless emissions. We then determine the incoming momenta
	and flavours in \lstinline!PhaseSpacePoint::reconstruct_incoming! and
	adjust the outgoing flavours to ensure an FKL configuration. Finally, we
	may reassign outgoing flavours to generate suppressed (for example
	unordered) configurations.

	\subsection{Unweighting}
	\label{sec:unweight}

	Straightforward event generation tends to produce many events with small
	weights. Those events have a negligible contribution to the final
	observables, but can take up considerable storage space and CPU time in
	later processing stages. This problem can be addressed by unweighting.

	For naive unweighting, one would determine the maximum weight
	$w_\text{max}$ of all events, discard each event with weight $w$ with a
	probability $p=w/w_\text{max}$, and set the weights of all remaining
	events to $w_\text{max}$. The downside to this procedure is that it also
	eliminates a sizeable fraction of events with moderate weight, so that
	the statistical convergence deteriorates.

	To ameliorate this problem, we perform unweighting only for events with
	sufficiently small weights. This is done by the
	\lstinline!Unweighter! class. In the constructor we estimate the
	mean and width of the weight-weight distribution from a sample of
	events. We use these estimates to determine the maximum weight below
	which unweighting is performed. The actual unweighting is the done in
	the \lstinline!Unweighter::unweight! function.

	\bibliographystyle{JHEP}
	\bibliography{biblio}


	\end{document}
	diff --git a/doc/sphinx/analyses.rst b/doc/sphinx/analyses.rst
	index 74a97c6..013a79f 100644
	--- a/doc/sphinx/analyses.rst
	+++ b/doc/sphinx/analyses.rst
	@@ -1,163 +1,179 @@
	.. _`Writing custom analyses`:

	Writing custom analyses
	=======================

	Reversed HEJ and the HEJ fixed-order generator can generate HepMC files,
	so you can always run a `rivet <https://rivet.hepforge.org/>`_ analysis
	-on these. Alternatively, you can provide a custom analysis inside a C++
	-library.
	+on these. However if you compiled reversed HEJ with rivet you can use
	+the native rivet interface. For example
	+
	+.. code-block:: YAML
	+
	+ analysis:
	+ rivet: [MC_XS, MC_JETS]
	+ output: RHEJ
	+
	+would call the generic
	+`MC_XS <https://rivet.hepforge.org/analyses/MC_XS.html>`_ and
	+`MC_JETS <https://rivet.hepforge.org/analyses/MC_JETS.html>`_ analysis
	+and write the result into :code:`RHEJ[.Scalename].yoda`.
	+Reversed HEJ will then run rivet over all different scales seperatly and
	+write out each into a different yoda file. Alternatively instead
	+of using rivet, you can provide a custom analysis inside a C++ library.

	An analysis is a class that derives from the abstract :code:`Analysis`
	base class provided by reversed HEJ. It has to implement three public
	functions:

	* The :code:`pass_cuts` member function return true if and only if the
	given event (first argument) passes the analysis cuts

	* The :code:`fill` member function adds an event to the analysis, which
	for example can be used to fill histograms. Reversed HEJ will only
	pass events for which :code:`pass_cuts` has returned true.

	* The :code:`finalise` member function is called after all events have
	been processed. It can be used, for example, to print out or save the
	analysis results.

	The :code:`pass_cuts` and :code:`fill` functions take two arguments: the
	resummation event generated by reversed HEJ and the original fixed-order
	input event. Usually, the second argument can be ignored. It can be
	used, for example, for implementing cuts that depend on the ratio of the
	weights between the fixed-order and the resummation event.

	In addition to the two member functions, there has to be a global
	make_analysis function that takes the analysis parameters in the form of
	a YAML :code:`Node` and returns a :code:`std::unique_ptr` to the
	Analysis.

