%Paper: 
%From: "Andrzej J. Buras" <buras@feynman.t30.physik.tu-muenchen.de>
%Date: Wed, 7 Sep 1994 09:43:46 +0200

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\def\vcb{\mid V_{cb} \mid}
\def\vtd{\mid V_{td} \mid}
\def\vub{\mid V_{ub}/V_{cb} \mid}
\def\f{\frac}
\def\o{\over}
\def\b{\begin{equation}}
\def\e{\end{equation}}
\def\l{\label}
\def\kpnn{K^+\rightarrow\pi^+\nu\bar\nu }
\def\kpn{K^+\rightarrow\pi^+\nu\bar\nu}
\def\klpnn{K_L\rightarrow\pi^0\nu\bar\nu}
\def\klpn{K_L\rightarrow\pi^0\nu\bar\nu}

\def\imlt{{\rm Im}\lambda_t}
\def\relt{{\rm Re}\lambda_t}
\def\relc{{\rm Re}\lambda_c}
\def\klmm{$K_L\rightarrow\mu^+\mu^-$\ }
\def\klm{K_L\rightarrow\mu^+\mu^-}

\def\r#1{(\ref{#1})}

\begin{document}

 \title{
 {\normalsize\rm
\rightline{MPI-PhT/94-57}
 \rightline{TUM--T31--70/94}
 \rightline{August 1994}
 \ \\
 \ \\
 \ \\}
 Towards Precise Determinations of the CKM \\
  Matrix without Hadronic Uncertainties*}

\author{Andrzej J. Buras}

\affil{ Technische Universit\"at M\"unchen, Physik Department\\
 D-85748 Garching, Germany \\
 Max-Planck-Institut f\"ur Physik
 -- Werner-Heisenberg-Institut --\\
 F\"ohringer Ring 6, D-80805 M\"unchen, Germany}

\abstract{
We illustrate how the measurements of the CP asymmetries in
$B^0_{d,s}$-decays together with a measurement of
$Br(K_L\to \pi^\circ\nu\bar\nu)$ or $Br(\kpnn)$
and the known value of $\mid V_{us}\mid $ can determine all elements
of the Cabibbo-Kobayashi-Maskawa matrix essentially without any hadronic
uncertainties. An analysis using the ratio $x_d/x_s$ of $B_d-\bar B_d$
to $B_s-\bar B_s$ mixings is also presented.}

\twocolumn[\maketitle]

\fnm{7}{Invited talk given at ICHEP '94, Glasgow, July 1994.
 Supported by the German
   Bundesministerium f\"ur Forschung und Technologie under contract
   06 TM 732 and by the CEC science project SC1--CT91--0729.}

\section{Setting the Scene}
An important target of particle physics is the determination of
the unitary $3\times 3$ Cabibbo-Kobayashi-Maskawa
matrix which parametrizes the charged current interactions of
 quarks:
\begin{equation}\label{1j}
J^{cc}_{\mu}=(\bar u,\bar c,\bar t)_L\gamma_{\mu}
\left(\begin{array}{ccc}
V_{ud}&V_{us}&V_{ub}\\
V_{cd}&V_{cs}&V_{cb}\\
V_{td}&V_{ts}&V_{tb}
\end{array}\right)
\left(\begin{array}{c}
d \\ s \\ b
\end{array}\right)_L
\end{equation}
It is customery these days to parametrize these matrix by the four Wolfenstein
parameters  $(\lambda, A, \varrho, \eta)$. In particular
one has
\begin{equation}\label{2.75}
\mid V_{us}\mid=\lambda
\qquad
\vcb=A \lambda^2
\end{equation}
and
\begin{equation}\label{2.75a}
V_{ub}=A\lambda^3 (\varrho-i\eta)
\qquad
V_{td}=A\lambda^3 (1-\bar\varrho-i\bar\eta)
\end{equation}
Here following \cite{BLO}
 we have introduced
\begin{equation}\label{3}
\bar\varrho=\varrho (1-\frac{\lambda^2}{2})
\qquad
\bar\eta=\eta (1-\frac{\lambda^2}{2}).
\end{equation}
which allows to improve the accuracy of the Wolfenstein parametrization.

{}From tree level K decays sensitive to $V_{us}$ and tree level B decays
 sensitive to $V_{cb}$ and $V_{ub}$ we have:
\begin{equation}\label{2}
\lambda=0.2205\pm0.0018
\qquad
\mid V_{cb} \mid=0.039\pm0.004
\end{equation}
\begin{equation}\label{2.94}
R_b \equiv  \sqrt{\bar\varrho^2 +\bar\eta^2}
= (1-\frac{\lambda^2}{2})\frac{1}{\lambda}
\left| \frac{V_{ub}}{V_{cb}} \right|=0.36\pm0.14
\end{equation}
corresponding to
\begin{equation}\label{2a}
\left| \frac{V_{ub}}{V_{cb}} \right|=0.08\pm0.03
\end{equation}
$R_b$ is just the length of one side of the rescaled unitarity triangle
in which the length of the side on the $\bar\varrho$ axis is equal
unity.
The length of the third side is governed by $\vtd$ and is given by
\begin{equation}\label{2.95}
R_t \equiv \sqrt{(1-\bar\varrho)^2 +\bar\eta^2}
=\frac{1}{\lambda} \left| \frac{V_{td}}{V_{cb}} \right|
\end{equation}
In order to find $R_t$ one has to go beyond tree level decays.

As we have seen at this conference a large part in the errors quoted in
(\ref{2}), (\ref{2.94}) and (\ref{2a}) results from theoretical (hadronic)
 uncertainties.
Consequently even if the data from CLEO II improves in the
future, it is difficult to imagine at present that in the tree level B-decays
a better accuracy than $\Delta\vcb=\pm 2\cdot 10^{-3}$ and
$\Delta\vub=\pm 0.01$ ($\Delta R_b=\pm 0.04$) could be achieved unless some
dramatic improvements in the theory will take place.

The question then arises whether it is possible at all to determine the
CKM parameters without any hadronic uncertainties.
The aim of this contribution is to demonstrate that this is indeed possible.
To this end one has to go to the loop induced decays or transitions
governed by short distance
physics. We will see that in this manner clean and
precise determinations of $\vcb$, $\vub$, $\vtd$, $\varrho$ and $\eta$
can be achieved. Since the relevant measurements will take place only
in the next decade, what follows is really a 21st century story.

