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diff --git a/doc/developer_manual/currents.tex b/doc/developer_manual/currents.tex
index 6968022..035941e 100644
--- a/doc/developer_manual/currents.tex
+++ b/doc/developer_manual/currents.tex
@@ -1,609 +1,609 @@
\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!).
\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/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]{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.
The FKL $W$ current is
\todo{Text. The following is what's currently implemented in \lstinline!jW!}
\begin{align}
\label{eq:jW-}
j^-_{W}(p_a, p_1, p_{\bar{l}}, p_{l}) ={}&
\frac{2 \spa 1.l}{(p_1+p_l+p_{\bar{l}})^2}\*\Big(
\spa 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 1.l j^-(p_l, p_a) + \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.
\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}} \\
+ \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}
+ (\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}} \\
+ \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}
+ (\slashed{p}_a-\slashed{p}_1)\nu |a\rangle}{s_{2W}t_{a1}}\,,
+ \end{split}\\
\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).
+\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}}, \\
\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/src/Wjets.cc b/src/Wjets.cc
index 102b7f5..57dca4f 100644
--- a/src/Wjets.cc
+++ b/src/Wjets.cc
@@ -1,1135 +1,1137 @@
/**
* \authors The HEJ collaboration (see AUTHORS for details)
* \date 2019
* \copyright GPLv2 or later
*/
#include "HEJ/Wjets.hh"
#include <array>
#include <iostream>
#include "HEJ/Constants.hh"
#include "HEJ/EWConstants.hh"
#include "HEJ/jets.hh"
#include "HEJ/Tensor.hh"
using HEJ::Tensor;
using HEJ::init_sigma_index;
using HEJ::metric;
using HEJ::rank3_current;
using HEJ::rank5_current;
using HEJ::eps;
using HEJ::to_tensor;
using HEJ::Helicity;
using HEJ::angle;
using HEJ::square;
using HEJ::flip;
using HEJ::ParticleProperties;
namespace helicity = HEJ::helicity;
namespace { // Helper Functions
// FKL W Helper Functions
double WProp (const HLV & plbar, const HLV & pl, ParticleProperties const & wprop){
COM propW = COM(0.,-1.)/( (pl+plbar).m2() - wprop.mass*wprop.mass
+ COM(0.,1.)*wprop.mass*wprop.width);
double PropFactor=(propW*conj(propW)).real();
return PropFactor;
}
namespace {
// FKL current including W emission off negative helicities
// See eq. (87) {eq:jW-} in developer manual
// Note that the terms are rearranged
Tensor<1> jW_minus(
HLV const & pa, HLV const & p1,
HLV const & plbar, HLV const & pl
){
using HEJ::helicity::minus;
const double tWin = (pa-pl-plbar).m2();
const double tWout = (p1+pl+plbar).m2();
// C++ arithmetic operators are evaluated left-to-right,
// so the following first computes complex scalar coefficients,
// which then multiply a current, reducing the number
// of multiplications
return 2.*(
+ angle(p1, pl)*square(p1, plbar)/tWout
+ square(pa, plbar)*angle(pa, pl)/tWin
)*HEJ::current(p1, pa, helicity::minus)
+ 2.*angle(p1, pl)*square(pl, plbar)/tWout
*HEJ::current(pl, pa, helicity::minus)
+ 2.*square(pa, plbar)*angle(pl, plbar)/tWin
*HEJ::current(p1, plbar, helicity::minus);
}
}
// FKL current including W emission
// see eqs. (87), (88) {eq:jW-}, {eq:jW+} in developer manual
Tensor<1> jW(
HLV const & pa, HLV const & p1,
HLV const & plbar, HLV const & pl,
Helicity h
){
if(h == helicity::minus) {
return jW_minus(pa, p1, plbar, pl);
}
return jW_minus(pa, p1, pl, plbar).complex_conj();
}
/**
* @brief W+Jets Unordered Contribution Helper Functions
* @returns result of equation (4.1.28) in Helen's Thesis (p.100)
*/
double jM2Wuno(HLV pg, HLV p1,HLV plbar, HLV pl, HLV pa, Helicity h1,
HLV p2, HLV pb, Helicity h2, Helicity pol,
ParticleProperties const & wprop
){
//@TODO Simplify the below (less Tensor class?)
init_sigma_index();
HLV pW = pl+plbar;
HLV q1g=pa-pW-p1-pg;
HLV q1 = pa-p1-pW;
HLV q2 = p2-pb;
const double taW = (pa-pW).m2();
const double taW1 = (pa-pW-p1).m2();
- const double tb2 = (pb-p2).m2();
const double s1W = (p1+pW).m2();
const double s1gW = (p1+pW+pg).m2();
const double s1g = (p1+pg).m2();
+ const double s2g = (p2+pg).m2();
+ const double sbg = (pb+pg).m2();
const double tag = (pa-pg).m2();
const double taWg = (pa-pW-pg).m2();
//use p1 as ref vec in pol tensor
Tensor<1> epsg = eps(pg,p2,pol);
Tensor<1> epsW = HEJ::current(pl,plbar,helicity::minus);
Tensor<1> j2b = HEJ::current(p2,pb,h2);
- Tensor<1> Tq1q2 = to_tensor((q1+q2)/taW1 + (pb/pb.dot(pg)
- +p2/p2.dot(pg)) * tb2/(2*taW1));
+ Tensor<1> Tq1q2 = to_tensor(
+ (pb/sbg + p2/s2g)*(q1 - pg).m2() + 2*q1 - pg
+ );
Tensor<3> J31a = rank3_current(p1, pa, h1);
- Tensor<2> J2_qaW =J31a.contract((pa-pW)/taW, 2);
- Tensor<2> J2_p1W =J31a.contract((p1+pW)/s1W, 2);
+ Tensor<2> J2_qaW =J31a.contract((pa-pW)/taW/taW1, 2);
+ Tensor<2> J2_p1W =J31a.contract((p1+pW)/s1W/taW1, 2);
Tensor<3> L1a = outer(Tq1q2, J2_qaW);
Tensor<3> L1b = outer(Tq1q2, J2_p1W);
- Tensor<3> L2a = outer(-pg-q1,J2_qaW)/taW1;
- Tensor<3> L2b = outer(-pg-q1, J2_p1W)/taW1;
- Tensor<3> L3 = outer(metric(), J2_qaW.contract(pg-q2,1)+J2_p1W.contract(pg-q2,2))/taW1;
+ Tensor<3> L2a = outer(-2*pg, J2_qaW);
+ Tensor<3> L2b = outer(-2*pg, J2_p1W);
+ Tensor<3> L3 = outer(metric(), J2_qaW.contract(2*pg-q1,1)+J2_p1W.contract(2*pg-q1,2));
Tensor<3> L(0.);
Tensor<5> J51a = rank5_current(p1, pa, h1);
Tensor<4> J_qaW = J51a.contract((pa-pW),4);
Tensor<4> J_qag = J51a.contract(pa-pg,4);
Tensor<4> J_p1gW = J51a.contract(p1+pg+pW,4);
Tensor<3> U1a = J_qaW.contract(p1+pg,2);
Tensor<3> U1b = J_p1gW.contract(p1+pg,2);
Tensor<3> U1c = J_p1gW.contract(p1+pW,2);
Tensor<3> U1(0.);
Tensor<3> U2a = J_qaW.contract(pa-pg-pW,2);
Tensor<3> U2b = J_qag.contract(pa-pg-pW,2);
Tensor<3> U2c = J_qag.contract(p1+pW,2);
Tensor<3> U2(0.);
for(int nu=0; nu<4;nu++){
for(int mu=0;mu<4;mu++){
for(int rho=0;rho<4;rho++){
L(nu, mu, rho) = L1a(nu,mu,rho) + L1b(nu,rho,mu)
+ L2a(mu,nu,rho) + L2b(mu,rho,nu) + L3(mu,nu,rho);
U1(nu, mu, rho) = U1a(nu, mu, rho) / (s1g*taW)
+ U1b(nu,rho,mu) / (s1g*s1gW) + U1c(rho,nu,mu) / (s1W*s1gW);
U2(nu,mu,rho) = U2a(mu,nu,rho) / (taWg*taW)
+ U2b(mu,rho,nu) / (taWg*tag) + U2c(rho,mu,nu) / (s1W*tag);
}
}
}
COM X = ((((U1-L).contract(epsW,3)).contract(j2b,2)).contract(epsg,1));
COM Y = ((((U2+L).contract(epsW,3)).contract(j2b,2)).contract(epsg,1));
double amp = HEJ::C_A*HEJ::C_F*HEJ::C_F/2.*(norm(X)+norm(Y)) - HEJ::C_F/2.*(X*conj(Y)).real();
double t1 = q1g.m2();
double t2 = q2.m2();
//Divide by WProp
amp*=WProp(plbar, pl, wprop);
//Divide by t-channels
amp/=(t1*t2);
return amp;
}
// Relevant Wqqx Helper Functions.
