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\pagestyle{empty}
\begin{titlepage}

\noindent
\begin{center}
\begin{small}
\begin{tabular}{llrr}
Submitted to & & &
\epsfig{file=/h1/www/images/H1logo_bw_small.epsi
,width=2.cm} \\[.2em] \hline
\multicolumn{4}{l}{{\bf
                32nd International Conference 
                on High Energy Physics, ICHEP04},
                August~16,~2004,~Beijing} \\
                 & Abstract:        & {\bf 12-0185}    &\\
                 & Parallel Session & {\bf 12}   &\\ \hline
 & \multicolumn{3}{r}{\footnotesize {\it
    www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
\end{tabular}
\end{small}
\end{center}
\vspace*{2cm}

\begin{center}
  \Large
  {\bf 
    A Direct Search for Magnetic Monopoles at HERA}

  \vspace*{1cm}
    {\Large H1 Collaboration} 
\end{center}

\begin{abstract}

\noindent


A direct search has been made for magnetic monopoles produced in 
$e^+p$ collisions at a centre of mass energy of 300 GeV at HERA.  
The beam pipe surrounding the interaction region during 1995-1997 
(integrated luminosity 60 pb$^{-1}$) was investigated 
using a SQUID magnetometer to look for stopped magnetic monopoles. 
No free magnetic charges were observed and charge-dependent upper limits 
on the cross section for the electro-production of magnetic monopoles have 
been set.


\end{abstract}

\end{titlepage}
%
\pagestyle{plain}

\section{Introduction}
\label{Vacuo}

One of the outstanding issues in modern physics is the possible 
existence of magnetic monopoles. Dirac showed that only one magnetic 
monopole is needed anywhere in the universe to explain the empirical 
fact of electric charge quantisation\cite{dirac}. Magnetic monopoles 
are also predicted from field theories which unify the fundamental 
forces\cite{gut1,gut2,mtheory1,mtheory2}. Furthermore,  the formation of 
a monopole condensate provides a possible mechanism for quark 
confinement\cite{confine}.  Nevertheless, despite a large number of 
searches\cite{searchgen} using a variety of experimental 
techniques no reproducible evidence has been found to support the 
existence of  monopoles. Recent searches for monopoles produced in 
high energy particle collisions have been made with 
$p\bar{p}$\cite{D01,D02,ppd0} and $e^+e^-$\cite{ee1,ee2,ee3,ee4,ee5,eegam}
interactions. 
This paper describes the first search for monopoles produced in high 
energy $e^+p$ scattering at HERA. 

The quantisation of the angular momentum of a system of an electron with 
electric charge $e$ and a monopole with magnetic charge $g$ leads to 
Dirac's celebrated charge quantisation condition $eg=n{h}c/4\pi$, where 
$h$ is Planck's constant, $c$ is the speed of light and $n$ is an 
integer\cite{dirac}. Within this approach, taking $n=1$ sets the 
theoretical minimum magnetic charge which can be possessed by a 
particle (known as the Dirac charge $g_d$). However, if the elementary 
electric charge is considered to be held by the down quark then the minimum 
value of $g_d$ will be three times larger. The value of $g_d$ could be 
even higher since the application of the Dirac argument to a particle 
possessing both electric and magnetic charge (a so-called 
dyon\cite{schwinger,othersw}) restricts the values of $n$ to be 
even\cite{schwinger}.

Monopoles are also features of current unification theories such as 
M-theory\cite{mtheory1,mtheory2} and Supersymmetric Grand Unified 
Theories\cite{gut1,gut2}. Both of these approaches tend to predict 
superheavy primordial monopoles with mass values in excess of $10^{15}$ 
GeV.  However, in some Grand Unified scenarios values of monopole mass 
as low as $10^4$ GeV\cite{so103,so101,so102} are allowed. Light 
monopoles are also predicted in other 
approaches\cite{other0,other1,other2,other3} and postulates on values of 
the classical radius of a monopole lead to estimates of mass of $\cal O$(10) 
GeV\cite{search2}.  

Since the value of the coupling constant of a photon to a monopole 
($\alpha_m \approx 34n^2$) is substantially larger than for a 
photon-electron interaction ($\alpha_e \approx 1/137$) perturbative 
field theory cannot be reliably used to calculate the rates of monopole 
processes.  The large coupling also implies that ionisation energy losses 
will be typically several orders of magnitude greater for monopoles than 
for minimum ionising electrically charged particles\cite{ahlen1,ahlen,ahlen2}.

