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{\bf
SCALING PROPERTIES OF HADRON PRODUCTION \\[0.1cm]
IN $\pi^--p$ AND  $\pi^--A$ COLLISIONS AT HIGH-$P_T$ }

% TITLE OF THE ARTICLE (IN CAPITAL LETTERS)}

\vskip 5mm
G.P. \v {S}koro $^{1,*}$,
 M.V. Tokarev $^{2, \natural}$,
Yu.A. Panebratsev $^{2, \heartsuit}$
and  I.Zborovsk\'{y} $^{3, \clubsuit}$\footnote{The work is partially
supported by the  grant No. 020475 of the Czech Ministry of Education,
Youth and  Physical  Training.}


\vskip 5mm

{\small

(1) { \it Institute of Nuclear Sciences "Vin\v {c}a",\\
Faculty of Physics, University of Belgrade,\\
Belgrade, Yugoslavia}

\vskip 0.2cm

(2) {\it Laboratory of High Energies,\\
Joint Institute for Nuclear Research,\\
141980, Dubna, Moscow region, Russia}

\vskip 0.2cm

(3)  {\it Nuclear Physics Institute,\\
Academy of Sciences of the Czech Republic, \\
\v {R}e\v {z}, Czech Republic}


$^{*}$  E-mail: {\it {goran@rudjer.ff.bg.ac.yu}}

$^{\natural}$ {\it  E-mail: {tokarev@sunhe.jinr.ru}}

$^{\heartsuit}$ {\it  E-mail: {panebrat@sunhe.jinr.ru}}

$^{\clubsuit}$ {\it E-mail: {zborovsky@ujf.cas.cz}}

}
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\vskip 5mm

\begin{center}
\begin{minipage}{150mm}
\centerline{\bf Abstract}
  Scaling features of  particles
  produced in $\pi^--p$ and $\pi^--A$ collisions over a high-$p_T$
  range at high energies are studied. The general concept of
  $z$-scaling is applied  for the analysis of $\pi^--p$ and
  $\pi^--A$ experimental data on the $Ed^3\sigma/dq^3$ inclusive
  cross section. The scaling function $\psi(z)$ and scaling variable
  $z$ are constructed and the anomalous dimension $\delta_{\pi}$ is found.
  %to be $\sim 0.1$.
  The $A$-dependence of particle production
  in pion-nucleus collisions is studied.
% and
%  the scale transformations
%  $z\rightarrow \alpha (A) \cdot z$ and
%  $\psi \rightarrow \alpha^{-1}(A) \cdot \psi$  are  used for the analysis
%  of $\psi(z)$ for different nucleus targets
%  $(Be, Cu, W)$.
The predictions
 of the inclusive cross section of the $\pi^{0}$-mesons produced
  in $\pi^--A$ collisions in the central rapidity range at
  high energies have been made.
\\
{\bf Key-words:}
pion-proton and pion-nucleus collisions, high energy, scaling
\end{minipage}
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%\begin{center}
%    Submitted to "International Journal of Modern Physics A"
%\end{center}


%\end{document}

%\newpage

{\section{Introduction}}

  Particle production with a high transverse momentum is traditionally
  connected with fundamental phenomena of
  elementary constituent interactions. The hypothesis of parton-hadron
  duality \cite{DPM} states, in particular,
  that the features of high-$p_T$ hadron spectra reflect the features
  of hard parton-parton interactions. It
  means that partons retain information about the collision during
  particle formation. Therefore, the features
  of single inclusive particle spectra in hadron-hadron and
  hadron-nucleus collisions of particle having a
  different flavour content are of interest to search for unusual
  properties of particle itself and its
  formation. Such features could be very useful to search for
  complementary signatures of unusual phenomena such
  as the phase transition of nuclear matter, new type of particle
  interactions and quark compositeness.

  One of the methods to study the properties of nuclear matter is
  to search for the violation of known scaling laws established
  in elementary collisions such as
  the Bjorken  and  Feynman  scaling laws.

  In this paper we study scaling features of hadron production
  in $\pi^--p$  and $\pi^--A$ collisions
  over a high $p_{T}$ range.
 Experimental data on
  cross section \cite{fris83,donal76,marzo87,turch93}
  and \cite{alver93,E706}   are used for the analysis.

 The $z$-scaling  was proposed in \cite{Z96} to
  describe the features of charged hadron production in $p-p$ and
  $\bar p-p$ collisions.
  New presentation ($z$-presentation) of experimental data can be obtained
  using the experimental observables,
  the inclusive cross section $Ed^3\sigma/dq^3$, the multiplicity
  density of charged particles
  $dN/d{\eta}|_{\eta=0}=\rho(s)$  and kinematical quantities of the
  reaction (collision energy, momenta and masses of initial  and produced
  particles).
  As shown in \cite{Z96,Z99,Z97,Z01} the data $z$-presentation
  reveals the symmetry properties,
  the  independence on  center-of-mass energy ${\sqrt s}$ and the angle
  of produced particle ${\theta}$ over a wide kinematical range.
  The energy dependence  of the $\pi^--p$ experimental data
  is used to find the anomalous dimension $\delta_{\pi}$.
  The scaling function $\psi(z)$ describes the
  probability density to form a particle with
  formation length $z$. The scaling variable $z$ reveals the property
  of fractal measure $z = z_0
  \epsilon^{-\delta}$, where $\epsilon $ is the scale resolution, and
  has a relevance to the geometry of
  space-time \cite{Zb,Z00}. It was shown \cite{Z01} that the A-dependence
  of high-$p_T$ hadron production in the
  framework of $z$-presentation is described by the function $\alpha (A)$
  depending on the single parameter, the  atomic weight $A$.

  The existence of the scaling  and its properties
  is assumed to reflect the fundamental features of
  particle structure, constituent interaction and particle
  production such as self-similarity, locality,
  fractality and scale-relativity.


\vskip 0.5cm
  {\section{ Z-scaling}}

 The idea of $z$-scaling is based on the assumption \cite{Stavinsky}
 that the  gross features of the inclusive particle
  distributions for reaction  (\ref{eq:r1}) at high energies
  \begin{equation}
  P_{1}+P_{2} \rightarrow q + X.
  \label{eq:r1}
  \end{equation}
can be described  in  terms of the corresponding kinematic
characteristics of the exclusive subprocess written in the symbolic
form
\begin{equation}
(x_{1}M_{1}) + (x_{2}M_{2}) \rightarrow m_{1} +
(x_{1}M_{1}+x_{2}M_{2} + m_{2}).
\label{eq:r2}
\end{equation}
The scale-invariant  fractions
$x_{1}$ and $x_{2}$ of the incoming four-momenta of colliding
objects are expressed via  momenta and masses of incident and produced
particles ($P_{1}, P_{2}, q$ and $M_{1}, M_{2}, m_1$) and determine
a minimum energy, which
 is necessary for the production of the secondary particle with mass $m_1$
 and  four-momentum $q$.
  The parameter $m_{2}$ is introduced  to satisfy the  internal conservation
  laws (for isospin, baryon number, and strangeness).

  \vskip 0.5cm
  {\subsection{Fractions $x_1$ and $x_2$}}

  The elementary parton-parton collision is considered  as a binary
  sub-process which satisfies the condition
  \begin{equation}
  (x_{1}P_{1} + x_{2}P_{2} - q)^{2} = (x_{1}M_{1} + x_{2}M_{2} +
  m_{2})^{2}.
  \label{eq:r5}
  \end{equation}
  The equation reflects minimum recoil mass hypothesis in the
  elementary sub-process. To connect kinematic and structural
  characteristics of the interaction, the coefficient
  $\Omega$ is introduced. It is chosen in the form
  \begin{equation}
  \Omega(x_1,x_2) = m(1-x_{1})^{\delta_1}(1-x_{2})^{\delta_2},
  \label{eq:r8}
  \end{equation}
  where $m$ is a mass constant and $\delta_1$ and $\delta_2$
  are factors relating to the fractal structure of
  the colliding objects \cite{Z99}\footnote{The anomalous dimensions
  are found to be  $\delta_{1,2} = \delta_h$ and
  $\delta_1 = \delta_h$, $\delta_2 = \delta_A = \delta_N \cdot A$
  for $h-h $ and $h-A$ collisions, respectively.}.
  The fractions $x_{1}$ and
  $x_{2}$  are determined  to maximize the value of $\Omega(x_1,x_2)$,
  simultaneously fulfilling condition
  $
  {d\Omega(x_1,x_2)/ dx_1}|_{x_2=x_2(x_1)} = 0.
  $
  Expressions for $x_{1}$ and $x_{2}$ as a
  function of the momenta and masses of
  the colliding and produced particles are given in \cite{Z99}.
  The variables
  $x_{1,2}$ are equal to unity along the phase space limit and
  cover the full phase space accessible at any
  energy.