It is known that many loop induced decays contain also hadronic uncertainties
\cite{AB94A}.
Examples are $B^0-\bar B^0$ mixing, $\varepsilon_K$ and
 $\varepsilon'/\varepsilon$.
Let us in this connection recall the expectations from a "standard" analysis
of the unitarity triangle which is based on $\varepsilon_K$, $x_d$
giving the size of $B^0-\bar B^0$ mixing,
$\vcb$ and $\vub$ with the last two extracted from tree level decays.
As a recent analysis \cite{BLO} shows, even with optimistic assumptions
about the theoretical and experimental errors it will be difficult to
achieve the accuracy better than $\Delta\varrho=\pm 0.15$ and
$\Delta\eta=\pm 0.05$ this way. Therefore in what follows we will
only discuss the four finalists
in the field of weak decays which
essentially are free of hadronic uncertainties.
\section{Finalists}
\subsection{CP-Asymmetries in $B^o$-Decays}
The CP-asymmetry in the decay $B_d^\circ \rightarrow \psi K_S$ allows
 in the standard model
a direct measurement of the angle $\beta$ in the unitarity triangle
without any theoretical uncertainties
\cite{NQ}. Similarly the decay
$B_d^\circ \rightarrow \pi^+ \pi^-$ gives the angle $\alpha$, although
 in this case strategies involving
other channels are necessary in order to remove hadronic
uncertainties related to penguin contributions
\cite{CPASYM}.
The determination of the angle~$\gamma$ from CP asymmetries in neutral
B-decays is more difficult but not impossible
\cite{RF}. Also charged B decays could be useful in
this respect \cite{Wyler}.
We have for instance
%
\begin{equation}\label{113c}
 A_{CP}(\psi K_S)=-\sin(2\beta) \frac{x_d}{1+x_d^2},
\end{equation}
\begin{equation}\label{113d}
   A_{CP}(\pi^+\pi^-)=-\sin(2\alpha) \frac{x_d}{1+x_d^2}
\end{equation}
where we have neglected QCD penguins in $A_{CP}(\pi^+\pi^-)$.
Since in the usual unitarity triangle  one side is known,
it suffices to measure
two angles to determine the triangle completely. This means that
the measurements of $\sin 2\alpha$ and $\sin 2\beta$ can determine
the parameters $\varrho$ and $\eta$.
The main virtues of this determination are as follows:
\begin{itemize}
\item No hadronic or $\Lambda_{\overline{MS}}$ uncertainties.
\item No dependence on $m_t$ and $V_{cb}$ (or A).
\end{itemize}
\subsection{$K_L\to\pi^o\nu\bar\nu$}
$K_L\to\pi^o\nu\bar\nu$ is the theoretically
cleanest decay in the field of rare K-decays.
$K_L\to\pi^o\nu\bar\nu$ is dominated by short distance loop diagrams
involving
the top quark and proceeds almost entirely through direct CP violation.
The last year calculations
\cite{BB1,BB2} of next-to-leading QCD corrections to this decay
considerably reduced the theoretical uncertainty
due to the choice of the renormalization scales present in the
leading order expression \cite{DDG}.
Typically the uncertainty in $Br(\klpnn$) of $\pm 10\%$ in the
leading order is reduced to $\pm 1\%$.  Since the relevant hadronic matrix
elements of the weak current $\bar {s} \gamma_{\mu} (1- \gamma _{5})d $
can be measured in the leading
decay $K^+ \rightarrow \pi^0 e^+ \nu$, the resulting theoretical
expression for Br( $K_L\to\pi^o\nu\bar\nu$)
is
only a function of the CKM parameters, the QCD scale
 $\Lambda \overline{_{MS}}$
 and  $m_t$.
The long distance contributions to $K_L\to\pi^o\nu\bar\nu$ are negligible.
We have then:
\begin{equation}\label{3c}
Br(\klpnn)=1.50 \cdot 10^{-5}\eta^2\mid V_{cb}\mid^4 x_t^{1.15}
\end{equation}
where $x_t=m_t^2/M_W^2$ with
$m_t\equiv\bar m_t(m_t)$. The main features of this decay are:
\begin{itemize}
\item No hadronic uncertainties
\item  $\Lambda_{\overline{MS}}$ and renormalization scale uncertainties
at most $\pm 1\%$.
\item Strong dependence on $m_t$ and $V_{cb}$ (or A).
\end{itemize}
\subsection{$\kpnn$}
$K^+\to\pi^+\nu\bar\nu$ is CP conserving and receives
contributions from
both internal top and charm exchanges.
The last year calculations
\cite{BB1,BB2,BB3} of next-to-leading QCD corrections to this decay
considerably reduced the theoretical uncertainty
due to the choice of the renormalization scales present in the
leading order expression \cite{DDG}.
Typically the uncertainty in $Br(\kpnn$) of $\pm 20\%$ in the
leading order is reduced to $\pm 5\%$.
The long distance contributions to
$K^+ \rightarrow \pi^+ \nu \bar{\nu}$ have been
considered in \cite{RS} and found to be very small: two to three
orders of magnitude smaller than the short distance contribution
at the level of the branching ratio.
$K^+\to\pi^+\nu\bar\nu$ is then the second best decay in the field
of rare decays. Compared to $\klpnn$ it receives additional uncertainties
due to $m_c$ and the related renormalization scale. Also its QCD scale
dependence is stronger. Explicit expressions can be found in
\cite{BB3,BB4}.
The main features of this decay are:
\begin{itemize}
\item Hadronic uncertainties below $1\%$
\item  $\Lambda_{\overline{MS}}$, $m_c$ and renormalization scales
 uncertainties at most $\pm (5-10)\%$.
\item Strong dependence on $m_t$ and $V_{cb}$ (or A).
\end{itemize}
\subsection{$B^o-\bar B^o$ Mixing}
Measurement of $B^o_d-\bar B^o_d$ mixing parametrized by $x_d$ together
with  $B^o_s-\bar B^o_s$ mixing parametrized by $x_s$ allows to
determine $R_t$:
%
\begin{equation}\label{107b}
R_t = \frac{1}{\sqrt{R_{ds}}} \sqrt{\frac{x_d}{x_s}} \frac{1}{\lambda}
\end{equation}
with $R_{d,s}$ summarizing SU(3)--flavour breaking effects.
Note that $m_t$ and $V_{cb}$ dependences have been eliminated this way
 and $R_{ds}$
contains much smaller theoretical
uncertainties than the hadronic matrix elements in $x_d$ and $x_s$
separately.
Provided $x_d/x_s$ has been accurately measured a determination
of $R_t$ within $\pm 10\%$ should be possible.
The main features of $x_d/x_s$ are:
\begin{itemize}
\item No $\Lambda_{\overline{MS}}$, $m_t$ and $V_{cb}$ dependence.
\item Hadronic uncertainty in SU(3)--flavour breaking effects of
      roughly $\pm 10\%$.
\end{itemize}
Because of the last feature, $x_d/x_s$ cannot fully compete in the clean
determination of CKM parameters with CP asymmetries in B-decays and
with $\klpnn$. Although $\kpnn$ has smaller hadronic uncertainties
than $x_d/x_s$, its dependence on $\Lambda_{\overline{MS}}$ and  $m_c$
puts it in the same class as $x_d/x_s$ \cite{AB94A}.
\section{$\sin (2\beta)$ from $K\to \pi\nu\bar\nu$}
It has been pointed out in \cite{BH} that
measurements of $Br(\kpn)$ and $Br(\klpn)$ could determine the
unitarity triangle completely provided $m_t$ and $V_{cb}$ are known.
In view of the strong dependence of these branching ratios on
$m_t$ and $V_{cb}$ this determination is not precise however \cite{BB4}.
On the other hand it has been noticed recently \cite{BB4} that the $m_t$ and
$V_{cb}$ dependences drop out in the evaluation of $\sin(2\beta)$.
Introducing the "reduced" branching ratios
\begin{equation}\label{19}
B_+={Br(\kpn)\o 4.64\cdot 10^{-11}}\qquad
B_L={Br(\klpn)\o 1.94\cdot 10^{-10}}
\end{equation}
one finds
\begin{equation}\label{22}
\sin (2\beta)=\frac{2 r_s(B_+, B_L)}{1+r^2_s(B_+, B_L)}
\end{equation}
where
\begin{equation}\label{21}
r_s(B_+, B_L)=
{\sqrt{(B_+-B_L)}-P_0(K^+)\o\sqrt{B_L}}
\end{equation}
so that $\sin (2\beta)$
does not depend on $m_t$ and $V_{cb}$.
Here $P_0(K^+)=0.40\pm0.09$ \cite{BB3,BB4} is a function of $m_c$ and
 $\Lambda_{\overline{MS}}$ and includes the residual uncertainty
due to the renormalization scale $\mu$.
Consequently $\kpnn$ and $\klpnn$ offer a
clean
determination of $\sin (2\beta)$ which can be confronted with
the one possible in $B^0\to\psi K_S$ discussed above.
Any difference in these two determinations
would signal new physics.
Choosing
$Br(\kpn)=(1.0\pm 0.1)\cdot 10^{-10}$ and
$Br(\klpn)=(2.5\pm 0.25)\cdot 10^{-11}$,
one finds \cite{BB4}
\begin{equation}\label{26}
\sin(2 \beta)=0.60\pm 0.06 \pm 0.03 \pm 0.02
\end{equation}
where the first error is "experimental", the second represents the
uncertainty in $m_c$ and  $\Lambda_{\overline{MS}}$ and the last
is due to the residual renormalization scale uncertainties. This
determination of $\sin(2\beta)$ is competitive with the one
expected at the B-factories at the beginning of the next decade.
\section{Precise Determinations of the CKM Matrix}
Using the first two finalists and $\lambda=0.2205\pm 0.0018$
\cite{LR}
it is possible to determine all the parameters
of the CKM matrix without any hadronic uncertainties
\cite{AB94}.
With $a\equiv \sin(2\alpha)$, $b\equiv \sin(2\beta)$
and $Br(K_L)\equiv Br(\klpnn)$
one determines $\varrho$, $\eta$
and $\vcb$ as follows \cite{AB94}:
\begin{equation}\label{5}
\bar\varrho = 1-\bar\eta r_{+}(b)\quad ,\quad
\bar\eta=\frac{r_{-}(a)+r_{+}(b)}{1+r_{+}^2(b)}
\end{equation}
\begin{equation}\label{9b}
\mid V_{cb}\mid=0.039\sqrt\frac{0.39}{\eta}
\left[ \frac{170 ~GeV}{m_t} \right]^{0.575}
\left[ \frac{Br(K_L)}{3\cdot 10^{-11}} \right]^{1/4}
\end{equation}
where
\begin{equation}\label{7}
r_{\pm}(z)=\frac{1}{z}(1\pm\sqrt{1-z^2})
\qquad
z=a,b
\end{equation}
We note that the weak dependence of $\mid V_{cb}\mid$ on $Br(\klpnn)$
allows to achieve high accuracy for this CKM element even when $Br(\klpnn)$
is not measured precisely.

