%================================================================
% LaTeX file with preferred layout for the contributed papers to
% the ICHEP Conference 98 in Vancouver
% process with:  latex hep98.tex
%                dvips -D600 hep98
%================================================================
\documentclass[12pt]{article}
\usepackage{epsfig}
\usepackage{amsmath}
\usepackage{hhline}
\usepackage{amssymb}
\usepackage{times}

\renewcommand{\topfraction}{1.0}
\renewcommand{\bottomfraction}{1.0}
\renewcommand{\textfraction}{0.0}
\newlength{\dinwidth}
\newlength{\dinmargin}
\setlength{\dinwidth}{21.0cm}
\textheight23.5cm \textwidth16.0cm
\setlength{\dinmargin}{\dinwidth}
\setlength{\unitlength}{1mm}
\addtolength{\dinmargin}{-\textwidth}
\setlength{\dinmargin}{0.5\dinmargin}
\oddsidemargin -1.0in
\addtolength{\oddsidemargin}{\dinmargin}
\setlength{\evensidemargin}{\oddsidemargin}
\setlength{\marginparwidth}{0.9\dinmargin}
\marginparsep 8pt \marginparpush 5pt
\topmargin -42pt
\headheight 12pt
\headsep 30pt \footskip 24pt
\parskip 3mm plus 2mm minus 2mm

%===============================title page=============================

% Some useful tex commands
%
\newcommand{\GeV}{\rm GeV}
\newcommand{\TeV}{\rm TeV}
\newcommand{\pb}{\rm pb}
\newcommand{\cm}{\rm cm}
\newcommand{\hdick}{\noalign{\hrule height1.4pt}}

\newcommand{\ra}{\rightarrow}
\newcommand{\ccb}{c\bar{c}}
\newcommand{\bbb}{b\bar{b}}
\newcommand{\pbp}{\bar{p}p}
\newcommand{\epem}{e^+e^-}

\begin{document}

\pagestyle{empty}
\begin{titlepage}

\noindent
\begin{center}
%{\it {\large version of \today}} \\[.3em] 
\begin{small}
\begin{tabular}{llrr}
%Submitted to & \multicolumn{3}{r}{\footnotesize Electronic Access: {\it http://www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] \hline 
%Submitted to & \multicolumn{3}{r}{\footnotesize {\it www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] \hline 
Submitted to & & &
\epsfig{file=/h1/www/images/H1logo_bw_small.epsi
,width=2.cm} \\[.2em] \hline
\multicolumn{4}{l}{{\bf
                International Europhysics
                Conference on High Energy Physics},
                July~12,~2001,~Budapest} \\
 {\bf EPS 2001:} 
                 & Abstract:        & {\bf 807}    &\\
                 & Parallel Session & {\bf 1, 4}   &\\ [.7em]
\multicolumn{4}{l}{{\bf
               XX International Symposium on Lepton and Photon Interactions}, 
               July~23,~2001,~Rome} \\ 
{\bf LP 2001:}  
                 & Abstract:        & {\bf 484} &\\
                 & Plenary Session  & {\bf S05, S07, S08}   &\\ \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 
Beauty Production in Deep Inelastic {\boldmath ep} Scattering}

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

\begin{abstract}

\noindent
We report the first observation of beauty production  
in deep inelastic $ep$ scattering (DIS).
Hadrons with $b$~fla\-vour are observed 
with the H1 detector at HERA 
through their semi-leptonic decay.
The cross section is extracted using the distributions 
of the impact parameter and of the transverse momentum of 
muons relative to jets 
in the kinematic range $2<Q^2<100$~GeV$^2$, $0.05<y<0.7$,
for muon polar angles and transverse momenta
$35^\circ<\theta<130^\circ$ and $p_T>2$~GeV.
The result,
$\sigma = [39\,\pm\,8\,(stat.)\,\pm 10\,(syst.)\,]\,{\rm pb}$ 
is found to be significantly 
% next-to-leading order 
above NLO QCD predictions.   
%We present the first measurement of beauty production in DIS. 
%The analysis is performed with a sample of DIS events with 2 jets 
%($E_T>5\,$ GeV) accompanied by a muon which is identified in
%the instrumented iron and well measured in the central silicon vertex 
%detector. The contribution of $b$-events to the sample is determined with 
%a likelihood fit to the two-dimensional distribution
%in the impact parameter and the muon transverse momentum relative to the 
%jet axis, as applied previously in the photoproduction regime. 
%The measured cross section is found to be
%significantly larger than predicted by LO and NLO QCD calculations. 
\end{abstract}


