diff --git a/current_generator/j_Wqqbar_j.frm b/current_generator/j_Wqqbar_j.frm
index eaa8e0f..afe808c 100644
--- a/current_generator/j_Wqqbar_j.frm
+++ b/current_generator/j_Wqqbar_j.frm
@@ -1,116 +1,116 @@
 */**
 *  \brief Contraction of FKL current with central qqbar+W emission and FKL current
 *
 *  TODO: unify conventions with developer manual
 *  the current dictionary is as follows:
 *
 *  code  | manual
 *  pq    | p_2
 *  pqbar | p_3
 *  pl    | p_A
 *  plbar | p_B
 *
 *  \authors   The HEJ collaboration (see AUTHORS for details)
 *  \date      2020
 *  \copyright GPLv2 or later
 */
 #include- include/helspin.frm
 #include- include/write.frm
 
 i mu,nu,rho,sigma;
 cf T1a, T4b, Xunc, Xcro, X1a, X4b, V3g, jv;
 v p1,pa,p4,pb,pq,pqbar,pl,plbar,q1,q3,q11,q12;
 s h;
 s tunc1,tunc2,tcro1,tcro2,s2AB,s3AB,s23AB;
 s t1,t3,s12,s13,s1A,s1B,sa2,sa3,saA,saB,s42,s43,s4A,s4B,sb2,sb3,sbA,sbB;
 
 #do h1={+,-}
    #do h2={+,-}
       l [M_uncross_W `h1'`h2'] = T1a(`h1'1, mu)*T4b(`h2'1, nu)*Xunc(mu, nu);
       l [M_cross_W `h1'`h2'] = T1a(`h1'1, mu)*T4b(`h2'1, nu)*Xcro(mu, nu);
       l [M_sym_W `h1'`h2'] = T1a(`h1'1, mu)*T4b(`h2'1, nu)*(
          X1a(mu, nu, sigma) - X4b(mu, nu, sigma) + V3g(mu, nu, sigma)
       )/s23AB * jv(sigma);
    #enddo
 #enddo
 
 id T1a(h?, mu?) = Current(h, p1, mu, pa);
 id T4b(h?, mu?) = Current(h, p4, mu, pb);
 * see eq:X_Unc in developer manual, multiplied by -t1*t3
 id Xunc(mu, nu) = -Current(-1, pl, sigma, plbar)*(
    - Current(-1, pq, sigma, pq + pl + plbar, mu, q3 + pqbar, nu, pqbar)/s2AB/tunc2
    + Current(-1, pq, mu, q1 - pq, sigma, q3 + pqbar, nu, pqbar)/tunc1/tunc2
    + Current(-1, pq, mu, q1 - pq, nu, pqbar + pl + plbar, sigma, pqbar)/tunc1/s3AB
 );
 * see eq:X_Cro in developer manual, multiplied by -t1*t3
 id Xcro(mu, nu) = -Current(-1, pl, sigma, plbar)*(
    - Current(-1, pq, nu, q3 + pq, mu, pqbar + pl + plbar, sigma, pqbar)/tcro1/s3AB
    + Current(-1, pq, nu, q3 + pq, sigma, q1 - pqbar, mu, pqbar)/tcro1/tcro2
    + Current(-1, pq, sigma, pq + pl + plbar, nu, q1 - pqbar, mu, pqbar)/s2AB/tcro2
 );
-* see eq:X_1a in developer manual, multiplied by -t1*t3
+* see eq:X_1a in developer manual, multiplied by -t1*s23AB*t3
 id X1a(mu, nu, sigma) = t1*d_(mu, nu)*(
    + p1(sigma)/(s12 + s13 + s1A + s1B)
    + pa(sigma)/(sa2 + sa3 + saA + saB)
 );
-* see eq:X_4b in developer manual, multiplied by t1*t3
+* see eq:X_4b in developer manual, multiplied by t1*s23AB*t3
 id X4b(mu, nu, sigma) = t3*d_(mu, nu)*(
    + p4(sigma)/(s42 + s43 + s4A + s4B)
    + pb(sigma)/(sb2 + sb3 + sbA + sbB)
 );
 * see eq:3GluonWEmit in developer manual, multiplied by t1*s23AB*t3
 id V3g(mu, nu, sigma) = (
    + (q1(nu) + pq(nu) + pqbar(nu) + pl(nu) + plbar(nu))*d_(mu, sigma)
    + (q3(mu) - pq(mu) - pqbar(mu) - pl(mu) - plbar(mu))*d_(nu, sigma)
    - (q1(sigma) + q3(sigma))*d_(mu, nu)
 );
 * see eq:J_V in developer manual
 * this is actually JW (eq:Weffcur1), but we can't use the built-in
 * because it cannot deal with two outgoing momenta, i.e. negative-energy spinors
 id jv(sigma?) = -i_*(
    + Current(-1, pq, rho, pq + pl + plbar, sigma, pqbar)/s2AB
    - Current(-1, pq, sigma, pqbar + pl + plbar, rho, pqbar)/s3AB
 )*Current(-1, pl, rho, plbar);
 