As illustrative examples we consider in table 1 three scenarios.
The first four rows give the assumed input parameters and their
experimental errors. The remaining rows give the results for
selected parameters. Further results can be found in \cite{AB94}.
The accuracy in the scenario I should be achieved at B-factories,
HERA-B,
at KAMI and at KEK.
 Scenarios II and
III correspond to B-physics at Fermilab during the Main Injector
era and at LHC
respectively.
At that time an improved measurement of $Br(\klpnn)$ should be aimed for.
\begin{table}
\begin{center}
\begin{tabular}{|c||c||c|c|c|}\hline
& Central &$I$&$II$&$III$\\ \hline
$\sin(2\alpha)$ & $0.40$ &$\pm 0.08$ &$\pm 0.04$ & $\pm 0.02 $\\ \hline
$\sin(2\beta)$ & $0.70$ &$\pm 0.06$ &$\pm 0.02$ & $\pm 0.01 $\\ \hline
$m_t$ & $170$ &$\pm 5$ &$\pm 3$ & $\pm 3 $\\ \hline
$10^{11} Br(K_L)$ & $3$ &$\pm 0.30$ &$\pm 0.15$ & $\pm 0.15 $\\ \hline\hline
$\varrho$ &$0.072$ &$\pm 0.040$&$\pm 0.016$ &$\pm 0.008$\\ \hline
$\eta$ &$0.389$ &$\pm 0.044$ &$\pm 0.016$&$\pm 0.008$ \\ \hline
$\mid V_{ub}/V_{cb}\mid$ &$0.087$ &$\pm 0.010$ &$\pm 0.003$&$\pm 0.002$
 \\ \hline
$\mid V_{cb}\mid/10^{-3}$ &$39.2$ &$\pm 3.9$ &$\pm 1.7$&$\pm 1.3$\\ \hline
$\mid V_{td}\mid/10^{-3}$ &$8.7$ &$\pm 0.9$ &$\pm 0.4$ &$\pm 0.3$ \\
 \hline \hline
$\mid V_{cb}\mid/10^{-3}$ &$41.2$ &$\pm 4.3$ &$\pm 3.0$&$\pm 2.8$\\ \hline
$\mid V_{td}\mid/10^{-3}$ &$9.1$ &$\pm 0.9$ &$\pm 0.6$ &$\pm 0.6$ \\
 \hline
\end{tabular}
\end{center}
\centerline{}
\caption{Determinations of various parameters in scenarios I-III }
\end{table}
Table 1 shows very clearly the potential of CP asymmetries
in B-decays and of $\klpnn$ in the determination of CKM parameters.
It should be stressed that this high accuracy is not only achieved
because of our assumptions about future experimental errors in the
scenarios considered, but also because $\sin(2\alpha)$ is a
very sensitive function of $\varrho$ and $\eta$ \cite{BLO},
$Br(\klpnn)$
depends strongly on $\mid V_{cb}\mid$ and most importantly because
of the clean character of the quantities considered.

It is instructive to investigate whether the use of
$\kpnn$ instead of $\klpnn$ would also give interesting results for
$V_{cb}$ and $V_{td}$.
 We again consider scenarios I-III with
$Br(\kpnn)= (1.0\pm 0.1)\cdot 10^{-10}$ for the scenario I and
$Br(\kpnn)= (1.0\pm 0.05)\cdot 10^{-10}$ for scenarios II and III
in place of $Br(\klpnn)$ with all other input parameters unchanged.
An analytic formula for $\vcb$ can be found in \cite{AB94}.
The results for $\varrho$, $\eta$, and $\mid V_{ub}/V_{cb}\mid$
remain of course unchanged. In the last two rows of table 1 we show the
results for $\mid V_{cb} \mid$ and $\mid V_{td}\mid$ .
We observe that
due to the uncertainties present in the charm contribution to
$\kpnn$, which was absent in $\klpnn$, the determinations of
 $\mid V_{cb}\mid$ and  $\mid V_{td}\mid$  are less accurate.
 If the uncertainties due to the charm mass
and $\Lambda_{\overline{MS}}$ are removed one day this analysis
will be improved \cite{AB94}.

An alternative strategy is to use the measured value of $R_t$ instead
of $\sin(2\alpha)$. Then (\ref{5})
is replaced by
\begin{equation}\label{5a}
\bar\varrho = 1-\bar\eta r_{+}(b)\quad ,\quad
\bar\eta=\frac{R_t}{\sqrt{2}}\sqrt{b r_{-}(b)}
\end{equation}
The result of this exercise is shown in table 2. We observe that even
with rather optimistic assumptions on the accuracy of
$R_t$, this determination of
CKM parameters cannot fully compete with the previous one.
Again the last two rows give the results when $\klpnn$ is replaced
by $\kpnn$.
\begin{table}
\begin{center}
\begin{tabular}{|c||c||c|c|c|}\hline
& Central &$I$&$II$&$III$\\ \hline
$R_t$ & $1.00$ &$\pm 0.10$ &$\pm 0.05$ & $\pm 0.03 $\\ \hline
$\sin(2\beta)$ & $0.70$ &$\pm 0.06$ &$\pm 0.02$ & $\pm 0.01 $\\ \hline
$m_t$ & $170$ &$\pm 5$ &$\pm 3$ & $\pm 3 $\\ \hline
$10^{11} Br(K_L)$ & $3$ &$\pm 0.30$ &$\pm 0.15$ & $\pm 0.15 $\\ \hline\hline
$\varrho$ &$0.076$ &$\pm 0.111$&$\pm 0.053$ &$\pm 0.031$\\ \hline
$\eta$ &$0.388$ &$\pm 0.079$ &$\pm 0.033$&$\pm 0.019$ \\ \hline
$\mid V_{ub}/V_{cb}\mid$ &$0.087$ &$\pm 0.014$ &$\pm 0.005$&$\pm 0.003$
 \\ \hline
$\mid V_{cb}\mid/10^{-3}$ &$39.3$ &$\pm 5.7$ &$\pm 2.6$&$\pm 1.8$\\ \hline
$\mid V_{td}\mid/10^{-3}$ &$8.7$ &$\pm 1.2$ &$\pm 0.6$ &$\pm 0.4$ \\
 \hline \hline
$\mid V_{cb}\mid/10^{-3}$ &$41.3$ &$\pm 5.8$ &$\pm 3.7$&$\pm 3.3$\\ \hline
$\mid V_{td}\mid/10^{-3}$ &$9.1$ &$\pm 1.3$ &$\pm 0.8$ &$\pm 0.7$ \\
 \hline
\end{tabular}
\end{center}
\centerline{}
\caption{ As in table 1 but with $\sin(2\alpha)$ replaced by $R_t$.}
\end{table}
\section{Final Remarks}
\begin{itemize}
\item Precise measurements of all CKM parameters without hadronic
uncertainties are possible.
\item Such measurements are essential for the tests of the
standard model.
Of particular interest will be the comparison of $\mid V_{cb}\mid$
determined as suggested here with the value of this CKM element extracted
from tree level semi-leptonic  B-decays.
 Since in contrast to
$\klpnn$ and $\kpnn$, the tree-level decays are to an excellent approximation
insensitive to any new physics contributions from very high energy scales,
the comparison of these two determinations of $\mid V_{cb}\mid$ would
be a good test of the standard model and of a possible physics
beyond it.
\end{itemize}
Precise determinations of all CKM parameters without hadronic uncertainties
 along the lines presented
here can only be realized if the measurements of CP asymmetries in
B-decays and the measurements of $Br(\klpnn)$, $Br(\kpnn)$ and $x_d/x_s$
can reach the desired accuracy.
All efforts should be made to achieve this goal.