Direct experimental searches using a variety of tracking devices to detect 
the passage of highly ionising particles with monopole properties have 
been made\cite{searchgen}. Monopoles which stop in matter such as material 
at accelerators\cite{D02} and lunar rock\cite{lunar1,lunar2,lunar3} and 
monopoles 
in 
cosmic 
rays\cite{cabrera} have been sought via the induction of a persistent 
current within a superconducting loop\cite{lunar1, griffiths}, the method 
adopted here. Measurements of 
multi-photon production\cite{ppd0,eegam} allow indirect searches to be
made. However, the inapplicability of perturbative field theory
renders these limits unreliable\cite{dracula,kimc}. 

%This paper describes a direct search for monopoles produced in 
%$e^+p$ collisions which become trapped in material surrounding the 
%H1 detector. The search is sensitive to monopoles with values of mass 
%up to 320 GeV and is based on an integrated luminosity of 62pb$^{-1}$. A 
%SQUID magnetometer\cite{SQUID} has been used to provide a sensitivity to  
%magnetic monopoles of charge $g>0.2g_d$. 

%Magnetic monopoles are thought to exist. Dirac \cite{dirac} showed from an
%argument linking electromagnetism and quantum mechanics 
%that a magnetic monopole of a strength 
%\begin{equation}
% g = n/2 e = 3.3~10^{-9} \textrm{n~amp-metre} 
%\label{Dirac}
%\end{equation}
%(where n is an integer) should exist. The existence of a monopole would then 
%lead to an explanation of the quantisation of 
%electric charge.  Further consideration by Schwinger \cite{schwinger}
%suggests that n is at least 2. 
%Magnetic monopoles are also firmly predicted in many 
%gauge theories but their masses are unknown. In consequence each time 
%a new energy region is entered in Particle Physics a search for 
%magnetic monopoles is usually made \cite{PDG}. We report here the first 
%direct search made in Deep Inelastic Scattering (DIS). Many 
%indirect searches have been made for magnetic monopoles \cite{PDG} in 
%other channels. These all suffer from the problem that it is usually 
%impossible to compute cross sections for Feynman graphs involving 
%monopoles since the coupling constants involved are so large that 
%perturbation theory is inapplicable. The coupling constant for electric 
%charges $\alpha_e = e^2 = 1/137$ whereas that for a magnetic 
%charge is $\alpha_g = g^2 = n^2/e^2 =137 n^2/4 =34 n^2$.   

For the direct search reported here we use the fact that heavily ionising 
magnetic monopoles produced in $e^+p$ collisions may stop in the beam 
pipe surrounding the H1 interaction point at HERA. The binding energy of 
monopoles in the material is expected to be large \cite{kimc} and so they 
should remain permanently trapped providing they are stable. The beam pipe 
has been measured using a SQUID magnetometer with a sensitivity of
$0.2g_d$ after a single traversal of a sample to look for the 
persistent currents from such trapped monopoles.

\section{The Experimental Method}

A section of the aluminium beam pipe used in 1996-1998 of length 58 cm 
centred on the interaction point was cut into 15 longitudinal strips. 
%Two of these were cut into 37 small samples of 
%a few cm$^2$ area each.  
The strips were passed through the 2G Enterprises type 760 magnetometer 
\cite{2G} at the Southampton Oceanography Centre. This is a warm bore 
device with high sensitivity and low noise level. The strips were passed 
axially once through the magnetometer in steps, pausing for 1 second 
after each step, to look for a persistent change in current in the coil 
oriented perpendicular to the direction of the traversal. Such a change 
in the final current would be induced by the passage of a monopole 
whereas dipole 
impurities cause a current which returns to zero after the traversal of 
the strip. The reading for each strip was repeated several times. This 
allowed the reproducibility of the results to be studied so that random 
flux jumps and base line drifts could be identified. Any real monopole 
in the pipe would give a consistent and reproducible current step.  