//g->qxqlxl (Calculates gluon to qqx Current. See JV_\mu in WSubleading Notes)
Tensor <1> gtqqxW(HLV pq,HLV pqbar,HLV pl,HLV plbar){
//@TODO Simplify the calculation below (Less Tensor class use?)
double s2AB=(pl+plbar+pq).m2();
double s3AB=(pl+plbar+pqbar).m2();
// Define llx current.
Tensor<1> ABCur = HEJ::current(pl, plbar, helicity::minus);
//blank 3 Gamma Current
Tensor<3> JV23 = rank3_current(pq,pqbar,helicity::minus);
// Components of g->qqW before W Contraction
Tensor<2> JV1 = JV23.contract((pq + pl + plbar),2)/(s2AB);
Tensor<2> JV2 = JV23.contract((pqbar + pl + plbar),2)/(s3AB);
// g->qqW Current. Note Minus between terms due to momentum flow.
// Also note: (-I)^2 from W vert. (I) from Quark prop.
Tensor<1> JVCur = (JV1.contract(ABCur,1) - JV2.contract(ABCur,2))*COM(0.,-1.);
return JVCur;
}
// Helper Functions Calculate the Crossed Contribution
Tensor <2> MCrossW(HLV pa, HLV, HLV, HLV, HLV pq, HLV pqbar, HLV pl,
HLV plbar, std::vector<HLV> partons, int nabove
){
//@TODO Simplify the calculation below Maybe combine with MCross?
// Useful propagator factors
double s2AB=(pl+plbar+pq).m2();
double s3AB=(pl+plbar+pqbar).m2();
HLV q1, q3;
q1=pa;
for(int i=0; i<nabove+1;i++){
q1=q1-partons.at(i);
}
q3 = q1 - pq - pqbar - pl - plbar;
double tcro1=(q3+pq).m2();
double tcro2=(q1-pqbar).m2();
// Define llx current.
Tensor<1> ABCur = HEJ::current(pl, plbar,helicity::minus);
//Blank 5 gamma Current
Tensor<5> J523 = rank5_current(pq,pqbar,helicity::minus);
// 4 gamma currents (with 1 contraction already).
Tensor<4> J_q3q = J523.contract((q3 + pq),2);
Tensor<4> J_2AB = J523.contract((pq + pl + plbar),2);
// Components of Crossed Vertex Contribution
Tensor<3> Xcro1 = J_q3q.contract((pqbar + pl + plbar),3);
Tensor<3> Xcro2 = J_q3q.contract((q1 - pqbar),3);
Tensor<3> Xcro3 = J_2AB.contract((q1 - pqbar),3);
// Term Denominators Taken Care of at this stage
Tensor<2> Xcro1Cont = Xcro1.contract(ABCur,3)/(tcro1*s3AB);
Tensor<2> Xcro2Cont = Xcro2.contract(ABCur,2)/(tcro1*tcro2);
Tensor<2> Xcro3Cont = Xcro3.contract(ABCur,1)/(s2AB*tcro2);
//Initialise the Crossed Vertex Object
Tensor<2> Xcro(0.);
for(int mu=0; mu<4;mu++){
for(int nu=0;nu<4;nu++){
Xcro(mu,nu) = -(-Xcro1Cont(nu,mu)+Xcro2Cont(nu,mu)+Xcro3Cont(nu,mu));
}
}
return Xcro;
}
// Helper Functions Calculate the Uncrossed Contribution
Tensor <2> MUncrossW(HLV pa, HLV, HLV, HLV, HLV pq, HLV pqbar,
HLV pl, HLV plbar, std::vector<HLV> partons, int nabove
){
//@TODO Simplify the calculation below Maybe combine with MUncross?
double s2AB=(pl+plbar+pq).m2();
double s3AB=(pl+plbar+pqbar).m2();
HLV q1, q3;
q1=pa;
for(int i=0; i<nabove+1;i++){
q1=q1-partons.at(i);
}
q3 = q1 - pl - plbar - pq - pqbar;
double tunc1 = (q1-pq).m2();
double tunc2 = (q3+pqbar).m2();
// Define llx current.
Tensor<1> ABCur = HEJ::current(pl, plbar, helicity::minus);
//Blank 5 gamma Current
Tensor<5> J523 = rank5_current(pq,pqbar,helicity::minus);
// 4 gamma currents (with 1 contraction already).
Tensor<4> J_2AB = J523.contract((pq + pl + plbar),2);
Tensor<4> J_q1q = J523.contract((q1 - pq),2);
// 2 Contractions taken care of.
Tensor<3> Xunc1 = J_2AB.contract((q3 + pqbar),3);
Tensor<3> Xunc2 = J_q1q.contract((q3 + pqbar),3);
Tensor<3> Xunc3 = J_q1q.contract((pqbar + pl + plbar),3);
// Term Denominators Taken Care of at this stage
Tensor<2> Xunc1Cont = Xunc1.contract(ABCur,1)/(s2AB*tunc2);
Tensor<2> Xunc2Cont = Xunc2.contract(ABCur,2)/(tunc1*tunc2);
Tensor<2> Xunc3Cont = Xunc3.contract(ABCur,3)/(tunc1*s3AB);
//Initialise the Uncrossed Vertex Object
Tensor<2> Xunc(0.);
for(int mu=0; mu<4;mu++){
for(int nu=0;nu<4;nu++){
Xunc(mu,nu) = -(- Xunc1Cont(mu,nu)+Xunc2Cont(mu,nu) +Xunc3Cont(mu,nu));
}
}
return Xunc;
}
// Helper Functions Calculate the g->qqxW (Eikonal) Contributions
Tensor <2> MSymW(HLV pa, HLV p1, HLV pb, HLV p4, HLV pq, HLV pqbar,
HLV pl,HLV plbar, std::vector<HLV> partons, int nabove
){
//@TODO Simplify the calculation below Maybe combine with MSym?
double sa2=(pa+pq).m2();
double s12=(p1+pq).m2();
double sa3=(pa+pqbar).m2();
double s13=(p1+pqbar).m2();
double saA=(pa+pl).m2();
double s1A=(p1+pl).m2();
double saB=(pa+plbar).m2();
double s1B=(p1+plbar).m2();
double sb2=(pb+pq).m2();
double s42=(p4+pq).m2();
double sb3=(pb+pqbar).m2();
double s43=(p4+pqbar).m2();
double sbA=(pb+pl).m2();
double s4A=(p4+pl).m2();
double sbB=(pb+plbar).m2();
double s4B=(p4+plbar).m2();
double s23AB=(pl+plbar+pq+pqbar).m2();
HLV q1,q3;
q1=pa;
for(int i=0;i<nabove+1;i++){
q1-=partons.at(i);
}
q3=q1-pq-pqbar-plbar-pl;
double t1 = (q1).m2();
double t3 = (q3).m2();
// g->qqW Current (Factors of sqrt2 dealt with in this function.)