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\bibitem{LR}
H. Leutwyler and M. Roos, {\sl Zeitschr. f.  Physik} {\bf C25} (1984) 91;
J.F. Donoghue, B.R. Holstein and S.W. Klimt, {\sl Phys. Rev.} {\bf D 35}
 (1987) 934.
\bibitem{AB94}
A.J. Buras, {\sl Phys. Lett.} {\bf B 333} (1994) 476.

\end{thebibliography}
\end{document}

HERE STARTS: ICHEP.STY
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%                                                                      %%%
%%%    INSTITUTE OF PHYSICS PUBLISHING                                   %%%
%%%                                                                      %%%
%%%    ICHEP.STY  LaTeX CRC style file for ICHEP94 conference            %%%
%%%                                                                      %%%
%%%    Copyright 1994 IOP Publishing Ltd                                 %%%
%%%                                                                      %%%
%%%    Permission is hereby given to use this file for                   %%%
%%%    material to be submitted to or published by                       %%%
%%%    Institute of Physics Publishing                                   %%%
%%%                                                                      %%%
%%%    Version 1.2  1 July 1994                                          %%%
%%%                                                                      %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% First we have a character check
%
% ! exclamation mark    " double quote
% # hash                ` opening quote (grave)
% & ampersand           ' closing quote (acute)
% $ dollar              % percent
% ( open parenthesis    ) close paren.
% - hyphen              = equals sign
% | vertical bar        ~ tilde
% @ at sign             _ underscore
% { open curly brace    } close curly
% [ open square         ] close square bracket
% + plus sign           ; semi-colon
% * asterisk            : colon
% < open angle bracket  > close angle
% , comma               . full stop
% ? question mark       / forward slash
% \ backslash           ^ circumflex
%
% ABCDEFGHIJKLMNOPQRSTUVWXYZ
% abcdefghijklmnopqrstuvwxyz
% 1234567890
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\typeout{Document Style `ichep.sty'. IOP camera-ready copy
style file for ICHEP Conference Proceedings}

\let\reset@font\empty

\def\refname{References}
\def\figurename{Figure}
\def\tablename{Table}
\def\abstractname{Abstract}

\def\@ptsize{0}
\@namedef{ds@11pt}{\def\@ptsize{0}}
\@namedef{ds@12pt}{\def\@ptsize{0}}
\def\ds@twoside{\@twosidetrue
           \@mparswitchtrue}

\def\ds@draft{\overfullrule 5\p@}

\newif\if@titlepage \@titlepagefalse
\def\ds@titlepage{\@titlepagetrue}

\def\ds@twocolumn{\@twocolumntrue}

%
\newdimen\mathindent
\newlength{\digitwidth}
\newlength{\indentedwidth}
\newcounter{firstpage}
\newbox{\captionbox}
\newcounter{eqnval}
%
\@twosidetrue
%\@mparswitchtrue
\def\ds@draft{\overfullrule 5\p@}
\@options
%
\def\hexnumber@#1{\ifcase#1 0\or 1\or 2\or 3\or 4\or 5\or 6\or 7\or 8\or
 9\or A\or B\or C\or D\or E\or F\fi}
%
\lineskip 1pt \normallineskip 1pt
\def\baselinestretch{1}
\def\@normalsize{\@setsize\normalsize{12pt}\xpt\@xpt
\abovedisplayskip 10pt plus2pt minus5pt
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip \z@ plus3pt
\belowdisplayshortskip 6pt plus3pt minus3pt}
\def\small{\@setsize\small{11pt}\ixpt\@ixpt
\abovedisplayskip 8.5pt plus 3pt minus 4pt
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip \z@ plus2pt
\belowdisplayshortskip 4pt plus2pt minus 2pt
\def\@listi{\topsep 4pt plus 2pt minus 2pt\parsep 0pt plus 1pt
\itemsep \parsep}}
\def\footnotesize{\@setsize\footnotesize{9.5pt}\viiipt\@viiipt
\abovedisplayskip 6pt plus 2pt minus 4pt
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip \z@ plus 1pt
\belowdisplayshortskip 3pt plus 1pt minus 2pt
\def\@listi{\topsep 3pt plus 1pt minus 1pt\parsep 0pt plus 1pt
\itemsep \parsep}}
\def\scriptsize{\@setsize\scriptsize{8pt}\viipt\@viipt}
\def\tiny{\@setsize\tiny{6pt}\vpt\@vpt}
\def\large{\@setsize\large{14pt}\xiipt\@xiipt}
\def\Large{\@setsize\Large{18pt}\xivpt\@xivpt}
\def\LARGE{\@setsize\LARGE{22pt}\xviipt\@xviipt}
\def\huge{\@setsize\huge{25pt}\xxpt\@xxpt}
\def\Huge{\@setsize\Huge{30pt}\xxvpt\@xxvpt}
\normalsize
\oddsidemargin -3pc
\evensidemargin -3pc
\marginparwidth .75in
\marginparsep 7\p@
\topmargin=-72\p@
\headheight=12\p@
\headsep=12\p@
\footheight=12\p@
\footskip=25\p@

\textheight 55pc
\textwidth 18cm
\indentedwidth 15.9cm
\columnsep 1cm
\columnseprule 0\p@
\mathindent = 2pc

\newcommand{\onecol}{\parfillskip=0pt\par\eject
   \onecolumn\parfillskip=0pt plus1fil\noindent}
\newcommand{\twocol}{\parfillskip=0pt\par\eject
   \twocolumn\parfillskip=0pt plus1fil\noindent}
\footnotesep 6.65\p@
\skip\footins 9\p@ plus 4\p@ minus 2\p@
\floatsep 12\p@ plus 2\p@ minus 2\p@
\textfloatsep 18\p@ plus 2\p@ minus 4\p@
\intextsep 12\p@ plus 2\p@ minus 2\p@
\@maxsep 20\p@
\dblfloatsep 12\p@ plus 2\p@ minus 2\p@
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\@fpbot 0\p@ plus 1fil
\@dblfptop 0\p@
\@dblfpsep 8\p@ plus 1fil
\@dblfpbot 0\p@
\marginparpush 5\p@

\parskip 0\p@
\parindent 16\p@
\topsep 4\p@ plus 2\p@ minus 2\p@
\partopsep 2\p@ plus 1\p@ minus 1\p@
\itemsep 0\p@ plus 2\p@
\@lowpenalty 51
\@medpenalty 151
\@highpenalty 301
\@beginparpenalty -\@lowpenalty
\@endparpenalty -\@lowpenalty
\@itempenalty -\@lowpenalty

\@noskipsecfalse   % new version

%
\def\section{\@startsection{section}{1}{\z@}{-3.5ex plus -1ex minus
 -.2ex}{2.3ex plus .2ex}{\noindent\reset@font\normalsize\bf\raggedright}}
\def\subsection{\@startsection{subsection}{2}{\z@}{-3.25ex plus -1ex minus
 -.2ex}{1.5ex plus .2ex}{\noindent\reset@font
  \normalsize\it\raggedright\nohyphens}}
\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-3.25ex plus
-1ex minus -.2ex}{-1em}{\reset@font\normalsize\it\nohyphens}}
\def\paragraph{\@startsection
 {paragraph}{4}{\z@}{3.25ex plus 1ex minus .2ex}{-1em}
                                                {\reset@font\normalsize\it}}
\def\subparagraph{\@startsection
 {subparagraph}{4}{\parindent}{3.25ex plus 1ex minus
 .2ex}{-1em}{\reset@font\normalsize\it}}

\def\@sect#1#2#3#4#5#6[#7]#8{\ifnum #2>\c@secnumdepth
     \let\@svsec\@empty\else
     \refstepcounter{#1}\edef\@svsec{\csname the#1\endcsname.\hskip 1em}\fi
     \@tempskipa #5\relax
      \ifdim \@tempskipa>\z@
        \begingroup #6\relax
          \noindent{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par}%
        \endgroup
       \csname #1mark\endcsname{#7}\addcontentsline
         {toc}{#1}{\ifnum #2>\c@secnumdepth \else
                      \protect\numberline{\csname the#1\endcsname}\fi
                    #7}\else
        \def\@svsechd{#6\hskip #3\relax  %% \relax added 2 May 90
                   \@svsec #8\csname #1mark\endcsname
                      {#7}\addcontentsline
                           {toc}{#1}{\ifnum #2>\c@secnumdepth \else
                             \protect\numberline{\csname the#1\endcsname}\fi
                       #7}}\fi
     \@xsect{#5}}
%
\def\@ssect#1#2#3#4#5{\@tempskipa #3\relax
   \ifdim \@tempskipa>\z@
     \begingroup #4\noindent{\hskip #1}{\interlinepenalty \@M #5\par}\endgroup
   \else \def\@svsechd{#4\hskip #1\relax #5}\fi
    \@xsect{#3}}


