\documentstyle[12pt,epsfig]{article}
\parskip 2mm plus 2mm minus 2mm
\newlength{\dinwidth}
\newlength{\dinmargin}
\setlength{\dinwidth}{21.0cm}
\textheight23.0cm \textwidth15.0cm
\setlength{\dinmargin}{\dinwidth}
\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 \footheight 12pt \footskip 24pt
%\parindent=20pt
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
%{\noindent
\vskip 3cm
\begin{center}
{\large \bf Some Properties of the CCFM Monte Carlo - SMALLX}
\vskip 0.5cm
{L. Goerlich\footnote{E-mail: goerlich@chall.ifj.edu.pl}} {\it and} 
{J. Turnau\footnote{E-mail: turnau@chall.ifj.edu.pl}} 
\vskip0.5cm
{\it 
H. Niewodnicza\'nski Institute of Nuclear Physics,}

{\it ul. Radzikowskiego 152, 31-342 Krak\'ow, Poland}
\vskip1cm
(\today)
\end{center}
\vskip1cm 
\begin{abstract}
 Properties of the B.Webber Monte-Carlo generator for DIS -
          SMALLX are investigated. We compare CCFM evolution
          implemented by the generator with the structure function $F_2$
          measured at HERA. In addition, having implemented JETSET
          hadronization of the final partonic state provided by SMALLX
          we compare basic characteristics of the hadronic states with
          the HERA data.
\end{abstract}

In a recent paper \cite{NASZ} we described a study of the Monte Carlo program
SMALLX  \cite{SMALLX}. This program generates
the deep inelastic lepton-nucleon scattering (DIS) events at small
values of the Bjorken variable $x_B$ using CCFM  \cite{MARCH} branching
scheme with angular ordering of the gluon emissions. Our study was confined
to open charm production and the partonic final states. We fixed the 
generation parameters by requirement that charm structure function 
$F_{2}^{c\bar{c}}(x,Q^{2})$ measured at HERA \cite{HERACC} is correctly  
described.
This includes the parameters of the initial gluon distribution ${\cal F}^0$,
 for which the following form is postulated:
 \begin{displaymath}
x_{0}{\cal F}^{0}(x_0,{\bf k}_{\bot 0},Q_s)=A_0x_0^{-p_0}(1 - x_0)^{p_1}
exp(-2  {\bf k}_{\bot 0}^{2}/Q_s^{2})
 \end{displaymath}
where the parameter $Q_s$ also plays the role of the collinear cutoff $q_0$
for the first real gluon emission, and the normalization constant $A_0$
is determined from the momentum sum rule
\begin{displaymath}
  P(Q_s)= \int_0^1 dx~x F(x,Q_s) = 0.5.
\end{displaymath}
 Above $F(x,Q)$ is the usual gluon structure function (gluon density) :
\begin{displaymath}
 F(x,Q) = F(x,Q,q_0) \equiv \int d^2 {\bf k_{\bot}}~{\cal F}
(x,{\bf k_{\bot}},Q,q_0)\Theta(Q-|{\bf k_{\bot}}|).
\end{displaymath}
We have fixed $Q_s = 1$ GeV and $p_1 = 5$ motivated by large $x$ behavior
of the conventional gluon distribution.  The parameter $p_0 = 0$ was chosen
to obtain best possible  description of $F_2^{c \bar c}$ at $Q^2 = 12$ GeV$^2$.
The infrared cutoff parameter $Q_0$ has been set to 1 GeV.
\par
Our studies have shown relevance of the CCFM approximation in the description 
 of exclusive processes in DIS at HERA. The most spectacular results are the 
azimuthal angle decorrelation for the heavy quarks \-- a direct consequence of
$k_{\bot}$ \-- diffusion along the gluon chain in CCFM scheme, and 
forward jet production.
\par
The present study is an extension of the previous work to production of the
light quarks. In addition we provided the original Webber code with 
hadronisation via JETSET7.4. This has been done in the usual way, by 
connection of 
the quark and the diquark in the proton remnant with anti-quark and quark from
boson gluon fusion into two chains which include gluons emitted along the 
chain.
\par
The first obstacle  we encountered was inability to  find any set of 
parameters $p_0, p_1, Q_s $ and $Q_0$ which would provide a good or even 
passable description of the proton structure function $F_2(x,Q^2)$. 
