Flavor violation in theories with TeV scale quantum gravity

We study the effects of possible flavor-violating operators in theories with the TeV scale quantum gravity, in which the ordinary matter is localized on a 3-brane embedded in the space with N extra dimensions, whereas gravity propagates in the bulk. These operators are scaled by the fundamental Planck mass M_pf ∼ TeV and must be suppressed by the gauge family symmetries. We study suppression of the most dangerous and model-independent operators. Several points emerge. First, we show that the Abelian symmetries can not do the job and one has to invoke non-Abelian U(2)_F (or U(3)_F) symmetries. However, even in this case there emerge severe restrictions on the fermion mixing pattern and the whole structure of the theory. In order not to be immediately excluded by the well-known bounds, the horizontal gauge fields must be the bulk modes, like gravitons. For the generic hierarchical breaking pattern the four-fermion operators induced by the tree-level exchange of the bulk gauge fields are unsuppressed for N = 2. For N > 3 the suppression factor goes as a square of the largest U(2)_F-non-invariant Yukawa coupling, which implies the lower bound M_pf> 10 TeV or so from the K⁰ - K̄⁰ system. Situation is different in the scenarios when flavor Higgs fields (and thus familons) live on a (3 + N′)-brane of lower dimensionality than the gauge fields. The further suppression of gauge-mediated operators can be achieved by an explicit construction: for instance, if U(2)_F is broken by a vacuum expectation value of the doublet, the troublesome operators are suppressed in the leading order, due to custodial SO(4) symmetry of the Higgs-gauge quartic coupling.