\setcounter{secnumdepth}{3}

\def\appendix{\@@par
 \setcounter{section}{0}
 \setcounter{subsection}{0}
 \setcounter{subsubsection}{0}
 \setcounter{equation}{0}
 \setcounter{figure}{0}
 \setcounter{table}{0}
 \def\thesection{Appendix \Alph{section}}
 \def\theequation{\ifnumbysec
      \Alph{section}.\arabic{equation}\else
      \Alph{section}\arabic{equation}\fi}
 \def\thetable{\ifnumbysec
      \Alph{section}\arabic{table}\else
      A\arabic{table}\fi}
 \def\thefigure{\ifnumbysec
      \Alph{section}\arabic{figure}\else
      A\arabic{figure}\fi}}



\labelsep 4\p@

\leftmargini 16\p@
\leftmarginii 18\p@
\leftmarginiii 16\p@
\leftmarginiv 14\p@
\leftmarginv 10\p@
\leftmarginvi 10\p@
\leftmargin\leftmargini
\labelwidth\leftmargini\advance\labelwidth-\labelsep
\parsep 0\p@ plus 1\p@
\def\@listI{\leftmargin\leftmargini \parsep 4\p@ plus2\p@ minus\p@
\topsep 8\p@ plus2\p@ minus4\p@
\itemsep 4\p@ plus2\p@ minus\p@}

\let\@listi\@listI
\@listi

\def\@listii{\leftmargin\leftmarginii
 \labelwidth\leftmarginii\advance\labelwidth-\labelsep
 \topsep 3\p@ plus 1\p@ minus 1\p@
 \parsep 0\p@ plus 1\p@
 \itemsep \parsep}
\def\@listiii{\leftmargin\leftmarginiii
 \labelwidth\leftmarginiii\advance\labelwidth-\labelsep
 \topsep 2\p@ plus 1\p@ minus 1\p@
 \parsep \z@ \partopsep 1\p@ plus 0\p@ minus 1\p@
 \itemsep \topsep}
\def\@listiv{\leftmargin\leftmarginiv
 \labelwidth\leftmarginiv\advance\labelwidth-\labelsep}
\def\@listv{\leftmargin\leftmarginv
 \labelwidth\leftmarginv\advance\labelwidth-\labelsep}
\def\@listvi{\leftmargin\leftmarginvi
 \labelwidth\leftmarginvi\advance\labelwidth-\labelsep}

\pretolerance=5000
\tolerance=8000
\hbadness=5000
\vbadness=5000
%
\def\labelenumi{\theenumi}
\def\theenumi{\arabic{enumi}}
\def\labelenumii{\theenumii}
\def\theenumii{\alpha{enumii}}
\def\p@enumii{\theenumi.}
\def\labelenumiii{\theenumiii.}
\def\theenumiii{\arabic{enumiii}}
\def\p@enumiii{\p@enumii.\theenumii}
\def\labelenumiv{\theenumiv.}
\def\theenumiv{\arabic{enumiv}}
\def\p@enumiv{\p@enumiii.\theenumiii}

\def\labelitemi{$\m@th\bullet$}
\def\labelitemii{\bf --}
\def\labelitemiii{$\m@th\ast$}
\def\labelitemiv{$\m@th\cdot$}

\def\verse{\let\\=\@centercr
 \list{}{\itemsep\z@ \itemindent -1.5em\listparindent \itemindent
 \rightmargin\leftmargin\advance\leftmargin 1.5em}\item[]}
\let\endverse\endlist
\def\quotation{\list{}{\listparindent 1.5em
 \itemindent\listparindent
 \rightmargin\leftmargin\parsep 0\p@ plus 1\p@}\item[]}
\let\endquotation=\endlist
\def\quote{\list{}{\rightmargin\leftmargin}\item[]}
\let\endquote=\endlist

\def\descriptionlabel#1{\hspace\labelsep \bf #1}
\def\description{\list{}{\labelwidth\z@ \itemindent-\leftmargin
 \let\makelabel\descriptionlabel}}
\let\enddescription\endlist
%
\def\enumerate{\ifnum \@enumdepth >3 \@toodeep\else
      \advance\@enumdepth \@ne
      \edef\@enumctr{enum\romannumeral\the\@enumdepth}\list
      {\csname label\@enumctr\endcsname}{\usecounter
        {\@enumctr}\def\makelabel##1{##1\hss}}\fi}
%
\def\itemize{\ifnum \@itemdepth >3 \@toodeep\else \advance\@itemdepth \@ne
\edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%
\list{\csname\@itemitem\endcsname}{\def\makelabel##1{##1\hss}\topsep=3pt
  \parsep=0pt\listparindent=0pt\itemsep=0pt\partopsep=0pt\rightmargin=0pt
  }\fi}
%
\newenvironment{leqnarray}{\begin{leqnarray}}{\end{leqnarray}}
\def\leqnarray{\stepcounter{equation}\let\@currentlabel=\theequation
\global\@eqnswtrue
\global\@eqcnt\z@\tabskip\mathindent\let\\=\@eqncr
\abovedisplayskip\topsep\ifvmode\advance\abovedisplayskip\partopsep\fi
\belowdisplayskip\abovedisplayskip
\belowdisplayshortskip\abovedisplayskip
\abovedisplayshortskip\abovedisplayskip
$$\halign to
\columnwidth\bgroup\@eqnsel$\displaystyle\tabskip\z@
 {##{}}$&\global\@eqcnt\@ne
                    $\displaystyle{{}##{}}$\hfil    %\hfil delete before 2nd $
 &\global\@eqcnt\tw@ $\displaystyle{{}##}$\hfil
 \tabskip\@centering&\llap{##}\tabskip\z@\cr}
%
\def\endleqnarray{\@@eqncr\egroup
 \global\advance\c@equation\m@ne$$\global\@ignoretrue }
%
\arraycolsep 5\p@
\tabcolsep=6\p@
\arrayrulewidth .4\p@
\doublerulesep 2\p@
\tabbingsep \labelsep
\skip\@mpfootins = \skip\footins
\fboxsep = 3\p@
\fboxrule = .4\p@
\def\titlepage{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn
     \else \newpage \fi \thispagestyle{myheadings}\c@page\z@}

\def\endtitlepage{\if@restonecol\twocolumn \else \newpage \fi}

\newcounter {section}
\newcounter {subsection}[section]
\newcounter {subsubsection}[subsection]
\newcounter {paragraph}[subsubsection]
\newcounter {subparagraph}[paragraph]



\def\thesection {\arabic{section}}
\def\thesubsection {\thesection.\arabic{subsection}}
\def\thesubsubsection {\thesubsection .\arabic{subsubsection}}
\def\theparagraph {\thesubsubsection.\arabic{paragraph}}
\def\thesubparagraph {\theparagraph.\arabic{subparagraph}}
\def\@chapapp{Section}


\def\@pnumwidth{1.55em}
\def\@tocrmarg {2.55em}
\def\@dotsep{4.5}
\setcounter{tocdepth}{2}


\def\tableofcontents{\@restonecolfalse\if@twocolumn\@restonecoltrue
 \onecolumn\fi\section*{Contents}{}\thispagestyle{empty}
 \@starttoc{toc}\if@restonecol\twocolumn\fi}
%
\def\l@section{\@dottedtocline{1}{1.5em}{2.3em}}
\def\l@subsection{\@dottedtocline{2}{3.8em}{3.2em}}
\def\l@subsubsection{\@dottedtocline{3}{7.0em}{4.1em}}
\def\l@paragraph{\@dottedtocline{4}{10em}{5em}}
\def\l@subparagraph{\@dottedtocline{5}{12em}{6em}}
\def\listoffigures{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn
 \fi\section*{List of Figures\@mkboth
 {LIST OF FIGURES}{LIST OF FIGURES}}\@starttoc{lof}\if@restonecol\twocolumn
 \fi}
\def\l@figure{\@dottedtocline{1}{1.5em}{2.3em}}
\def\listoftables{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn
 \fi\section*{List of Tables\@mkboth
 {LIST OF TABLES}{LIST OF TABLES}}\@starttoc{lot}\if@restonecol\twocolumn
 \fi}
\let\l@table\l@figure
%
% Redefinition to remove dotted lines from \@dottedtocline
%
\def\@dottedtocline#1#2#3#4#5{\ifnum #1>\c@tocdepth \else
  \vskip \z@ plus .2\p@
  {\leftskip #2\relax \rightskip \@tocrmarg \parfillskip -\rightskip
    \parindent #2\relax\@afterindenttrue
   \interlinepenalty\@M
   \leavevmode
   \@tempdima #3\relax \advance\leftskip \@tempdima
   \hbox{}\hskip -\leftskip
    #4\nobreak\hfill \nobreak \hbox to\@pnumwidth{\hfil
   \rm #5}\@@par}\fi}

