
\newcommand{\captionwidth}{14cm}

\newcommand{\agt}{\,\rlap{\lower 3.5 pt \hbox{$\mathchar \sim$}} \raise 1pt
 \hbox {$>$}\,}
\newcommand{\alt}{\,\rlap{\lower 3.5 pt \hbox{$\mathchar \sim$}} \raise 1pt
 \hbox {$<$}\,}

\newcommand{\gsim}{\;\rlap{\lower 3.5 pt \hbox{$\mathchar \sim$}} \raise 1pt
 \hbox {$>$}\;}
\newcommand{\lsim}{\;\rlap{\lower 3.5 pt \hbox{$\mathchar \sim$}} \raise 1pt
 \hbox {$<$}\;}
\newcommand{\dd}{{\rm d}}                  % differential
\newcommand{\bld}[1]{\boldmath{$#1$}}      % bold math symbols
\newcommand{\sprod}[2]{#1\hspace{-.1em}\cdot\hspace{-.1em}#2}   % dot-product
\newcommand{\llangle}{\left\langle}        
\newcommand{\rrangle}{\right\rangle}

\renewcommand{\Re}{{\rm Re}}
\renewcommand{\Im}{{\rm Im}}
\newcommand{\msbar}{$\overline{\rm MS}$}

\newcommand{\yp}{y}
\newcommand{\logtwos}{L_{tW}}
\newcommand{\logtwms}{l_{tW}}
\newcommand{\logctheta}{l_\Theta}
\newcommand{\logmuW}{l_{\mu W}}

\newcommand{\logqmms}{l_{qm}}
\newcommand{\logqmos}{L_m}
\newcommand{\logmsms}{l_s}
\newcommand{\logmsos}{L_{ms}}
\newcommand{\logmusos}{L_{s\mu}}
\newcommand{\logqmums}{l_{q\mu}}
\newcommand{\logmum}{l_{\mu m}}