 multiply replace_(
    s2AB, m2(pl+plbar+pq),
    s3AB, m2(pl+plbar+pqbar),
    s23AB, m2(pl+plbar+pq+pqbar),
    tunc1, m2(q1-pq),
    tunc2, m2(q3+pqbar),
    tcro1, m2(q3+pq),
    tcro2, m2(q1-pqbar),
    t1, m2(q1),
    t3, m2(q3),
    s12, m2(p1+pq),
    s13, m2(p1+pqbar),
    s1A, m2(p1+pl),
    s1B, m2(p1+plbar),
    sa2, m2(pa+pq),
    sa3, m2(pa+pqbar),
    saA, m2(pa+pl),
    saB, m2(pa+plbar),
    s42, m2(p4+pq),
    s43, m2(p4+pqbar),
    s4A, m2(p4+pl),
    s4B, m2(p4+plbar),
    sb2, m2(pb+pq),
    sb3, m2(pb+pqbar),
    sbA, m2(pb+pl),
    sbB, m2(pb+plbar)
 );
 multiply replace_(q3, q1-pl-plbar-pq-pqbar);
 * replace q1 by sum of lightlike momenta
 * @TODO: choose q11 as collinear to some other vector
 multiply replace_(q1, q11-q12);
 .sort
 #call ContractCurrents()
 .sort
 format O4;
 format c;
 #call WriteHeader(`OUTPUT')
 #call WriteOptimised(`OUTPUT',M_uncross_W,2,pa,p1,pb,p4,pq,pqbar,pl,plbar,q11,q12)
 #call WriteOptimised(`OUTPUT',M_cross_W,2,pa,p1,pb,p4,pq,pqbar,pl,plbar,q11,q12)
 #call WriteOptimised(`OUTPUT',M_sym_W,2,pa,p1,pb,p4,pq,pqbar,pl,plbar,q11,q12)
 #call WriteFooter(`OUTPUT')
 .end
diff --git a/doc/developer_manual/currents.tex b/doc/developer_manual/currents.tex
index 8f0dc12..94c8b61 100644
--- a/doc/developer_manual/currents.tex
+++ b/doc/developer_manual/currents.tex
@@ -1,693 +1,694 @@
 \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 Higgs+Jets currents are
 defined in \texttt{src/Hjets.cc}, and pure jet currents are defined in
 in \texttt{src/jets.cc}. All of these have their own separate header
 files: \texttt{include/HEJ/Wjets.hh}, \texttt{include/HEJ/Hjets.hh} and
 \texttt{include/HEJ/jets.hh} respectively.
 
 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!ME_unob_XX!).
 
 \subsubsection{Extremal $q\bar{q}$}
 In Pure jets we also include the subleading process which arises when
 an incoming gluon splits into a $q\bar{q}$ pair. This splitting impact
 factor is related to the unordered current by simple means of a
 crossing symmetry.
 
