%Paper: 
%From: luw@bepc3.ihep.ac.cn
%Date: Fri, 16 Jun 1995 17:02:25 CDT
%Date (revised): Wed, 21 Jun 1995 08:33:26 CDT
%Date (revised): Sat, 09 Sep 1995 05:52:43 CDT
%Date (revised): Sat, 09 Sep 1995 06:01:29 CDT

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\begin{document}
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\begin{title}
Symmetry analysis of the hadronic tensor for the semi-inclusive
  pseudoscalar meson leptoproduction from an unpolarized nucleon target
\end{title}


\author{Wei Lu}

\begin{instit}
CCAST (World Laboratory),  P.O. Box 8730, Beijing 100080, China

and Institute of High Energy Physics,
 P.O. Box 918(4), Beijing 100039, China\footnote{Mailing address}
\end{instit}


\begin{abstract}



By examining the symmetry constraints on the semi-inclusive
pseudoscalar  particle production in unpolarized inelastic  lepton-hadron
scattering, we  present a complete, exact Lorentz decomposition
for the corresponding hadronic tensor. As a result, we find that
it contains       five  independent terms, instead of the four
as have been suggested before. The newly identified  one is odd under the
naive time reversal transformation,  and the corresponding
structure function is directly related to the
single spin asymmetry in the semi-inclusive pseudoscalar meson
production by a polarized  lepton beam off an unpolarized target.
\end{abstract}
\pacs{PACS Number(s): 11.30.Er, 13.85.Ni, 13.85.+e}

In the particle physics, the symmetry  analysis plays
a very important role, since it can forbid or allow for
the existence of physical quantities  before we set
about the details of dynamics.
Although the  principles and methods
involved  in the symmetry analysis  are usually
not complicated, in some circumstances it is a
highly nontrivial matter to
arrive at a complete result.
As the time reversal (${\cal T} $) invariance
of interactions  is involved,  this is  even the case.
In fact, most mistakes associated with
the symmetry  analysis
can be traced to  the  confusion
the  so-called  naive ${\cal T} $ transformation
with the full ${\cal T} $ transformation.
In other words,  the constraints due to time reversal
invariance  are often not properly considered.



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