Tensor<1> JV = gtqqxW(pq,pqbar,pl,plbar);
// 1a gluon emisson Contribution
Tensor<3> X1a = outer(metric(), p1*(t1/(s12+s13+s1A+s1B))
+ pa*(t1/(sa2+sa3+saA+saB)) );
Tensor<2> X1aCont = X1a.contract(JV,3);
//4b gluon emission Contribution
Tensor<3> X4b = outer(metric(), p4*(t3/(s42+s43+s4A+s4B))
+ pb*(t3/(sb2+sb3+sbA+sbB)) );
Tensor<2> X4bCont = X4b.contract(JV,3);
//Set up each term of 3G diagram.
Tensor<3> X3g1 = outer(q1+pq+pqbar+pl+plbar, metric());
Tensor<3> X3g2 = outer(q3-pq-pqbar-pl-plbar, metric());
Tensor<3> X3g3 = outer(q1+q3, metric());
// Note the contraction of indices changes term by term
Tensor<2> X3g1Cont = X3g1.contract(JV,3);
Tensor<2> X3g2Cont = X3g2.contract(JV,2);
Tensor<2> X3g3Cont = X3g3.contract(JV,1);
// XSym is an amalgamation of x1a, X4b and X3g.
// Makes sense from a colour factor point of view.
Tensor<2>Xsym(0.);
for(int mu=0; mu<4;mu++){
for(int nu=0;nu<4;nu++){
Xsym(mu,nu) = (X3g1Cont(nu,mu) + X3g2Cont(mu,nu) - X3g3Cont(nu,mu))
+ (X1aCont(mu,nu) - X4bCont(mu,nu));
}
}
return Xsym/s23AB;
}
Tensor <2> MCross(HLV pa, HLV pq, HLV pqbar, std::vector<HLV> partons,
Helicity hq, int nabove
){
//@TODO Simplify the calculation below Maybe combine with MCrossW?
HLV q1;
q1=pa;
for(int i=0;i<nabove+1;i++){
q1-=partons.at(i);
}
double t2=(q1-pqbar).m2();
//Blank 3 gamma Current
Tensor<3> J323 = rank3_current(pq,pqbar,hq);
// 2 gamma current (with 1 contraction already).
Tensor<2> XCroCont = J323.contract((q1-pqbar),2)/(t2);
//Initialise the Crossed Vertex
Tensor<2> Xcro(0.);
for(int mu=0; mu<4;mu++){
for(int nu=0;nu<4;nu++){
Xcro(mu,nu) = XCroCont(nu,mu);
}
}
return Xcro;
}
// Helper Functions Calculate the Uncrossed Contribution
Tensor <2> MUncross(HLV pa, HLV pq,HLV pqbar, std::vector<HLV> partons,
Helicity hq, int nabove
){
//@TODO Simplify the calculation below Maybe combine with MUncrossW?
HLV q1;
q1=pa;
for(int i=0;i<nabove+1;i++){
q1-=partons.at(i);
}
double t2 = (q1-pq).m2();
//Blank 3 gamma Current
Tensor<3> J323 = rank3_current(pq,pqbar,hq);
// 2 gamma currents (with 1 contraction already).
Tensor<2> XUncCont = J323.contract((q1-pq),2)/t2;
//Initialise the Uncrossed Vertex
Tensor<2> Xunc(0.);
for(int mu=0; mu<4;mu++){
for(int nu=0;nu<4;nu++){
Xunc(mu,nu) = -XUncCont(mu,nu);
}
}
return Xunc;
}
// Helper Functions Calculate the Eikonal Contributions
Tensor <2> MSym(HLV pa, HLV p1, HLV pb, HLV p4, HLV pq, HLV pqbar,
std::vector<HLV> partons, Helicity hq, int nabove
){
//@TODO Simplify the calculation below Maybe combine with MsymW?
HLV q1, q3;
q1=pa;
for(int i=0;i<nabove+1;i++){
q1-=partons.at(i);
}
q3 = q1-pq-pqbar;
double t1 = (q1).m2();
double t3 = (q3).m2();
double s23 = (pq+pqbar).m2();
double sa2 = (pa+pq).m2();
double sa3 = (pa+pqbar).m2();
double s12 = (p1+pq).m2();
double s13 = (p1+pqbar).m2();
double sb2 = (pb+pq).m2();
double sb3 = (pb+pqbar).m2();
double s42 = (p4+pq).m2();
double s43 = (p4+pqbar).m2();
Tensor<1> qqxCur = HEJ::current(pq, pqbar, hq);
// // 1a gluon emisson Contribution
Tensor<3> X1a = outer(metric(), p1*(t1/(s12+s13))+ pa*(t1/(sa2+sa3)));
Tensor<2> X1aCont = X1a.contract(qqxCur,3);
// //4b gluon emission Contribution
Tensor<3> X4b = outer(metric(), p4*(t3/(s42+s43)) + pb*(t3/(sb2+sb3)));
Tensor<2> X4bCont = X4b.contract(qqxCur,3);
// New Formulation Corresponding to New Analytics
Tensor<3> X3g1 = outer(q1+pq+pqbar, metric());
Tensor<3> X3g2 = outer(q3-pq-pqbar, metric());
Tensor<3> X3g3 = outer(q1+q3, metric());
// Note the contraction of indices changes term by term
Tensor<2> X3g1Cont = X3g1.contract(qqxCur,3);
Tensor<2> X3g2Cont = X3g2.contract(qqxCur,2);
Tensor<2> X3g3Cont = X3g3.contract(qqxCur,1);
Tensor<2>Xsym(0.);
for(int mu=0; mu<4;mu++){
for(int nu=0;nu<4;nu++){
Xsym(mu, nu) = COM(0,1) * ( (X3g1Cont(nu,mu) + X3g2Cont(mu,nu)
- X3g3Cont(nu,mu)) + (X1aCont(mu,nu) - X4bCont(mu,nu)) );
}
}
return Xsym/s23;
}
//! W+Jets FKL Contributions
/**
* @brief W+Jets FKL Contributions, function to handle all incoming types.
* @param p1out Outgoing Particle 1. (W emission)
* @param plbar Outgoing election momenta
* @param pl Outgoing neutrino momenta
* @param p1in Incoming Particle 1. (W emission)
* @param p2out Outgoing Particle 2
* @param p2in Incoming Particle 2
* @param aqlineb Bool. Is Backwards quark line an anti-quark line?
