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diff --git a/doc/developer_manual/currents.tex b/doc/developer_manual/currents.tex
index 074cf43..141ca73 100644
--- a/doc/developer_manual/currents.tex
+++ b/doc/developer_manual/currents.tex
@@ -1,582 +1,590 @@
\section{Currents}
\label{sec:currents_impl}
The following section contains a list of all the currents implemented
in \HEJ. Clean up of the code structure is ongoing. All $W$+Jet currents
are located in \texttt{src/Wjets.cc}. All other currents are defined
in \texttt{src/currents.cc}. There is a common header between these
files located at \texttt{include/HEJ/currents.hh}.
-\subsection{Pure Jets}
+The naming convention for the current contraction $\left\|S_{f_1 f_2\to f_1
+f_2}\right\|^2$ is \lstinline!ME_[Boson]_[subleading-type]_[incoming]!. For
+example \lstinline!ME_W_unob_qq! corresponds to the contraction $j_W^\mu
+j_{\text{uno}, \mu}$ ($qQ\to \bar{q}WQg$). For bosons on the same side as the
+subleading we drop the connecting underscore, e.g. \lstinline!ME_Wuno_qq!
+gives $j_{W,\text{uno}}^\mu j_\mu$ ($qQ\to g\bar{q}WQ$).
+
+\subsection{Pure Jets}
\subsubsection{Quark}
\label{sec:current_quark}
+
\begin{align}
j_\mu(p_i,p_j)=\bar{u}(p_i)\gamma_\mu u(p_j)
\end{align}
The exact for depends on the helicity and direction (forward/backwards) for the quarks. Currently all different contractions of incoming and outgoing states are defined in \lstinline!joi!, \lstinline!jio! and \lstinline!joo!.
\subsubsection{Gluon}
In \HEJ the currents for gluons and quarks are the same, up to a colour factor $K_g/C_F$, where
\begin{align}
K_g(p_1^-, p_a^-) = \frac{1}{2}\left(\frac{p_1^-}{p_a^-} + \frac{p_a^-}{p_1^-}\right)\left(C_A -
\frac{1}{C_A}\right)+\frac{1}{C_A}.
\end{align}
Thus we can just reuse the results from sec.~\ref{sec:current_quark}.
\subsubsection{Single unordered gluon}
Configuration $q(p_a) \to g(p_1) q(p_2) g^*(\tilde{q}_2)$~\cite{Andersen:2017kfc}
\begin{align}
\label{eq:juno}
\begin{split}
&j^{{\rm uno}\; \mu\ cd}(p_2,p_1,p_a) = i \varepsilon_{1\nu} \left( T_{2i}^{c}T_{ia}^d\
\left(U_1^{\mu\nu}-L^{\mu\nu} \right) + T_{2i}^{d}T_{ia}^c\ \left(U_2^{\mu\nu} +
L^{\mu\nu} \right) \right). \\
U_1^{\mu\nu} &= \frac1{s_{21}} \left( j_{21}^\nu j_{1a}^\mu + 2 p_2^\nu
j_{2a}^\mu \right) \qquad \qquad U_2^{\mu\nu} = \frac1{t_{a1}} \left( 2
j_{2a}^\mu p_a^\nu - j_{21}^\mu j_{1a}^\nu \right) \\
L^{\mu\nu} &= \frac1{t_{a2}} \left(-2p_1^\mu j_{2a}^\nu+2p_1.j_{2a}
g^{\mu\nu} + (\tilde{q}_1+\tilde{q}_2)^\nu j_{2a}^\mu + \frac{t_{b2}}{2} j_{2a}^\mu \left(
\frac{p_2^\nu}{p_1.p_2} + \frac{p_b^\nu}{p_1.p_b} \right) \right) ,
\end{split}
\end{align}
$j^{{\rm uno}\; \mu}$ is currently not calculated as a separate current, but always as needed for the ME (i.e. in \lstinline!jM2unoXXX!).
\subsection{Higgs}
Different rapidity orderings \todo{give name of functions}
\begin{enumerate}
\item $qQ\to HqQ/qHQ/qQH$ (any rapidity order, full LO ME) $\Rightarrow$ see~\ref{sec:V_H}
\item $qg\to Hqg$ (Higgs outside quark) $\Rightarrow$ see~\ref{sec:V_H}
\item $qg\to qHg$ (central Higgs) $\Rightarrow$ see~\ref{sec:V_H}
\item $qg\to qgH$ (Higgs outside gluon) $\Rightarrow$ see~\ref{sec:jH_mt}
\item $gg\to gHg$ (central Higgs) $\Rightarrow$ see~\ref{sec:V_H}
\item $gg\to ggH$ (Higgs outside gluon) $\Rightarrow$ see~\ref{sec:jH_mt}
\end{enumerate}
\subsubsection{Higgs gluon vertex}
\label{sec:V_H}
The coupling of the Higgs boson to gluons via a virtual quark loop can be written as
\begin{align}
\label{eq:VH}
V^{\mu\nu}_H(q_1, q_2) = \mathgraphics{build/figures/V_H.pdf} &=
\frac{\alpha_s m^2}{\pi v}\big[
g^{\mu\nu} T_1(q_1, q_2) - q_2^\mu q_1^\nu T_2(q_1, q_2)
\big]\, \\
&\xrightarrow{m \to \infty} \frac{\alpha_s}{3\pi
v} \left(g^{\mu\nu} q_1\cdot q_2 - q_2^\mu q_1^\nu\right).
\end{align}
The outgoing momentum of the Higgs boson is $p_H = q_1 - q_2$.
As a contraction with two currents this by implemented in \lstinline!cHdot! inside \texttt{src/currents.cc}.