In general $F_2$ 
is much too steep at very small values of $x$. In principle we could achieve
some reduction of the cross section at small $x$ increasing the value of $Q_0$
however even 1 GeV seems to be rather high for the infrared cutoff. In 
addition such a change makes the discrepancy at high values of $x$ even worse. 
\begin{figure}[!htb]
\begin{center}
\epsfig{file=f2.ps,bbllx=40pt,bblly=276pt,bburx=586pt,bbury=816pt,width=15cm,
angle=0}
\end{center}
\caption{ The $F_2(x,Q^2)$ structure function : H1 data compared to the
SMALLX generator results (full line) in several  $(x,Q^2)$ bins.}
\end{figure}
 The fact that SMALLX gives a passable description of $F_2^{c \bar c}$ and
at the same time completely misses $F_2$ data (Fig. 1)  can be only
partially attributed to the higher  $x$-range covered by the charm production
data and much bigger errors on the data points. 
 In spite of the failure to explain the differential cross section for DIS, we
decided to investigate some properties of the final hadronic states produced
by the  SMALLX generator. In  Fig.2 
\begin{figure}[!htb]
\begin{center}
\epsfig{file=etflow.ps,bbllx=40pt,bblly=276pt,bburx=586pt,bbury=816pt,
width=15cm,angle=0}
\end{center}
\caption{ The flow of transverse energy $E_T$ in the CMS as a function of
pseudorapidity $\eta$. The proton remnant direction is to the left. 
Shown are nine 
different kinematic bins. The distributions are normalized to the number of 
events $N$ in each case. Together with the  H1 data points simulations by
SMALLX, ARIADNE and LEPTO generators are shown.}
\end{figure}
we show the transverse energy flow in 
several bins of $x$ and $Q^2$ compared with the H1 data \cite{H1FLOW}, ARIADNE
\cite{ARIADNE} and LEPTO \cite{LEPTO} simulations. While ARIADNE describes the
data very well indeed, SMALLX gives too much transverse energy in the  
central and forward (i.e. in the direction of incoming proton) region of 
pseudorapidity. 
\par
As SMALLX does not describe correctly  DIS cross section, its 
results concerning  cross section  of the
forward jet  production, are not meaningful.
However some features  of the hadronic final states it generates
are still of interest. As we have shown in \cite{NASZ}, there are 
significantly more gluons in  the angular ordering mode (CCFM) of the
SMALLX generation in comparison with DGLAP-like mode. This leads directly
to significant  difference of the total forward jet cross sections for the two 
generation modes.    
Is it possible to observe enhanced gluon emission accompanying forward jet
production ? How does CCFM compare in this respect with the other generation 
schemes (ARIADNE, LEPTO) ? 
\par
To answer these questions we studied the transverse energy flow in presence
of the fast forward high transverse momentum $p_t$ particle. As shown 
in \cite{H1FORW} a
particle with $p_t \geq 1.0$ GeV, proton momentum fraction $p/p_{proton} 
\geq 0.01$ and the angle with respect to proton direction in the range 
$5 \leq\Theta \leq 25$ degree (LAB frame) is strongly correlated with presence
of the forward jet. In Fig.3
\begin{figure}[!htb]
\begin{center}
\epsfig{file=diff_pi0.ps,bbllx=7pt,bblly=151pt,bburx=560pt,bbury=708pt,
width=15cm,angle=0}
\end{center}
\caption{The difference between transverse energy flow for events selected by
fast forward particle and  events without selection. It is shown as a function
of the $\gamma$p CMS pseudorapidity. The proton remnant is to the left.}
\end{figure} 
we show the difference between 
the transverse energy flow  for events which contain fast forward particle 
defined as above (excluding this particle) and the transverse energy flow 
for all events in the same
kinematic range ($ 0.0002 \leq x \leq 0.00235$). We may expect that
substraction operation  reduces effects of  the above mentioned flaw in 
the description of $E_t$-flow by SMALLX and LEPTO.
The curves representing 
SMALLX, ARIADNE and LEPTO generator results differ significantly. Comparing 
ARIADNE with LEPTO we see that in LEPTO case transverse momentum of the 
fast forward particle is compensated mainly in the backward region 
($\eta \geq 0$) while in ARIADNE case we observe increased emission of
hadrons in the  forward direction i.e. transverse momentum compensation
is mostly local. This should be expected, because with $p_t$-ordered
emission along the gluon ladder (LEPTO) large part of the transverse
momentum compensation is due to the  $q \bar{q}$ pair from the
box. The compensation pattern in the SMALLX generator is similar to that
of ARIADNE - the difference is mainly in the $E_t$-flow level.