  A long ($0.7$ m length) solenoid was used to assess the sensitivity 
of the SQUID Magnetometer to a monopole.  
The magnetic field outside of the ends of a long solenoid is similar to
that produced by a monopole. A solenoid can thus be considered as
possessing two oppositely charged ``pseudopoles'' of pole strength 
$g_d = n i S/3.3~10^{-9}$ in units of the Dirac charge. Here $n$ 
is the number of turns per metre length, $i$ is the current 
and $S$ is the cross sectional area of the coil and the factor 
$3.3~10^{-9}$ Am is the Dirac charge. Hence the current and radius of 
the solenoid can be chosen to mimic the desired pole
strength.\footnote{A study integrating the Biot
Savart Law for the magnetic field outside the dimensions of the magnetometer 
coil shows that this simple formula is accurate to $\sim \pm 3\%$.} 
To calibrate the solenoid was stepped through the magnetometer. Data
were taken with different currents subtracting the measurements with 
zero current to correct for the dipole impurities in it. The measured
increase in current in the magnetometer following
the passage of one end of the solenoid is shown in Fig. \ref{calib} as a
function of pseudopole strength (in units of $g_d$). 


To simulate trapped monopole behaviour the long calibration solenoid 
was placed along a strip and passed through the magnetometer. 
Only one end of the calibration solenoid was allowed to traverse the 
magnetometer hence simulating the passage of a monopole in the strip. 
Fig. \ref{dummy} shows the absolute value of the measured 
magnetometer current as the strip alone was stepped through and when 
pseudopoles of values $g_d$ and $-g_d$ were attached.  The large
structure at the centre comes from the dipole impurities in the aluminium. 
The final persistent magnetometer current is consistent with the value 
expected (shown as the the dashed lines). Shown inset, on a linear scale,
is the value of the measured current as the strip leaves 
the magnetometer pickup coil. The values of current for $g_d$ and $-g_d$
pseudopoles are approximately equal and opposite and at the value expected
from the calibration performed purely with the solenoid. The  
deviations are due to small dipole impurities in the former of the 
copper coil. 
 
Fig. \ref{dummy} illustrates 
that if a monopole of strength greater than a fraction of a Dirac monopole 
had been trapped by the beam pipe its persistent current would have been seen. 

\section{Results}

The data were taken in two separate runs. In the first run 13 of the strips 
were passed through the magnetometer once for each strip. Two of the strips 
showed persistent currents of a value expected from the passage of a magnetic 
charge of strength 1 $g_d$ each with a sign equivalent to a North seeking
pole 
i.e. one that is accelerated in the $+z$ direction by the H1 magnetic field 
of 1.15 Tesla. The strips were then remeasured several times during a 
second run. In this run none of the strips showed any persistent current 
after traversal through the magnetometer. It was therefore assumed that the 
two observed persistent currents during the first run had been caused by 
random flux jumps (which occurred during about 10$\%$ of the readings). 
The binding energy of monopoles in solids is thought to be hundreds of 
kilovolts \cite{kimc} compared to those of atoms which are at the eV level. 
Nevertheless the strips were carefully stored between the two runs to avoid 
dislodging any monopole present. They had also been carefully stored and 
not been subject to heat or strong magnetising or demagnetising fields 
after removal from the H1 apparatus. 

Fig \ref{overview} shows a summary of all the readings from the second 
run. The values of the monopole strength on 
the vertical axis were computed by taking the difference between the 
first reading as the moving table entered the magnetometer (before the 
strip entered) and the last reading which came 40 cm after the strip 
left the magnetometer coil. Strips 1 and 3 show 
some activity in one reading each, at the level of 0.2 $g_d$. This 
activity was compatible with zero on all other passes and it was 
compatible with zero if the penultimate reading is used for the exit 
current rather than the last reading. It is concluded therefore that 
this reading is spurious possibly caused by something such as a speck 
of dust falling on the table. The overall root mean square 
deviation of the readings was 0.07 $g_d$ (shown as the dashed lines in 
Fig. \ref{overview}). This illustrates the remarkable improvements 
in SQUID technology since previous measurements using this technique 
(e.g. see \cite{lunar1,lunar2,lunar3}) where many traversals were needed
to 
achieve noise levels approaching this value compared to the single
traverals reported here. 

It is concluded therefore that no consistently repeatable monopole 
signal was seen in any of the beam pipe strips examined. From Fig. 
\ref{overview} it can be seen that the magnetometer was sensitive to 
monopole strengths above about 0.2 $g_d$. 