The form factors $T_1$ and $T_2$ are then given by~\cite{DelDuca:2003ba}
\begin{align}
\label{eq:T_1}
T_1(q_1, q_2) ={}& -C_0(q_1, q_2)\*\left[2\*m^2+\frac{1}{2}\*\left(q_1^2+q_2^2-p_H^2\right)+\frac{2\*q_1^2\*q_2^2\*p_H^2}{\lambda}\right]\notag\\
&-\left[B_0(q_2)-B_0(p_H)\right]\*\frac{q_2^2}{\lambda}\*\left(q_2^2-q_1^2-p_H^2\right)\notag\\
&-\left[B_0(q_1)-B_0(p_H)\right]\*\frac{q_1^2}{\lambda}\*\left(q_1^2-q_2^2-p_H^2\right)-1\,,\displaybreak[0]\\
\label{eq:T_2}
T_2(q_1, q_2) ={}& C_0(q_1,
q_2)\*\left[\frac{4\*m^2}{\lambda}\*\left(p_H^2-q_1^2-q_2^2\right)-1-\frac{4\*q_1^2\*q_2^2}{\lambda}
-
\frac{12\*q_1^2\*q_2^2\*p_H^2}{\lambda^2}\*\left(q_1^2+q_2^2-p_H^2\right)\right]\notag\\
&-\left[B_0(q_2)-B_0(p_H)\right]\*\left[\frac{2\*q_2^2}{\lambda}+\frac{12\*q_1^2\*q_2^2}{\lambda^2}\*\left(q_2^2-q_1^2+p_H^2\right)\right]\notag\\
&-\left[B_0(q_1)-B_0(p_H)\right]\*\left[\frac{2\*q_1^2}{\lambda}+\frac{12\*q_1^2\*q_2^2}{\lambda^2}\*\left(q_1^2-q_2^2+p_H^2\right)\right]\notag\\
&-\frac{2}{\lambda}\*\left(q_1^2+q_2^2-p_H^2\right)\,,
\end{align}
where we have used the scalar bubble and triangle integrals
\begin{align}
\label{eq:B0}
B_0\left(p\right) ={}& \int \frac{d^dl}{i\pi^{\frac{d}{2}}}
\frac{1}{\left(l^2-m^2\right)\left((l+p)^2-m^2\right)}\,,\\
\label{eq:C0}
C_0\left(p,q\right) ={}& \int \frac{d^dl}{i\pi^{\frac{d}{2}}} \frac{1}{\left(l^2-m^2\right)\left((l+p)^2-m^2\right)\left((l+p-q)^2-m^2\right)}\,,
\end{align}
and the K\"{a}ll\'{e}n function
\begin{equation}
\label{eq:lambda}
\lambda = q_1^4 + q_2^4 + p_H^4 - 2\*q_1^2\*q_2^2 - 2\*q_1^2\*p_H^2- 2\*q_2^2\*p_H^2\,.
\end{equation}
The Integrals as such are provided by \QCDloop{} (see wrapper functions \lstinline!B0DD! and \lstinline!C0DD! in \texttt{src/currents.cc}).
In the code we are sticking to the convention of~\cite{DelDuca:2003ba}, thus instead of the $T_{1/2}$ we implement (in the functions \lstinline!A1! and \lstinline!A2!)
\begin{align}
\label{eq:A_1}
A_1(q_1, q_2) ={}& \frac{i}{16\pi^2}\*T_2(-q_1, q_2)\,,\\
\label{eq:A_2}
A_2(q_1, q_2) ={}& -\frac{i}{16\pi^2}\*T_1(-q_1, q_2)\,.
\end{align}
\subsubsection{Peripheral Higgs emission - Finite quark mass}
\label{sec:jH_mt}
We describe the emission of a peripheral Higgs boson close to a
scattering gluon with an effective current. In the following we consider
a lightcone decomposition of the gluon momenta, i.e. $p^\pm = E \pm p_z$
and $p_\perp = p_x + i p_y$. The incoming gluon momentum $p_a$ defines
the $-$ direction, so that $p_a^+ = p_{a\perp} = 0$. The outgoing
momenta are $p_1$ for the gluon and $p_H$ for the Higgs boson. We choose
the following polarisation vectors:
\begin{equation}
\label{eq:pol_vectors}
\epsilon_\mu^\pm(p_a) = \frac{j_\mu^\pm(p_1, p_a)}{\sqrt{2}
\bar{u}^\pm(p_a)u^\mp(p_1)}\,, \quad \epsilon_\mu^{\pm,*}(p_1) = -\frac{j_\mu^\pm(p_1, p_a)}{\sqrt{2}
\bar{u}^\mp(p_1)u^\pm(p_a)}\,.
\end{equation}
Following~\cite{DelDuca:2001fn}, we introduce effective polarisation
vectors to describe the contraction with the Higgs-boson production
vertex eq.~\eqref{eq:VH}:
\begin{align}
\label{eq:eps_H}
\epsilon_{H,\mu}(p_a) = \frac{T_2(p_a, p_a-p_H)}{(p_a-p_H)^2}\big[p_a\cdot
p_H\epsilon_\mu(p_a) - p_H\cdot\epsilon(p_a) p_{a,\mu}\big]\,,\\
\epsilon_{H,\mu}^*(p_1) = -\frac{T_2(p_1+p_H, p_1)}{(p_1+p_H)^2}\big[p_1\cdot
p_H\epsilon_\mu^*(p_1) - p_H\cdot\epsilon^*(p_1) p_{1,\mu}\big]\,,
\end{align}
We also employ the usual short-hand notation
\begin{equation}
\label{eq:spinor_helicity}
\spa i.j = \bar{u}^-(p_i)u^+(p_j)\,,\qquad \spb i.j =
\bar{u}^+(p_i)u^-(p_j)\,, \qquad[ i | H | j\rangle = j_\mu^+(p_i, p_j)p_H^\mu\,.
\end{equation}
Without loss of generality, we consider only the case where the incoming
gluon has positive helicity. The remaining helicity configurations can
be obtained through parity transformation.
