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%%%%%%%%%%%% Begin Cover Page %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\preprint

\title{Erratum: Next-to-leading order supersymmetric QCD predictions for
 associated production of gauginos and gluinos [Phys.\ Rev.\ D 62, 095014
 (2000)]}

\author{Edmond L.\ Berger, Michael Klasen, and Tim M.\ P.\ Tait}

\date{\today}

\pacs{12.60.Jv, 12.38.Bx, 13.85.Fb}

\maketitle
%%%%%%%%%%%% End of Cover Page %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%% Begin Section I %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Within the curly brackets of Eq.\ (C1), a term $-\pi^2/4$ from the expansion of
the relative factor $\Gamma(1-\epsilon)/\Gamma(1-2\epsilon)$ between the
virtual (Eq.\ (21)) and the soft corrections (Eq.\ (28)) should be included.
Equation (C1) then reads
\renewcommand{\theequation}{C1}
\bea
   \frac{d^2\hat{\sigma}^S}{dt_2 \, du_2} &=& 
   \frac{d^2 {\hat{\sigma}}^B}{dt_2 \, du_2} 
   \left( \frac{C_F \, \alphas}{\pi} \right) \left\{
     {\rm Li}_2 \left( \frac{ u_2 \, t_2 - s \, m_2^2}{(s+t_2)(s+u_2)} \right) 
   + \frac{1}{2} \log^2 \left( \frac{ \mu^2}{m_1^2 \delta^2} \right)
   + \log \left(\frac{(s+t_2)(s+u_2)}{s \, m_1^2} \right)
     \log \left( \frac{ \mu^2}{m_1^2 \delta^2} \right) \right. 
   \nonumber \\[0.3cm]
   & & \left.
   + \frac{1}{2}\log^2 \left( \frac{(s+t_2)(s+u_2)}{s \, m_1^2} \right)
   - {\pi^2\over4} \right\}.
\eea
Correct inclusion of the missing term changes the total NLO cross section and
its renormalization and factorization scale dependence, since the term
$-\pi^2/4$ is multiplied by $\alpha_s$ and the parton densities. Figures\ 16
and 17 should therefore be replaced by Fig.\ 1 below. The corrected
%
%%%%%%%%%%%%%% Begin Figure I %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
 \centering
 \includegraphics[width=0.49\columnwidth]{ppbar2gln2_qg.eps}
 \includegraphics[width=0.49\columnwidth]{pp2gln2_qg.eps}
 \caption{\label{fig:1}Dependence of the predicted NLO, LO, and $qg$ initiated
  total cross sections at the Tevatron (left) and LHC (right) on the
  renormalization and factorization scale. We show the case of $\gluino
  \neutralino_2$ associated production in the SUGRA model, with $m_{\gluino} =
  410 $ GeV and $m_{\neutralino_2} = 104$ GeV. This figure replaces Figs.\ 16
  and 17 in Ref.\ \cite{Berger:2000iu} and agrees with the results in Ref.\
  \cite{Spira:2002rd}.}
\end{figure}
%%%%%%%%%%%%%% End of Figure I %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
results agree with those in Ref.\ \cite{Spira:2002rd}, if we use CTEQ5M parton
densities \cite{Lai:1999wy} and the two-loop expression for $\alpha_s$ with
$\Lambda^{(5)}=226$ MeV. Our implementation of the intermediate on-shell squark
subtraction in Eq.\ (41) differs from that in Ref.\ \cite{Spira:2002rd}, 
and both approaches are arguably equally valid.  The difference is insignificant 
quantitatively in this case, so that all other numerical results in Ref.\
\cite{Berger:2000iu} remain valid, if the renormalization and factorization
scales are properly adjusted.

Specific predictions for the Tevatron and LHC will be provided on request
\cite{request}. For example, we show in Fig.\ 2 the predicted total cross
sections at the current Tevatron center-of-mass energy of
%
%%%%%%%%%%%%%% Begin Figure II %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
 \centering
 \includegraphics[width=0.49\columnwidth]{ppbar2glxx_xsec.eps}
 \includegraphics[width=0.49\columnwidth]{ppbar2glxx_lg.eps}
 \caption{\label{fig:2}Predicted total cross sections at the Tevatron with 
  total center-of-mass energy $\sqrt{S}=1.96$ TeV and CTEQ6 parton densities 
  for all six $\gluino\gaugino$ channels in the SUGRA model as functions of
  the mass of the gluino (left) and for a gluino with mass 30 GeV as functions
  of $m_{1/2}$ (right).}
\end{figure}
%%%%%%%%%%%%%% End of Figure II %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
$\sqrt{S}=1.96$ TeV for all six $\gluino \gaugino$ channels in the SUGRA model
as functions of the mass of the gluino (left) and for a gluino with mass 30 GeV
as functions of $m_{1/2}$ (right). In Fig.\ 2, we use CTEQ6M (NLO) and CTEQ6L
(LO) parton densities \cite{Pumplin:2002vw} and the two-loop expression for
$\alpha_s$ with $\Lambda^{(5)}=226$ MeV (LO {\em and} NLO).

