  A search is presented for the four-body decay $B^0\rightarrow p p \bar{p}
\bar{p}$ in a sample of $471$ million $B\bar{B}$ pairs collected with the BaBar
detector, operated at the SLAC PEP-II asymmetric-energy $e^+e^-$ collider. The
center-of-mass energy is $10.58$ GeV. From a fit to the distribution of the
energy-substituted mass $m_{\mathrm{ES}}$, the result
$\mathcal{B}(B^0\rightarrow p p \bar{p} \bar{p})=(1.1 \pm 0.5 \pm 0.2) \times
10^{-7}$ is extracted, where the first uncertainty is statistical and the
second is systematic. The significance of the signal is $2.9$ standard
deviations. The upper limit on the branching fraction is determined to be $2.0
\times 10^{-7}$ at $90\%$ confidence level.

High Energy Physics - Experiment