\section{Upper Limits on the measured Cross Sections}

To derive an upper limit on the measured cross section it is necessary 
to compute the acceptance, i.e. the fraction of the monopoles produced 
which would have been detected. A model of the production process is 
therefore needed. A simple model was used here to compute the  
acceptance by Monte Carlo technique. This model assumed that a 
monopole($M$)-antimonopole ($\bar M$) pair are produced by the 
photoproduction process $\gamma p \rightarrow M \bar M p $  
through a $\gamma - \gamma$ interaction with a photon radiated from 
each of the electron and proton. The model depends on perturbation
theory to compute the cross sections which are therefore unreliable as 
noted previously. However, it is assumed that computations of the
acceptance will be roughly correct since these mainly depend on 
the kinematics. 
Events were generated according to this model using the programme 
CompHep \cite{CompHep} and the final 
state particles tracked through the H1 magnetic field (B=1.15 Tesla)
and the beam pipe to determine the fraction of the monopoles which stop.

  Monopoles have a parabolic trajectory in a magnetic field of the form
\begin{equation}
z-z_v = 0.5 \frac{gB r^2}{e p_T \beta_T} + \frac{r}{\tan\theta_0} 
\end{equation}
where $z_v$ is the z coordinate of the vertex and $z$ 
is the coordinate of a point on the trajectory at distance $r$ from the 
proton beam (taken to define the $+z$ axis). The transverse momentum 
and tranverse velocity of the monopole are $p_T$ and $\beta_T$, 
respectively. The electric charge is $e$ and $\theta_0$ is the
initial angle of the monopole to the proton beam direction.  
In this equation $g$ is negative(positive) for South(North) poles 
which decelerate (accelerate) in the $+z$ direction in the H1 magnetic field.
The geometric acceptance is the fraction of the monopoles which traverse 
the beam pipe in the cut length. The total acceptance is this fraction 
times the fraction which stop in the pipe. The range of 
monopoles in aluminium was computed by 
integrating the stopping power, $dE/dx$, given in 
\cite{ahlen} adjusted for the electron density in aluminium. 
Fig. \ref{RErel} shows the computed range (normalised to mass) for
monopoles of strength 
1 $g_d$ versus $p/m=\beta \gamma$ where $p$ and $m$ are the momentum and 
mass of the monopole, respectively, and $\beta,\gamma$ are its velocity 
factors. The stopping power was 
computed in \cite{ahlen1,ahlen,ahlen2} by classically considering the
long range monopole interactions with atomic electrons.   


Fig \ref{DISacc} shows the total efficiency for stopping a monopole in the
section of beampipe under investigation. This was computed from the 
model for magnetic charges of 1,2,3 and 6 $g_d$ using the range calculations
given in the previous figure divided by the square of the monopole charge 
considered. The mass values extend out to about $120$ GeV albeit with lower 
efficiencies in these regions since heavier monopoles are
preferentially produced in the foward region due to the phase space
limitations caused by the asymmetry in the momenta of the colliding beams
at HERA. Since the value of the ionisation energy loss increases as the
square of the monopole charge this similarly leads to a rapid increase of
stopping efficiency. For monopoles of charge $6g_d$ and above the
efficiency becomes limited by the geometric acceptance of the beam-pipe
section considered.  


The upper limit on the cross section for monopole-antimonopole pair 
production was derived as follows. Observation of zero 
monopole candidates means that we must have had less than 3 events at 
95 $\%$ confidence level. It is assumed that the flux of monopoles 
is not so high that there is an equal number of pairs in each strip  
to cancel the signal. The pipe was exposed to a total luminosity of 60
pb$^{-1}$. A total of 13 strips have been analysed to date
corresponding to 75$\%$ of the mass of the pipe after cutting.
\footnote{The remaining 2 strips were cut into smaller pieces which 
will be studied in the future.}    
The acceptance was computed from the model described 
above. Fig. \ref{figure6} shows the upper limit on the cross section 
at 95$\%$ confidence for monopoles of strength $1$,$2$, $3$ and $6$ $g_d$.   

Other experiments have also produced limits on monopole production
cross-sections for different masses and
charges\cite{D01,D02,ee1,ee2,ee3,ee4,ee5}.
However, owing to the lack of a reliable field theory for monopole
production different model assumptions were made in their derivations. 
Furthermore, although a universal production mechanism for monopole
production can be postulated, comparisons of cross-section limits in
processes as diverse as $e^+p$, $p\bar{p}$ and $e^+e^-$ should be treated
with care. Nevertheless, the regions of charge and mass which are excluded 
are largely determined by acceptance effects.    