\vskip 0.5cm
{\subsection{Scaling function $\psi(z)$ and variable $z$}}

 The scaling function $\psi$ expressed via the invariant differential
 cross section for the production of
 the inclusive particle $m_{1}$  is introduced as follows (see \cite{Z99})
 \begin{equation}
 \psi(z) = - \frac{\pi s_A}{\rho_A(s, \eta) \sigma_{inel}}J^{-1}
 E\frac{d\sigma}{dq^{3}}.
 \label{eq:r20}
 \end{equation}
 Here, $s_A \simeq s \cdot A$ and $ s $ are the center-of-mass energy
  squared of the corresponding $ h-A $
 and $ h-N $ systems and  $A$ is the atomic weight. The factor $J$ is
 a known function of kinematic variables
 \cite{Z99}. The expression (\ref{eq:r20}) relates the inclusive differential
  cross section and the average
 multiplicity density $\rho_A(s,\eta)$ to the scaling function $\psi(z)$.

The scaling function  is normalized as
\begin{equation}
\int_{z_{min}}^{\infty} \psi(z) dz = 1.
\label{eq:b6}
\end{equation}
The equation allow us to give the physical meaning
of the scaling function $\psi$ as a probability density to form
a particle  with a corresponding value of the variable $z$.


  The variable $z$ as argued in \cite{Z99}  can be interpreted
  as a particle formation length. It is chosen  in the form
\begin{equation}
z = \frac{ \sqrt{ {\hat s}_{\bot} }} {\Omega \cdot \rho_A(s) },
\label{eq:r28}
\end{equation}
where ${\hat{s}}^{1/2}_{\bot}$
is the transverse kinetic energy
of subprocess (\ref{eq:r2});
$\Omega$ is the measure given by (\ref{eq:r8}) and
$\rho_A(s) = \rho_A(s, \eta=0)$.
 We would like to note that the form of $z$ determines its variation range.
 The boundaries of the range are 0
 and $\infty$, as defined by (\ref{eq:r28})  and (\ref{eq:r8}).
 These values are scale independent and
 kinematically accessible at any energy.

%***********************************************************************

%%  Thus, one of the features of the procedure described above
% is the joint use of
% the experimental observables characterizing hard and soft processes.
%  The scaling variable $z$ and the scaling function  $\psi(z)$
%  are expressed via experimental quantities,
%  inclusive cross section and multiplicity
%  particle density.  The first one describes the hard
%  and the second one describes the soft regimes of particle formation.
%  The physical features of hard and soft processes
%  are very different. Therefore there is a real problem
%  for the theoretical description of $z$-scaling in the
%%  framework of perturbative QCD. We would like to note that
%%  $z$-construction is not direct mathematical consequence of
%%  parton model of strong interaction but this is a new
%  data presentation motivated by parton-parton and string-like
%  scenarios of particle interactions.
%
%
%%***********************************
%
%
%    Let us consider the definition of the variable
%  $z=\sqrt{\hat s_{\bot}}/(\Omega\rho_A)$  more closely
%   and clarify its physical meaning.
%  %Here we would like to argue that $z$ is the hadron formation length.
%  We assume that the gross features of the inclusive
%  particle distribution for the reactions (\ref{eq:r1})
%  at high energies can be described  via the
%  corresponding characteristics of exclusive  subprocess (\ref{eq:r2}).
%  The value $ \sqrt {\hat s_{\bot}}$ is the minimal transverse energy of
%  colliding constituents necessary to produce a real hadron in the reaction
%  (\ref{eq:r1}). It is assumed that two point-like and massless
%  elementary constituents interact each other in the initial state and
%  convert into real hadrons in the final state. The conversion is not
%  instant process and is usually called  hadronization.
%  Space-time microscopic picture of the process is not
%  understood enough at present time.
%  We assume that a number of hadrons produced
%  in the hard interaction of constituents
%  is proportional to $\rho_A$. Therefore the value
%   $ \sqrt {\hat s_{\bot}}/\rho_A$ corresponds to the energy density
%  per one hadron produced in the subprocess.
%  The factor $\Omega \simeq M_1+M_2 - x_1 M_1- x_2 M_2  $
%  is the missing mass for the process (\ref{eq:r1})
%   expressed via the kinematic characteristics of the
%  subprocess (\ref{eq:r2}). It corresponds to the energy
%  consumed on creation
%  of the associative particle multiplicity and characterizes
%  the property of hadron environment such
%  as energy tension of nuclear matter.
%  Taking into account the qualitative scenario of hadron formation
%  as a conversion of a point-like constituent into a real hadron
%  we interpreted the value $z$ as a hadron formation length.
%  It increases with $p_{\bot}$ at fixed $\sqrt s$ and  takes into account
%  kinematic and dynamic features of hadron formation in
%  the elementary subprocess (\ref{eq:r2}).
%
%
  \vskip 0.5cm
  {\subsection{Fractality and scale-relativity}}

  Fractality in particle and nuclear physics concerns the internal
  structure of particles and their interactions. It is manifested
  by their self-similarity on any scale.
  This general principle is described by power law dependencies of
  the corresponding quantities \cite{Nottale,Z99}.


 The equation (\ref{eq:r5}) written in the form
  $x_1 x_2 - x_1 \lambda_2 - x_2 \lambda_1 = \lambda_0 $,
  does not change under the scale transformation
$
  \lambda_{1,2} \rightarrow \rho_{1,2} \cdot \lambda_{1,2},\ \ \
  x_{1,2} \rightarrow \rho_{1,2} \cdot x_{1,2}, \ \ \
  \lambda_0 \rightarrow  \rho_1 \cdot  \rho_2 \cdot  \lambda_0.$
   The transformation with the scale parameters
   $\rho_{1,2}$ allows us to consider the collisions of the complex
   objects in terms of suitable sub-processes of the
   interacting elementary constituents.
%It is reasonable to use
%   $\rho_1=1$, $\rho_2=1$ and $\rho_1=1$, $\rho_2=A$ for
%  the description of $p-p$ and  $p-A$ interactions,
%  respectively. Here, $A$ is the  corresponding atomic weight.
The coefficient $\Omega$, given by (\ref{eq:r8}),
 connects the kinematic and fractal characteristics of
 the interaction.
 The factors $\delta_1$ and $\delta_2$ are
 anomalous fractal dimensions of the colliding objects.
 The fractal structure itself is defined by the structure
  of the interacting constituents, which is not an elementary one either.
  In this scheme, high energy hadron-hadron, hadron-nucleus and
  nucleus-nucleus interactions are considered as interactions of fractals.

%  For the collisions of pions with nuclei we have
%  $\delta_{\pi}=\delta_1<<\delta_2=\delta_A$, what is demonstrated
%  on the experimental data below.

  The variable  $z$ written in the form
  $ z=z_0\cdot {\epsilon}^{-\delta}$ (where
   $z_0=\sqrt{{\hat s}_{\bot}}/\rho(s)$ and
 $\epsilon ^{-1} =[m(1-x_1)^{A_1}(1-x_2)^{A_2}]^{-1} $)
 reveals the properties  of a fractal measure
 and $\delta $ is the anomalous fractal dimension describing
 the intrinsic structure of the interaction constituents
 revealed at high energies. The nontrivial features of
 mechanism of particle formation is that the formation length $z$
 increases with resolution $\epsilon ^{-1}$.


%  The factor $V$ is the relative part of the full phase-space
%  volume corresponding to such parton-parton
%  collisions in which the inclusive particle can be produced.
%  The fractal property of the collision reveals itself so that
%  only the part of all multi-scattering corresponding to the phase space
%  $V^{\delta}$ produces the inclusive particle.


  \vskip 0.5cm
 { \section{ $\pi^-p$,  $\pi^--$nucleus collisions and $z$-scaling}}

   Experimental data sets
   of cross sections for $\pi^{\pm,0}, K^{\pm}, \bar p$ hadrons
   produced  in $\pi^--p$ and $\pi^--A$ collisions at high transverse
   momentum $p_T$  are presented in
   \cite{fris83,donal76,marzo87,turch93} and \cite{alver93,E706},
   respectively.
   The measurements were made at
   pion momentum $p_{lab}=40, 200, 300~GeV/c$  over the
   range  $0.8<p_T<10.~GeV/c$. The nuclear  targets  $Be, Cu$
   and $W$ were used.