 \subsubsection{Central $q\bar{q}$}
 The final subleading process type in the Pure Jets case is Central
 $q\bar{q}$. In this process type, we have two currents scattering off
 of each other, but this time, via an effective vertex, which connects
 together two FKL chains. Each FKL chain t-channel gluon splits into a
 $q\bar{q}$ and this results in a quark and anti-quark in between the
 most forward and backward jets. One can see an example of such a
 process in Figure \ref{fig:qqbarcen_example}.
 
 \begin{figure}[ht]
 \centering
 \includegraphics[]{Cenqqbar_jx}
 \caption{Momentum labeling for a central $q\bar{q}$ process.}
 \label{fig:qqbarcen_example}
 \end{figure}
 
 As the new central $q\bar{q}$ piece contains the quark propagator, we will treat
 this as part of the skeleton process.  This means that we do not impose strong ordering
 between the $q\bar{q}$-pair taking
 \begin{align}
 \label{eq:cenqqbarraporder}
   y_1 \ll y_q,y_{\bar{q}} \ll y_n.
 \end{align}
 The HEJ Matrix element for this process can be calculated as:
   \begin{align}
   \label{eq:Mcentral}
     i\mathcal{M} &= g_s^4 T^d_{1a} T^e_{nb}\ \frac{j_{\mu}(p_a,p_1)\ X^{ab\, \mu
     \nu}_{{\rm cen}}(p_q,p_{\bar{q}},q_1,q_3)\
     j_{\nu}(p_b,p_n)}{t_{a1}t_{bn}}.
   \end{align}
 where $X^{\mu \nu}_{\rm cen}$ is given by:
 \begin{equation}
   \label{eq:Xcen}
   \begin{split}
   X^{\mu \nu}_{\rm cen} ={}&\frac{f^{ced}T^c_{q\bar{q}}}{s_{q\bar{q}}}
      \left(\eta^{\mu \nu} X_{sym}^\sigma + V^{\mu \nu \sigma}_{\bar{q}g} \right)
      \bar{u}(p_q) \gamma^\sigma u(p_{\bar{q}}) \\ & \qquad + \frac{i
      T^d_{qj}T^e_{j\bar{q}}}{(q_1-p_q)^2} X^{\mu\nu}_{\text{qprop}} - \frac{i
      T^e_{qj}T^d_{j\bar{q}}}{(q_1-p_{\bar{q}})^2} X^{\mu\nu}_{\text{crossed}}\,,
  \end{split}
 \end{equation}
 with
 \begin{align}
   \label{eq:Xsym}
   X_{sym}^\sigma ={}& q_1^2 \left(
   \frac{p_a^\sigma}{s_{aq} + s_{a\bar{q}}} +  \frac{p_1^\sigma}{s_{1q} + s_{1\bar{q}}}
   \right) - q_3^2 \left(
   \frac{p_b^\sigma}{s_{bq} + s_{b\bar{q}}} +  \frac{p_n^\sigma}{s_{nq} + s_{n\bar{q}}}
   \right)\,,\\
   \label{eq:V3g}
   V_{3g}^{\mu\nu\sigma} ={}& (q_1 + p_q + p_{\bar{q}})^\nu \eta^{\mu\sigma}
   + (q_3 - p_q - p_{\bar{q}})^\mu \eta^{\nu\sigma}
   - (q_1 + q_3)^\sigma \eta^{\mu\nu}\,,\\
   \label{eq:Xqprop}
   X^{\mu\nu}_{\text{qprop}} ={}& \frac{\langle p_q | \mu (q_1-p_q) \nu | p_{\bar{q}}\rangle}{(q_1-p_q)^2}\,,\\
   \label{eq:Xcrossed}
   X^{\mu\nu}_{\text{crossed}} ={}& \frac{\langle p_q | \nu (q_1-p_{\bar{q}}) \mu | p_{\bar{q}}\rangle}{(q_1-p_{\bar{q}})^2}\,,
 \end{align}
 and $q_3 = q_1 - p_q - p_{\bar{q}}$.
 