* @param aqlinef Bool. Is Forwards quark line an anti-quark line?
*
* Calculates j_W ^\mu j_\mu.
* Handles all possible incoming states.
*/
double jW_j( HLV p1out, HLV plbar, HLV pl, HLV p1in, HLV p2out, HLV p2in,
bool aqlineb, bool /* aqlinef */,
ParticleProperties const & wprop
){
using helicity::minus;
using helicity::plus;
const HLV q1=p1in-p1out-plbar-pl;
const HLV q2=-(p2in-p2out);
const double WPropfact = WProp(plbar, pl, wprop);
const auto j_W = COM{0,-1}*jW(p1in, p1out, plbar, pl, aqlineb?plus:minus);
double Msqr = 0.;
for(const auto h: {plus, minus}) {
const auto j = HEJ::current(p2out, p2in, h);
Msqr += abs2(j_W.contract(j, 1));
}
// Division by colour and Helicity average (Nc2-1)(4)
// Multiply by Cf^2
return HEJ::C_F*HEJ::C_F*WPropfact*Msqr/(q1.m2()*q2.m2()*(HEJ::N_C*HEJ::N_C - 1)*4);
}
} // Anonymous Namespace
double ME_W_qQ (HLV p1out, HLV plbar, HLV pl,HLV p1in, HLV p2out, HLV p2in,
ParticleProperties const & wprop
){
return jW_j(p1out, plbar, pl, p1in, p2out, p2in, false, false, wprop);
}
double ME_W_qQbar (HLV p1out, HLV plbar, HLV pl,HLV p1in, HLV p2out, HLV p2in,
ParticleProperties const & wprop
){
return jW_j(p1out, plbar, pl, p1in, p2out, p2in, false, true, wprop);
}
double ME_W_qbarQ (HLV p1out, HLV plbar, HLV pl,HLV p1in, HLV p2out, HLV p2in,
ParticleProperties const & wprop
){
return jW_j(p1out, plbar, pl, p1in, p2out, p2in, true, false, wprop);
}
double ME_W_qbarQbar (HLV p1out, HLV plbar, HLV pl,HLV p1in, HLV p2out, HLV p2in,
ParticleProperties const & wprop
){
return jW_j(p1out, plbar, pl, p1in, p2out, p2in, true, true, wprop);
}
double ME_W_qg (HLV p1out, HLV plbar, HLV pl,HLV p1in, HLV p2out, HLV p2in,
ParticleProperties const & wprop
){
return jW_j(p1out, plbar, pl, p1in, p2out, p2in, false, false, wprop)
*K_g(p2out, p2in)/HEJ::C_F;
}
double ME_W_qbarg (HLV p1out, HLV plbar, HLV pl,HLV p1in, HLV p2out, HLV p2in,
ParticleProperties const & wprop
){
return jW_j(p1out, plbar, pl, p1in, p2out, p2in, true, false, wprop)
*K_g(p2out, p2in)/HEJ::C_F;
}
namespace{
/**
* @brief W+Jets Unordered Contributions, function to handle all incoming types.
* @param p1out Outgoing Particle 1. (W emission)
* @param plbar Outgoing election momenta
* @param pl Outgoing neutrino momenta
* @param p1in Incoming Particle 1. (W emission)
* @param p2out Outgoing Particle 2 (Quark, unordered emission this side.)
* @param p2in Incoming Particle 2 (Quark, unordered emission this side.)
* @param pg Unordered Gluon momenta
* @param aqlineb Bool. Is Backwards quark line an anti-quark line?
* @param aqlinef Bool. Is Forwards quark line an anti-quark line?
*
* Calculates j_W ^\mu j_{uno}_\mu. Ie, unordered with W emission opposite side.
* Handles all possible incoming states.
*/
double jW_juno(HLV p1out, HLV plbar, HLV pl,HLV p1in, HLV p2out,
HLV p2in, HLV pg, bool aqlineb, bool aqlinef,
ParticleProperties const & wprop
){
using helicity::minus;
using helicity::plus;
const HLV q1=p1in-p1out-plbar-pl;
const HLV q2=-(p2in-p2out-pg);
const HLV q3=-(p2in-p2out);
const Helicity fhel = aqlinef?plus:minus;
const auto j_W = jW(p1in, p1out, plbar, pl, aqlineb?plus:minus);
const auto mj2p = HEJ::current(p2out, p2in, flip(fhel));
const auto mj2m = HEJ::current(p2out, p2in, fhel);
const auto jgbp = HEJ::current(pg, p2in, flip(fhel));
const auto jgbm = HEJ::current(pg, p2in, fhel);
const auto j2gp = HEJ::current(p2out, pg, flip(fhel));
const auto j2gm = HEJ::current(p2out, pg, fhel);
// Dot products of these which occur again and again
COM MWmp=j_W.dot(mj2p); // And now for the Higgs ones
COM MWmm=j_W.dot(mj2m);
const auto qsum = to_tensor(q2+q3);
const auto p1o = to_tensor(p1out);
const auto p1i = to_tensor(p1in);
const auto p2o = to_tensor(p2out);
const auto p2i = to_tensor(p2in);
const auto Lmm=( (-1.)*qsum*(MWmm) + (-2.*COM{j_W.dot(pg)})*mj2m + 2.*COM{mj2m.dot(pg)}*j_W
+ ( p1o/pg.dot(p1out) + p1i/pg.dot(p1in) )*( q2.m2()*MWmm/2. ) )/q3.m2();
const auto Lmp=( (-1.)*qsum*(MWmp) + (-2.*COM{j_W.dot(pg)})*mj2p + 2.*COM{mj2p.dot(pg)}*j_W
+ ( p1o/pg.dot(p1out) + p1i/pg.dot(p1in) )*( q2.m2()*MWmp/2. ) )/q3.m2();
const auto U1mm=(COM{jgbm.dot(j_W)}*j2gm+2.*p2o*MWmm)/(p2out+pg).m2();
const auto U1mp=(COM{jgbp.dot(j_W)}*j2gp+2.*p2o*MWmp)/(p2out+pg).m2();
const auto U2mm=((-1.)*COM{j2gm.dot(j_W)}*jgbm+2.*p2i*MWmm)/(p2in-pg).m2();
const auto U2mp=((-1.)*COM{j2gp.dot(j_W)}*jgbp+2.*p2i*MWmp)/(p2in-pg).m2();
double amm,amp;
amm=HEJ::C_F*(2.*vre(Lmm-U1mm,Lmm+U2mm))+2.*HEJ::C_F*HEJ::C_F/3.*abs2(U1mm+U2mm);
amp=HEJ::C_F*(2.*vre(Lmp-U1mp,Lmp+U2mp))+2.*HEJ::C_F*HEJ::C_F/3.*abs2(U1mp+U2mp);
double ampsq=-(amm+amp);
//Divide by WProp
ampsq*=WProp(plbar, pl, wprop);
return ampsq/((16)*(q2.m2()*q1.m2()));
}
}
double ME_W_unob_qQ(HLV p1out, HLV p1in, HLV p2out, HLV p2in,
HLV pg, HLV plbar, HLV pl,
ParticleProperties const & wprop
){
return jW_juno(p2out, plbar, pl, p2in, p1out, p1in, pg, false, false, wprop);
}
double ME_W_unob_qQbar(HLV p1out, HLV p1in, HLV p2out, HLV p2in,
HLV pg, HLV plbar, HLV pl,
ParticleProperties const & wprop
){
return jW_juno(p2out, plbar, pl, p2in, p1out, p1in, pg, false, true, wprop);
}
double ME_W_unob_qbarQ(HLV p1out, HLV p1in, HLV p2out, HLV p2in,
HLV pg, HLV plbar, HLV pl,
ParticleProperties const & wprop
){
return jW_juno(p2out, plbar, pl, p2in, p1out, p1in, pg, true, false, wprop);
}
double ME_W_unob_qbarQbar(HLV p1out, HLV p1in, HLV p2out, HLV p2in,
HLV pg, HLV plbar, HLV pl,
ParticleProperties const & wprop
){
return jW_juno(p2out, plbar, pl, p2in, p1out, p1in, pg, true, true, wprop);
}
namespace{
/**
* @brief W+Jets Unordered Contributions, function to handle all incoming types.