Fig. \ref{figure7_1} shows the cross-section upper limit as a function
of mass for monopoles of charge $g_d$ produced in $e^+p$ scattering in
this analysis, $p\bar{p}$  
interactions at the Tevatron\cite{D01,D02} and $e^+e^-$ interactions at
LEP\cite{ee5},Tristan\cite{ee3} and Petra\cite{ee1}. The regions which are
excluded are denoted. The results from H1
extend over a larger mass region than in $e^+e^-$ although these latter
results exclude lower values of the cross-section. The results from the
Tevatron extend to larger values of mass and cover lower cross-section
values than H1. However, the most recent of these results \cite{D02}
relies on
assumptions of the stability of monopole 
binding which are far more stringent than ours\footnote{In 
order to attempt to reduce the dipole moment background the samples were
degaussed and heat treated\cite{grkpriv} procedures which we have 
avoided here due to the unknown chemistry of magnetic monopoles.}. 

The same curves are shown in Fig. \ref{figure7_2} with an additional
limit derived from studies of lunar soil \cite{lunar3}. Here, the
interactions of the cosmic rays with the surface of the moon over 500
Myears is used to derive an upper limit for monopole pair production for
$pn$ scattering. This relies on a number of assumptions including
the stability of energy distributions of cosmic rays over a
large period of time and  of the churning rate of the lunar surface.
Nevertheless it provides the best limit. 

Fig. \ref{figure8_1} shows the same curves as in Fig. \ref{figure7_1}
but for
monopoles of charge $2g_d$. Again the H1 masslimit extends beyond that
from $e^+e^-$ results but below that from $p\bar{p}$ interactions.
However, the H1 results are able to exclude lower values of cross-section
than either experiment. 

Limits from monopoles of charge $3g_d$ are shown in 
Fig. \ref{figure9_1}. At this charge it is seen that 
$e^+e^-$ results are only able to exclude low values of mass ($<$10 GeV). 
%The lunar limit derived for large magnetic charges is added in Fig.
%\ref{figure9_2} which is again the most stringent. 
Similar conclusions can be drawn from the upper limits for monopoles 
of charge $6g_d$ which are shown in Figs. \ref{figure10_1}.
% and
%\ref{figure10_2}. 
 
\section{Conclusions}

A search for magnetic monopoles produced in $e^+p$ collisions
at HERA at a centre of mass energy of $\sqrt s=300$ GeV has been made for 
the first time. 
Monopoles trapped in the beam pipe were directly sought by examining it
with a 
sensitive SQUID magnetometer. No reproducible signal was observed 
allowing upper limits on the monopole pair production cross section to
be set for monopoles with values of charges and masses from $1$ to $6$
$g_d$ and up to about 150 GeV, respectively. 

The search is sensitive to a greater range of monopole mass and charge
than in studies of $e^+e^-$ interactions. Limits from $p\bar{p}$
interactions exclude larger values of mass albeit with more
model assumptions than used here.  

In the future we hope to extend the mass range of the limits  
and improve the sensitivity by examining a further 
length of the beam pipe. 


\begin{thebibliography}{99}

\bibitem{dirac}    P.A.M.~Dirac, \Journal{\PRSL}{133}{60}{1931}, 
\Journal{\PR}{74}{817}{1948}; \\
Alternative derivations of the Dirac quantisation condition can be found 
in\\
J.D.~Jackson, {\it Classical Electrodynamics}, $3^{rd}$ edition (John 
Wiley, New York, 1999); 
M.~Kaku, {\it Quantum Field Theory, a Modern Introduction}, $1^{st}$ 
edition (Oxford University Press, New York, 1993).
\bibitem{mtheory1} R.D.~Sorkin, \Journal{\PRL}{51}{87}{1983}; \\
D.J.~Gross and M.~Perry, \Journal{\NPB}{226}{29}{1983}. 
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\end{thebibliography}
\newpage

% PLOTS FROM DAVE MILSTEAD'S DIRECTORY

\begin{figure}
\begin{center}
\vspace{-20mm}
\epsfig{file=H1prelim-03-062.fig1.eps,width=14.2cm}
\caption{The magnitude of the observed steps versus pole strength for
each calibration coil current (the conversion accuracy is
$\pm3\%$ point to point with a further overall normalisation accuracy
of $\pm3\%$ due to the uncertainty in the coil diameter). The solid line
shows a linear fit to the data which gives the calibration
constant to be $0.045$ units per unit Dirac monopole charge.}
\label{calib} 
\end{center}  
\end{figure}  



\begin{figure}
\begin{center}
\vspace{-30mm}
\epsfig{file=H1prelim-03-062.fig2.eps,width=14.2cm}
\caption[junk]{ The absolute value of the magnetometer current on a 
logarithmic scale versus step position ($z$) from a strip with a solenoid  
mounted on it. The solenoid current was chosen to simulate a pole strength 
of 1 $g_d$ (red dashed curve) and -1 $g_d$ (blue dotted curve). The
solid black curve shows the readings with the solenoid removed. The inset 
shows the signed measurements of the same currents on a linear scale.}
\label{dummy}
\end{center}
\end{figure}