    We would like to note that all the cross section data
    demonstrate  the strong energy dependence of
 the cross section on transverse momentum,
 the tendency  that  difference between hadron yields increases
 with transverse momentum and energy $\sqrt s$ and
 the non-exponential behavior of the spectra
 at $p_{T}>1~GeV/c$.

  \vskip 0.5cm
{\subsection{$\pi^--p$ collisions}}

 In this section we study the properties of $z$-scaling
 for hadrons produced in $\pi^--p$ collisions.
% General formulas (\ref{eq:r20}) and (\ref{eq:r28}) are
% used to calculate the scaling function $\psi(z)$ and the variable
% $z$. The quantities $\rho (s,\eta) $ and $\sigma_{inel}$ are the
% average charged particle multiplicity density and the inelastic
% cross section of $\pi^--p$-collisions, respectively.
%** ***** Goran MC simulation **********
  The charged particle density $\rho (s,\eta) $  in $\pi^--p$ collisions was simulated
 by PYTHIA \cite{PYTHIA} in the energy range $\sqrt s = 10-200~GeV$.
 The results of simulations show that the energy dependence of the
 density $\rho (s)$ for processes  $\pi^--p$ and $p-p$ is practically
 the same one (taking into account the errors)
 and can be parameterized in the form $\rho = a s^b$.
 The values of the parameters were found to be
 $a = 0.74\pm 0.12,\ b =0.105\pm 0.011$ and
 $a = 0.59\pm 0.08,\ b =0.126\pm 0.017$ for  $p-p$ and  $\pi^--p$,
 respectively. The PYTHIA results give the relation
 $\sigma_{\pi p} = 0.67 \sigma_{pp}$ expected from quark counting rule too.
 We do not have enough experimental data for $\rho(s) $ of
 $\pi^--p$ at high  $\sqrt s$ and $p_T$ and the available
 experimental data \cite{NA22} are not in disagreement with MC
 results. Therefore we use in our analysis of $z$-scaling
 in $\pi^--p$  collisions
 the experimentally measured dependence of the average charged particle
 multiplicity density  for $p-p$ collisions. As we will show later
 the replacement does not destroy the general properties of
 $z$-scaling  in $\pi^--p$ particle production.


 We verify the hypothesis of energy scaling for data
 $z$-presentation for hadron production
 in $\pi^--p$ collisions using the available experimental data.

 Figures 1(a)-2(a)  show the dependence of the cross section
 $Ed^3\sigma/dq^3$  of  $\pi^{+}$ and $K^{-}$-mesons produced
 in $\pi^--p$
 on transverse momentum $p_{T}$ at $p_{lab} = 40, 200 ,300~GeV$
 and the produced angle $\theta_{cm}$ near $90^0$.
 Note that the data cover the  wide
 transverse momentum range, $p_{T}=1-6~GeV/c$.



%%%% The similar energy dependence of cross section
%%%% for $\pi^0$-mesons produced in $\pi^--p$
%%%% collisions at $p_{lab}=100,200$ and $300~GeV/c$
%%%% and the angle  $\theta_{cm}^{\pi N}$ of $90^0$  is shown in Figure 6(a).

 Figures 1(b)-2(b) show $z$-presentation of the same data sets.
 Taking into account the experimental errors we can conclude that
 the scaling function $\psi(z)$ demonstrates an energy
 independence over a wide energy and transverse momentum
 range at $\theta_{cm}^{\pi N} \simeq 90^0$.
 The energy dependence  of the $\pi^--p$ experimental data
 is used to find the value of the anomalous dimension $\delta_{\pi}$.
 It is equal to 0.1.
% The similar results are found for $\pi^{-}, K^{+}, \bar p$
% produced in $\pi -p$ collisions too.


% Figures 7-10 demonstrate
% the energy dependence of $\psi(z)$
% for $\pi^{\pm}, K^{\pm}$ produced in $p-p$ collisions,
% as a comparison with the $\pi^--p$ case.
% Experimental cross section  data were obtained
% at Batavia \cite{Cronin} and Protvino \cite{Protvino}.
% One can see that both data $z$-presentations reveal
% similar properties.


%\vskip 0.5cm
%{\subsection {Angular dependence  of $\psi(z)$}}


 To analyze the angular dependence
 of the scaling function $\psi(z)$ of charged hadrons
 $\pi^{\pm}, K^{\pm}, \bar p$ produced
 in $\pi^--p$ collisions  we use the data set obtained
 at Protvino \cite{turch93}.
 The data set includes the results
 of measurements of the invariant cross section
 $Ed^3\sigma/dq^3$  at the pion incident momentum
 $p_{lab} = 40~GeV$ over the momentum and angular ranges of
 $p_{T}=1.05-3.75~GeV/c$ and $\theta_{cm}^{\pi N} = 49^0-93^0$.
 The obtained results show that experimental errors are large enough
 and more high accuracy data on the
 cross section are necessary to verify carefully the
 angular independence of the scaling function $\psi(z)$ of hadrons
 produced in $\pi^--p$ collisions  as a function
 of energy $\sqrt s $, transverse momentum $p_T$ and
 and $\theta_{cm}^{\pi N}$.


\vskip  0.5cm
{\subsection{$\pi^--A$ collisions} }

 In this section, we study the properties of $z$-scaling for
 hadron  production  in $\pi^--$nucleus
 collisions. The  experimental data sets \cite{fris83,alver93} and
 \cite{E706} are used in the analysis.

  According to the procedure of
  $z$-analysis of the $p-A$ experimental data, the function $\psi$
  is calculated for every nucleus using the normalization  factor
  $\sigma_{inel}^{pA}/\sigma_{inel}^{pp}$ \cite{Z01}
  in the expression for the inclusive cross section
  \footnote{The other normalization  factor,
  $\sigma_{inel}$, was used in \cite{Z99}.}.
  The factor $\sigma_{inel}^{pA}$ is the total inelastic
 cross section for $pA$ interactions.
 The $A$-dependence of the ratio $\sigma_{inel}^{pA}/\sigma_{inel}^{pp}$
 is taken from \cite{Carroll}.
  The relevant multiplicity
 densities of charged particles obtained  by the Monte Carlo
 simulation generator  HIJING \cite{Hij1} for different nuclei
 ($A=7-197$) are taken in the form  $\rho_A(s) {\simeq }0.67{\cdot}
 A^{0.18}{\cdot }s^{0.105} $ \cite{Z99}.
 In the present analysis  we use for the
 multiplicity density $\rho_A(s)$
 and the $A$-dependence of the ratio $\sigma_{inel}^{\pi A}/\sigma_{inel}^{\pi p}$
 of $\pi^--A$
 the results obtained for $p-A$ collisions. The possibility of such replacement
 will be argued by obtained results for data $z$-presentation.

 The symmetry
 transformations
$ z \rightarrow \alpha (A) \cdot z,
 \ \psi \rightarrow \alpha^{-1} (A) \cdot \psi $
 of the function  $\psi(z)$  and the argument $z$ are used to
 compare the functions $\psi$  for different nuclei.



 Figures 3(a),4(a) show the dependence of the inclusive cross
 section  for $\pi^{+}, K^{-}$
 produced in $\pi^--Be, Cu$, and $W$ collisions on the transverse
 momentum $p_{T}$ at $p_{lab} = 200$ and $300~GeV/c$.
 The incisive cross section data for $W$ nucleus demonstrate the
 energy dependence, which enhances as the transfers momentum of
 produced particle increases.

 Figure 5(a) presents cross sections for $\pi^0$-mesons produced
 on $Be$ and $Cu$ nuclear targets at $\sqrt s \simeq  31~GeV$.

 The dependencies of the scaling function $\psi$ on $z$ of the same
 experimental data are shown in Figures 3(b)-5(b).
 As seen from Figure 5(b) the asymptotic regime
 (the power law for the scaling function, $\psi(z)\sim
 z^{-\beta}$) is achieved over a high-$p_T$ range for $\pi^0$-meson
 production on nuclei $Be$ and $Cu$ at $\sqrt s \simeq 31~GeV$.
 The value of the slope parameter $\beta$
 is found to be $\simeq 9.37$  over a wide range of
 high transverse momentum ($3<q_{T}<7.5~GeV/c$).


