\section{Introduction}
The Standard Model (SM) is well established and in agreement with all present
collider data. The only part of the model, not explored so far, is the
Higgs sector. Because this sector plays a distinguished role in the
theory, being responsible for the masses and mixings of all particles,
the search for the Higgs boson is one of the highest priorities at the
LHC. Within the Standard Model all properties of the Higgs boson are
fixed when its mass is known. From indirect limits the Higgs boson is
expected to have a mass in the range 114.4~GeV\ $< m_H <$ 246~GeV\
(95\% C.L.) \cite{Eidelman:2004wy}. When the Higgs mass is above the
$Z$ pair threshold, it decays with a large branching fraction into $Z$
bosons, that can be discovered in the ``golden"
$\ell^+\ell^+\ell^-\ell^-$ decay mode. As long as $m_H \gtrsim$
130~GeV\ the decay into four leptons can still be used. Within the
region 155~GeV\ $< m_H <$ 170~GeV\ the $ZZ^*$ branching fraction
goes through a minimum, while the $WW^*$ decay mode opens up. In this
mass range the $gg \to H \to WW \to \ell \nu \ \ell \nu$
\cite{Dittmar:1996ss} and the recently established vector boson fusion mode
$qq \to qq H \to qq WW \to qq \ \ell \nu \ \ell \nu$
\cite{Rainwater:1999sd,Asai:2004ws,cms-higgs} have the largest discovery
potential.
In recent papers \cite{Buszello:2002uu, Choi:2002jk} we discussed
the possible determination of the spin/CP
properties of the Higgs boson. To analyse these properties we introduced
hypothetical couplings to the Z-bosons corresponding to a Higgs-like
particle with non Standard Model spin and CP. To distinguish different
spin/CP eigenstates we considered the decay chain $H\to ZZ \to
\ell^+\ell^-\ell^+\ell^-$ and analysed the angular correlations between the leptons.
In \cite{Buszello:2002uu} we discuss pure spin/CP states up to spin 1,
\cite{Choi:2002jk} also considers spin 2 particles performing a similar
analysis. In addition we also consider mixed CP states for spin 0
particles in \cite{Buszello:2004be}. These analyses showed that the
spin/CP properties can easily be determined for a Higgs mass above the
threshold for Z pair production. Below the threshold it is more
challenging to obtain a significant separation.
To cover this mass region we now investigate Higgs
production via WBF and the subsequent decay chain $H\to WW\to \ell\nu\,\ell\nu$. Promising observables in this case are the angle
between the two forward jets and the invariant mass of the charged leptons.
A similar analysis using only the angle between the tag jets has already
been performed in \cite{Rainwater:1999sd}. They considered additional
dimension six operators to couple a spin 0 Higgs boson to vector bosons
including a CP odd and a CP even coupling not present in the Standard Model.
The NLO corrections to Higgs production via WBF are given in
\cite{Figy:2003nv}. They do not significantly
change the shape of the distributions and therefore we limit ourselves
to the leading order approximation.
The paper is organized as follows. In chapter 2 we briefly review the
model used for the non Standard Model couplings, in chapter 3 we
discuss the angular distributions of the tag jets and the invariant
mass of the lepton pair and finally we conclude.
\section{Model}
We use the same parametrisation as introduced in
\cite{Buszello:2002uu} and only repeat it here for completeness.
The most general coupling of a (pseudo) scalar Higgs boson with mass $M_h$
to two on-shell vector bosons is of the following form:
\begin{equation}
{\cal L}_{scalar}=
\mathbf{X} \delta_{\mu \nu}+
\mathbf{Y} k_{\mu} k_{\nu}/M_h^2 +i \mathbf{P} \epsilon_{\mu \nu p_{Z}
q_{Z}}/M_h^2 .
\label{scalar}
\end{equation}
Here the momentum of the first boson is $p_Z^{\mu}$,
that of the second boson is $q_Z^{\nu}$.
The momentum of the Higgs boson is $k$ and $\epsilon_{\mu\nu \rho\sigma}$ is the total antisymmetric tensor with $\epsilon_{1234} = i$.
Within the Standard Model one has $\mathbf{X}=1$, $\mathbf{Y}=\mathbf{P}=0$.
For a pure pseudoscalar particle one has $\mathbf{P} \not= 0, \mathbf{X}=\mathbf{Y}=0$.
If both $\mathbf{P}$ and one of the other interactions are present,
one cannot assign a definite parity to the Higgs boson.
A similar formula for a (pseudo) vector with momentum
$k_{\rho}$ reads:
\begin{equation}
{\cal L}_{vector}=
\mathbf{X} (\delta_{\rho \mu} p_Z^{\nu}+\delta_{\rho \nu} q_Z^{\mu})
+\mathbf{P} (i \epsilon_{\mu \nu \rho p_Z}
-i \epsilon_{\mu \nu \rho q_Z}) .
\label{vector}
\end{equation}
It is to be noted that the coupling to the vector field
actually contains only two parameters and is therefore simpler
than to the scalar.
Using the generalised couplings given above we calculated the matrix
elements for $qQ\to q'Q' H $ where the primed and unprimed quarks
belong to the same $SU(2)$ doublet. In combination with the matrix
elements for $H\to WW\to \ell\nu\,\ell\nu$ given in \cite{Buszello:2002uu}
the full matrix element for $qQ \to q'Q' \ell\nu\,\ell\nu$ can be
obtained. Using this result an event generator was written to study
the effects of the various cuts.
The QCD background has been simulated using
Pythia\cite{Sjostrand:2003wg}
while we used Madgraph/Madevent\cite{Maltoni:2002qb} for the electroweak
background.