* @param pg Unordered Gluon momenta
* @param p1out Outgoing Particle 1. (Quark - W and Uno emission)
* @param plbar Outgoing election momenta
* @param pl Outgoing neutrino momenta
* @param p1in Incoming Particle 1. (Quark - W and Uno emission)
* @param p2out Outgoing Particle 2
* @param p2in Incoming Particle 2
* @param aqlineb Bool. Is Backwards quark line an anti-quark line?
*
* Calculates j_W_{uno} ^\mu j_\mu. Ie, unordered with W emission same side.
* Handles all possible incoming states. Note this handles both forward and back-
* -ward Wuno emission. For forward, ensure p1out is the uno and W emission parton.
* @TODO: Include separate wrapper functions for forward and backward to clean up
* ME_W_unof_current in `MatrixElement.cc`.
*/
double jWuno_j(HLV pg, HLV p1out, HLV plbar, HLV pl, HLV p1in,
HLV p2out, HLV p2in, bool aqlineb,
ParticleProperties const & wprop
){
//Calculate different Helicity choices
const Helicity h = aqlineb?helicity::plus:helicity::minus;
double ME2mpp = jM2Wuno(pg, p1out,plbar,pl,p1in,h,p2out,p2in,
helicity::plus,helicity::plus, wprop);
double ME2mpm = jM2Wuno(pg, p1out,plbar,pl,p1in,h,p2out,p2in,
helicity::plus,helicity::minus, wprop);
double ME2mmp = jM2Wuno(pg, p1out,plbar,pl,p1in,h,p2out,p2in,
helicity::minus,helicity::plus, wprop);
double ME2mmm = jM2Wuno(pg, p1out,plbar,pl,p1in,h,p2out,p2in,
helicity::minus,helicity::minus, wprop);
//Helicity sum and average over initial states
return (ME2mpp + ME2mpm + ME2mmp + ME2mmm)/(4.*HEJ::C_A*HEJ::C_A);
}
}
double ME_Wuno_qQ(HLV p1out, HLV p1in, HLV p2out, HLV p2in,
HLV pg, HLV plbar, HLV pl, ParticleProperties const & wprop
){
return jWuno_j(pg, p1out, plbar, pl, p1in, p2out, p2in, false, wprop);
}
double ME_Wuno_qQbar(HLV p1out, HLV p1in, HLV p2out, HLV p2in,
HLV pg, HLV plbar, HLV pl,
ParticleProperties const & wprop
){
return jWuno_j(pg, p1out, plbar, pl, p1in, p2out, p2in, false, wprop);
}
double ME_Wuno_qbarQ(HLV p1out, HLV p1in, HLV p2out, HLV p2in,
HLV pg, HLV plbar, HLV pl,
ParticleProperties const & wprop
){
return jWuno_j(pg, p1out, plbar, pl, p1in, p2out, p2in, true, wprop);
}
double ME_Wuno_qbarQbar(HLV p1out, HLV p1in, HLV p2out, HLV p2in,
HLV pg, HLV plbar, HLV pl,
ParticleProperties const & wprop
){
return jWuno_j(pg, p1out, plbar, pl, p1in, p2out, p2in, true, wprop);
}
double ME_Wuno_qg(HLV p1out, HLV p1in, HLV p2out, HLV p2in,
HLV pg, HLV plbar, HLV pl, ParticleProperties const & wprop
){
return jWuno_j(pg, p1out, plbar, pl, p1in, p2out, p2in, false, wprop)
*K_g(p2out, p2in)/HEJ::C_F;
}
double ME_Wuno_qbarg(HLV p1out, HLV p1in, HLV p2out, HLV p2in,
HLV pg, HLV plbar, HLV pl,
ParticleProperties const & wprop
){
return jWuno_j(pg, p1out, plbar, pl, p1in, p2out, p2in, true, wprop)
*K_g(p2out, p2in)/HEJ::C_F;
}
/**
* @brief W+Jets Extremal qqx Contributions, function to handle all incoming types.
* @param pgin Incoming gluon which will split into qqx.
* @param pqout Quark of extremal qqx outgoing (W-Emission).
* @param plbar Outgoing anti-lepton momenta
* @param pl Outgoing lepton momenta
* @param pqbarout Anti-quark of extremal qqx pair. (W-Emission)
* @param pout Outgoing Particle 2 (end of FKL chain)
* @param p2in Incoming Particle 2
* @param aqlinef Bool. Is Forwards quark line an anti-quark line?
*
* Calculates j_W_{qqx} ^\mu j_\mu. Ie, Ex-QQX with W emission same side.
* Handles all possible incoming states. Calculated via crossing symmetry from jWuno_j.
*/
double jWqqx_j(HLV pgin, HLV pqout, HLV plbar, HLV pl,
HLV pqbarout, HLV p2out, HLV p2in, bool aqlinef,
ParticleProperties const & wprop
){
//Calculate Different Helicity Configurations.
const Helicity h = aqlinef?helicity::plus:helicity::minus;
double ME2mpp = jM2Wuno(-pgin, pqout,plbar,pl,-pqbarout,h,p2out,p2in,
helicity::plus,helicity::plus, wprop);
double ME2mpm = jM2Wuno(-pgin, pqout,plbar,pl,-pqbarout,h,p2out,p2in,
helicity::plus,helicity::minus, wprop);
double ME2mmp = jM2Wuno(-pgin, pqout,plbar,pl,-pqbarout,h,p2out,p2in,
helicity::minus,helicity::plus, wprop);
double ME2mmm = jM2Wuno(-pgin, pqout,plbar,pl,-pqbarout,h,p2out,p2in,
helicity::minus,helicity::minus, wprop);
//Helicity sum and average over initial states.
double ME2 = (ME2mpp + ME2mpm + ME2mmp + ME2mmm)/(4.*HEJ::C_A*HEJ::C_A);
//Correct colour averaging after crossing:
ME2*=(3.0/8.0);
return ME2;
}
double ME_WExqqx_qbarqQ(HLV pgin, HLV pqout, HLV plbar, HLV pl,
HLV pqbarout, HLV p2out, HLV p2in,
ParticleProperties const & wprop
){
return jWqqx_j(pgin, pqout, plbar, pl, pqbarout, p2out, p2in, false, wprop);
}
double ME_WExqqx_qqbarQ(HLV pgin, HLV pqbarout, HLV plbar, HLV pl,
HLV pqout, HLV p2out, HLV p2in,
ParticleProperties const & wprop
){
return jWqqx_j(pgin, pqbarout, plbar, pl, pqout, p2out, p2in, true, wprop);
}
double ME_WExqqx_qbarqg(HLV pgin, HLV pqout, HLV plbar, HLV pl,
HLV pqbarout, HLV p2out, HLV p2in,
ParticleProperties const & wprop
){
return jWqqx_j(pgin, pqout, plbar, pl, pqbarout, p2out, p2in, false, wprop)
*K_g(p2out,p2in)/HEJ::C_F;
}
double ME_WExqqx_qqbarg(HLV pgin, HLV pqbarout, HLV plbar, HLV pl,
HLV pqout, HLV p2out, HLV p2in,
ParticleProperties const & wprop
){
return jWqqx_j(pgin, pqbarout, plbar, pl, pqout, p2out, p2in, true, wprop)
*K_g(p2out,p2in)/HEJ::C_F;
}
namespace {
//Function to calculate Term 1 in Equation 3.23 in James Cockburn's Thesis.