Labelling the effective current by the helicities of the gluons we obtain
for the same-helicity case
\begin{equation}
\label{eq:jH_same_helicity}
\begin{split}
j_{H,\mu}^{++}{}&(p_1,p_a,p_H) =
\frac{m^2}{\pi v}\bigg[\\
&-\sqrt{\frac{2p_1^-}{p_a^-}}\frac{p_{1\perp}^*}{|p_{1\perp}|}\frac{t_2}{\spb a.1}\epsilon^{+,*}_{H,\mu}(p_1)
+\sqrt{\frac{2p_a^-}{p_1^-}}\frac{p_{1\perp}^*}{|p_{1\perp}|}\frac{t_2}{\spa 1.a}\epsilon^{+}_{H,\mu}(p_a)\\
&+ [1|H|a\rangle \bigg(
\frac{\sqrt{2}}{\spa 1.a}\epsilon^{+}_{H,\mu}(p_a)
+ \frac{\sqrt{2}}{\spb a.1}\epsilon^{+,*}_{H,\mu}(p_1)-\frac{\spa 1.a T_2(p_a, p_a-p_H)}{\sqrt{2}(p_a-p_H)^2}\epsilon^{+,*}_{\mu}(p_1)\\
&
\qquad
-\frac{\spb a.1 T_2(p_1+p_H,
p_1)}{\sqrt{2}(p_1+p_H)^2}\epsilon^{+}_{\mu}(p_a)-\frac{RH_4}{\sqrt{2}\spb a.1}\epsilon^{+,*}_{\mu}(p_1)+\frac{RH_5}{\sqrt{2}\spa 1.a}\epsilon^{+}_{\mu}(p_a)
\bigg)\\
&
- \frac{[1|H|a\rangle^2}{2 t_1}(p_{a,\mu} RH_{10} - p_{1,\mu} RH_{12})\bigg]
\end{split}
\end{equation}
with $t_1 = (p_a-p_1)^2$, $t_2 = (p_a-p_1-p_H)^2$ and $R = 8 \pi^2$. Eq.~\eqref{eq:jH_same_helicity}
is implemented by \lstinline!g_gH_HC! in \texttt{src/currents.cc}
\footnote{\lstinline!g_gH_HC! and \lstinline!g_gH_HNC! includes an additional
$1/t_2$ factor, which should be in the Matrix element instead.}.
The currents with a helicity flip is given through
\begin{equation}
\label{eq:jH_helicity_flip}
\begin{split}
j_{H,\mu}^{+-}{}&(p_1,p_a,p_H) =
\frac{m^2}{\pi v}\bigg[\\
&-\sqrt{\frac{2p_1^-}{p_a^-}}\frac{p_{1\perp}^*}{|p_{1\perp}|}\frac{t_2}{\spb
a.1}\epsilon^{-,*}_{H,\mu}(p_1)
+\sqrt{\frac{2p_a^-}{p_1^-}}\frac{p_{1\perp}}{|p_{1\perp}|}\frac{t_2}{\spb a.1}\epsilon^{+}_{H,\mu}(p_a)\\
&+ [1|H|a\rangle \left(
\frac{\sqrt{2}}{\spb a.1} \epsilon^{-,*}_{H,\mu}(p_1)
-\frac{\spa 1.a T_2(p_a, p_a-p_H)}{\sqrt{2}(p_a-p_H)^2}\epsilon^{-,*}_{\mu}(p_1)
- \frac{RH_4}{\sqrt{2}\spb a.1}\epsilon^{-,*}_{\mu}(p_1)\right)
\\
&+ [a|H|1\rangle \left(
\frac{\sqrt{2}}{\spb a.1}\epsilon^{+}_{H,\mu}(p_a)
-\frac{\spa 1.a
T_2(p_1+p_H,p_1)}{\sqrt{2}(p_1+p_H)^2}\epsilon^{+}_{\mu}(p_a)
+\frac{RH_5}{\sqrt{2}\spb a.1}\epsilon^{+}_{\mu}(p_a)
\right)\\
& - \frac{[1|H|a\rangle [a|H|1\rangle}{2 \spb a.1 ^2}(p_{a,\mu} RH_{10} - p_{1,\mu}
RH_{12})\\
&+ \frac{\spa 1.a}{\spb a.1}\bigg(RH_1p_{1,\mu}-RH_2p_{a,\mu}+2
p_1\cdot p_H \frac{T_2(p_1+p_H, p_1)}{(p_1+p_H)^2} p_{a,\mu}
\\
&
\qquad- 2p_a \cdot p_H \frac{T_2(p_a, p_a-p_H)}{(p_a-p_H)^2} p_{1,\mu}+ T_1(p_a-p_1, p_a-p_1-p_H)\frac{(p_1 + p_a)_\mu}{t_1}\\
&\qquad-\frac{(p_1+p_a)\cdot p_H}{t_1} T_2(p_a-p_1, p_a-p_1-p_H)(p_1 - p_a)_\mu
\bigg)
\bigg]\,,
\end{split}
\end{equation}
and implemented by \lstinline!g_gH_HNC! again in \texttt{src/currents.cc}.
If we instead choose the gluon momentum in the $+$ direction, so that
$p_a^- = p_{a\perp} = 0$, the corresponding currents are obtained by
replacing $p_1^- \to p_1^+, p_a^- \to p_a^+,
\frac{p_{1\perp}}{|p_{1\perp}|} \to -1$ in the second line of
eq.~\eqref{eq:jH_same_helicity} and eq.~\eqref{eq:jH_helicity_flip} (see variables \lstinline!ang1a! and \lstinline!sqa1! in the implementation).
The form factors $H_1,H_2,H_4,H_5, H_{10}, H_{12}$ are given in~\cite{DelDuca:2003ba}, and are implemented under their name in \texttt{src/currents.cc}. They reduce down to fundamental QCD integrals, which are again provided by \QCDloop.
