It is interesting to search for new physics beyond the standard model at LHCb. We suggest that weak decays of doubly charmed baryon such as $Xi_{cc}(3520)^+, Xi_{cc}^{++}$ to charmless final states would be a possible signal for new physics. In this work, we consider two models, i.e. the unparticle and $Z$ as examples to study such possibilities. We also discuss the cases for $Xi^0_{bb}, Xi_{bb}^-$ which have not been observed yet, but one can expect to find them when LHCb begins running. Our numerical results show that these two models cannot result in sufficiently large decay widths, therefore if such modes are observed at LHCb, there must be a new physics other than the unparticle or $Z$ models.
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