Tensor<1> qggm1(HLV pb, HLV p2, HLV p3, Helicity hel2, Helicity helg, HLV refmom){
//@TODO Simplify the calculation below. (Less Tensor class use?)
double t1 = (p3-pb)*(p3-pb);
// Gauge choice in polarisation tensor. (see JC's Thesis)
Tensor<1> epsg = eps(pb, refmom, helg);
Tensor<3> qqCurBlank = rank3_current(p2,p3,hel2);
Tensor<2> qqCur = qqCurBlank.contract(p3-pb,2);
Tensor<1> gqqCur = qqCur.contract(epsg,2)/t1;
return gqqCur*(-1);
}
//Function to calculate Term 2 in Equation 3.23 in James Cockburn's Thesis.
Tensor<1> qggm2(HLV pb, HLV p2, HLV p3, Helicity hel2, Helicity helg, HLV refmom){
//@TODO Simplify the calculation below (Less Tensor class use?)
double t1 = (p2-pb)*(p2-pb);
// Gauge choice in polarisation tensor. (see JC's Thesis)
Tensor<1> epsg = eps(pb,refmom, helg);
Tensor<3> qqCurBlank = rank3_current(p2,p3,hel2);
Tensor<2> qqCur = qqCurBlank.contract(p2-pb,2);
Tensor<1> gqqCur = qqCur.contract(epsg,1)/t1;
return gqqCur;
}
//Function to calculate Term 3 in Equation 3.23 in James Cockburn's Thesis.
Tensor<1> qggm3(HLV pb, HLV p2, HLV p3, Helicity hel2, Helicity helg, HLV refmom){
//@TODO Simplify the calculation below (Less Tensor class use?)
double s23 = (p2+p3)*(p2+p3);
// Gauge choice in polarisation tensor. (see JC's Thesis)
Tensor<1> epsg = eps(pb, refmom, helg);
Tensor<3> qqCurBlank1 = outer(p2+p3, metric())/s23;
Tensor<3> qqCurBlank2 = outer(pb, metric())/s23;
Tensor<1> Cur23 = HEJ::current(p2, p3,hel2);
Tensor<2> qqCur1 = qqCurBlank1.contract(Cur23,3);
Tensor<2> qqCur2 = qqCurBlank2.contract(Cur23,3);
Tensor<2> qqCur3 = qqCurBlank2.contract(Cur23,1);
Tensor<1> gqqCur = (qqCur1.contract(epsg,1)
- qqCur2.contract(epsg,2)
+ qqCur3.contract(epsg,1))*2*COM(0,1);
return gqqCur;
}
}
// no wqq emission
double ME_W_Exqqx_QQq(HLV pa, HLV pb, HLV p1, HLV p2,
HLV p3,HLV plbar, HLV pl, bool aqlinepa,
ParticleProperties const & wprop
){
using helicity::minus;
using helicity::plus;
init_sigma_index();
// 2 independent helicity choices (complex conjugation related).
Tensor<1> TMmmm1 = qggm1(pb,p2,p3,minus,minus, pa);
Tensor<1> TMmmm2 = qggm2(pb,p2,p3,minus,minus, pa);
Tensor<1> TMmmm3 = qggm3(pb,p2,p3,minus,minus, pa);
Tensor<1> TMpmm1 = qggm1(pb,p2,p3,minus,plus, pa);
Tensor<1> TMpmm2 = qggm2(pb,p2,p3,minus,plus, pa);
Tensor<1> TMpmm3 = qggm3(pb,p2,p3,minus,plus, pa);
// Build the external quark line W Emmision
Tensor<1> cur1a = jW(pa,p1,plbar,pl, aqlinepa?plus:minus);
//Contract with the qqxCurrent.
COM Mmmm1 = TMmmm1.contract(cur1a,1);
COM Mmmm2 = TMmmm2.contract(cur1a,1);
COM Mmmm3 = TMmmm3.contract(cur1a,1);
COM Mpmm1 = TMpmm1.contract(cur1a,1);
COM Mpmm2 = TMpmm2.contract(cur1a,1);
COM Mpmm3 = TMpmm3.contract(cur1a,1);
//Colour factors:
COM cm1m1,cm2m2,cm3m3,cm1m2,cm1m3,cm2m3;
cm1m1=8./3.;
cm2m2=8./3.;
cm3m3=6.;
cm1m2 =-1./3.;
cm1m3 = -3.*COM(0.,1.);
cm2m3 = 3.*COM(0.,1.);
//Sqaure and sum for each helicity config:
double Mmmm = real( cm1m1*pow(abs(Mmmm1),2) + cm2m2*pow(abs(Mmmm2),2)
+ cm3m3*pow(abs(Mmmm3),2) + 2.*real(cm1m2*Mmmm1*conj(Mmmm2))
+ 2.*real(cm1m3*Mmmm1*conj(Mmmm3))
+ 2.*real(cm2m3*Mmmm2*conj(Mmmm3)) );
double Mpmm = real( cm1m1*pow(abs(Mpmm1),2) + cm2m2*pow(abs(Mpmm2),2)
+ cm3m3*pow(abs(Mpmm3),2) + 2.*real(cm1m2*Mpmm1*conj(Mpmm2))
+ 2.*real(cm1m3*Mpmm1*conj(Mpmm3))
+ 2.*real(cm2m3*Mpmm2*conj(Mpmm3)) );
// Divide by WProp
const double WPropfact = WProp(plbar, pl, wprop);
return (2*WPropfact*(Mmmm+Mpmm)/24./4.)/(pa-p1-pl-plbar).m2()/(p2+p3-pb).m2();
}
// W+Jets qqxCentral
double ME_WCenqqx_qq(HLV pa, HLV pb,HLV pl, HLV plbar, std::vector<HLV> partons,
bool aqlinepa, bool aqlinepb, bool qqxmarker, int nabove,
ParticleProperties const & wprop
){
init_sigma_index();
HLV pq, pqbar, p1, p4;
if (qqxmarker){
pqbar = partons[nabove+1];
pq = partons[nabove+2];}
else{
pq = partons[nabove+1];
pqbar = partons[nabove+2];}
p1 = partons.front();
p4 = partons.back();
Tensor<1> T1am, T4bm, T1ap, T4bp;
if(!(aqlinepa)){
T1ap = HEJ::current(p1, pa, helicity::plus);
T1am = HEJ::current(p1, pa, helicity::minus);}
else if(aqlinepa){
T1ap = HEJ::current(pa, p1, helicity::plus);
T1am = HEJ::current(pa, p1, helicity::minus);}
if(!(aqlinepb)){
T4bp = HEJ::current(p4, pb, helicity::plus);
T4bm = HEJ::current(p4, pb, helicity::minus);}
else if(aqlinepb){
T4bp = HEJ::current(pb, p4, helicity::plus);
T4bm = HEJ::current(pb, p4, helicity::minus);}
// Calculate the 3 separate contributions to the effective vertex
Tensor<2> Xunc = MUncrossW(pa, p1, pb, p4, pq, pqbar, pl, plbar, partons, nabove);
Tensor<2> Xcro = MCrossW( pa, p1, pb, p4, pq, pqbar, pl, plbar, partons, nabove);
Tensor<2> Xsym = MSymW( pa, p1, pb, p4, pq, pqbar, pl, plbar, partons, nabove);
// 4 Different Helicity Choices (Differs from Pure Jet Case, where there is
// also the choice in qqbar helicity.