 We use the properties of $z$-scaling to calculate the
 cross section of $\pi^0$-meson production in $\pi^-Be$ and
 $\pi^-Cu$ collisions at high energies. The results are shown in
 Figures 6(a,b).


%  777777777777777778888888888888888888888****************

% It is usually assumed that high energy-density
% nucleon matter produced in
% heavy-ion collisions could give an indication of phase transition to
% a quark-gluon plasma and high-$p_T$ $\pi^0$-meson  spectra
% should be sensitive to the transition \cite{Wang1}.
% Therefore the verification of the predicted results
% is of interest for
% a more detailed study of the $A$-dependence of $\pi^0$ spectra
% over a high-$p_T$ range and for a search for signatures of
% nuclear matter phase transition.


%
%
%
%\vskip  0.5cm
%{\section{Discussion}}
%
% In this section we discuss the obtained results. First of all,
% it should be emphasized that the scaling properties of
% $\pi^{\pm,0}, K^{\pm}, \bar p$ produced in $\pi^--p$ and
% $\pi^--A$  collisions were observed at a high colliding energy and
% transverse momentum of produced hadron. This means that the
% scaling function describes the fragmentation process of point-like
% produced partons into observable hadrons.
%
%% **************************************************
%
%   In Section II  we described
%    the qualitative scenario that is useful to
%    construct the scaling function $\psi$ and variable $z$.
%    In the scenario the reaction $P_1 + P_2 \to q + X$ is treated
%    as a binary parton-parton collision process which leads to
%   (\ref{eq:r5}).
%    The remnant $X$ is treated as an elementary particle
%    with a mass $x_1 M_1+x_2 M_2+m_2$. The 4-momentum conservation law
%   (\ref{eq:r5}) is an important part of the construction.
%    We show that $z$-presentation of experimental
%    data demonstrate self-similarity of particle production.
%   This fact is independent of theoretical scenario of constituent
%   interaction. In the analysis we use  the experimental
%   data but not the results of microscopic calculations.
%   However there are and widely used
%   different string-like models
%   (Lund model \cite{Lund},
%   Dual Parton Model \cite{DPM},
%   Monte Carlo String Fusion Model \cite{MCSFM} etc.).
%   Such string-like models of particle
%   production allow ones to describe
%   satisfactorily different experimental data, as well
%   \cite{QM96,QM93,HOT,Schukraft,Schmidt,QM99}.
%  It means that string-like scenarios of particle formation
%  reflect also some
%  features of particle structure, constituent interaction
%  and particle formation.
%  At present time we do not know
% the real mechanism of particle formation. We assume that
% the process can reveal  different features
% corresponding to binary parton-parton
%  and string-like interactions.
% Therefore we hope that such
% joint models can be developed in future to describe,
% in particular, $z$-scaling too.
%
%
%
%% ***************************************************
%
% The measure $\Omega(x_1,x_2)$ defining the scaling variable $z$
% given by (\ref{eq:r8}) determines all possible configurations of
% elementary interactions that lead to the production of the
%  inclusive particle. In  our case, the measure is factorized:
% $\Omega(x_1,x_2)=\Omega_1(x_1)\cdot \Omega_2(x_2)$ \footnote{The factorization  of
% $\Omega(x_1,x_2)$
% is assumed to be violated for the cumulative processes
% \cite{Stavinsky,Zolin,Strikman,Bondarev}.}.
%  A single
% measure $\Omega_i(x_i)$ described by a power dependence in the
% space of fractions $\{x_1, x_2\}$ reflects the number of
% constituent configurations in the colliding object involved in the
% production of the inclusive particle. The measure is characterized
% by the fractal dimension $\delta_i$.
% The $z$-presentation of experimental data for
% $\pi^{\pm,0}, K^{\pm}, \bar p$ produced in $\pi^--p$ collisions
% and presented in Figures 1(b)-6(b) corresponds to the anomalous
% dimensions $\delta_N = 0.5$ and $\delta_{\pi} = 0.1$. The fractal
% dimension of the nucleus $\delta_A $ is expressed via the nucleon
% fractal dimension $\delta_A = \delta_N \cdot A $.
%
% We would like to note that the same values of $\delta_N$
% (see Figure 7(b)-10(b))
% and $\delta_A $ were used in our previous  analysis of charged and
% neutral hadrons produced in $p-p$ and  $p-A$ collisions \cite{Rog2,Z01}. The
% relation  $\delta_{\pi} < \delta_{N} < \delta_{A}$ means that a
% fractal structure of nucleon and nucleus is more richer
% than a pion  one. We assume that the dimension of a point-like
% particle should be zero. In reality the point-likeness of the
% interacting constituents is defined by a colliding energy
% $\sqrt s$ and a transverse momentum of a registered  particle.
% Therefore the determination of the anomalous dimension $\delta_h$
% of different kind of particles
% ($p, \pi, K, \gamma, e, \mu$  etc.) is of interest to study elementary constituents and
% search for quark and gluon substructure.
%
%   The property of scale covariance
%   of the function $\psi$ under  scale transformation (\ref{eq:r50})
%   shows that hadron formation (hadronization)
%   as a process reveals self-similarity in a nuclear environment.
%   The fractal dimension  $\delta_A $
%   is a quantitative characteristic of
%   the hadron structure in  surrounding matter.
%   Therefore, the change of the fractal dimension of
%   particle formation is assumed to be a
%   signature of new physics phenomena
%   (quark compositeness, new type of interaction,
%   phase transition etc.).
%
%   In the framework of the proposed scenario, the interaction of
%   colliding objects is the interaction of fractals and the mechanism
%   of hadron formation is considered as a process of construction  of
%   complex fractal (hadron) from elementary fractal blocks. The size
%   and structure of blocks depend on the colliding energy and
%   transverse momentum of the produced hadron. The multiple scattering of
%   elementary constituents is the main feature of heavy ion
%   collisions. Fractality is the reflection of this property
%   described by a power law.
%
%   One of the important properties of the scaling function $\psi(z)$
%   is the power law, $\psi(z) \sim z^{-\beta}$. The power regime is
%   found for $\pi^0$-meson production in $\pi^--A $ collisions  at a
%   high transverse momentum of $p_{T} > 2~GeV/c$ and $\sqrt s \simeq
%   31~GeV$ and shown in Figure 16(b).
%    The asymptotic value of the slope
%    parameter $\beta \simeq 9.37$ is determined
%    over the  transverse momentum range $3 <p_{T}< 7.5~GeV/c$.
%
%   The $A$-dependence of $z$-scaling obtained in our analysis
%   confirms the general features of  $z$-scaling construction  found
% for charged hadron production in $p-p$ and $p-A$ collisions
% \cite{Z96,Z99}. Thus, the influence of surrounding matter on the
% mechanism of particle formation both in $\pi^--A$ and  $p-A$ is
% described by a smooth function $\alpha(A)$ depending on the atomic
%  weight $A$. The obtained results give indication  that the fractal
%  dimension is not changed by a nuclear medium and the relation
% $\delta_A = \delta_N \cdot A$ is valid for hadron production
% in $\pi^--A$ collisions too.
%
%
%    We would like to note that the different data presentations
%    are used to study the $A$-dependence of particle
%    production. One of
%    them is $\sigma_A = \sigma_N \cdot A^{\alpha(x_F, p_T)}$.
%    Here  $\sigma_A $, $\sigma_N $ and $x_F$ are the cross section for
%    nucleus, nucleon and Feynman scaling variable, respectively; $A$ is the atomic weight.
%   The function  $\alpha (x_F , p_T)$ describes the
%   nuclear matter influence and reveals a nontrivial
%   $x_F$ and $p_T$ dependence  as found for example in \cite{Cronin}
%  (see \cite{Schukraft,Schmidt} also).
%   There are the problem how to
%   normalize the  experimental nucleus cross section in order
%   to compare  the cross sections
%   (or the scaling functions as in the present paper) for different nuclei.
%   One can use the normalization per pair participants in soft region
%   (low $p_T$)
%   or per one collisions in hard region (high $p_T$).
%   Both of them are model dependent  and there are not
%   strong criteria for the procedure.
%   Therefore in the paper we described one of the possible
%   procedures to study the $A$-dependence of $z$-scaling.
%   The normalization per nucleon for $z$
%   (not per nucleus $\rho_A$ as in the present paper)
%   and per nucleus cross section  $\sigma_{pA}^{inel}$ for $\psi(z)$ were used
%   in \cite{Z99}. In the present paper we used the normalization
%   conditions for $z$ and $\psi $ as in \cite{Rog2}.
%
%%   *******************************************
%
%  The other problem for data analysis is due to
%  multiplicity selection  of events.
%   In the paper we presumably treat the minimum bias data of
%   $\pi-A$ collisions.
%   The $A$-dependence of the parameter $\alpha$ is found by the fit.
%   It is the same as for $p-A$ collisions \cite{Z01}.
%   The comparison of $\psi$ for the different nuclei
%   is  performed  by "shifting"  of $z \rightarrow \alpha z$ and
%   the scaling function  $\psi \rightarrow \alpha^{-1} \psi$.
%    We would like to note that the centrality of the collision
%   is characterized by the multiplicity of particles produced.
%   It corresponds to the different value of the impact
%   parameter. The impact parameter is the model dependent
%   quantity and characterizes the collision geometry.
%   We do not have enough information (cross section data and
%    corresponding multiplicity particle density data)
%   for analysis. Therefore we use the procedure to construct
%   data $z$-presentation without taking into account the
%   multiplicity selection.
%   We assume that high-$p_T$
%   collisions over a central rapidity range for different nuclei
%   can be described by the same function $\alpha (A)$.
%   The obtained results shown in Figures 11(b)-16(b) confirm the assumption.
%   In the general case the multiplicity independence of $\alpha (A)$
%   for the particle production in collisions with different
%   multiplicity at the same energy $\sqrt s$  can be violated
%   due to spectator contribution.
%   However there is the indication \cite{WA80,WA98}
%   that the shape of $p_T$ spectra of $\pi^0$-mesons produced in the
%   central and  minimum bias nucleus-nucleus collisions
%   is practically  the same.
%     It is not true for the peripheral collisions.
%   It means that the dynamic mechanism
%   describing  the particle formation is the same
%   for different multiplicity  too.
%   The multiplicity (or impact parameter) selection from
%   this point of view is the some kind of cross
%   section renormalization.
%     Therefore we consider that for construction
%     of $z$-presentation the inclusive cross section
%    and multiplicity
%     particle density should be taken in a consistent manner.
%   The change of the $p_T$ spectrum shape  as a function of
%   multiplicity at the same $\sqrt s$ and
%   different atomic weight  $A$  can
%   indicate the modification of nuclear matter state and
%   can be one of the complementary criteria to search for
%   nuclear phase transition.
%  %******************************************************
%
%   We emphasize that
%   the scaling function $\psi(z)$ describes the transformation
%(or hadronization) of
%   point-like partons  to  real particles $\pi^{\pm,0},
%   K^{\pm}, \bar p$.
%    Therefore, we assume that
%   the search for scaling violation of hadron production in $\pi-A$
%   collisions at high energies, especially  in the region of high
%    transverse momenta, could be very interesting for our
%   understanding of a $\pi$-meson substructure itself, interaction of
%   pion and nucleon elementary constituents and mechanism of particle
%   formation in nuclear medium.
%
%
%  % ****************   Z-p_T plot  ***********************
%
%   Figure 18 shows a $z-p_{T}$ plot for $\pi^--p$, $\pi^--Be$ and
%   $\pi^--Au$ collisions at $\sqrt s = 20,30 $ and $40~GeV$.
%   The plot allows us to determine  a transverse
%   momentum range where the scaling can be violated. The value $z=20$
%   for $\pi^--p$ collisions  corresponds to the value of the
%   transverse momentum $p_{T}$ of 7.2, 9 and $10.5~GeV/c$, at
%   $\sqrt s = 20$, 30 and $40~GeV$, respectively. The available
%   experimental data \cite{donal76,marzo87} for $\pi^--p$ (Figure
%   6(b)), and  the data \cite{alver93,E706} for $\pi^--Be$ (Figure 16(b))
%   give
%   us the indication that the kinematic range $z>10$ is of more
%   preferable for experimental investigations of $z$-scaling violation.