\end{titlepage}

\pagestyle{plain}
Beauty production has not yet been observed 
in deep inelastic scattering (DIS).
The process is considered to be reliably calculable in perturbative QCD
since the $b$ quark mass sets a hard scale. 
Particular interest in 
confronting the theory with 
experiment in a yet unexplored production environment
stems from the fact that
$b$ cross sections are 
found in excess of QCD expectations in $\bar{p}p$~\cite{hadronb}, 
$\gamma p$~\cite{h1openb,blto,zeusopenb} and, recently,  $\gamma\gamma$~\cite{ggb}
interactions, 
where the calculations follow the same principles. 
Moreover, since charm accounts for about a quarter of the inclusive DIS rate
in the HERA domain~\cite{f2ch1zeus},
the proton structure analysis of inclusive DIS data~\cite{f2h1zeus}
relies heavily on the understanding of heavy quark production,
for which $b$ production constitutes a new testing ground. 

In electron proton collisions,
$b$ quarks are predominantly produced, in QCD,  via  
the interaction of a photon coupling to the incoming electron with 
a gluon in the proton by forming a quark-anti-quark pair.
The case of small photon virtuality, $Q^2<1$~GeV$^2$ corresponds 
to photoproduction ($\gamma p$). 
The DIS case of larger $Q^2$ is complementary, because 
resolved contributions involving the partonic structure of the photon
are expected to be suppressed~\cite{grs}.
Thus theoretical 
uncertainties due to imperfect knowledge of hadronic structures 
are smaller in DIS than in the other reactions.  

The result presented here is an extension of our 
measurement of the beauty production cross section~\cite{blto},
from the photoproduction regime 
to DIS. 
The analysis starts with a sample of DIS events collected in 1997. 
The same reconstruction 
and selection procedures as in~\cite{blto} are used 
to obtain a dijet event sample with a muon identified
in the instrumented iron and well measured in the 
central silicon tracker (CST)~\cite{cst}.

Here the electron is scattered into the main detector. 
Its signature is used in the trigger which requires
electromagnetic energy deposition signals 
from the backward calorimeter SpaCal 
in coincidence with tracking information 
from proportional and drift chambers. The integrated luminosity 
corresponds to ${\cal L}=10.5$~pb$^{-1}$.

The selection of DIS events follows the methods described in~\cite{gluon}. 
The scattered electron candidate reconstructed in the 
SpaCal must be 
detected with a polar angle  
$\theta_{e'}<177^o$ relative to the incoming proton momentum vector
and is required to 
have an energy $E_{e'} >$ 9 GeV. 
The DIS kinematic variables $Q^2$ and $y$ are reconstructed from 
the scattered electron.
The cross section is determined for 
the visible kinematic range 
$2<Q^2<100$ GeV$^2$, 
$0.05<y<0.7\,$, 
$p_T(\mu)>2$ GeV
and $35^\circ<\theta(\mu)<130^\circ$.
$p_T(\mu)$ and $\theta(\mu)$ denote the transverse momentum and 
the polar angle of the muon with respect to the beam axis.
168 events are selected which contain $N_{\mu} = 171$ muon candidates.

The composition of the sample, in terms of muons from $\bbb$ events, 
$\ccb$ events, or background from misidentified hadrons (``fake muons'') 
is analyzed using  
AROMA Monte Carlo~\cite{aroma} event samples as in~\cite{blto}.
The hadron sample used to model the fake muon background is 
selected using the same requirements as for the signal, except for the 
muon identification, and using the same trigger for DIS events. 
%This is in contrast to the photoproduction case, 
%where the trigger for the signal is based on the muon signature
%in the instrumented iron and cannot be used for this purpose. 

In the photoproduction case, it has been shown that the 
impact parameter $\delta$ and the 
transverse momentum $p_T^{rel}$ relative to the jet axis
provide independent and consistent signatures for $b$ production.
The analysis of the smaller DIS sample relies on the 
combination of the two observables, which also provided the most precise 
photoproduction result.
  