// (- - hel choice)
COM M_mmUnc = (((Xunc).contract(T1am,1)).contract(T4bm,1));
COM M_mmCro = (((Xcro).contract(T1am,1)).contract(T4bm,1));
COM M_mmSym = (((Xsym).contract(T1am,1)).contract(T4bm,1));
// (- + hel choice)
COM M_mpUnc = (((Xunc).contract(T1am,1)).contract(T4bp,1));
COM M_mpCro = (((Xcro).contract(T1am,1)).contract(T4bp,1));
COM M_mpSym = (((Xsym).contract(T1am,1)).contract(T4bp,1));
// (+ - hel choice)
COM M_pmUnc = (((Xunc).contract(T1ap,1)).contract(T4bm,1));
COM M_pmCro = (((Xcro).contract(T1ap,1)).contract(T4bm,1));
COM M_pmSym = (((Xsym).contract(T1ap,1)).contract(T4bm,1));
// (+ + hel choice)
COM M_ppUnc = (((Xunc).contract(T1ap,1)).contract(T4bp,1));
COM M_ppCro = (((Xcro).contract(T1ap,1)).contract(T4bp,1));
COM M_ppSym = (((Xsym).contract(T1ap,1)).contract(T4bp,1));
//Colour factors:
COM cmsms,cmumu,cmcmc,cmsmu,cmsmc,cmumc;
cmsms=3.;
cmumu=4./3.;
cmcmc=4./3.;
cmsmu =3./2.*COM(0.,1.);
cmsmc = -3./2.*COM(0.,1.);
cmumc = -1./6.;
// Work Out Interference in each case of helicity:
double amp_mm = real(cmsms*pow(abs(M_mmSym),2)
+cmumu*pow(abs(M_mmUnc),2)
+cmcmc*pow(abs(M_mmCro),2)
+2.*real(cmsmu*M_mmSym*conj(M_mmUnc))
+2.*real(cmsmc*M_mmSym*conj(M_mmCro))
+2.*real(cmumc*M_mmUnc*conj(M_mmCro)));
double amp_mp = real(cmsms*pow(abs(M_mpSym),2)
+cmumu*pow(abs(M_mpUnc),2)
+cmcmc*pow(abs(M_mpCro),2)
+2.*real(cmsmu*M_mpSym*conj(M_mpUnc))
+2.*real(cmsmc*M_mpSym*conj(M_mpCro))
+2.*real(cmumc*M_mpUnc*conj(M_mpCro)));
double amp_pm = real(cmsms*pow(abs(M_pmSym),2)
+cmumu*pow(abs(M_pmUnc),2)
+cmcmc*pow(abs(M_pmCro),2)
+2.*real(cmsmu*M_pmSym*conj(M_pmUnc))
+2.*real(cmsmc*M_pmSym*conj(M_pmCro))
+2.*real(cmumc*M_pmUnc*conj(M_pmCro)));
double amp_pp = real(cmsms*pow(abs(M_ppSym),2)
+cmumu*pow(abs(M_ppUnc),2)
+cmcmc*pow(abs(M_ppCro),2)
+2.*real(cmsmu*M_ppSym*conj(M_ppUnc))
+2.*real(cmsmc*M_ppSym*conj(M_ppCro))
+2.*real(cmumc*M_ppUnc*conj(M_ppCro)));
double amp=((amp_mm+amp_mp+amp_pm+amp_pp)/(9.*4.));
HLV q1,q3;
q1=pa;
for(int i=0;i<nabove+1;i++){
q1-=partons.at(i);
}
q3 = q1 - pq - pqbar - pl - plbar;
double t1 = (q1).m2();
double t3 = (q3).m2();
//Divide by t-channels
amp/=(t1*t1*t3*t3);
//Divide by WProp
amp*=WProp(plbar, pl, wprop);
return amp;
}
// no wqq emission
double ME_W_Cenqqx_qq(HLV pa, HLV pb,HLV pl,HLV plbar, std::vector<HLV> partons,
bool aqlinepa, bool aqlinepb, bool qqxmarker, int nabove,
int nbelow, bool forwards, ParticleProperties const & wprop
){
using helicity::minus;
using helicity::plus;
init_sigma_index();
if (!forwards){ //If Emission from Leg a instead, flip process.
