The pentaquark $Theta^+$ has been searched for via the $pi^-p to K^-X$ reaction with beam momenta of 1.92 and 2.01 GeV/$c$ at J-PARC. A missing mass resolution of 2 MeV (FWHM) was achieved but no sharp peak structure was observed. The upper limits on the production cross section averaged over the scattering angle from 2$^{circ}$ to 15$^{circ}$ in the laboratory frame were found to be less than 0.28 $mu$b/sr at the 90% confidence level for both the 1.92- and 2.01-GeV/$c$ data. The systematic uncertainty of the upper limits was controlled within 10%. Constraints on the $Theta^+$ decay width were also evaluated with a theoretical calculation using effective Lagrangian. The present result implies that the width should be less than 0.36 and 1.9 MeV for the spin-parity of $1/2^+$ and $1/2^-$, respectively.
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