%The likelihood fit of the $\bbb$, $\ccb$ and fake muon 
%reference spectra to the two-dimensional 
%distribution in $\delta$ and $p_T^{rel}$ 
%yields a $\bbb$ fraction of $f_b = (43\pm 8)\,\%$.
A likelihood fit of $\bbb$, $\ccb$ and fake muon 
reference spectra to the two-dimensional 
distribution in $\delta$ and $p_T^{rel}$ 
adjusts the relative weights of all three components in the data.
It yields a $\bbb$ fraction of $f_b = (43\pm 8)\,\%$.

The projections of this distribution are shown in Fig.~\ref{fig:disptdelta}
together with the decomposition from the fit. The distributions of 
both variables are well described. The need for a $\bbb$ component 
is evident from the lifetime based signature as well as from the 
$p_T^{rel}$ spectrum. 
%
%
\begin{figure}[t]
\begin{center}
\unitlength5mm
\begin{picture}(24,18)
\put(-4.,-0.){\epsfig{figure=H1prelim-01-072_fig1a.eps,height=9cm}}
\put(12.,-0.){\epsfig{figure=H1prelim-01-072_fig1b.eps,height=9cm}}
%
\end{picture}
\caption{\label{fig:disptdelta}
Distributions of the muon impact parameter (left)
and transverse momentum relative to the jet axis (right), 
with decomposition from the likelihood fit.}
\end{center}
\end{figure}         
%
%
%
%\begin{figure}[t]
%\begin{center}
%\unitlength5mm
%\begin{picture}(24,20)
%\put(0., 0.){\epsfig{figure=dis_ptrel.eps,height=12cm}}
%%
%\end{picture}
%\caption{\label{fig:ptrel}
%Impact parameter distribution and decomposition from the likelihood fit.}
%\end{center}
%\end{figure}         
%
The charm and fake muon fractions are varied independently in the fit, 
but have large, correlated errors. The fit yields 
$f_{fake} = (11 \pm 22)\,\%$. 
Within the large error this is consistent with the expectation using 
fake probabilities determined in Monte Carlo simulations to reweight 
the hadron track sample, $f_{fake} = 43\,\%$.
Fixing the fake muon fraction to this value in the fit changes the result 
for $f_b$
by less than half the statistical error. 
%The same holds true if $p_T^{rel}$ alone is used in this constraint fit.   
The fits to the one-dimensional distributions were performed 
as cross checks, as in~\cite{blto} and yield consistent results.  
%Due to the small statistics, one cannot expect to obtain a reliable
%independent measurement using a free fit to the impact parameter $\delta$ 
%alone, as was possible in photoproduction. 

The sources of systematic uncertainty are the same as in the photoproduction 
case, except for a small contribution ascribed to the electron 
reconstruction.  The dominant contribution is due to 
the Monte Carlo Model used to extrapolate the cross section.
The biggest experimental errors, arising from the stability with respect to 
variations of the impact parameter analysis and the change of the jet energy 
scale,
% and the Monte Carlo Model used to extrapolate the cross section
were checked separately for the DIS sample and confirmed. 

%The cross section in the visible range 
%is defined as in~\cite{blto,h1openb} as 
%$\sigma = f_b N_{\mu} / (2\epsilon{\cal L})$,
%where $\epsilon$ denotes the efficiency for a $\bbb$ event with a muon 
%in the visible range to fulfill the selection requirements. 
The cross section for the production of muons from 
$b$ decays 
is defined as in~\cite{h1openb} as 
\[\sigma_{ep}^{vis} (ep\ra bX\ra\mu X)= 
f_b N_{\mu} / (2\epsilon{\cal L})\, ,\]
where $\epsilon$ denotes the efficiency for a $\bbb$ event with a 
primary or secondary muon 
in the visible range to fulfill the selection and trigger requirements. 
The factor of 2 accounts for the fact 
that the experiment measures muons from $b$ and $\bar{b}$ decays. 
We find 
\[ \sigma_{ep}^{vis} = 
[\;39\;\pm\;8\;(stat.)\; \pm 10\;(syst.)\;]\;{\rm pb}\ . \]
This measurement can be directly compared to a NLO QCD calculation using 
the standard HVQDIS program~\cite{hvqdis} with a Peterson fragmentation 
function~\cite{peterson}
used to scale the quark momenta in order to obtain $b$ hadron
momenta. The distributions were then folded with a lepton spectrum 
extracted from the aroma Monte Carlo generator. 
The GRV98 parton densities~\cite{grv98}
are used, the $b$ quark mass was set to 4.75 GeV, 
and the renormalization and factorization scales to $\mu = \sqrt{Q^2+4m_b^2}$.
The Peterson fragmentation parameter to $\epsilon_b = 0.0033$
as obtained from a fit of a fixed order QCD calculation~\cite{olearimerged}
in the same (massive) scheme to the $b$ production spectrum~\cite{alephb} 
measured in $\epem$ annihilation. 
The QCD result is $(11\pm 2)$ pb, where the error has been estimated 
by varying the scale $\mu$ by factors of two, $\epsilon_b$ between 0.0016 and 
0.0069, and $m_b$ between 4.5 and 5 GeV. The $b$ mass has the 
strongest influence ($\pm 11\,\%$). 
The AROMA prediction is 9~pb. A LO calculation with the 
CASCADE program~\cite{cascade} based on the CCFM evolution 
equation yields 15~pb.