\def\footnoterule{}%
\setcounter{footnote}{0}
\@addtoreset{footnote}{page}
\long\def\@makefntext#1{\parindent 1em\noindent
 \makebox[1em][l]{\footnotesize\rm$\m@th{\fnsymbol{footnote}}$}%
 \footnotesize\rm #1}
\def\@makefnmark{\hbox{${\fnsymbol{footnote}}\m@th$}}
\def\@thefnmark{\fnsymbol{footnote}}
\def\footnote{\@ifnextchar[{\@xfootnote}{\stepcounter{\@mpfn}%
     \begingroup\let\protect\noexpand
       \xdef\@thefnmark{\thempfn}\endgroup
     \@footnotemark\@footnotetext}}
\def\@fnsymbol#1{\ifcase#1\or \dagger\or \ddagger\or \S\or
   \|\or \P\or ^{+}\or ^{\tsty *}\or \sharp
   \or \dagger\dagger \else\@ctrerr\fi\relax}
\newcommand\ftnote[1]{\setcounter{footnote}{#1}%
   \addtocounter{footnote}{-1}\footnote}
\newcommand{\fnm}[1]{\setcounter{footnote}{#1}\footnotetext}
%
\def\center{\trivlist\topsep=0\p@\partopsep=0\p@
   \parsep=0\p@\itemsep=0\p@\centering\item[]}
%
\newenvironment{indented}{\begin{indented}}{\end{indented}}
\def\indented{\list{}{\itemsep=0\p@\labelsep=0\p@\itemindent=0\p@
   \labelwidth=0\p@\leftmargin=1.5cm\rightmargin=1.5cm
   \topsep=0\p@\partopsep=0\p@
   \parsep=0\p@\listparindent=0\p@}\rm}

\let\endindented=\endlist
%
\def\catchline{\hfill}

\def\cpyrtline{\hfill}
%
\def\maketitle{\thispagestyle{myheadings}%
   \vspace*{1.8cm}
   \begin{center}\@title\end{center}
   \vspace*{1.1cm}
   \normalsize\rm
   \begin{center}\@author\end{center}
   \begin{center}\@address\end{center}
   \@collab
   \@abstract}
%
%  Title
%
\def\title#1{\def\@title{\exhyphenpenalty=10000\hyphenpenalty=10000
    \Large\bf#1\par}}
\def\shortitle#1{\def\@shorttitle{#1}}
\let\paper=\title
%
% Authors
%
\renewcommand{\author}[1]{\def\@author{{\large #1\par}}}
%
% Affiliation
%
\newcommand{\address}[1]{\def\@address{\rm #1\par}}
\let\affil=\address
%
\newcommand{\collab}[1]{\def\@collab{\begin{center}%
   {\large\rm #1}\par
   \end{center}}}
%
% Default
%
\def\@collab{}
%
% Abstract
%
\def\abstract#1{\def\@abstract{\begin{center}
{\bf\abstractname}\end{center}%
\begin{indented}
\item[]#1\par
\end{indented}
\vspace{2cm minus1cm}}}%
%
\def\endabstract{}
%
% Command for second and subsequent paragraphs in abstract
%
\def\cabs{\\\hspace*{16\p@}}
%
\def\nosections{\vspace{30\p@ plus12\p@ minus12\p@}
    \noindent\ignorespaces}
%
\def\ack{\ifletter\bigskip\noindent\ignorespaces\else
    \section*{Acknowledgments}\fi}
\def\ackn{\ifletter\bigskip\noindent\ignorespaces\else
    \section*{Acknowledgment}\fi}
%
\newif\ifnumbysec
\def\theequation{\ifnumbysec
      \arabic{section}.\arabic{equation}\else
      \arabic{equation}\fi}
\def\eqnobysec{\numbysectrue\@addtoreset{equation}{section}}
%
\def\eqalign#1{\null\vcenter{\def\\{\cr}\openup\jot\m@th
  \ialign{\strut\hfil$\displaystyle{##{}}$&$\displaystyle{{}##}$\hfil
      \crcr#1\crcr}}\,}
%
\def\eqalignno#1{\displ@y \tabskip\z@skip
  \halign to\if@twocolumn\columnwidth\else\displaywidth\fi
   {\hfil$\@lign\displaystyle{##}$%
    \tabskip\z@skip
    &$\@lign\displaystyle{{}##}$\hfill\tabskip\@centering
    &\llap{$\@lign\hbox{\rm##}$}\tabskip\z@skip\crcr
    #1\crcr}}
%
\def\numparts{\addtocounter{equation}{1}%
     \setcounter{eqnval}{\value{equation}}%
     \setcounter{equation}{0}%
     \def\theequation{\ifnumbysec
     \arabic{section}.\arabic{eqnval}{\it\alph{equation}}%
     \else\arabic{eqnval}{\it\alph{equation}}\fi}}