\vskip  0.5cm
{\section{Conclusions}}

 The scaling features of $\pi^{+}, K^{-}$ hadrons
 produced in $\pi^--p$ and $\pi^--A$ collisions at high energies in
 terms of $z$-scaling are studied. The experimental data sets
 \cite{fris83,donal76,marzo87,turch93} and \cite{alver93,E706} on
 the inclusive cross sections are used in the analysis. The
 momentum of incident pion beam $p_{lab}$ changes from 40 to $515~GeV/c$
 over the high transverse momentum range $(p_{T}=0.2-10~GeV/c)$.

 The $z$-presentation  of experimental data is constructed
 and  the anomalous fractal dimension $\delta_{\pi}$ is found
 to be 0.1.
 The value is allowed us to reproduce the general properties of
 $z$-scaling established in $p-p$, $\bar p-p$ and $p-A$ collisions.

%  The symmetry transformations of the function  $\psi$ and its
%  argument,  $\psi \rightarrow \alpha^{-1}(A)  \psi $ and $z\rightarrow
%  \alpha (A) z$, are used to compare $\psi(z)$  of different nuclei
%  $(A = Be, Cu, W)$.

 The $A$-dependence of data $z$-presentation is studied
 and it is shown that the dependence is described by the
 function  $\alpha = \alpha(A)$. The fractal
 dimension of nuclei $\delta_A$ for $\pi^--A$ is found to be the
 same  $\delta_A= A\cdot \delta_N$ as for the
 hadrons produced in $p-A$ collisions.

 The asymptotic regime of the scaling function, $\psi(z)\sim
 z^{-\beta}$, is observed  and the asymptotic value of the slope
 parameter  $\beta $ is determined  to be  $\simeq 9.37$
 at $\sqrt s \simeq  31~GeV$ and over the range
 $3 <p_{T}< 7.5~GeV/c$.

 Using the properties of $z$-scaling, the dependence of the cross
 sections of $\pi^{0}$-mesons produced in $\pi^--Be$, $\pi^--Cu$
 and $\pi^--Au$ collisions on transverse momentum over the central
 rapidity range at high energy $\sqrt s = 60, 200$ and $500~GeV$ is
 predicted.

%The dependence of $z$ on transverse momentum $p_{T}$ ($z-p_{T}$
% plot ) as a function of an atomic weight $(A)$, an angle of produced
% particle $(\theta)$ and a colliding energy $\sqrt s $
% is suggested to use as a joint kinematic and dynamic criterion
% to select the domain where new physical phenomena can be found.

 Thus, the obtained results show that data $z$-presentation of
 hadrons  produced in $\pi^--p$ and
 $\pi^--A$ collisions demonstrates general properties of the
 particle formation mechanism such as self-similarity, locality,
 scale relativity and fractality.  As one can assume the properties
 reflect through the anomalous dimension $\delta_{\pi}$
 the features of elementary constituent substructure too.

% \vskip 1cm
%Acknowledgments

%This work has been partially  supported by the grant
%No. 020475  of the Czech Ministry of Education, Youth and Physical
%Training.

%for useful discussions of the present work
%and M.Zielinski from the E706 Collaboration
%for providing one of the authors (M.T.)
%with the experimental data.


%{\Large \bf Acknowledgments}

%\vskip 0.5cm

%This work has been partially supported
%by Grant of the Czech Academy of Sciences No. 1048703.
%
%\vskip 1cm
%

%\newpage
{\small
\begin{thebibliography}{99}


\bibitem{DPM}
A. Capella, U. Sukhatme, C.I. Tan, and J. Tran Thanh Van,
%Dual Parton Model,
%Orsay preprint LPTHE 92-38.
Phys. Rep. {\bf 236}, 225 (1994).


\bibitem{fris83}
N. D. Giokaris et al.,  Phys. Rev. Lett.  {\bf 47}, 1690 (1981);\\
 H. J. Frisch et al.,  Phys. Rev. {\bf D27}, 1001 (1983).


\bibitem{donal76}G. J. Donaldson  et al.,
 Phys. Rev. Lett.  {\bf 36}, 1110 (1976);
 Phys. Rev. Lett.  {\bf 40}, 917 (1978);
 Phys. Lett.  {\bf B73}, 375 (1978).

\bibitem{marzo87} C. DeMarzo et al.,  Phys. Rev. {\bf D36}, 16 (1987).

\bibitem{turch93} L. K. Turchanovich et al.,
Yad.Fiz. {\bf 56(10)}, 116 (1993).
%; IFVE-93-8, 1993; PAN {\bf 56}, 1367 (1993).