%
% --- HERA b
%
\begin{figure}[tbp]
\begin{center}
\unitlength5mm
\begin{picture}(24,19)
\put(1.,-0.3){\epsfig{figure=H1prelim-01-072_fig2.eps,height=10cm}}
%
%\put(6.,2.){$\underbrace{\;\;\;\;\;\;\;\;\;\;\;\;}$}
%\put(4.7,0.5){\large\sf Q$^2<1\,$GeV$^2$}
\end{picture}
\caption{\label{fig:herab}
Ratio of measured $b$ production cross sections at HERA 
over theoretical expectation, as a function of $Q^2$.
The inner (outer) error bars represent the statistical (total experimental) 
error, the shaded band the theoretical uncertainty.}  
\end{center}
\end{figure}         
%
We summarize the HERA results 
as a function of $Q^2$ in Fig.~\ref{fig:herab}. 
Displayed is the ratio of measured visible cross sections over 
theoretical expectations,
which for the photoproduction case have been 
calculated~\cite{h1openb,zeusopenb} using the FMNR program~\cite{frixi}.
%\footnote{The result of the NLO QCD calculation for the visible 
%photoproduction cross section  given in our first publication~\cite{h1openb}
%could not be reproduced. 
%The measured value of 
%$\sigma_{ep}^{vis}=
%[176\;\pm\;16\;^{+27}_{-17}\; ] \;{\rm pb}$
%must be compared with the NLO QCD expectation of $(48\pm 5)$ pb 
%obtained using the FMNR program~\cite{frixi} with a 
%Peterson fragmentation function. 
%The extrapolated total $ep$ and $\gamma p$ cross sections in~\cite{h1openb}
%scale accordingly.}
The ratio is consistent with being independent of $Q^2$; 
the discrepancy between data and theory is thus not a feature 
of the photoproduction regime alone. 

\newpage 
In conclusion, the $b$ cross section in DIS is measured for the first time 
and is found to be above QCD expectations.
A similar excess as observed in $\bar{p}p$~\cite{hadronb}, 
$\gamma p$~\cite{h1openb,zeusopenb} and $\gamma\gamma$~\cite{ggb} 
interactions is now also seen in $ep$ scattering. 
     
\begin{thebibliography}{99}
\bibitem{hadronb} 
% CDF, D0 open b
CDF Coll., F. Abe {\it et al.}, 
Phys.\ Rev.\ Let. 71 (1993) 2396, Phys.\ Rev.\ D 53 (1996) 1051; \\
D0 Coll., S. Abachi {\it et al.}, 
Phys.\ Rev.\ Let 74 (1995) 3548, Phys.\ Let.\ B 370 (1996) 239.

\bibitem{h1openb} 
%% H1 openb
H1 Coll., C. Adloff {\it et al.},  Phys.\ Lett.\ B467 (1999) 156,
and Erratum (to be published). 

\bibitem{blto}
F. Sefkow, talk presented at ICHEP 2000, July 2000, 
and contrib.\ paper \\
http://www-h1.desy.de/psfiles/confpap/ICHEP2000/H1prelim-00-171.ps

\bibitem{zeusopenb} 
%% Zeus openb
J.~Breitweg {\it et al.}  [ZEUS Collaboration],
%``Measurement of open beauty production in photoproduction at HERA,''
hep-ex/0011081.