\def\endnumparts{\def\theequation{\ifnumbysec
     \arabic{section}.\arabic{equation}\else
     \arabic{equation}\fi}%
     \setcounter{equation}{\value{eqnval}}}
%
\def\cases#1{%
     \left\{\,\vcenter{\def\\{\cr}\normalbaselines\openup1\jot\m@th%
     \ialign{\strut$\displaystyle{##}\hfil$&\tqs
     \rm##\hfil\crcr#1\crcr}}\right.}%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  Floats
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  \c@topnumber            : Number of floats allowed at the top of a column.
%
\setcounter{topnumber}{4}
%
%  \topfraction            : Fraction of column that can be devoted to floats.
%
\def\topfraction{1}
%
%  \c@dbltopnumber, \dbltopfraction : Same as above, but for double-column
%                          floats.
%
\setcounter{dbltopnumber}{4}
\def\dbltopfraction{1}
%
%  \c@bottomnumber, \bottomfraction : Same as above for bottom of page.
%
\setcounter{bottomnumber}{2}
\def\bottomfraction{.8}
%
%  \c@totalnumber          : Number of floats allowed in a single column,
%                          including in-text floats.
%
\setcounter{totalnumber}{5}
%
%  \textfraction         : Minimum fraction of column that must contain text.
%
\def\textfraction{0}
%
%  \floatpagefraction    : Minimum fraction of page that must be taken
%                          up by float page.
%
\def\floatpagefraction{.8}
%
%  \dblfloatpagefraction : Same as above, for double-column floats.
%
\def\dblfloatpagefraction{.8}
%
\newcounter{figure}
\def\thefigure{\@arabic\c@figure}
\def\figure{\let\@makecaption\@makeonecolcaption\@float{figure}}
\let\endfigure\end@float
%
\@namedef{figure*}{\let\@makecaption\@makewidecaption
      \@dblfloat{figure}}
\@namedef{endfigure*}{\end@dblfloat}
%
\def\@makewidecaption#1#2{\vspace{10\p@}%
     \sbox{\captionbox}{\noindent\footnotesize\rm\raggedright{\bf #1.} #2}%
     \ifdim\wd\captionbox > \indentedwidth
     \begin{indented}
     \item[]\footnotesize\rm\raggedright{\bf #1.} #2\par
     \end{indented}%
     \else
     \hbox to \hsize{\hfil\box\captionbox\hfil}\fi}
%
\def\@makeonecolcaption#1#2{\vspace{10pt}%
     \parbox{\columnwidth}{\noindent
     \footnotesize\rm\raggedright{\bf #1.} #2}\par}
%
%
% The document style must define the following.
%
%    \fps@TYPE   : The default placement specifier for floats of type TYPE.
%
\def\fps@figure{tb}
\def\fps@table{tb}
%
%    \ftype@TYPE : The type number for floats of type TYPE.
%
\def\ftype@figure{1}
\def\ftype@table{2}
%
%    \ext@TYPE   : The file extension indicating the file on which the
%                  contents list for float type TYPE is stored.  For example,
%                  \ext@figure = 'lof'.
%
\def\ext@table{aux}
\def\ext@figure{aux}
%
%    \fnum@TYPE  : A macro to generate the figure number for a caption.
%                  For example, \fnum@TYPE == Figure \thefigure.
%
\def\fnum@table{\tablename~\thetable}
\def\fnum@figure{\figurename~\thefigure}
%
%    \@makecaption{NUM}{TEXT} : A macro to make a caption, with NUM the value
%                  produced by \fnum@... and TEXT the text of the caption.
%                  It can assume it's in a \parbox of the appropriate width.
%
\newcommand{\Figure}[2]{\def\figspace{\vspace*{#1}}%
    \def\figcap{\caption{#2}}%
    \futurelet\next\@figplace}
\def\@figplace{\ifx\next[\let\next=\@figpl
                 \else\let\next=\@fignopl\fi\next}
\def\@figpl[#1]{\begin{figure}[#1]
   \figspace
   \figcap
   \end{figure}}
\def\@fignopl{\begin{figure}
   \figspace
   \figcap
   \end{figure}}
%
\newcommand{\widefigure}[2]{\def\figspace{\vspace*{#1}}%
    \def\figcap{\caption{#2}}%
    \futurelet\next\@wfigplace}
\def\@wfigplace{\ifx\next[\let\next=\@wfigpl
                 \else\let\next=\@wfignopl\fi\next}
\def\@wfigpl[#1]{\begin{figure*}[#1]
   \figspace
   \figcap
   \end{figure*}}
\def\@wfignopl{\begin{figure*}
   \figspace
   \figcap
   \end{figure*}}
%
% \@float{TYPE}[PLACEMENT] : This macro begins a float environment for a
%     single-column float of type TYPE with PLACEMENT as the placement
%     specifier.  The default value of PLACEMENT is defined by \fps@TYPE.
%     The environment is ended by \end@float.
%     E.g., \figure == \@float{figure}, \endfigure == \end@float.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  Tables
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newcounter{table}
%
\def\thetable{\@arabic\c@table}
\def\table{\let\@makecaption\@makeonecolcaption
    \footnotesize\rm\@float{table}}
\let\endtable\end@float
%
\@namedef{table*}{\let\@makecaption\@makewidecaption
   \footnotesize\rm
   \@dblfloat{table}}
\@namedef{endtable*}{\end@dblfloat}
%
\def\tabular{\def\@halignto{}\@tabular}
\def\endtabular{\crcr\egroup\egroup $\egroup}
\expandafter \let \csname endtabular*\endcsname = \endtabular
%
\newsavebox{\tablebox}
%
\newcommand{\Table}[2]{\begin{center}
    \lineup
    \begin{tabular}{#1}%
    \hline
    #2
    \hline
    \end{tabular}
    \end{center}}
%
\newcommand{\tabnote}[1]{\begin{indented}
     \item[]\footnotesize\rm\raggedright #1\par
     \end{indented}}
%
% Definitions for centring headings over several columns
% \centre{4}{Results for helium} will centre
% Results for helium over four columns
% \crule{4} will produce a rule centred over four columns
% to go below a centred heading
%
\newcommand{\centre}[2]{\multicolumn{#1}{c}{#2}}
\newcommand{\crule}[1]{\multispan{#1}{\hrulefill}}
%
\def\lineup{\def\0{\hbox{\phantom{\footnotesize\rm 0}}}%
    \def\m{\hbox{$\phantom{-}$}}%
    \def\-{\llap{$-$}}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% References
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newcommand{\Bibliography}[1]{\section*{References}\par\numrefs{#1}}
\newcommand{\References}[1]{\section*{References}\footnotesize\rm}
%
\def\thebibliography#1{\list
 {\hfil[\arabic{enumi}]}{\topsep=0\p@\parsep=0\p@
 \partopsep=0\p@\itemsep=0\p@
 \labelsep=5\p@\itemindent=0\p@                %-10
 \settowidth\labelwidth{\footnotesize[#1]}%
 \leftmargin\labelwidth
 \advance\leftmargin\labelsep
% \advance\leftmargin -\itemindent
 \usecounter{enumi}}%
 \def\newblock{\ }
 \sloppy\clubpenalty4000\widowpenalty4000
 \sfcode`\.=1000\footnotesize\rm\relax}
\let\endthebibliography=\endlist
%
\def\numrefs#1{\begin{thebibliography}{#1}}
\def\endnumrefs{\end{thebibliography}}
\let\endbib=\endnumrefs

\mark{{}{}}

\def\ps@headings{\let\@mkboth\markboth
 \def\@oddfoot{}%
 \def\@evenfoot{}%
 \def\@evenhead{\makebox[\mathindent][l]{\normalsize\rm \thepage}%
  \normalsize\it\rightmark\hfill}%
 \def\@oddhead{\makebox[\mathindent][r]{\hfill}{\normalsize\it\leftmark}\hfill
  \normalsize\rm\thepage}%
}%

\def\ps@myheadings{\let\@mkboth\markboth
 \def\@oddhead{\catchline}%
 \def\@oddfoot{\cpyrtline}%
 \def\@evenhead{}%
 \def\@evenfoot{}%
}


\def\today{\ifcase\month\or
 January\or February\or March\or April\or May\or June\or
 July\or August\or September\or October\or November\or December\fi
 \space\number\day, \number\year}

\def\@begintheorem#1#2{\rm \trivlist \item[\hskip \labelsep{\it #1\ #2.}]}
\def\@opargbegintheorem#1#2#3{\rm \trivlist
      \item[\hskip \labelsep{\it #1\ #2\ (#3).}]}

\let\scap=\sc
\renewcommand{\sc}{\protect\scriptsize}
\newcommand{\itsc}{\protect\scriptsize\it}
\newcommand{\bfsc}{\protect\scriptsize\bf}
\def\p@LaTeX{{L\kern-.3em\lower.1em\hbox{$^{\rm A}$}\kern-.15em%
    T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}}
%
\newcommand{\nohyphens}{\hyphenpenalty=10000\exhyphenpenalty=10000}
\newcommand{\fl}{\hspace*{-\mathindent}}
\newcommand{\Tr}{\mathop{\rm Tr}\nolimits}
\newcommand{\tr}{\mathop{\rm tr}\nolimits}
\newcommand{\Or}{\mathop{\rm O}\nolimits}
\newcommand{\lshad}{[\![}
\newcommand{\rshad}{]\!]}
\newcommand{\case}[2]{{\textstyle\frac{#1}{#2}}}
\def\pt(#1){({\it #1\/})}
\newcommand{\dsty}{\displaystyle}
\newcommand{\tsty}{\textstyle}
\newcommand{\ssty}{\scriptstyle}
\newcommand{\sssty}{\scriptscriptstyle}
\def\lo#1{\llap{${}#1{}$}}
\def\eql{\llap{${}={}$}}
\def\lsim{\llap{${}\sim{}$}}
\def\lsimeq{\llap{${}\simeq{}$}}
\def\lequiv{\llap{${}\equiv{}$}}
%
\def\;{\protect\psemicolon}
\def\psemicolon{\relax\ifmmode\mskip\thickmuskip\else\kern .3333em\fi}
%
\newcommand{\eref}[1]{(\ref{#1})}
\newcommand{\sref}[1]{section~\ref{#1}}
\newcommand{\fref}[1]{figure~\ref{#1}}
\newcommand{\tref}[1]{table~\ref{#1}}
\newcommand{\Eref}[1]{Equation~(\ref{#1})}
\newcommand{\Sref}[1]{Section~\ref{#1}}
\newcommand{\Fref}[1]{Figure~\ref{#1}}
\newcommand{\Tref}[1]{Table~\ref{#1}}