\par
The above example shows, that correlations provide powerful tool to 
discriminate between models of the particle production in DIS. The failure of 
the present version of SMALLX to describe the basic properties of the
DIS at smallx $x$ in not a surprise (see e.g. \cite{SALAM}). The better 
implementation of the CCFM evolution scheme is on the way \cite{JUNG}.    
 
%------------------------------------------------------------------------

%------------------------------------------------------------------------
\begin{thebibliography}{999}
\bibitem{NASZ}
K. Golec-Biernat, L. Goerlich, J. Turnau, Nucl.Phys.B527(1998)289
\bibitem{HERACC}
 H1 Collaboration, C. Adloff et al., Z.Phys. C 72 (1996)593
\bibitem{SMALLX} 
  G.Marchesini,  B.Webber,  Nucl. Phys. {\bf B386} (1992) 215.
\bibitem{DGLAP} 
  V.N.Gribov, L.N.Lipatov, Sov.J.Nucl.Phys. {\bf 15} 
  (1992) 438, 675;\\ 
  G.Altarelli, G.Parisi, Nucl.Phys.{\bf B126} (1977) 297;\\              
  Yu.L.Dokshitzer, Sov.Phys.JETP {\bf 46} (1977) 641.
\bibitem{BFKL}  
  L.N.Lipatov, Sov.J.Nucl.Phys. {\bf 23} (1976) 642;\\
  V.S.Fadin, E.A.Kuraev, L.N.Lipatov, Phys. Lett. {\bf B60} (1975) 50;\\
  E.A.Kuraev, L.N.Lipatov, V.S.Fadin, Sov. Phys. JETP {\bf 44} (1976) 45,
  Sov. Phys. JETP {\bf 45} (1977) 199;\\
  Ya.Ya.Balitsky, L.N.Lipatov, Sov. J. Nucl.Phys. {\bf 28} (1978) 822.
\bibitem{MARCH} 
  M.Ciafaloni,  Nucl.Phys. {\bf B296} (1988) 49;\\
  S.Catani, F.Fiorani,  G.Marchesini, Phys. Lett. {\bf B234} (1990) 339, 
  Nucl.Phys. {\bf B336} (1990) 18.
\bibitem{LARGCOH} 
  A.Basseto, M.Ciafaloni,  G.Marchesini, Phys. Rep. {\bf 100} (1983) 201;\\
  Yu.I.Dokshitzer, V.A.Khoze, S.L.Troyan, A.H.Mueller, 
  Rev. Mod. Phys. {\bf 60} (1988) 373.
\bibitem{CAT1} 
  S.Catani, F.Fiorani, G.Marchesini,  G.Oriani, 
  Nucl. Phys. {\bf B361} (1991) 645; 
  G.Marchesini, Nucl. Phys. {\bf B445} (1995) 49.
\bibitem{KTFAC1} 
  S.Catani, M.Ciafaloni, F.Hautmann, Phys. Lett {\bf 242} (1990) 97,
   Nucl. Phys. {\bf 366} (1991) 135;\\
  J.C.Collins, R.K.Ellis, {\bf 360} (1991) 3.
\bibitem{KTFAC2}  
   E.M.Levin, M.G.Ryskin, Yu.M.Shabelskii, A.G.Shuvaev, 
   Sov. J. Nucl.Phys. {\bf 54} (1991) 867.
\bibitem{ARIADNE}
 L. L\"onnblad, Computer Phys. Comm. 71 (1992) 15.
\bibitem{LEPTO}
 G.Ingelman, Proc. of the Workshop on Physics at HERA, Hamburg 
1991, eds. W.Buchm\"uller and G.Ingelman, vol. 3, p. 1366
\bibitem{H1FLOW}
H1 Collaboration, S. Aid et al., Nucl. Phys. B356(1995)118
\bibitem{H1FORW}
H1 Collaboration, C. Adloff et al., Nucl.Phys. B538(1999)3  
\bibitem{SALAM}
G.Bottazzi, G.Marchesini, G.P. Salam and M. Scorletti, hep-ph/9810546
\bibitem{JUNG}
H. Jung, these proceedings
\end{thebibliography}
\end{document}