\bibitem{alver93}G. Alverson et al.,  Phys. Rev. {\bf D48}, 5 (1993).
%\bibitem{alver92}G. Alverson et al.,  Phys. Rev. {\bf D45}, 3889 (1992).

%\bibitem{Alverson} E706 Collaboration G.Alverson  et al.
% Phys. Rev. {\bf D48}, 5 (1993).

\bibitem{E706}  L. Apanasevich  et al.
 Phys. Rev. Lett. {\bf 81}, 2642 (1998).





\bibitem{Z96}
I.Zborovsk\'{y}, Yu.A.Panebratsev, M.V.Tokarev, G.P.Skoro, Phys.
Rev. {\bf D54} (1996) 5548.

%\bibitem{pag}
%M.V.Tokarev, JINR Preprint  E2-98-161, Dubna, 1998.
%
%\bibitem{Dedovich}  M.V.Tokarev, T.G.Dedovich,
%JINR Preprint  E2-99-300, Dubna, 1999;
% Int. J. Mod. Phys. {\bf A15} (2000) 3495.
%
%\bibitem{Rog1}  M.V.Tokarev, O.V.Rogachevski, T.G.Dedovich,
%JINR Preprint  E2-99-313, Dubna, 1999;
%J. Phys. G: Nucl. Part. Phys. {\bf 26} (2000) 1671.
%
%
%\bibitem{Rog2}  M.V.Tokarev, O.V.Rogachevski, T.G.Dedovich,
%JINR Preprint  E2-2000-90, Dubna, 2000.
%

\bibitem{Nottale}
L.Nottale, Fractal Space-Time and Microphysics. World Scientific
Publishing Co.Pte. Ltd. 1993.


\bibitem{Z99}
I.Zborovsk\'{y}, M.V.Tokarev, Yu.A.Panebratsev, and G.P.\v{S}koro,
% JINR Preprint  E2-98-250, Dubna, 1998;
Phys. Rev. {\bf C59}, 2227 (1999).

\bibitem{Z01}
 M.Tokarev, I.Zborovsk\'{y}, Yu.Panebratsev, G.Skoro,
% JINR Preprint  E2-99-113, Dubna, 1999;
 Int. J. Mod. Phys. {\bf A16} (2001) 1281.

\bibitem{Zb}
I.Zborovsk\'{y}, 

\bibitem{Z00}
I.Zborovsk\'{y}, M.Tokarev, Yu.Panebratsev, G.Skoro,
  JINR Preprint  E2-2001-41, Dubna, 2001.


\bibitem{Z97}
    I.Zborovsky, M.Tokarev, Yu.Panebratsev, G.Skoro,
  JINR Preprint  E2-97-24, Dubna, 1997.

%   EXP DATA ******************************


\bibitem{Stavinsky} V.S. Stavinsky,
Physics of Elementary Particles and Atomic Nuclei
{\bf 10}, 949 (1979).


%\bibitem{matveev}
%  V.A. Matveev, R.M. Muradyan, and A.N. Tavkhelidze,
%  Part. Nuclei {\bf 2}, 7 (1971);
%  Lett. Nuovo Cimento {\bf 5}, 907 (1972);
%  Lett. Nuovo Cimento {\bf 7}, 719 (1973).
%
%\bibitem{brodsky}
%  S. Brodsky, and G. Farrar, Phys. Rev. Lett. {\bf 31}, 1153 (1973);
%  Phys. Rev. {\bf D11}, 1309 (1975).


%\bibitem{Cronin}
%J.W.Cronin {\it et al.}, Phys.Rev. {\bf D11} (1975) 3105;\\
%D.Antreasyan {\it et al.}, Phys. Rev. {\bf D19} (1979) 764.


\bibitem{Carroll}
 J. Carroll {\it et al.}, Phys. Lett. B {\bf 80}, 319 (1979).

\bibitem{Hij1}
 X.N. Wang and M. Gyulassy, Phys. Rev. D {\bf 44}, 3501 (1991);
 Phys. Rev. D {\bf 45}, 844 (1992).


%\bibitem{Hij2}
% X.N. Wang and M. Gyulassy, Phys. Rev. D {\bf 45}, 844 (1992).
%\bibitem{Wang1}  X.-N. Wang,  22 July, 1999.

\bibitem{PYTHIA}
 T. Sjostrand, Computer Physics Communications, {\bf 82}, 74  (1994).

 \bibitem{NA22}
 M. Adamus et al., IHEP preprint 88-121, Serpukhov, 1988.

% \bibitem{Lund}
% B. Andersson, G. Gustafson, G. Ingelman, and  T. Sjostrand,
% Phys. Rep. {\bf 97}, 31 (1983);
% B. Andersson, The Lund Model, Cambridge University Press, Cambridge, 1998;
% B. Andersson, In: Proc. XXII International Symposium on Multiparticle Dynamics, p.428
% Edited by C.Pajares, Santiago de Compostela, Spain, July 13-17, 1992, World Scientific Publishing
% Co. Pte. Ltd.


% \bibitem{MCSFM}
% N.S. Amelin, M. Braun, and C.Pojares,
% Z. Phys. C {\bf 63}, 507 (1994).

 %In: Proc. XXII International Symposium
 % on Multiparticle Dynamics, p.482,
 % Edited by C.Pajares, Santiago de Compostela, Spain, July 13-17, 1992,
 % World Scientific Publishing
 % Co. Pte. Ltd.


\end{thebibliography}

% *************************************************************
% *************    1(a,b),   2(a,b)   *************************
% *************************************************************

\newpage
\begin{minipage}{4cm}

\end{minipage}

\vskip 4cm
\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{sbepi0.ps}{}}
%{cppip.ps}{}}
{fig1a.ps}{}}
\hspace*{3cm}
%\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[55 55 400 400]
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{hppip_t.ps}{}}
{fig1b.ps}{}}
\vskip -0.5cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}


 {\bf Figure 1.}
 (a) Dependence of  the
 inclusive cross section of $\pi^+$-meson  production
 on transverse momentum $q_{T}$ at $p_{lab} = 40, 200$ and $300~GeV/c$
 and $\theta_{cm}^{\pi p} \simeq 90^{0}$
 in  $\pi^--p$ collisions.
 Experimental data are taken from
 \cite{fris83,turch93}.
 %\cite{Povlis}-\cite{E706}.
 (b) The corresponding scaling function $\psi(z)$.

%\end{center}

\vskip 5cm

\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{cpkm.ps}{}}
{fig2a.ps}{}}
\hspace*{3cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{hpkm.ps}{}}
{fig2b.ps}{}}
\vskip -1.cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}

 {\bf Figure 2.}
 (a) Dependence of  the
 inclusive cross section of $K^-$-meson  production
 on transverse momentum $q_{T}$ at $p_{lab} = 40, 200$ and $300~GeV/c$
 and $\theta_{cm}^{\pi p} \simeq 90^{0}$
 in  $\pi^--p$ collisions.
 Experimental data are taken from
 \cite{fris83,turch93}.
 (b) The corresponding scaling function $\psi(z)$.


% *************************************************************
% *************    3(a,b),   4(a,b)   *************************
% *************************************************************

\newpage
\begin{minipage}{4cm}

\end{minipage}

\vskip 4cm
\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{cwip.ps}{}}
{fig3a.ps}{}}
\hspace*{3cm}
%\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[55 55 400 400]
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{hwip.ps}{}}
{fig3b.ps}{}}
\vskip -0.5cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}



{\bf Figure 3.}
(a) Dependence of  the
inclusive cross section of $\pi^+$-meson  production
on transverse momentum $q_{T}$
in  $\pi^--A$ collisions
at $p_{lab} = 200, 300~GeV/c$.
Experimental data are taken from
\cite{fris83}.
(b) The corresponding scaling function $\psi(z)$.



%\end{center}

\vskip 5cm

\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{cwkm.ps}{}}
{fig4a.ps}{}}
\hspace*{3cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{hwkm.ps}{}}
{fig4b.ps}{}}
\vskip -1.cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}

{\bf Figure 4.}
(a) Dependence of  the
inclusive cross section of $K^-$-meson  production
on transverse momentum $q_{T}$
in  $\pi^--A$ collisions
at $p_{lab} = 200, 300~GeV/c$.
Experimental data are taken from
\cite{fris83}.
(b) The corresponding scaling function $\psi(z)$.