\subsubsection{Peripheral Higgs emission - Infinite top mass}
\label{sec:jH_eff}
To get the result with infinite top mass we could either take the limit $m_t\to \infty$ in~\eqref{eq:jH_helicity_flip} and~\eqref{eq:jH_same_helicity}, or use the \textit{impact factors} as given in~\cite{DelDuca:2003ba}. Both methods are equivalent, and lead to the same result. For the first one would find
\begin{align}
\lim_{m_t\to\infty} m_t^2 H_1 &= i \frac{1}{24 \pi^2}\\
\lim_{m_t\to\infty} m_t^2 H_2 &=-i \frac{1}{24 \pi^2}\\
\lim_{m_t\to\infty} m_t^2 H_4 &= i \frac{1}{24 \pi^2}\\
\lim_{m_t\to\infty} m_t^2 H_5 &=-i \frac{1}{24 \pi^2}\\
\lim_{m_t\to\infty} m_t^2 H_{10} &= 0 \\
\lim_{m_t\to\infty} m_t^2 H_{12} &= 0.
\end{align}
\todo{double check this, see James thesis eq. 4.33}
However only the second method is implemented in the code through \lstinline!C2gHgp!
and \lstinline!C2gHgm! inside \texttt{src/currents.cc}, each function
calculates the square of eq. (4.23) and (4.22) from~\cite{DelDuca:2003ba} respectively.
\subsection{$W$+Jets}
\label{sec:currents_W}
\subsubsection{Quark+$W$}
\begin{figure}
\centering
\begin{minipage}[b]{0.2\textwidth}
\includegraphics[width=\textwidth]{figures/Wbits.pdf}
\end{minipage}
\begin{minipage}[b]{0.1\textwidth}
\centering{=}
\vspace{0.7cm}
\end{minipage}
\begin{minipage}[b]{0.2\textwidth}
\includegraphics[width=\textwidth]{figures/Wbits2.pdf}
\end{minipage}
\begin{minipage}[b]{0.1\textwidth}
\centering{+}
\vspace{0.7cm}
\end{minipage}
\begin{minipage}[b]{0.2\textwidth}
\includegraphics[width=\textwidth]{figures/Wbits3.pdf}
\end{minipage}
\caption{The $j_W$ current is constructed from the two diagrams which
contribute to the emission of a $W$-boson from a given quark line.}
\label{fig:jW}
\end{figure}
For a $W$ emission we require a fermion. The $j_W$ current is actually a sum of
two separate contributions, see figure~\ref{fig:jW}, one with a $W$-emission
from the initial state, and one with the $W$-emission from the final state.
Mathematically this can be seen as the following two
terms~\cite{Andersen:2012gk}\todo{cite W subleading paper}:
\begin{align}
\label{eq:Weffcur1}
j_W^\mu(p_a,p_{\ell},p_{\bar{\ell}}, p_1) =&\ \frac{g_W^2}{2}\
\frac1{p_W^2-M_W^2+i\ \Gamma_W M_W}\ \bar{u}^-(p_\ell) \gamma_\alpha
v^-(p_{\bar\ell})\nonumber \\
& \cdot \left( \frac{ \bar{u}^-(p_1) \gamma^\alpha (\slashed{p}_W +
\slashed{p}_1)\gamma^\mu u^-(p_a)}{(p_W+p_1)^2} +
\frac{ \bar{u}^-(p_1)\gamma^\mu (\slashed{p}_a + \slashed{p}_W)\gamma^\alpha u^-(p_a)}{(p_a-p_W)^2} \right).
\end{align}
There are a couple of subtleties here. There is a minus sign
distinction between the quark-anti-quark cases due to the fermion flow
of the propagator in the current. Note that the type of $W$ emission
(+ or -) will depend on the quark flavour, and that the handedness of
the quark-line is given by whether its a quark or anti-quark.
\subsubsection{$W$+uno}
\begin{figure}
\centering
\begin{subfigure}{0.45\textwidth}
\centering
\includegraphics{figures/wuno1}
\caption{}
\label{fig:U1diags}
\end{subfigure}
\begin{subfigure}{0.45\textwidth}
\centering
\includegraphics{figures/wuno2}
\caption{}
\label{fig:U2diags}
\end{subfigure}
\begin{subfigure}{0.45\textwidth}
\centering
\includegraphics{figures/wuno3}
\caption{}
\label{fig:Cdiags}
\end{subfigure}
\begin{subfigure}{0.45\textwidth}
\centering
\includegraphics{figures/wuno4}
\caption{}
\label{fig:Ddiags}
\end{subfigure}
\vspace{0.4cm}
\caption{Examples of each of the four categories of Feynman diagram which
contribute to at leading-order; there are twelve in total. (a) is an example where the gluon and $W$
boson are emitted from the same quark line and the gluon comes after the
$t$-channel propagator. In (b), the gluon and $W$ boson are emitted from
the same quark line and the gluon comes before the $t$-channel proagator.
