A search for baryon and lepton number violation in $B$ decays using the BaBar dataset

A search is performed for the decay $B \rightarrow \textrm{baryon } \textrm{lepton}$, where the baryon is either a $\Lambda_c^+$ or $\Lambda^0$ and the lepton is a muon or electron. This decay would violate baryon (B) and lepton (L) number individually. In some of the decays in which we search, the difference (B-L) is conserved. The $B-L$-conserving process is generally interpreted as being mediated by a boson that carries both color and lepton number and is fractionally charged. This boson is a signature of some unification theories. The flavor/generation dependence of this type of interaction can be constrained by a comprehensive search for decays involving different flavors of quarks and leptons. At the SLAC National Accelerator Laboratory, the PEP-II storage rings provided $e^+/e^-$ beams from 1999-2008, during which time the {\sl B{\scriptsize A}B{\scriptsize AR}} experiment collected 429 fb$^{-1}$ of data at the $\Upsilon(4S)$ resonance giving this analysis access to 1 billion $B$ mesons. In the event of a null result, upper limits on the $B$ branching fractions for these processes will be calculated in order to provide experimental constraints. The status of the search will be presented.