% *************************************************************
% *************    5(a,b),   6(a,b)   *************************
% *************************************************************

\newpage
\begin{minipage}{4cm}

\end{minipage}

\vskip 4cm
\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{cbepi0.ps}{}}
{fig5a.ps}{}}
\hspace*{3cm}
%\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[55 55 400 400]
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{hbepi0f.ps}{}}
{fig5b.ps}{}}
\vskip -0.5cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}

{\bf Figure 5.}
(a) Dependence of  the
inclusive cross section of $\pi^0$-meson  production
on transverse momentum $q_{T}$
in  $\pi^--A$ collisions
at $\sqrt s =31~GeV$.
Experimental data are taken from
\cite{alver93,E706}.
(b) The corresponding scaling function $\psi(z)$.


%\end{center}

\vskip 5cm

\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{cbepi0f.ps}{}}
{fig6a.ps}{}}
\hspace*{3cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{ccupi0f.ps}{}}
{fig6b.ps}{}}
\vskip -1.cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}

 {\bf Figure 6.}
  Dependence of the inclusive cross section of
 $\pi^0$-meson  production
 on transverse momentum $q_{T}$
 at $\theta_{cm}^{\pi N} \simeq 90^{0}$
 in
 $\pi^--Be$ (a),  $\pi^--Cu$ (b) and  $\pi^--Au$ (c) collisions.
 The calculated results are shown by
 points and solid lines $(\diamond - 60~GeV, \circ - 200~GeV,
 + - 500~GeV)$.
 Experimental data $(\triangle)$ are taken from \cite{alver93,E706}.


\end{document}


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% *************    1(a,b),   2(a,b)   *************************
% *************************************************************

\newpage
\begin{minipage}{4cm}

\end{minipage}

\vskip 4cm
\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{sbepi0.ps}{}}
{cppip.ps}{}}
\hspace*{3cm}
%\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[55 55 400 400]
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{ssipi0.ps}{}}
{hppip_t.ps}{}}
\vskip -0.5cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}


 {\bf Figure 1.}
 (a) Dependence of  the
 inclusive cross section of $\pi^+$-meson  production
 on transverse momentum $q_{T}$ at $p_{lab} = 40, 200$ and $300~GeV/c$
 and $\theta_{cm}^{\pi p} \simeq 90^{0}$
 in  $\pi^--p$ collisions.
 Experimental data are taken from
 \cite{fris83,turch93}.
 %\cite{Povlis}-\cite{E706}.
 (b) The corresponding scaling function $\psi(z)$.

%\end{center}

\vskip 5cm

\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{scupi0f.ps}{}}
{cppim.ps}{}}
\hspace*{3cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{saupi0.ps}{}}
{hppim_t.ps}{}}
\vskip -1.cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}

 {\bf Figure 2.}
 (a) Dependence of  the
 inclusive cross section of $\pi^-$-meson  production
 on transverse momentum $q_{T}$ at $p_{lab} = 40, 200$ and $300~GeV/c$
 and $\theta_{cm}^{\pi p} \simeq 90^{0}$
 in  $\pi^--p$ collisions.
 Experimental data are taken from
 \cite{fris83,turch93}.
 (b) The corresponding scaling function $\psi(z)$.


% *************************************************************
% *************    3(a,b),   4(a,b)   *************************
% *************************************************************

\newpage
\begin{minipage}{4cm}

\end{minipage}

\vskip 4cm
\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{sbepi0.ps}{}}
{cpkp.ps}{}}
\hspace*{3cm}
%\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[55 55 400 400]
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{ssipi0.ps}{}}
{hpkp.ps}{}}
\vskip -0.5cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}




 {\bf Figure 3.}
 (a) Dependence of  the
 inclusive cross section of $K^+$-meson  production
 on transverse momentum $q_{T}$ at $p_{lab} = 40, 200$ and $300~GeV/c$
 and $\theta_{cm}^{\pi p} \simeq 90^{0}$
 in  $\pi^--p$ collisions.
 Experimental data are taken from
 \cite{fris83,turch93}.
 %\cite{Povlis}-\cite{E706}.
 (b) The corresponding scaling function $\psi(z)$.


%\end{center}

\vskip 5cm

\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{scupi0f.ps}{}}
{cpkm.ps}{}}
\hspace*{3cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{saupi0.ps}{}}
{hpkm.ps}{}}
\vskip -1.cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}



 {\bf Figure 4.}
 (a) Dependence of  the
 inclusive cross section of $K^-$-meson  production
 on transverse momentum $q_{T}$ at $p_{lab} = 40, 200$ and $300~GeV/c$
 and $\theta_{cm}^{\pi p} \simeq 90^{0}$
 in  $\pi^--p$ collisions.
 Experimental data are taken from
 \cite{fris83,turch93}.
 (b) The corresponding scaling function $\psi(z)$.


% *************************************************************
% *************    5(a,b),   6(a,b)   *************************
% *************************************************************

\newpage
\begin{minipage}{4cm}

\end{minipage}

\vskip 4cm
\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{sbepi0.ps}{}}
{cpbp.ps}{}}
\hspace*{3cm}
%\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[55 55 400 400]
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{ssipi0.ps}{}}
{hpbp.ps}{}}
\vskip -0.5cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}



 {\bf Figure 5.}
 (a) Dependence of  the
 inclusive cross section of $\bar p$  production
 on transverse momentum $q_{T}$ at $p_{lab} = 40, 200$ and $300~GeV/c$
 and $\theta_{cm}^{\pi p} \simeq 90^{0}$
 in  $\pi^--p$ collisions.
 Experimental data are taken from
 \cite{fris83,turch93}.
 (b) The corresponding scaling function $\psi(z)$.



%\end{center}

\vskip 5cm

\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{scupi0f.ps}{}}
{cppi02.ps}{}}
\hspace*{3cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{saupi0.ps}{}}
{hppi0_t2.ps}{}}
\vskip -1.cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}


 {\bf Figure 6.}
 (a) Dependence of  the
 inclusive cross section of $\pi^0$-meson  production
 on transverse momentum $q_{T}$ at $p_{lab} = 100, 200$ and $300~GeV/c$
 and $\theta_{cm}^{\pi p} \simeq 90^{0}$
 in  $\pi^--p$ collisions.
 Experimental data $(\diamond - 100~GeV/c, \circ - 200~GeV/c,
 +  - 300~GeV/c)$  are taken from
 \cite{donal76} and \cite{marzo87}.
 (b) The corresponding scaling function $\psi(z)$.



% *************************************************************
% *************    7(a,b),   8(a,b)   *************************
% *************************************************************

\newpage
\begin{minipage}{4cm}

\end{minipage}

\vskip 3cm
\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{sbepi0.ps}{}}
{cpppip.ps}{}}
\hspace*{3cm}
%\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[55 55 400 400]
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{ssipi0.ps}{}}
{hpppip.ps}{}}
\vskip -0.5cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}



{\bf Figure 7.}
(a) The  inclusive differential cross sections
for the $\pi^+$-mesons produced
in $p-p$ collisions at $p_{lab} = 70, 200, 300$ and
$ 400~GeV/c$ and
$\theta_{pp} \simeq 90^{0}$ as functions of the
transverse momentum  $q_{T}$.
(b) The corresponding scaling function $\psi(z)$.
Solid lines are obtained by fitting  of the data
at  $p_{lab} = 70$, and $400$.
Experimental data are taken from
\cite{Cronin,Protvino}.




%\end{center}

\vskip 5cm

\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{scupi0f.ps}{}}
{cpppim.ps}{}}
\hspace*{3cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{saupi0.ps}{}}
{hpppim.ps}{}}
\vskip -1.cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}


{\bf Figure 8.}
(a) The  inclusive differential cross sections
for the $\pi^-$-mesons produced
in $p-p$ collisions at $p_{lab} = 70, 200, 300$ and
$ 400~GeV/c$ and
$\theta_{pp} \simeq 90^{0}$ as functions of the
transverse momentum  $q_{T}$.
(b) The corresponding scaling function $\psi(z)$.
Solid lines are obtained by fitting  of the data
at  $p_{lab} = 70$, and $400$.
Experimental data are taken from \cite{Cronin,Protvino}.