In (c) the gluon is emitted from the $t$-channel gluon and in (d) the gluon
is emitted from the $b$--$3$ quark line.}
\label{fig:Wunodiags}
\end{figure}
It is necessary to include subleading processes in $W$+Jets also. All of
these currents have been built for the \lstinline!Tensor! Class detailed in
section~\ref{sec:tensor}. Similarly to the pure jet case, the uno currents are
not calculated separately, and only in the ME functions when required
in the \texttt{src/Wjets.cc} file. For unordered emissions a new
current is required, $j_{W,{\rm uno}}$, it is only non-zero for
$h_a=h_1=-$ and hence we have suppressed its helicity indices. It is
derived from the 12 leading-order Feynman diagrams in the QMRK
limit (see figure~\ref{fig:Wunodiags}). Using $T^m_{ij}$ represent fundamental
colour matrices between quark state $i$ and $j$ with adjoint index $m$ we find
\begin{align}\label{eq:wunocurrent}
\begin{split}
j^{d\,\mu}_{\rm W,uno}(p_a,p_1,p_2,p_\ell,p_{\bar{\ell}}) =& \ i \varepsilon_{\nu}(p_1)\
\bar{u}^-(p_\ell) \gamma_\rho v^-(p_{\bar \ell}) \\ & \quad \times\
\left(T^1_{2i} T^d_{ia} (\tilde U_1^{\nu\mu\rho}-\tilde L^{\nu\mu\rho}) +
T^d_{2i} T^1_{ia} (\tilde U_2^{\nu\mu\rho}+\tilde L^{\nu\mu\rho}) \right),
\end{split}
\end{align}
where expressions for $\tilde U_{1,2}^{\nu\mu\rho}$ and $\tilde L^{\nu\mu\rho}$
are given as:
\begin{align}
\label{eq:U1tensor}
\begin{split}
\tilde U_1^{\nu\mu\rho} =&\frac{\langle 2|\nu (\slashed{p}_2+ \slashed{p}_1)\mu (\slashed{p}_a - \slashed{p}_W)\rho P_L |a\rangle }{s_{12}t_{aW}} + \frac{\langle 2|\nu (\slashed{p}_2+ \slashed{p}_1)\rho P_L (\slashed{p}_2+\slashed{p}_1 + \slashed{p}_W)\mu |a\rangle }{s_{12}s_{12W}} \\
&+ \frac{\langle 2|\rho P_L (\slashed{p}_2+ \slashed{p}_W) \nu
(\slashed{p}_1 + \slashed{p}_2+\slashed{p}_W)\mu |a\rangle}{s_{2W}s_{12W}}.
\end{split}
\end{align}
\begin{align}
\label{eq:U2tensor}
\begin{split}
\tilde U_2^{\nu\mu\rho} =&\frac{\langle 2|\mu (\slashed{p}_a-\slashed{p}_W-\slashed{p}_1)\nu (\slashed{p}_a - \slashed{p}_W)\rho P_L |a\rangle }{t_{aW1}t_{aW}} + \frac{\langle 2|\mu (\slashed{p}_a-\slashed{p}_W- \slashed{p}_1)\rho P_L (\slashed{p}_a-\slashed{p}_1) \nu |a\rangle }{t_{a1W}t_{a1}} \\
&+ \frac{\langle 2|\rho P_L (\slashed{p}_2+ \slashed{p}_W) \mu
(\slashed{p}_a-\slashed{p}_1)\nu |a\rangle}{s_{2W}t_{a1}}.
\end{split}
\end{align}
\begin{align}
\label{eq:Ltensor}
\tilde L^{\nu\mu\rho} &= \frac{q_2^2}{2t_{aW2}} \left[\frac{\langle 2 |\mu (\slashed{p}_a - \slashed{p}_W) \rho P_L | a\rangle}{t_{aW}} + \frac{\langle 2 |\rho P_L (\slashed{p}_2 + \slashed{p}_W) \mu | a\rangle }{s_{2W}} \right]
\cdot \left( \frac{p_b^{\nu}}{p_b\cdot p_1} + \frac{p_3^{\nu}}{p_3\cdot p_1} \right) \nonumber \\
&\quad+\frac{1}{t_{aW2}}\left[\frac{\langle 2 |\sigma (\slashed{p}_a - \slashed{p}_W) \rho P_L | a\rangle}{t_{aW}} + \frac{\langle 2 |\rho P_L (\slashed{p}_2 + \slashed{p}_W) \sigma | a\rangle }{s_{2W}} \right] \nonumber \\
&\vphantom{+\frac{1}{t_{aW2}}}\quad\cdot \left( g^{\sigma \mu} (q_1 +q_2)^\nu + g^{\mu \nu}(-q_2 +p_1)^\sigma+ g^{\nu \sigma}(-p_1 -q_1)^\mu \right).
\end{align}
\subsubsection{$W$+Extremal $\mathbf{q\bar{q}}$}
The $W$+Jet sub-leading processes containing an extremal $q\bar{q}$ are
related by crossing symmetry to the $W$+Jet unordered processes. This
means that one can simply perform a crossing symmetry argument on
eq.~\ref{eq:wunocurrent} to arrive at the extremal $q\bar{q}$ current
required.We show the basic structure of the extremal $q\bar{q}$
current in figure~\ref{fig:qgimp}, neglecting the $W$-emission for
simplicity.
\begin{figure}
\centering
\includegraphics[width=0.3\textwidth]{{qqbarex_schem}}
\caption{Schematic structure of the $gq \to \bar{Q}Qq$ amplitude in the limit
$y_1 \sim y_2 \ll y_3$}
\label{fig:qgimp}
\end{figure}
\begin{figure}
\centering
\begin{subfigure}{0.45\textwidth}
\centering
\includegraphics{qqbarex1}
\end{subfigure}
\begin{subfigure}{0.45\textwidth}
\centering
\includegraphics{qqbarex2}
\end{subfigure}
\begin{subfigure}{0.45\textwidth}
\centering
\includegraphics{qqbarex4}
\end{subfigure}
\begin{subfigure}{0.45\textwidth}
\centering
\includegraphics{qqbarex5}
\end{subfigure}
\begin{subfigure}{0.45\textwidth}
\centering
\includegraphics{qqbarex3}
\end{subfigure}
\caption{The five tree-level graphs which contribute to the process $gq \to \bar{Q}Qq$.}
\label{fig:qg_qQQ_graphs}
\end{figure}
We can obtain the current for $g\rightarrow W q \bar{q}$ by evaluating
the current for $W$ plus unordered emissions with the normal arguments
$p_a \leftrightarrow -p_1 $ interchanged. This is a non-trivial
statement: due to the minimality of the approximations made, the
crossing symmetry normally present in the full amplitude may be
extended to the factorised current.
We must again note that swapping $p_a \leftrightarrow -p_1$ will lead
to $u$-spinors with momenta with negative energy. These are identical
to $v$-spinors with momenta with positive energy, up to an overall
phase which is common to all terms, and can therefore be neglected.