	-The following code creates the simplest conceivable analysis.::
	+The following code creates the simplest conceivable analysis.
	+::

	#include <memory> // for std::unique_ptr

	#include "RHEJ/Analysis.hh"

	class MyAnalysis: public RHEJ::Analysis {
	public:
	MyAnalysis(YAML::Node const & /* config */) {}

	void fill(
	RHEJ::Event const & /* event */,
	RHEJ::Event const & /* FO_event */
	) override {
	}

	bool pass_cuts(
	RHEJ::Event const & /* event */,
	RHEJ::Event const & /* FO_event */
	) override {
	return true;
	}

	void finalise() override {
	}

	};

	extern "C"
	std::unique_ptr<RHEJ::Analysis> make_analysis(
	YAML::Node const & config
	){
	return std::make_unique<MyAnalysis>(config);
	}

	You can save this code to a file, for example :code:`myanalysis.cc`, and
	compile it into a shared library. Using the :code:`g++` compiler, the
	library can be built with

	.. code-block:: sh

	g++ -fPIC -shared -Wl,-soname,libmyanalysis.so -o libmyanalysis.so myanalysis.cc

	With :code:`g++` it is also good practice to add
	:code:`__attribute__((visibility("default")))` after :code:`extern "C"`
	in the above code snippet and then compile with the additional flag
	:code:`-fvisibility=hidden` to prevent name clashes.

	You can use the analysis in reversed HEJ or the HEJ fixed-order
	generator by adding

	.. code-block:: YAML

	analysis:
	plugin: /path/to/libmyanalysis.so

	to the .yml configuration file.

	As a more interesting example, here is the code for an analysis that
	sums up the total cross section and prints the result to both standard
	output and a file specified in the .yml config with

	.. code-block:: YAML

	analysis:
	plugin: analysis/build/directory/src/libmy_analysis.so
	output: outfile

	To access the configuration at run time, reversed HEJ uses the yaml-cpp
	library; for more details see the `yaml-cpp tutorial
	<https://github.com/jbeder/yaml-cpp/wiki/Tutorial>`_. The analysis code
	-itself is::
	+itself is
	+::

	#include <memory>
	#include <iostream>
	#include <fstream>
	#include <string>
	#include <cmath>

	#include "RHEJ/Analysis.hh"
	#include "RHEJ/Event.hh"

	#include "yaml-cpp/yaml.h"

	class MyAnalysis: public RHEJ::Analysis {
	public:
	MyAnalysis(YAML::Node const & config):
	xsection_{0.}, xsection_error_{0.},
	outfile_{config["output"].as<std::string>()}
	{}

	void fill(
	RHEJ::Event const & event,
	RHEJ::Event const & /* FO_event */
	) override {
	const double wt = event.central().weight;
	xsection_ += wt;
	xsection_error_ += wt*wt;
	}

	bool pass_cuts(
	RHEJ::Event const & /* event */,
	RHEJ::Event const & /* FO_event */
	) override {
	return true;
	}

	void finalise() override {
	std::cout << "cross section: " << xsection_ << " +- "
	<< std::sqrt(xsection_error_) << "\n";
	std::ofstream fout{outfile_};
	fout << "cross section: " << xsection_ << " +- "
	<< std::sqrt(xsection_error_) << "\n";
	}

	private:
	double xsection_, xsection_error_;
	std::string outfile_;

	};

	extern "C"
	std::unique_ptr<RHEJ::Analysis> make_analysis(
	YAML::Node const & config
	){
	return std::make_unique<MyAnalysis>(config);
	}
	diff --git a/doc/sphinx/rHEJ.rst b/doc/sphinx/rHEJ.rst
	index 38ec918..6caec96 100644
	--- a/doc/sphinx/rHEJ.rst
	+++ b/doc/sphinx/rHEJ.rst
	@@ -1,280 +1,282 @@
	.. _`Running reversed HEJ`:

	Running reversed HEJ
	====================

	Quick start
	-----------

	In order to run reversed HEJ, you need a configuration file and a file
	containing fixed-order events. A sample configuration is given by the
	:file:`config.yml` file distributed together with reversed HEJ. Events
	in the Les Houches Event File format can be generated with standard
	Monte Carlo generators like `MadGraph5_aMC@NLO
	<https://launchpad.net/mg5amcnlo>`_ or `Sherpa
	<https://sherpa.hepforge.org/trac/wiki>`_. Reversed HEJ assumes that the
	cross section is given by the sum of the event weights. Depending on the
	fixed-order generator it may be necessary to adjust the weights in the
	Les Houches Event File accordingly.

	The processes supported by reversed HEJ are

	- Pure multijet production
	- Production of a Higgs boson with jets

	..
	- TODO Production of a W boson with jets
	- TODO Production of a Z boson or photon with jets

	where at least two jets are required in each case. For the time being,
	only leading-order events are supported.