\newcommand{\opencirc}{\raisebox{2\p@}{\;\circle{5}}}
\newcommand{\opensqr}{\mbox{$\Box$}}
\newcommand{\fullcirc}{\raisebox{-2\p@}{\Large$\bullet$}}
\newcommand{\fullsqr}{\mbox{\vrule height6pt width6pt}}
\newcommand{\dotted}
                 {\mbox{${\mathinner{\cdotp\cdotp\cdotp\cdotp\cdotp\cdotp}}$}}
\newcommand{\dashed}{\mbox{-\; -\; -\; -}}
\newcommand{\broken}{\mbox{-- -- --}}
\newcommand{\longbroken}{\mbox{--- --- ---}}
\newcommand{\chain}{\mbox{--- $\cdot$ ---}}
\newcommand{\dashddot}{\mbox{--- $\cdot$ $\cdot$ ---}}
\newcommand{\full}{\mbox{------}}
%
\newcommand{\etal}{{\it et al\/}\ }
\newcommand{\nonum}{\item[]}
%
% abbreviations for IOPP journals
%
\newcommand{\CQG}{{\em Class. Quantum Grav.} }
\newcommand{\HPP}{{\em High Perform. Polym.} }              % added 4/5/93
\newcommand{\IP}{{\em Inverse Problems\/} }
\newcommand{\JHM}{{\em J. Hard Mater.} }                    % added 4/5/93
\newcommand{\JPA}{{\em J. Phys. A: Math. Gen.} }
\newcommand{\JPB}{{\em J. Phys. B: At. Mol. Phys.} }      %1968-87
\newcommand{\jpb}{{\em J. Phys. B: At. Mol. Opt. Phys.} } %1988 and onwards
\newcommand{\JPC}{{\em J. Phys. C: Solid State Phys.} }   %1968--1988
\newcommand{\JPCM}{{\em J. Phys.: Condens. Matter\/} }    %1989 and onwards
\newcommand{\JPD}{{\em J. Phys. D: Appl. Phys.} }
\newcommand{\JPE}{{\em J. Phys. E: Sci. Instrum.} }
\newcommand{\JPF}{{\em J. Phys. F: Met. Phys.} }
\newcommand{\JPG}{{\em J. Phys. G: Nucl. Phys.} }         %1975--1988
\newcommand{\jpg}{{\em J. Phys. G: Nucl. Part. Phys.} }   %1989 and onwards
\newcommand{\MSMSE}{{\em Modelling Simulation Mater. Sci. Eng.} }
\newcommand{\MST}{{\em Meas. Sci. Technol.} }              %1990 and onwards
\newcommand{\NET}{{\em Network\/} }
\newcommand{\NL}{{\em Nonlinearity\/} }
\newcommand{\NT}{{\em Nanotechnology} }
\newcommand{\PAO}{{\em Pure Appl. Optics\/} }
\newcommand{\PM}{{\em Physiol. Meas.} }                        % added 4/5/93
\newcommand{\PMB}{{\em Phys. Med. Biol.} }
\newcommand{\PPCF}{{\em Plasma Phys. Control. Fusion\/} }      % added 4/5/93
\newcommand{\PSST}{{\em Plasma Sources Sci. Technol.} }
\newcommand{\QO}{{\em Quantum Opt.} }
\newcommand{\RPP}{{\em Rep. Prog. Phys.} }
\newcommand{\SLC}{{\em Sov. Lightwave Commun.} }               % added 4/5/93
\newcommand{\SST}{{\em Semicond. Sci. Technol.} }
\newcommand{\SUST}{{\em Supercond. Sci. Technol.} }
\newcommand{\WRM}{{\em Waves Random Media\/} }
%
% Other commonly quoted journals
%
\newcommand{\AC}{{\em Acta Crystallogr.} }
\newcommand{\AM}{{\em Acta Metall.} }
\newcommand{\AP}{{\em Ann. Phys., Lpz.} }
\newcommand{\APNY}{{\em Ann. Phys., NY\/} }
\newcommand{\APP}{{\em Ann. Phys., Paris\/} }
\newcommand{\CJP}{{\em Can. J. Phys.} }
\newcommand{\JAP}{{\em J. Appl. Phys.} }
\newcommand{\JCP}{{\em J. Chem. Phys.} }
\newcommand{\JJAP}{{\em Japan. J. Appl. Phys.} }
\newcommand{\JP}{{\em J. Physique\/} }
\newcommand{\JPhCh}{{\em J. Phys. Chem.} }
\newcommand{\JMMM}{{\em J. Magn. Magn. Mater.} }
\newcommand{\JMP}{{\em J. Math. Phys.} }
\newcommand{\JOSA}{{\em J. Opt. Soc. Am.} }
\newcommand{\JPSJ}{{\em J. Phys. Soc. Japan\/} }
\newcommand{\JQSRT}{{\em J. Quant. Spectrosc. Radiat. Transfer\/} }
\newcommand{\NC}{{\em Nuovo Cimento\/} }
\newcommand{\NIM}{{\em Nucl. Instrum. Methods\/} }
\newcommand{\NP}{{\em Nucl. Phys.} }
\newcommand{\PL}{{\em Phys. Lett.} }
\newcommand{\PR}{{\em Phys. Rev.} }
\newcommand{\PRL}{{\em Phys. Rev. Lett.} }
\newcommand{\PRS}{{\em Proc. R. Soc.} }
\newcommand{\PS}{{\em Phys. Scr.} }
\newcommand{\PSS}{{\em Phys. Status Solidi\/} }
\newcommand{\PTRS}{{\em Phil. Trans. R. Soc.} }
\newcommand{\RMP}{{\em Rev. Mod. Phys.} }
\newcommand{\RSI}{{\em Rev. Sci. Instrum.} }
\newcommand{\SSC}{{\em Solid State Commun.} }
\newcommand{\ZP}{{\em Z. Phys.} }
%

\def\ap#1#2#3 {Ann. Phys. (NY) {\bf#1} (19#2) #3}
\def\apj#1#2#3 {Astrophys. J. {\bf#1} (19#2) #3}
\def\apjl#1#2#3 {Astrophys. J. Lett. {\bf#1} (19#2) #3}
\def\app#1#2#3 {Acta. Phys. Pol. {\bf#1} (19#2) #3}
\def\ar#1#2#3 {Ann. Rev. Nucl. Part. Sci. {\bf#1} (19#2) #3}
\def\cpc#1#2#3 {Computer Phys. Comm. {\bf#1} (19#2) #3}
\def\err#1#2#3 {{\it Erratum} {\bf#1} (19#2) #3}
\def\ib#1#2#3 {{\it ibid.} {\bf#1} (19#2) #3}
\def\jmp#1#2#3 {J. Math. Phys. {\bf#1} (19#2) #3}
\def\ijmp#1#2#3 {Int. J. Mod. Phys. {\bf#1} (19#2) #3}
\def\jetp#1#2#3 {JETP Lett. {\bf#1} (19#2) #3}
\def\jpg#1#2#3 {J. Phys. G. {\bf#1} (19#2) #3}
\def\mpl#1#2#3 {Mod. Phys. Lett. {\bf#1} (19#2) #3}
\def\nat#1#2#3 {Nature (London) {\bf#1} (19#2) #3}
\def\nc#1#2#3 {Nuovo Cim. {\bf#1} (19#2) #3}
\def\nim#1#2#3 {Nucl. Instr. Meth. {\bf#1} (19#2) #3}
\def\np#1#2#3 {Nucl. Phys. {\bf#1} (19#2) #3}
\def\pcps#1#2#3 {Proc. Cam. Phil. Soc. {\bf#1} (#2) #3}
\def\pl#1#2#3 {Phys. Lett. {\bf#1} (19#2) #3}
\def\prep#1#2#3 {Phys. Rep. {\bf#1} (19#2) #3}
\def\prev#1#2#3 {Phys. Rev. {\bf#1} (19#2) #3}
\def\prl#1#2#3 {Phys. Rev. Lett. {\bf#1} (19#2) #3}
\def\prs#1#2#3 {Proc. Roy. Soc. {\bf#1} (19#2) #3}
\def\ptp#1#2#3 {Prog. Th. Phys. {\bf#1} (19#2) #3}
\def\ps#1#2#3 {Physica Scripta {\bf#1} (19#2) #3}
\def\rmp#1#2#3 {Rev. Mod. Phys. {\bf#1} (19#2) #3}
\def\rpp#1#2#3 {Rep. Prog. Phys. {\bf#1} (19#2) #3}
\def\sjnp#1#2#3 {Sov. J. Nucl. Phys. {\bf#1} (19#2) #3}
\def\spj#1#2#3 {Sov. Phys. JEPT {\bf#1} (19#2) #3}
\def\spu#1#2#3 {Sov. Phys.-Usp. {\bf#1} (19#2) #3}
\def\zp#1#2#3 {Zeit. Phys. {\bf#1} (19#2) #3}
%
\ps@headings \pagenumbering{arabic} \onecolumn