Mathematically, this is given by:
\begin{align}\label{eq:crossedJ}
j^\mu_{\rm W,g\to Q\bar{Q}}(p_a,p_1,p_2,p_\ell,p_{\bar{\ell}}) =i \varepsilon_{g\nu}
\langle \ell | \rho | \bar \ell \rangle_L
\left(T^1_{2i} T^d_{ia} (\tilde U_{1,X}^{\nu\mu\rho}-\tilde L^{\nu\mu\rho}_X) + T^d_{2i} T^1_{ia} (\tilde U_{2,X}^{\nu\mu\rho}+\tilde L_X^{\nu\mu\rho}) \right),
\end{align}
where the components are now given by
\begin{align}
\label{eq:U1tensorX}
\begin{split}
\tilde U_{1,X}^{\nu\mu\rho} =&\frac{\langle 2|\nu (\slashed{p}_a- \slashed{p}_2)\mu (\slashed{p}_1 + \slashed{p}_W)\rho P_L |1\rangle }{t_{a2}s_{1W}} + \frac{\langle 2|\nu (\slashed{p}_a- \slashed{p}_2)\rho P_L (\slashed{p}_a-\slashed{p}_2 - \slashed{p}_W)\mu |1\rangle }{t_{a2}t_{a2W}} \\
&- \frac{\langle 2|\rho P_L (\slashed{p}_2+ \slashed{p}_W) \nu
(\slashed{p}_a - \slashed{p}_2-\slashed{p}_W)\mu
|1\rangle}{s_{2W}t_{a2W}}, \\
\tilde U_{2,X}^{\nu\mu\rho} =&-\frac{\langle 2|\mu (\slashed{p}_a-\slashed{p}_W-\slashed{p}_1)\nu (\slashed{p}_1 + \slashed{p}_W)\rho P_L |1\rangle }{t_{aW1}s_{1W}} + \frac{\langle 2|\mu (\slashed{p}_a-\slashed{p}_W- \slashed{p}_1)\rho P_L (\slashed{p}_a-\slashed{p}_1) \nu |1\rangle }{t_{a1W}t_{a1}} \\
&+ \frac{\langle 2|\rho P_L (\slashed{p}_2+ \slashed{p}_W) \mu
(\slashed{p}_a-\slashed{p}_1)\nu |1\rangle}{s_{2W}t_{a1}}, \\
\tilde L^{\nu\mu\rho}_X &= \frac{q_2^2}{2s_{1W2}} \left[\frac{\langle 2 |\mu (\slashed{p}_1 + \slashed{p}_W) \rho P_L | 1\rangle}{s_{1W}} + \frac{\langle 2 |\rho P_L (\slashed{p}_2 + \slashed{p}_W) \mu | 1\rangle }{s_{2W}} \right]
\cdot \left( \frac{p_b^{\nu}}{p_a\cdot p_b} + \frac{p_3^{\nu}}{p_a\cdot p_3} \right) \\
&\quad+\frac{1}{s_{W12}}\left[-\frac{\langle 2 |\sigma (\slashed{p}_1 + \slashed{p}_W) \rho P_L | a\rangle}{t_{aW}} + \frac{\langle 2 |\rho P_L (\slashed{p}_2 + \slashed{p}_W) \sigma | 1\rangle }{s_{2W}} \right] \\
&\vphantom{+\frac{1}{t_{aW2}}}\quad\cdot \left( g^{\sigma \mu} (q_1 +q_2)^\nu + g^{\mu \nu}(-q_2 +p_1)^\sigma+ g^{\nu \sigma}(-p_1 -q_1)^\mu \right).
\end{split}
\end{align}
Notice in particular the similarity to the $W$+uno scenario (from which
this has been derived).
\subsubsection{Central $\mathbf{q\bar{q}}$ Vertex}
The final subleading process in the $W$+Jet case is the Central
$q\bar{q}$ vertex. This subleading process does not require an altered
current, but an effective vertex which is contracted with two regular
\HEJ currents. This complexity is dealt with nicely by the \lstinline!Tensor!
class, which is detailed in section~\ref{sec:tensor}.
The $W$-emission can be from the central effective vertex (scenario
dealt with by the function \texttt{jM2WqqtoqQQq()} in the file
\texttt{src/Wjets.cc}); or from either of the external quark legs
(scenario dealt with by \texttt{jM2WqqtoqQQqW()} in same file). In
the pure jets case, there are 7 separate diagrams which contribute to
this, which can be seen in figure~\ref{fig:qq_qQQq_graphs}. In the $W$+Jets
case, there are then 45 separate contributions.
\begin{figure}
\centering
\begin{subfigure}{0.45\textwidth}
\centering
\includegraphics{figures/qqbarcen1}
\end{subfigure}
\begin{subfigure}{0.45\textwidth}
\centering
\includegraphics{figures/qqbarcen2}
\end{subfigure}
\begin{subfigure}{0.45\textwidth}
\centering
\includegraphics{figures/qqbarcen3}
\end{subfigure}
\begin{subfigure}{0.45\textwidth}
\centering
\includegraphics{figures/qqbarcen4}
\end{subfigure}
\begin{subfigure}{0.45\textwidth}
\centering
\includegraphics{figures/qqbarcen5}
\end{subfigure}
\begin{subfigure}{0.45\textwidth}
\centering
\includegraphics{figures/qqbarcen6}
\end{subfigure}
\begin{subfigure}{0.45\textwidth}
\centering
\includegraphics{figures/qqbarcen7}
\end{subfigure}
\caption{All Feynman diagrams which contribute to $qq' \to qQ\bar{Q}q'$ at
leading order.}
\label{fig:qq_qQQq_graphs}
\end{figure}
The end result is of the effective vertex, after derivation, is:
\begin{align}
\label{eq:EffectiveVertexqqbar}
\begin{split}
V^{\mu\nu}_{\text{Eff}}=&
\frac{C_1}{s_{23AB}}\left(X^{\mu\nu\sigma}_{1a}\hat{t_1} + X^{\mu\nu\sigma}_{4b}\hat{t_3} +V^{\mu\nu\sigma}_{3g}\right)J_{\text{V} \sigma}(p_2,p_A,p_B,p_3)
\\
&\quad +iC_2X^{\mu\nu}_{Unc}+iC_3X^{\mu\nu}_{Cro},
\end{split}
\end{align}
where:
\begin{eqnarray}
\begin{split}
C_1=&T^e_{1q}T^g_{qa}T^e_{23}T^g_{4b} -
T^g_{1q}T^e_{qa}T^e_{23}T^g_{4b} = f^{egc}T^c_{1a}T^e_{23}T^g_{4b},
\\
C_2=&T^g_{1a}T^g_{2q}T^{g'}_{q3}T^{g'}_{4b}
\\
C_3=&T^g_{1a}T^{g'}_{2q}T^g_{q3}T^{g'}_{4b}
\end{split}
\end{eqnarray}
are the colour factors of different contributions. The following
tensor structures correspond to groupings of diagrams in
figure~\ref{fig:qq_qQQq_graphs}.