\bibitem{ggb} 
% L3 gg->bb
M.~Acciarri {\it et al.}  [L3 Collaboration],
%``Measurements of the cross sections for open charm and beauty  production in gamma gamma collisions at s**(1/2) = 189-GeV - 202-GeV,''
hep-ex/0011070. \\
OPAL Coll., {\em Beauty particle production in photon-photon scattering at LEP2}, presented at ICHEP2000, Osaka, Japan, 2000. 

\bibitem{f2ch1zeus}
H1 Coll., C. Adloff {\it et al.}, Z. Phys.\ C 72 (1996) 593;\\
% Zeus F2c
ZEUS Coll., J. Breitweg {\it et al.}, 
Eur.\, Phys.\, J.  C12 (2000) 1.

\bibitem{f2h1zeus}
C.~Adloff {\it et al.}  [H1 Collaboration],
%``Deep-inelastic inclusive e p scattering at low x and a determination of  alpha(s),''
hep-ex/0012053;\\
J.~Breitweg {\it et al.}  [ZEUS Collaboration],
%``ZEUS results on the measurement and phenomenology of F2 at low x and  low Q**2,''
Eur.\ Phys.\ J.\ C {\bf 7} (1999) 609
[hep-ex/9809005].

\bibitem{grs}
M.~Gluck, E.~Reya and M.~Stratmann,
%``Probing the Parton Densities of Virtual Photons at ep Colliders,''
Phys.\ Rev.\ D {\bf 54} (1996) 5515
[hep-ph/9605297].

\bibitem{cst}
D.~Pitzl {\it et al.},
%``The H1 silicon vertex detector,''
Nucl.\ Instrum.\ Meth.\ A {\bf 454} (2000) 334
[hep-ex/0002044].

\bibitem{gluon}
C.~Adloff {\it et al.}  [H1 Collaboration],
%``Measurement of D* meson cross sections at HERA and determination of the  gluon density in the proton using NLO QCD,''
Nucl.\ Phys.\ B {\bf 545} (1999) 21
[hep-ex/9812023].

\bibitem{aroma}
% aroma
G. Ingelman, J. Rathsman and G.A. Schuler,
Comput.\,Phys.\,Commun.\ 101 (1997) 135.

\bibitem{hvqdis}
B.W. Harris and J. Smith, 
Nucl.\,Phys.\ B452 (1995) 109;      
Phys.\,Lett.\ B353 (1995) 535;
Phys.\,Rev.\ D57 (1998) 2806.

\bibitem{peterson}
% Peterson
C. Peterson, D. Schlatter, I. Schmitt, and P.M. Zerwas,
Phys.\,Rev.\ D 27 (1983) 105.
 
\bibitem{grv98}
M.~Gluck, E.~Reya and A.~Vogt,
%``Dynamical parton distributions revisited,''
Eur.\ Phys.\ J.\ C {\bf 5} (1998) 461
[hep-ph/9806404].

\bibitem{olearimerged}
P.~Nason and C.~Oleari,
%``A phenomenological study of heavy-quark fragmentation functions in  e+ e- annihilation,''
Nucl.\ Phys.\ B {\bf 565} (2000) 245
[hep-ph/9903541].

\bibitem{alephb}
D.~Buskulic {\it et al.}  [ALEPH Collaboration],
%``Measurement of the effective b quark fragmentation function at the Z resonance,''
Phys.\ Lett.\ B {\bf 357} (1995) 699.

\bibitem{cascade}
H.~Jung, \mbox{G.P.} Salam, {\em Eur. Phys. J. {\bf C}} (2001)\nolinebreak
  [2]\,DOI 10.1007/s100520100604, hep-ph/0012143. \\
H.~Jung, {\em \mbox{T}he CASCADE Monte Carlo Generator,
  version 0.5}, Lund University, 1999,
  \verb+http://www-h1.desy.de/~jung/cascade+.

\bibitem{frixi} 
% fmnr 
S. Frixione, M.L. Mangano, P. Nason, and G. Ridolfi,
Phys.\ Lett.\ B348 (1995) 633.

\end{thebibliography}

\end{document}


\end{document}

