Left-right symmetry at LHC

We revisit the issue of the limit on the scale of left-right symmetry breaking. We focus on the minimal $\mathrm{SU}(2{)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2{)}_{R}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1{)}_{B\ensuremath{-}L}$ gauge theory with the seesaw mechanism and discuss the two possibilities of defining left-right symmetry as parity or charge conjugation. In the commonly adopted case of parity, we perform a complete numerical study of the quark mass matrices and the associated left and right mixing matrices without any assumptions usually made in the literature about the ratio of vacuum expectation values. We find that the usual lower limit on the mass of the right-handed gauge boson from the $K$ mass difference, ${M}_{{W}_{R}}>2.5\text{ }\text{ }\mathrm{TeV}$, is subject to a possible small reduction due to the difference between right and left Cabibbo angles. In the case of charge conjugation the limit on ${M}_{{W}_{R}}$ is somewhat more robust. However, the more severe bounds from $CP$-violating observables are absent in this case. In fact, the free phases can also resolve the present mild discrepancy between the standard model and $CP$ violation in the $B$ sector. Thus, even in the minimal case, both charged and neutral gauge bosons may be accessible at the Large Hadron Collider with spectacular signatures of lepton number violation.