\begin{eqnarray}
\label{eq:1aFixed}
X_{1a}^{\mu\nu\sigma} &=
\frac{-g^{\mu\nu}}{s_{23AB}\hat{t_3}}\left(\frac{p^\sigma_a}{(s_{a23AB})} +
\frac{p^\sigma_1}{(s_{123AB})}\right)
\\
\label{eq:4bFixed}
X_{4b}^{\mu\nu\sigma}
&=\frac{g^{\mu\nu}}{s_{23AB}\hat{t_1}}\left(\frac{p^\sigma_b}{(s_{23bAB})}+\frac{p^\sigma_4}{(s_{234AB}}\right)
\end{eqnarray}
correspond to the first and second row of diagrams in figure~\ref{fig:qq_qQQq_graphs}.
\begin{align}
\label{eq:3GluonWEmit}
\begin{split}
X^{\mu\nu}_{3g}=\frac{1}{
\hat{t}_1s_{23AB}\,\hat{t}_3}
\bigg[&\left(q_1+p_2+p_3+p_A+p_B\right)^\nu
g^{\mu\sigma}+
\\
&\quad\left(q_3-p_2-p_3-p_A-p_B\right)^\mu g^{\sigma\nu}-
\\
& \qquad\left(q_1+q_3\right)^\sigma g^{\mu\nu}\bigg]J_{\text{V} \sigma}(p_2,p_A,p_B,p_3)
\end{split}
\end{align}
corresponds to the left diagram on the third row in
figure~\ref{fig:qq_qQQq_graphs}. One notes that all of these contributions have
the same colour factor, and as such we can group them together nicely
before summing over helicities etc. As such, the function
\texttt{MSymW()} in \texttt{src/Wjets.cc} returns a \lstinline!Tensor!
containing the information from these 5 groupings of contributions (30 diagrams
in total).
\begin{align}
\begin{split}
X^{\mu\nu}_{Unc}=\frac{\langle A|\sigma P_L|B\rangle}{\hat{t_1}\hat{t_3}} \bar{u}_2&\left[-\frac{
\gamma^\sigma P_L(\slashed{p}_2+\slashed{p}_A+\slashed{p}_B)\gamma^\mu
(\slashed{q}_3+ \slashed{p}_3)\gamma^\nu}{(s_{2AB})(t_{unc_{2}})}\right.+
\\
&\qquad\left. \frac{\gamma^\mu(\slashed{q}_1-\slashed{p}_2)\gamma^\sigma
P_L(\slashed{q}_3+\slashed{p}_3)\gamma^\nu}{(t_{unc_{1}})(t_{unc_{2}})}\right. +
\\
&\qquad\qquad\left. \frac{\gamma^\mu(\slashed{q}_1-\slashed{p}_2)\gamma^\nu(\slashed{p}_3+\slashed{p}_A+\slashed{p}_B)\gamma^\sigma P_L
}{(t_{unc_1})(s_{3AB})}\right]v_3
\end{split}
\end{align}
corresponds to the diagram on the right of row three in
figure~\ref{fig:qq_qQQq_graphs}. This contribution to the effective vertex can
be obtained in the code with the function \texttt{MUncW()} in file
\texttt{src/Wjets.cc}.
\begin{align}
\begin{split}
X^{\mu\nu}_{Cro}=\frac{\langle
A|\sigma P_L|B\rangle}{\hat{t_1}\hat{t_3}} \bar{u}_2&\left[-\frac{
\gamma^\nu(\slashed{q}_3+\slashed{p}_2)\gamma^\mu
(\slashed{p}_3+\slashed{p}_A+\slashed{p}_B)\gamma^\sigma P_L}{(t_{cro_1})(s_{3AB})}\right.+
\\
&\qquad\left. \frac{\gamma^\nu(\slashed{q}_3+\slashed{p}_2)\gamma^\sigma
P_L(\slashed{q}_1-\slashed{p}_3)\gamma^\mu}{(t_{cro_{1}})(t_{cro_{2}})}\right.+
\\ &\qquad\qquad\left
. \frac{\gamma^\sigma P_L(\slashed{p}_2+\slashed{p}_A+\slashed{p}_B)\gamma^\nu(\slashed{q}_1-\slashed{p}_3)\gamma^\mu
}{(s_{2AB})(t_{cro_2})}\right]v_3
\end{split}
\end{align}
corresponds to the last diagram in figure~\ref{fig:qq_qQQq_graphs}. This
contribution to the effective vertex can be obtained in the code with
the function \texttt{MCroW()} in file \texttt{src/Wjets.cc}.
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "developer_manual"
%%% End:
diff --git a/include/HEJ/Tensor.hh b/include/HEJ/Tensor.hh
index 75e04cc..62b8dbc 100644
--- a/include/HEJ/Tensor.hh
+++ b/include/HEJ/Tensor.hh
@@ -1,180 +1,179 @@
/** \file
* \brief Tensor Template Class declaration.
