Limits on Extra Dimensions and New Particle Production in the Exclusive Photon and Missing Energy Signature in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi><mml:mover accent="true"><mml:mi>p</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math>Collisions at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msqrt><mml:mi>s</mml:mi></mml:msqrt><mml:mo>=</mml:mo><mml:mn>1.8</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">T</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">V</mml:mi></mml:math>

The exclusive $\ensuremath{\gamma}{\mathrm{E\ensuremath{\llap{\not\;}}}}_{T}$ signal has a small standard model cross section and is thus a channel sensitive to new physics. This signature is predicted by models with a superlight gravitino or with large extra spatial dimensions. We search for such signals at the Collider Detector at Fermilab, using $87\text{ }\mathrm{p}{\mathrm{b}}^{\mathrm{\ensuremath{-}}\mathrm{1}}$ of data at $\sqrt{s}=1.8\text{ }\mathrm{T}\mathrm{e}\mathrm{V}$, and extract 95% C.L. limits on these processes. A limit of 221 GeV is set on the scale $|F{|}^{1/2}$ in supersymmetric models. For 4, 6, and 8 extra dimensions, model-dependent limits on the fundamental mass scale ${M}_{D}$ of 0.55, 0.58, and 0.60 TeV, respectively, are found. We also specify a ``pseudo-model-independent'' method of comparing the results to theoretical predictions.

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