New results for light gravitinos at hadron colliders: Fermilab Tevatron limits and CERN LHC perspectives

Abstract

We derive Feynman rules for the interactions of a single gravitino with (s)quarks and gluons/gluinos from an effective supergravity Lagrangian in nonderivative form and use them to calculate the hadroproduction cross sections and decay widths of single gravitinos. We confirm the results obtained previously with a derivative Lagrangian as well as those obtained with the nonderivative Lagrangian in the high-energy limit and elaborate on the connection between gauge independence and the presence of quartic vertices. We perform extensive numerical studies of branching ratios, total cross sections, and transverse-momentum spectra at the Fermilab Tevatron and the CERN LHC. From the latest CDF monojet cross section limit, we derive a new and robust exclusion contour in the gravitino-squark/gluino mass plane, implying that gravitinos with masses below $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ to $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\text{ }\text{ }\mathrm{eV}$ are excluded for squark/gluino masses below 200 and 500 GeV, respectively. These limits are complementary to the one obtained by the CDF Collaboration, $1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\text{ }\text{ }\mathrm{eV}$, under the assumption of infinitely heavy squarks and gluinos. For the LHC, we conclude that supersymmetric scenarios with light gravitinos will lead to a striking monojet signal very quickly after its startup.