*
* This file contains the declaration of the Tensor Template class. This
* is used to calculate some of the more complex currents within the
* W+Jets implementation particularly.
*
* \authors The HEJ collaboration (see AUTHORS for details)
* \date 2019
* \copyright GPLv2 or later
*/
#pragma once
#include <array>
#include <complex>
#include <valarray>
namespace CLHEP {
class HepLorentzVector;
}
class CCurrent;
typedef std::complex<double> COM;
///@TODO put in some namespace
namespace detail {
static constexpr std::size_t d = 4;
//! \internal Compute integer powers at compile time
constexpr std::size_t power(unsigned base, unsigned exp) {
if(exp == 0) return 1;
// use exponentiation by squaring
// there are potentially faster implementations using bit shifts
// but we don't really care because everything's done at compile time
// and this is easier to understand
const std::size_t sqrt = power(base, exp/2);
return (exp % 2)?base*sqrt*sqrt:sqrt*sqrt;
}
}
template <unsigned int N>
class Tensor{
public:
static constexpr std::size_t d = detail::d;
//! Constructor
Tensor() = default;
explicit Tensor(COM x);
//! Rank of Tensor
constexpr unsigned rank() const{
return N;
};
//! total number of entries
std::size_t size() const {
return components.size();
};
//! Tensor element with given indices
template<typename... Indices>
COM const & operator()(Indices... i) const;
//! Tensor element with given indices
template<typename... Indices>
COM & operator()(Indices... rest);
//! implicit conversion to complex number for rank 0 tensors (scalars)
operator COM() const;
Tensor<N> & operator*=(COM const & x);
Tensor<N> & operator/=(COM const & x);
Tensor<N> & operator+=(Tensor<N> const & T2);
Tensor<N> & operator-=(Tensor<N> const & T2);
//! Outer product of two tensors
template<unsigned M>
Tensor<N+M> outer(Tensor<M> const & T2) const;
//! Outer product of two tensors
template<unsigned K, unsigned M>
friend Tensor<K+M> outer(Tensor<K> const & T1, Tensor<M> const & T2);
/**
* \brief T^(mu1...mk..mN)T2_(muk) contract kth index, where k member of [1,N]
* @param T2 Tensor of Rank 1 to contract with.
* @param k int to contract Tensor T2 with from original Tensor.
* @returns T1.contract(T2,1) -> T1^(mu,nu,rho...)T2_mu
*/
Tensor<N-1> contract(Tensor<1> const & T2, int k);
std::array<COM, detail::power(d, N)> components;
private:
};
template<unsigned N>
Tensor<N> operator*(Tensor<N> t, COM const & x);
template<unsigned N>
Tensor<N> operator/(Tensor<N> t, COM const & x);
template<unsigned N>
Tensor<N> operator+(Tensor<N> T1, Tensor<N> const & T2);
template<unsigned N>
Tensor<N> operator-(Tensor<N> T1, Tensor<N> const & T2);
-
/**
* \brief Returns diag(+---) Metric
* @returns Metric {(1,0,0,0),(0,-1,0,0),(0,0,-1,0),(0,0,0,-1)}
*/
Tensor<2> Metric();
/**
* \brief Calculates current <p1|mu|p2>
* @param p1 Momentum of Particle 1
* @param h1 Helicity of Particle 1 (Boolean, False = -h, True = +h)
* @param p2 Momentum of Particle 2
* @param h2 Helicity of Particle 2 (Boolean, False = -h, True = +h)
* @returns Tensor T^mu = <p1|mu|p2>
*
* @note in/out configuration considered in calculation
*/
Tensor<1> TCurrent(CLHEP::HepLorentzVector p1, bool h1,
CLHEP::HepLorentzVector p2, bool h2);
/**
* \brief Calculates current <p1|mu nu rho|p2>
* @param p1 Momentum of Particle 1
* @param h1 Helicity of Particle 1 (Boolean, False = -h, True = +h)
* @param p2 Momentum of Particle 2
* @param h2 Helicity of Particle 2 (Boolean, False = -h, True = +h)
* @returns Tensor T^mu^nu^rho = <p1|mu nu rho|p2>
*
* @note in/out configuration considered in calculation
*/
Tensor<3> T3Current(CLHEP::HepLorentzVector p1, bool h1,
CLHEP::HepLorentzVector p2, bool h2);
/**
* \brief Calculates current <p1|mu nu rho tau sigma|p2>
* @param p1 Momentum of Particle 1
* @param h1 Helicity of Particle 1 (Boolean, False = -h, True = +h)
* @param p2 Momentum of Particle 2
* @param h2 Helicity of Particle 2 (Boolean, False = -h, True = +h)
* @returns Tensor T^mu^nu^rho = <p1|mu nu rho tau sigma|p2>
*
* @note in/out configuration considered in calculation
*/
Tensor<5> T5Current(CLHEP::HepLorentzVector p1, bool h1,
CLHEP::HepLorentzVector p2, bool h2);
/**
* \brief Convert from CCurrent class
* @param j Current in CCurrent format
* @returns Current in Tensor Format
*/
Tensor<1> Construct1Tensor(CCurrent j);
/**
* \brief Convert from HLV class
* @param p Current in HLV format
* @returns Current in Tensor Format
*/
Tensor<1> Construct1Tensor(CLHEP::HepLorentzVector p);
/**
* \brief Construct Epsilon (Polarisation) Tensor
* @param k Momentum of incoming/outgoing boson
* @param ref Reference momentum for calculation
* @param pol Polarisation of boson
* @returns Polarisation Tensor E^mu
*/
Tensor<1> eps(CLHEP::HepLorentzVector k, CLHEP::HepLorentzVector ref, bool pol);
//! Initialises Tensor values by iterating over permutations of gamma matrices.
bool init_sigma_index();
// implementation of template functions
#include "HEJ/detail/Tensor_impl.hh"

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