Exploring the linear space of Feynman integrals via generating functions

Deriving a comprehensive set of reduction rules for Feynman integrals has been a longstanding challenge. In this paper, we present a proposed solution to this problem utilizing generating functions of Feynman integrals. By establishing and solving differential equations of these generating functions, we are able to derive a system of reduction rules that effectively reduce any associated Feynman integrals to their bases. We illustrate this method through various examples and observe its potential value in numerous scenarios.Comment: 11 pages, 4 figures, references adde

A Possibility of Search for New Physics at LHCb

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.Comment: 7 pages, 3 figures, 1 table. More references and discussion adde