Finally, we take the opportunity to correct two typographical errors in the
published version of Ref.\ \cite{Berger:2000iu}. In Eq.\ (C2), the arguments
of the squared and the last logarithm were interchanged. The correct form is
\renewcommand{\theequation}{C2}
\bea
   \frac{d^2\hat{\sigma}^S}{dt_2 \, du_2} &=& 
   -\frac{d^2 {\hat{\sigma}}^B}{dt_2 \, du_2} 
   \left( \frac{N_C \, \alphas}{2 \pi} \right) \left\{
     -2 + 
     {\rm Li}_2 \left( \frac{ u_2 \, t_2 - s \, m_2^2}{(s+t_2)(s+u_2)} \right) 
   + \frac{1}{2} \log^2 \left( \frac{(s+t_2)(s+u_2)}{s \, m_1^2} \right)
  \right. \nonumber \\[0.3cm] & & \left.
      + \left[ \log \left(\frac{(s+t_2)(s+u_2)}{s \, m_1^2} \right)
     - 1 \right]
     \log \left( \frac{ \mu^2}{m_1^2 \delta^2} \right) \right\}.
\eea
In Eq.\ (D2), $+$-signs were omitted between the two large brackets in the
third line and the first two fractions in the fourth line. The correct form is
\renewcommand{\theequation}{D2}
\bea
  \frac{d^3 \hat{\sigma}_1^{g}}{ds_4 \, dt_2 \, du_2} &=&
  \frac{ C_F \, \alphas \, \alphash \, \delta \, (s + t_2 + u_1 - s_4)}
  {36 \, \pi \, s^2}
  \log \left( \frac{\mu^2 (s_4 + m_1^2)}{s_4^2} \right) \\[0.3cm]
%
  & & \times \, \left\{
  \left( \frac{s_4^2 - 2 \, s_4 (s+u_2) + 2 (s+u_2)^2}{s_4 (s+u_2)} \right) 
%
  \, \left( \frac{X_t \, t_2}{(t - \msqu{t}^2)^2}
  + \frac{2 \, X_{t u} \, s \, m_1 \, m_2}
  {(t- \msqu{t}^2) [(\delu-s-t_2)(s+u_2) + s \, s_4]} 
  \right. \right. \nonumber \\[0.3cm]
%
  & & \left. \left.
%
  + \frac{X_u \, u_2 \, [s_4 \, u_2 - u_1 \, (s+u_2)]}
  {[(\delu-s-t_2)(s+u_2) + s \, s_4]^2} \right) \right.
+
  \left( \frac{s_4^2 - 2 \, s_4 (s+t_2) + 2 (s+t_2)^2}{s_4 (s+t_2)} \right) 
 \nonumber \\[0.3cm]
%
   & &  \left.
%
  \times \,\left( \frac{X_t \, t_2 \, [s_4 \, t_2 - t_1 \, (s+t_2)]}
  {[(\delt-s-u_2)(s+t_2) + s \, s_4]^2} +
  \frac{2 \, X_{t u} \, s \, m_1 \, m_2}
  {(u- \msqu{u}^2) [(\delt-s-u_2)(s+t_2) + s \, s_4]}
%
  + \frac{X_u \, u_2}{ (u - \msqu{u}^2)^2 }
  \right) \right\} . \nonumber
\eea
%%%%%%%%%%%%%% End of Section I %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%% Begin References %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{thebibliography}{1}

%\cite{Spira:2002rd}
\bibitem{Spira:2002rd}
M.~Spira,
%``Higgs and SUSY particle production at hadron colliders,''
arXiv:
%%CITATION = ;%%
and private communication. We thank M.~Spira for helpful discussions.

%\cite{Lai:1999wy}
\bibitem{Lai:1999wy}
CTEQ Collaboration, H.~L.~Lai {\it et al.},
%``Global {QCD} analysis of parton structure of the nucleon: CTEQ5 parton  distributions,''
Eur.\ Phys.\ J.\ C {\bf 12}, 375 (2000).
%.
%%CITATION = ;%%

%\cite{Berger:2000iu}
\bibitem{Berger:2000iu}
E.~L.~Berger, M.~Klasen, and T.~M.~P.~Tait,
%``Next-to-leading order SUSY-QCD predictions for associated production of  gauginos and gluinos,''
Phys.\ Rev.\ D {\bf 62}, 095014 (2000).
%.
%%CITATION = ;%%

\bibitem{request}
E-mail addresses: berger@anl.gov, michael.klasen@desy.de, tait@fnal.gov.

%\cite{Pumplin:2002vw}
\bibitem{Pumplin:2002vw}
J.~Pumplin, D.~R.~Stump, J.~Huston, H.~L.~Lai, P.~Nadolsky, and W.~K.~Tung,
%``New generation of parton distributions with uncertainties from global  QCD analysis,''
JHEP {\bf 0207}, 012 (2002).
%.
%%CITATION = ;%%

\end{thebibliography}
%%%%%%%%%%%%%% End of References %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\end{document}