 \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{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/Hjets.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/Hjets.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/Hjets.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/Hjets.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/Hjets.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/Hjets.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]{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]{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]{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.
 
 The FKL $W$ current is
 \begin{align}
   \label{eq:jW-}
     j^-_{W}(p_a, p_1, p_{\bar{l}}, p_{l}) ={}&
     \frac{2 \spa 1.l}{(p_1+p_W)^2}\*\Big(
     \spb 1.{\bar{l}} j^-(p_1, p_a) + \spb l.{\bar{l}}
     j^-(p_{l}, p_a)\Big)\notag\\
     & + \frac{2\spb a.{\bar{l}}}{(p_a-p_W)^2}\Big(
      \spa l.{\bar{l}} j^-(p_1, p_{\bar{l}}) + \spa a.l
     j^-(p_1, p_a)
       \Big)\,,\\
   \label{eq:jW+}
       j^+_{W}(p_a, p_1, p_{\bar{l}}, p_{l}) =& \big[j^-_{W}(p_a, p_1, p_l, p_{\bar{l}})\big]^*\,,
 \end{align}
 where the negative-helicity current is used for emission off a quark
 line and the positive-helicity current for emissions off antiquark. The
 implementation is in \texttt{include/currents.frm} inside the
 \texttt{current\_generator} (see section~\ref{sec:cur_gen}). To use it inside
 \FORM use the place-holder \lstinline!JW(h, mu, pa, p1, plbar, pl)!.
 
 \subsubsection{$W$+uno}
 \begin{figure}
   \centering
   \begin{subfigure}{0.45\textwidth}
   \centering
   \includegraphics{wuno1}
   \caption{}
   \label{fig:U1diags}
 \end{subfigure}
 \begin{subfigure}{0.45\textwidth}
   \centering
 \includegraphics{wuno2}
 \caption{}
 \label{fig:U2diags}
 \end{subfigure}
 \begin{subfigure}{0.45\textwidth}
   \centering
   \includegraphics{wuno3}
 \caption{}
 \label{fig:Cdiags}
 \end{subfigure}
 \begin{subfigure}{0.45\textwidth}
 \centering
 \includegraphics{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.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}\\
   \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}\\
 \label{eq:Ltensor}
 \begin{split}
   \tilde L^{\nu\mu\rho} ={}& \frac{1}{t_{aW2}}\left[
    \frac{\langle 2 | \sigma (\slashed{p}_a-\slashed{p}_W)\rho|a\rangle}{t_{aW}}
    +\frac{\langle 2 | \rho (\slashed{p}_2+\slashed{p}_W)\sigma|a\rangle}{s_{2W}}
 \right]\\
 &\times \left\{\left(\frac{p_b^\nu}{s_{1b}} + \frac{p_3^\nu}{s_{13}}\right)(q_1-p_1)^2g^{\mu\sigma}+(2q_1-p_1)^\nu g^{\mu\sigma} - 2p_1^\mu g^{\nu\sigma} + (2p_1-q_1)^\sigma g^{\mu\nu} \right\}\,,
 \end{split}
 \end{align}
 where $s_{ij\dots} = (p_i + p_j + \dots)^2, t_{ij\dots} = (p_i - p_j - \dots)^2$ and $q_1 = p_a-p_2-p_W$.
 
