%\documentstyle[aps]{revtex}
\documentstyle[12pt]{article}

\ifx\tocauthor\undefined\def\tocauthor#1{\relax}\fi
\ifx\toctitle\undefined\def\toctitle#1{\relax}\fi
\begin{document}
%\begin{center}
%{\Large \bf
\title{Relativistic Quark Model of Mesons with Current Quark  
Masses}

%\vspace{0.2cm}

\tocauthor{L. D. Soloviev}
\author{L. D. Soloviev\\
{\small\it Institute for High Energy Physics, 142284, Protvino, Russia}}
%\end{center}
\date{}
\maketitle

\vspace{0.5cm}

We consider a relativistic quantum model of mesons in which current
quarks and antiquarks confined in a meson are described by the Dirac
equations and the gluon field contribution at large distances is
approximated by the Nambu--Goto straight-line quantum string. The
current quark masses and the string tension are the main parameters of  
the model. Additional parameters are phenomenological constants which
approximate nonstring short-range quark-antiquark interactions not  
growing with the meson spin.

The model describes the masses of all the mesons from pion to $\Upsilon$ 
lying on the leading Regge trajectories (i.e. the lowest radial  
excitations in terms of the potential quark models; the higher radial  
excitatios, or the daughter trajectories, correspond to the string  
oscillations). The quantized string in the model accounts for two  
mechanisms of the potential quark models: confining potential and  
constituent quark masses. The comparison of the measured meson masses
with the model predictions allows one to determine the current quark  
masses (in $MeV$) to be $m_s =3D 224 \pm 7,~~m_c =3D 1440 \pm 10$ and
$m_b =3D 4715 \pm 20$. The universal string tension is found to be
$0.176 \pm 0.002 ~GeV^2$. The chiral $SU_3$ model makes it possible to
estimate from here the $u$- and $d$-quark masses to be
$m_u =3D 6.2 \pm 0.2 ~MeV$ and $m_d =3D 11.1 \pm 0.4 ~MeV$.

The Regge trajectories for the light-quark mesons beginnig at spin 1
are practically linear. The corresponding trajectories for the
heavy-light-quark mesons are not linear but can be reprisented by
approximate straight lines for spins less than 6 by replacing the 
argument $m^2$ by $(m - m_h)^2$ where $m_h$ is the heavy-meson mass.
The effective slopes of these straight line are bigger than for the
light-quark mesons and are growing with $m_h$. The trajectories for 
heavy quarkonia are essentially nonlinear. The Regge trajectories 
beginning at spin 0 are always nonlinear in the region of low spins.

The model predicts many masses of high-spin mesons. In some cases the
masses of unknown low-spin mesons can also be predicted by an  
extrapolation in quark masses of the phenomenological parameters of the  
model. In this way the model predicts the mass of $\eta_b(1S)(0^{-+})$  
to be $9500 \pm 30 ~MeV$ (bigger than the mass of
$\Upsilon$; a potential quark model predicts $9400 ~MeV$). The mass of
$B_c(0^-)$ is predicted to be $6400 \pm 30~MeV$ (to be compared with
the potential quark model prediction $6270~MeV$) and a new $K^*(1^-)$
meson with mass $1900~MeV$ is predicted.

The relativistic wave functions of composit mesons obtained within the  
model allow one to analyse the spin structure of polarized mesons. The
average spin projections of the $u$- and $\bar d$-quarks within the
$\rho^+$ devided by the same projection of the total spin of the meson
are found to be 0.22 and 0.23, respectively. These numbers are twice as  
small as the nonrelativistic quark model predictions 0.5. At the same  
time they are slightly different from 0.17 for zero quark masses,
so one can hope that future polarization experiments will be able to
estimate the light-quark current masses from experiment. The  
corresponding numbers for the $u$- and $\bar s$-quarks within the
$K^{*+}$ are 0.22 and 0.42 which shows an 80\% violation of the flaviour  
$SU_3$ for the spin structure within a relativistic model. The meson  
spin structure results suggest a new approach to understanding the  
nucleon spin structure obtained from polarized deep
inelastic lepton-nucleon scattering.
\begin{thebibliography}{9}
\bibitem{1}
The full text of this report is to be published in\\
L. D. Soloviev. Yadernaya Fizika, March 1999.
\bibitem{2}
Details of this approach can be found in\\
L. D. Soloviev. Proceedings of the 10th Int. Conf. "Problems of Quantum  
Field Theory", Alushta,1996, page 75 (JINR E-2-96-369, Dubna, 1996);  
IHEP reports 96-97, 97-81, 98-29, Protvino; Phys.Rev. D
$\bf 58$, 035005, 1998; Teoreticheskaya i Matematicheskaya Fizika,
$\bf 116$, No 2, 225-247, 1998.
\end{thebibliography}
\end{document}
------=_NextPart_000_000C_01BDE274.C4E55710--