% *************************************************************
% *************    9(a,b),   10(a,b)   *************************
% *************************************************************

\newpage
\begin{minipage}{4cm}

\end{minipage}

\vskip 3cm
\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{sbepi0.ps}{}}
{cppkp.ps}{}}
\hspace*{3cm}
%\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[55 55 400 400]
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{ssipi0.ps}{}}
{hppkp.ps}{}}
\vskip -0.5cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}



{\bf Figure 9.}
(a) The  inclusive differential cross sections
for the $K^+$-mesons produced
in $p-p$ collisions at $p_{lab} = 70, 200, 300$ and
$ 400~GeV/c$ and
$\theta_{pp} \simeq 90^{0}$ as functions of the
transverse momentum  $q_{T}$.
(b) The corresponding scaling function $\psi(z)$.
Solid lines are obtained by fitting  of the data
at  $p_{lab} = 70$, and $400$.
Experimental data are taken from \cite{Cronin,Protvino}.




%\end{center}

\vskip 5cm

\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{scupi0f.ps}{}}
{cppkm.ps}{}}
\hspace*{3cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{saupi0.ps}{}}
{hppkm.ps}{}}
\vskip -1.cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}


{\bf Figure 10.}
(a) The  inclusive differential cross sections
for the $K^-$-mesons produced
in $p-p$ collisions at $p_{lab} = 70, 200, 300$ and
$ 400~GeV/c$ and
$\theta_{pp} \simeq 90^{0}$ as functions of the
transverse momentum  $q_{T}$.
(b) The corresponding scaling function $\psi(z)$.
Solid lines are obtained by fitting  of the data
at  $p_{lab} = 70$, and $400$.
Experimental data are taken from \cite{Cronin,Protvino}.




% *************************************************************
% *************    11(a,b),   12(a,b)   *************************
% *************************************************************

\newpage
\begin{minipage}{4cm}

\end{minipage}

\vskip 4cm
\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{sbepi0.ps}{}}
{cwip.ps}{}}
\hspace*{3cm}
%\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[55 55 400 400]
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{ssipi0.ps}{}}
{hwip.ps}{}}
\vskip -0.5cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}



{\bf Figure 11.}
(a) Dependence of  the
inclusive cross section of $\pi^+$-meson  production
on transverse momentum $q_{T}$
in  $\pi^--A$ collisions
at $p_{lab} = 200, 300~GeV/c$.
Experimental data are taken from
\cite{fris83}.
(b) The corresponding scaling function $\psi(z)$.



%\end{center}

\vskip 5cm

\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{scupi0f.ps}{}}
{cwim.ps}{}}
\hspace*{3cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{saupi0.ps}{}}
{hwim.ps}{}}
\vskip -1.cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}

{\bf Figure 12.}
(a) Dependence of  the
inclusive cross section of $\pi^-$-meson  production
on transverse momentum $q_{T}$
in  $\pi^--A$ collisions
at $p_{lab} = 200, 300~GeV/c$.
Experimental data are taken from
\cite{fris83}.
(b) The corresponding scaling function $\psi(z)$.


% *************************************************************
% *************    13(a,b),   14(a,b)   *************************
% *************************************************************

\newpage
\begin{minipage}{4cm}

\end{minipage}

\vskip 4cm
\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{sbepi0.ps}{}}
{cwkp.ps}{}}
\hspace*{3cm}
%\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[55 55 400 400]
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{ssipi0.ps}{}}
{hwkp.ps}{}}
\vskip -0.5cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}


{\bf Figure 13.}
(a) Dependence of  the
inclusive cross section of $K^+$-meson  production
on transverse momentum $q_{T}$
in  $\pi^--A$ collisions
at $p_{lab} = 200, 300~GeV/c$.
Experimental data are taken from
\cite{fris83}.
(b) The corresponding scaling function $\psi(z)$.



%\end{center}

\vskip 5cm

\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{scupi0f.ps}{}}
{cwkm.ps}{}}
\hspace*{3cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{saupi0.ps}{}}
{hwkm.ps}{}}
\vskip -1.cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}

{\bf Figure 14.}
(a) Dependence of  the
inclusive cross section of $K^-$-meson  production
on transverse momentum $q_{T}$
in  $\pi^--A$ collisions
at $p_{lab} = 200, 300~GeV/c$.
Experimental data are taken from
\cite{fris83}.
(b) The corresponding scaling function $\psi(z)$.


% *************************************************************
% *************    15(a,b),   16(a,b)   *************************
% *************************************************************

\newpage
\begin{minipage}{4cm}

\end{minipage}

\vskip 4cm
\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{sbepi0.ps}{}}
{cwbp.ps}{}}
\hspace*{3cm}
%\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[55 55 400 400]
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{ssipi0.ps}{}}
{hwbp.ps}{}}
\vskip -0.5cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}


{\bf Figure 15.}
(a) Dependence of  the
inclusive cross section of $\bar p$  production
on transverse momentum $q_{T}$
in  $\pi^--A$ collisions
at $p_{lab} = 200, 300~GeV/c$.
Experimental data are taken from
\cite{fris83}.
(b) The corresponding scaling function $\psi(z)$.


%\end{center}

\vskip 5cm

\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{scupi0f.ps}{}}
{cbepi0.ps}{}}
\hspace*{3cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{saupi0.ps}{}}
{hbepi0f.ps}{}}
\vskip -1.cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}


{\bf Figure 16.}
(a) Dependence of  the
inclusive cross section of $\pi^0$-meson  production
on transverse momentum $q_{T}$
in  $\pi^--A$ collisions
at $\sqrt s =31~GeV$.
Experimental data are taken from
\cite{alver93,E706}.
(b) The corresponding scaling function $\psi(z)$.


% *************************************************************
% *************    17(a,b,c)   *************************
% *************************************************************

\newpage
\begin{minipage}{4cm}

\end{minipage}

\vskip 4cm
\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
{cbepi0f.ps}{}}
\hspace*{3cm}
%\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[55 55 400 400]
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
{ccupi0f.ps}{}}
\vskip -0.5cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}


%{\bf Figure 15.}
%(a) Dependence of  the
%inclusive cross section of $\bar p$  production
%on transverse momentum $q_{T}$
%in  $\pi^--A$ collisions
%at $p_{lab} = 200, 300~GeV/c$.
%Experimental data are taken from
%\cite{fris83}.
%(b) The corresponding scaling function $\psi(z)$.


%\end{center}

\vskip 5cm

\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{scupi0f.ps}{}}
{caupi0f.ps}{}}
%\hspace*{3cm}
%\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{hbepi0f.ps}{}}
\vskip -1.cm
\hspace*{0.cm} c)
\end{center}


 {\bf Figure 17.}
  Dependence of the inclusive cross section of
 $\pi^0$-meson  production
 on transverse momentum $q_{T}$
 at $\theta_{cm}^{\pi N} \simeq 90^{0}$
 in
 $\pi^--Be$ (a),  $\pi^--Cu$ (b) and  $\pi^--Au$ (c) collisions.
 The calculated results are shown by
 points and solid lines $(\diamond - 60~GeV, \circ - 200~GeV,
 + - 500~GeV)$.
 Experimental data $(\triangle)$ are taken from \cite{alver93,E706}.


% *************************************************************
% *************    18(a,b,c)   *************************
% *************************************************************

\newpage
\begin{minipage}{4cm}

\end{minipage}

\vskip 4cm
\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
{zp_pti.ps}{}}
\hspace*{3cm}
%\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[55 55 400 400]
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
{zbe_pti.ps}{}}
\vskip -0.5cm
\hspace*{0.cm} a) \hspace*{8.cm} b)\\[0.5cm]
\end{center}


%{\bf Figure 15.}
%(a) Dependence of  the
%inclusive cross section of $\bar p$  production
%on transverse momentum $q_{T}$
%in  $\pi^--A$ collisions
%at $p_{lab} = 200, 300~GeV/c$.
%Experimental data are taken from
%\cite{fris83}.
%(b) The corresponding scaling function $\psi(z)$.


%\end{center}

\vskip 5cm

\begin{center}
\hspace*{-2.5cm}
\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
{zau_pti.ps}{}}
%\hspace*{3cm}
%\parbox{5cm}{\epsfxsize=5.cm\epsfysize=5.cm\epsfbox[95 95 400 400]
%{hbepi0f.ps}{}}
\vskip -1.cm
\hspace*{0.cm} c)
\end{center}


{\bf Figure 18.}
 Dependence of the variable $z$ of $\pi^0$-meson production in
$\pi^--p$ (a), and $\pi^--Be$ (b)   and $\pi^--Au$ (c) collisions
on transverse momentum $p_{T}$ at different colliding energy
$\sqrt s$ and $\theta_{cm}^{\pi N} \simeq 90^0$. Points, $\star
-20$ , $\triangle - 30~GeV$, $\circ - 40~GeV$, are calculated
results.

\end{document}