	After generating an event file :file:`events.lhe` adjust the parameters
	under the `fixed order jets`_ setting in :file:`config.yml` to the
	settings in the fixed-order generation. Resummation can then be added by
	running::

	rHEJ config.yml events.lhe

	Using the default settings, this will produce an output event file
	:file:`RHEJ.lhe` with events including high-energy resummation.

	.. _`reversed HEJ settings`:

	Settings
	--------

	Reversed HEJ configuration files follow the `YAML <http://yaml.org/>`_
	format. The following configuration parameters are supported:

	.. _`trials`:

	trials
	High-energy resummation is performed by generating a number of
	resummation phase space configurations corresponding to the input
	fixed-order event. This parameter specifies how many such
	configurations reversed HEJ should try to generate for each input
	event. Typical values vary between 10 and 100.

	.. _`min extparton pt`:

	min extparton pt
	Specifies the minimum transverse momentum in GeV of the most forward
	and the most backward parton. This setting is needed to regulate an
	otherwise uncancelled divergence. Its value should be slightly below
	the minimum transverse momentum of jets specified by `resummation
	jets: min pt`_. See also the `max ext soft pt fraction`_ setting.

	.. _`max ext soft pt fraction`:

	max ext soft pt fraction
	Specifies the maximum fraction that soft radiation can contribute to
	the transverse momentum of each the most forward and the most backward
	jet. Values between around 0.05 and 0.1 are recommended. See also the
	`min extparton pt`_ setting.

	.. _`fixed order jets`:

	fixed order jets
	This tag collects a number of settings specifying the jet definition
	in the event input. The settings should correspond to the ones used in
	the fixed-order Monte Carlo that generated the input events.

	.. _`fixed order jets: min pt`:

	min pt
	Minimum transverse momentum in GeV of fixed-order jets.

	.. _`fixed order jets: algorithm`:

	algorithm
	The algorithm used to define jets. Allowed settings are
	:code:`kt`, :code:`cambridge`, :code:`antikt`, :code:`genkt`,
	:code:`cambridge for passive`, :code:`genkt for passive`,
	:code:`ee kt`, :code:`ee genkt`. See the `FastJet
	<http://fastjet.fr/>`_ documentation for a description of these
	algorithms.

	.. _`fixed order jets: R`:

	R
	The R parameter used in the jet algorithm, roughly corresponding
	to the jet radius in the plane spanned by the rapidity and the
	azimuthal angle.

	.. _`resummation jets`:

	resummation jets
	This tag collects a number of settings specifying the jet definition
	in the observed, i.e. resummed events. These settings are optional, by
	default the same values as for the `fixed order jets`_ are assumed.

	.. _`resummation jets: min pt`:

	min pt
	Minimum transverse momentum in GeV of resummation jets. This
	should be around 25% larger than the minimum transverse momentum
	of fixed order jets set by `fixed order jets: min pt`_.

	.. _`resummation jets: algorithm`:

	algorithm
	The algorithm used to define jets. The reversed HEJ approach to
	resummation relies on properties of :code:`antikt` jets, so this
	value is strongly recommended. For a list of possible other
	values, see the `fixed order jets: algorithm`_ setting.

	.. _`resummation jets: R`:

	R
	The R parameter used in the jet algorithm.

	.. _`FKL`:

	FKL
	Specifies how to treat FKL events. The possible values are
	:code:`reweight` to enable resummation, :code:`keep` to keep the
	events as they are up to a possible change of renormalisation and
	factorisation scale, and :code:`discard` to discard these events.

	.. _`unordered`:

	unordered
	Specifies how to treat events with one emission that does not respect
	FKL ordering. The possible values are the same as for the `FKL`_
	setting, but :code:`reweight` may not be supported for all process
	types.


	.. TODO: rename to non-HEJ
	.. _`non-FKL`:

	non-FKL
	Specifies how to treat events where no resummation is possible. The
	allowed values are :code:`keep` to keep the events as they are up to
	a possible change of renormalisation and factorisation scale and
	:code:`discard` to discard these events.

	.. _`scales`:

	scales
	Specifies the renormalisation and factorisation scales for the output
	events. This can either be a single entry or a list :code:`[scale1,
	scale2, ...]`. For the case of a list the first entry defines the
	central scale. Possible values are fixed numbers to set the scale in
	GeV or the following:

	- :code:`H_T`: The sum of the scalar transverse momenta of all
	final-state particles
	- :code:`max jet pperp`: The maximum transverse momentum of all jets
	- :code:`jet invariant mass`: Sum of the invariant masses of all jets
	- :code:`m_j1j2`: Invariant mass between the two hardest jets.