 \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}}\,,
   \end{split}\\
   \label{eq:U2tensorX}
   \begin{split}
     \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}}\,,
   \end{split}\\
   \label{eq:LtensorX}
   \begin{split}
     \tilde L^{\nu\mu\rho}_X &= \frac{1}{s_{W12}}\left[-\frac{\langle 2 |\sigma (\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) \sigma | 1\rangle }{s_{2W}} \right] \\
     &\vphantom{+\frac{1}{t_{aW2}}}\quad\cdot \left( -\left(
         \frac{p_b^\nu}{s_{ab}} + \frac{p_n^\nu}{s_{an}} \right) (q_1+p_a)^2 g^{\sigma\mu}+ g^{\sigma \mu} (2q_1 +p_a)^\nu - g^{\mu \nu}(2p_a+q_1)^\sigma+ 2g^{\nu \sigma}p_a^\mu \right)\,,
   \end{split}
 \end{align}
 where $q_1=-(p_1+p_2+p_W)$.  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 \FORM inside the
 \texttt{current\_generator/j\_Wqqbar\_j.frm}, which is detailed in
 section~\ref{sec:contr_calc}.
 
 The $W$-emission can be from the central effective vertex (scenario
 dealt with by the function \lstinline!ME_WCenqqx_qq! in the file
 \texttt{src/Wjets.cc}); or from either of the external quark legs
 (scenario dealt with by \lstinline!ME_W_Cenqqx_qq! 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{qqbarcen1}
 \end{subfigure}
 \begin{subfigure}{0.45\textwidth}
 \centering
 \includegraphics{qqbarcen2}
 \end{subfigure}
 \begin{subfigure}{0.45\textwidth}
 \centering
 \includegraphics{qqbarcen3}
 \end{subfigure}
 \begin{subfigure}{0.45\textwidth}
 \centering
 \includegraphics{qqbarcen4}
 \end{subfigure}
 \begin{subfigure}{0.45\textwidth}
 \centering
 \includegraphics{qqbarcen5}
 \end{subfigure}
 \begin{subfigure}{0.45\textwidth}
 \centering
 \includegraphics{qqbarcen6}
 \end{subfigure}
 \begin{subfigure}{0.45\textwidth}
 \centering
 \includegraphics{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 and
 \todo{Different convention for $J_V$}
 \begin{equation}
   \label{eq:J_V}
     J_V^\mu(p_2,p_l,p_{\bar{l}},p_3)=-i\left( \frac{ \bar{u}_2 \gamma^\nu (\slashed{p}_2 +
         \slashed{p}_l +
         \slashed{p}_{\bar{l}}) \gamma^\mu u_3}{s_{2l\bar{l}}} -  \frac{\bar u_2
         \gamma^\mu(\slashed{p}_3 + \slashed{p}_l + \slashed{p}_{\bar{l}}) \gamma^\nu
         u_3}{s_{3l\bar{l}}} \right) [\bar{u}_l \gamma_\nu u_{\bar{l}}].
 \end{equation}
 The following tensor structures correspond to groupings of diagrams in
 figure~\ref{fig:qq_qQQq_graphs}.
 \begin{eqnarray}
   \label{eq:X_1a}
   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)
+\frac{-g^{\mu\nu}}{s_{23AB}\hat{t_3}}\left(\frac{p^\sigma_a}{s_{a2} + s_{a3} + s_{aA} + s_{aB}} +
+                    \frac{p^\sigma_1}{s_{12} + s_{13} + s_{1A} + s_{1B}}\right)
   \\
   \label{eq:X_4b}
   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)
+                        &=\frac{g^{\mu\nu}}{s_{23AB}\hat{t_1}}\left(\frac{p^\sigma_b}{s_{b2} + s_{b3} + s_{bA} + s_{bB}}+
+                          \frac{p^\sigma_4}{s_{42} + s_{43} + s_{4A} + s_{4B}}\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}
   V^{\mu\nu\sigma}_{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
 \lstinline!M_sym_W! returns a contraction of the above tensor containing the
 information from these 5 groupings of contributions (30 diagrams in total). It
 is available through the generated header \texttt{j\_Wqqbar\_j.hh} (see
 section~\ref{sec:cur_gen}).
 \begin{align}
   \label{eq:X_Unc}
   \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 current
 contraction can be obtained in the code with the function
 \lstinline!M_uncross_W!.
 \begin{align}
   \begin{split}
   \label{eq:X_Cro}
     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 current
 contraction can be obtained in the code with the function
 \lstinline!M_cross_W!.
 
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