std::swap(pa, pb);
std::reverse(partons.begin(),partons.end());
std::swap(aqlinepa, aqlinepb);
qqxmarker = !qqxmarker;
std::swap(nabove,nbelow);
}
HLV pq, pqbar, p1,p4;
if (qqxmarker){
pqbar = partons[nabove+1];
pq = partons[nabove+2];}
else{
pq = partons[nabove+1];
pqbar = partons[nabove+2];}
p1 = partons.front();
p4 = partons.back();
Tensor<1> T1am(0.), T1ap(0.);
if(!(aqlinepa)){
T1ap = HEJ::current(p1, pa, plus);
T1am = HEJ::current(p1, pa, minus);}
else if(aqlinepa){
T1ap = HEJ::current(pa, p1, plus);
T1am = HEJ::current(pa, p1, minus);}
Tensor <1> T4bm = jW(pb, p4, plbar, pl, aqlinepb?plus:minus);
// Calculate the 3 separate contributions to the effective vertex
Tensor<2> Xunc_m = MUncross(pa, pq, pqbar,partons, minus, nabove);
Tensor<2> Xcro_m = MCross( pa, pq, pqbar,partons, minus, nabove);
Tensor<2> Xsym_m = MSym( pa, p1, pb, p4, pq, pqbar, partons, minus, nabove);
Tensor<2> Xunc_p = MUncross(pa, pq, pqbar,partons, plus, nabove);
Tensor<2> Xcro_p = MCross( pa, pq, pqbar,partons, plus, nabove);
Tensor<2> Xsym_p = MSym( pa, p1, pb, p4, pq, pqbar, partons, plus, nabove);
// (- - hel choice)
COM M_mmUnc = (((Xunc_m).contract(T1am,1)).contract(T4bm,1));
COM M_mmCro = (((Xcro_m).contract(T1am,1)).contract(T4bm,1));
COM M_mmSym = (((Xsym_m).contract(T1am,1)).contract(T4bm,1));
// (- + hel choice)
COM M_mpUnc = (((Xunc_p).contract(T1am,1)).contract(T4bm,1));
COM M_mpCro = (((Xcro_p).contract(T1am,1)).contract(T4bm,1));
COM M_mpSym = (((Xsym_p).contract(T1am,1)).contract(T4bm,1));
// (+ - hel choice)
COM M_pmUnc = (((Xunc_m).contract(T1ap,1)).contract(T4bm,1));
COM M_pmCro = (((Xcro_m).contract(T1ap,1)).contract(T4bm,1));
COM M_pmSym = (((Xsym_m).contract(T1ap,1)).contract(T4bm,1));
// (+ + hel choice)
COM M_ppUnc = (((Xunc_p).contract(T1ap,1)).contract(T4bm,1));
COM M_ppCro = (((Xcro_p).contract(T1ap,1)).contract(T4bm,1));
COM M_ppSym = (((Xsym_p).contract(T1ap,1)).contract(T4bm,1));
//Colour factors:
COM cmsms,cmumu,cmcmc,cmsmu,cmsmc,cmumc;
cmsms=3.;
cmumu=4./3.;
cmcmc=4./3.;
cmsmu =3./2.*COM(0.,1.);
cmsmc = -3./2.*COM(0.,1.);
cmumc = -1./6.;
// Work Out Interference in each case of helicity:
double amp_mm = real(cmsms*pow(abs(M_mmSym),2)
+cmumu*pow(abs(M_mmUnc),2)
+cmcmc*pow(abs(M_mmCro),2)
+2.*real(cmsmu*M_mmSym*conj(M_mmUnc))
+2.*real(cmsmc*M_mmSym*conj(M_mmCro))
+2.*real(cmumc*M_mmUnc*conj(M_mmCro)));
double amp_mp = real(cmsms*pow(abs(M_mpSym),2)
+cmumu*pow(abs(M_mpUnc),2)
+cmcmc*pow(abs(M_mpCro),2)
+2.*real(cmsmu*M_mpSym*conj(M_mpUnc))
+2.*real(cmsmc*M_mpSym*conj(M_mpCro))
+2.*real(cmumc*M_mpUnc*conj(M_mpCro)));
double amp_pm = real(cmsms*pow(abs(M_pmSym),2)
+cmumu*pow(abs(M_pmUnc),2)
+cmcmc*pow(abs(M_pmCro),2)
+2.*real(cmsmu*M_pmSym*conj(M_pmUnc))
+2.*real(cmsmc*M_pmSym*conj(M_pmCro))
+2.*real(cmumc*M_pmUnc*conj(M_pmCro)));
double amp_pp = real(cmsms*pow(abs(M_ppSym),2)
+cmumu*pow(abs(M_ppUnc),2)
+cmcmc*pow(abs(M_ppCro),2)
+2.*real(cmsmu*M_ppSym*conj(M_ppUnc))
+2.*real(cmsmc*M_ppSym*conj(M_ppCro))
+2.*real(cmumc*M_ppUnc*conj(M_ppCro)));
double amp=((amp_mm+amp_mp+amp_pm+amp_pp)/(9.*4.));
HLV q1,q3;
q1=pa;
for(int i=0;i<nabove+1;i++){
q1-=partons.at(i);
}
q3 = q1 - pq - pqbar;
double t1 = (q1).m2();
double t3 = (q3).m2();
//Divide by t-channels
amp/=(t1*t1*t3*t3);
//Divide by WProp
amp*=WProp(plbar, pl, wprop);
return amp;
}
diff --git a/t/ME_data/ME_Wm.dat b/t/ME_data/ME_Wm.dat
index c4a69f0..b1ad4a2 100644
--- a/t/ME_data/ME_Wm.dat
+++ b/t/ME_data/ME_Wm.dat
@@ -1,1308 +1,1308 @@
2.928617337e-06
1.647083496e-06
6.792718307e-07
8.309052795e-05
1.188563005e-09
7.418703203e-09
4.64176585e-07
4.469210588e-07
6.108953218e-06
2.937369558e-06
4.834662872e-06
8.222916804e-06
1.984842145e-06
4.724279533e-06
2.284467423e-07
6.086670249e-08
9.402694313e-07
2.134890127e-05
1.344127063e-06
6.325064033e-08
5.042105356e-06
0.0002284967536
2.294811317e-06
6.277634042e-05
1.336994329e-07
3.953756759e-06
9.658399826e-05
2.316822172e-06
2.819631851e-07
0.0001081195238
3.432930003e-06
3.368456504e-06
1.112864917e-08
3.295369143e-07
3.989490572e-10
1.948758233e-05
3.510758397e-07
3.210138517e-07
3.239664339e-06
8.604705327e-06
7.617690755e-10
1.878849261e-06
8.602382866e-09
2.905076666e-09
9.580640762e-08
2.761322408e-07
1.121735761e-05
8.305550955e-07
3.094512747e-06
9.008871903e-07
3.660037761e-07
4.545298754e-08
1.619265714e-09
0.01367608992
3.915696743e-06
2.025165585e-06
3.681426282e-09
4.179813437e-06
3.072778246e-08
8.896098616e-07
3.025899647e-08
1.817366927e-09
4.337353756e-10
1.271872323e-06
6.04489128e-06
9.893120074e-09
1.214081986e-05
2.958624219e-08
2.061238904e-09
1.930294996e-05
6.299188205e-07
2.643963602e-07
2.06132771e-06
4.342452252e-05
8.291567369e-07
2.498958153e-06
4.358403281e-06
9.241515571e-05
9.124195104e-05
0.000115945869
2.350206043e-06
7.845167967e-06
0.000638524343
4.723346316e-08
6.954346838e-09
5.357593527e-06
1.473700863e-07
1.053983829e-07
5.919949754e-07
1.175787989e-05
1.546190854e-07
0.0004236014522
3.617348006e-06
4.516789165e-05
3.955639799e-05
0.0001365301129
5.126068859e-05
1.077721123e-06
1.018738183e-08
2.31035007e-09
6.836601309e-07
5.827486967e-09
1.557627741e-09
6.04883445e-05
1.652825805e-07
2.956934131e-07
3.715517348e-06
1.403902522e-08
2.060672536e-07
0.001033124848
9.772923916e-07
2.935927964e-05
1.151232995e-05
7.794558457e-06
2.174319802e-05
4.056670359e-08
2.955320268e-08
8.030711247e-05
2.603164139e-07
0.0001681638933
2.93007525e-08
7.196892999e-05
1.920951539e-06
3.637534963e-09
7.893685649e-06
0.0001175194162
4.802829388e-10
4.835469293e-07
2.878769998e-05
1.898685256e-09
2.754462006e-08
1.403651125e-10
5.826442197e-07
2.43372504e-06
7.927550152e-06
1.020962274e-08
1.052564287e-07
7.737037652e-06
3.40057811e-06
2.714499296e-08
2.377749398e-09
0.0001490838408
9.612641064e-11
1.654718689e-05
1.570703582e-07
1.609375559e-06
6.94622935e-08
0.04337706424
9.860599192e-06
1.103383561e-05
0.01558774793
1.359111595e-06
2.104947148e-07
4.483240938e-08
2.52721137e-08
4.136183848e-07
1.75959296e-07
4.162277212e-07
3.660655583e-07
2.475053461e-06
2.142026381e-05
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diff --git a/t/ME_data/ME_Wp.dat b/t/ME_data/ME_Wp.dat
index 77b368a..99d9469 100644
--- a/t/ME_data/ME_Wp.dat
+++ b/t/ME_data/ME_Wp.dat
@@ -1,1289 +1,1289 @@
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