%%figure Data
\begin{figure}
\begin{center}
\vspace{-20mm}
\epsfig{file=H1prelim-03-062.fig3.eps,width=14.2cm}
\caption{The observed persistent currents in each strip against strip
number. The different measurements for the same strip are staggered
in strip number for visibility. The dashed lines show the root mean
square deviation of the readings.}
\label{overview}
\end{center}
\end{figure}


%%figure Data
\begin{figure}
\begin{center}
\vspace{-20mm}
\epsfig{file=H1prelim-03-062.fig4.eps,width=14.2cm}
\caption{Range/mass of a monopole in aluminium versus $\beta \gamma$
calculated from the stopping power, $dE/dx$, in Fig 1 of \cite{ahlen}
adjusted to the electron density in aluminium.}
\label{RErel}
\end{center}
\end{figure}


%%figure Data
\begin{figure}[htb]
\begin{center}
%\vspace{-10mm}
%\epsfig{file=geomc.eps,width=10.2cm}
%\epsfig{file=accep.eps,width=10.2cm}
\epsfig{file=H1prelim-03-062.fig5.eps,width=14.cm}
\caption{The total efficiency for stopping a monopole of strength $g_d$,
$2g_d$, $3g_d$ and $6g_d$. }
\label{DISacc}
\end{center}
\end{figure}

%%figure Data
\begin{figure}[htb]
\begin{center}
\epsfig{file=H1prelim-03-062.fig6.eps,width=14.cm}
\caption{Upper limits on the cross section for monopole-antimonopole
pair production as a function of monopole mass for monopoles of
strength $g_d$, $2g_d$, $3g_d$ and $6g_d$.}
\label{figure6}
\end{center}
\end{figure}


\begin{figure}[htb]
\begin{center}
\epsfig{file=H1prelim-03-062.fig7.eps,width=14.cm}
\caption{Upper limits on the cross section for monopole-antimonopole   
pair production as a function of monopole mass for monopoles of
strength $g_d$ compared with limits obtained in $p\bar{p}$ and $e^+e^-$
interactions.}
\label{figure7_1}
\end{center}
\end{figure}


\begin{figure}[htb]
\begin{center}
\epsfig{file=H1prelim-03-062.fig8.eps,width=14.cm}
\caption{Upper limits on the cross section for monopole-antimonopole
pair production as a function of monopole mass for monopoles of
strength $g_d$ compared with limits obtained in $p\bar{p}$ and $e^+e^-$   
interactions and from lunar rock.}
\label{figure7_2}
\end{center}
\end{figure}



\begin{figure}[htb]
\begin{center}
\epsfig{file=H1prelim-03-062.fig9.eps,width=14.cm}
\caption{Upper limits on the cross section for monopole-antimonopole
pair production as a function of monopole mass for monopoles of
strength $2g_d$ compared with limits obtained in $p\bar{p}$ and $e^+e^-$
interactions.}
\label{figure8_1}
\end{center}
\end{figure}



\begin{figure}[htb]
\begin{center}
\epsfig{file=H1prelim-03-062.fig10.eps,width=14.cm}
\caption{Upper limits on the cross section for monopole-antimonopole
pair production as a function of monopole mass for monopoles of
strength $3g_d$ compared with limits obtained in $p\bar{p}$ and $e^+e^-$
interactions.}
\label{figure9_1}
\end{center}
\end{figure}





\begin{figure}[htb]
\begin{center}
\epsfig{file=H1prelim-03-062.fig11.eps,width=14.cm}
\caption{Upper limits on the cross section for monopole-antimonopole
pair production as a function of monopole mass for monopoles of
strength $6g_d$ compared with limits obtained in $p\bar{p}$ and $e^+e^-$
interactions.}
\label{figure10_1}
\end{center}
\end{figure}




\end{document}