	Scales can be multiplied or divided by an overall factor,
	e.g. :code:`H_T/2`.

	It is also possible to import scales from an external library, see
	:ref:`Custom scales`

	.. _`scale factors`:

	scale factors
	A list of numeric factors by which each of the `scales`_ should be
	multiplied. Renormalisation and factorisation scales are varied
	independently. For example, a list with entries :code:`[0.5, 2]`
	would give the four scale choices (0.5μ\ :sub:`r`, 0.5μ\ :sub:`f`);
	(0.5μ\ :sub:`r`, 2μ\ :sub:`f`); (2μ\ :sub:`r`, 0.5μ\ :sub:`f`); (2μ\
	:sub:`r`, 2μ\ :sub:`f`) in this order. The ordering corresponds to
	the order of the final event weights.

	.. _`max scale ratio`:

	max scale ratio
	Specifies the maximum factor by which renormalisation and
	factorisation scales may difer. For a value of :code:`2` and the
	example given for the `scale factors`_ the scale choices
	(0.5μ\ :sub:`r`, 2μ\ :sub:`f`) and (2μ\ :sub:`r`, 0.5μ\ :sub:`f`)
	will be discarded.

	.. _`log correction`:

	log correction
	Whether to include corrections due to the evolution of the strong
	coupling constant in the virtual corrections. Allowed values are
	:code:`true` and :code:`false`.

	.. TODO: unweight

	.. _`event output`:

	event output
	Specifies the name of a single event output file or a list of such
	files. The file format is either specified explicitly or derived from
	the suffix. For example, :code:`events.lhe` or, equivalently
	:code:`Les Houches: events.lhe` generates an output event file
	:code:`events.lhe` in the Les Houches format. The supported formats
	are

	- :code:`file.lhe` or :code:`Les Houches: file`: The Les Houches
	event file format.
	- :code:`file.hepmc` or :code:`HepMC: file`: The HepMC format.

	.. _`random generator`:

	random generator
	Sets parameters for random number generation.

	.. _`random generator: name`:

	name
	Which random number generator to use. Currently, :code:`mixmax`
	and :code:`ranlux64` are implemented. Mixmax is recommended. See
	the `CLHEP documentation
	<http://proj-clhep.web.cern.ch/proj-clhep/index.html#docu>`_ for
	details on the generators.

	.. _`random generator: seed`:

	seed
	The seed for random generation. This should be a single number for
	mixmax and the name of a state file for ranlux64.

	.. _`analysis`:

	analysis
	- Specifies the name and settings for a custom analysis library. The
	- :code:`plugin` sub-entry should be set to the analysis file path. All
	- further entries are passed on to the analysis. See
	- :ref:`Writing custom analyses` for details.
	+ Name and Setting for the event analyses; either a custom
	+ analysis plugin or rivet. For the first the :code:`plugin` sub-entry
	+ should be set to the analysis file path. All further entries are passed on
	+ to the analysis. To use rivet a list of rivet-analysis have to be
	+ given in :code:`rivet` and prefix for the yoda file has to be set
	+ through :code:`output`. See :ref:`Writing custom analyses` for details.

	.. _`Higgs coupling`:

	Higgs coupling
	This collects a number of settings concerning the effective coupling
	of the Higgs boson to gluons. This is only relevant for the
	production process of a Higgs boson with jets and only supported if
	reversed HEJ was compiled with `QCDloop
	<https://github.com/scarrazza/qcdloop>`_ support.

	.. _`Higgs coupling: use impact factors`:

	use impact factors
	Whether to use impact factors for the coupling to the most forward
	and most backward partons. Impact factors imply the infinite
	top-quark mass limit.

	.. _`Higgs coupling: mt`:

	mt
	The value of the top-quark mass in GeV. If this is not specified,
	the limit of an infinite mass is taken.

	.. _`Higgs coupling: include bottom`:

	include bottom
	Whether to include the Higgs coupling to bottom quarks.

	.. _`Higgs coupling: mb`:

	mb
	The value of the bottom-quark mass in GeV.

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