Flavor violation in theories with TeV scale quantum gravity

We study the effects of possible flavor-violating operators in theories wit h 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 Plan ck mass M-pf similar to TeV and must be suppressed by the gauge family symm etries. We study suppression of the most dangerous and model-independent op erators. 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)) s ymmetries. However, even in this case there emerge severe restrictions on t he fermion mixing pattern and the whole structure of the theory. In order n ot to be immediately excluded by the well-known bounds, the horizontal gaug e fields must be the bulk modes, like gravitons. For the generic hierarchic al breaking pattern the four-fermion operators induced by the tree-level ex change of the bulk gauge fields are unsuppressed for N = 2. For N > 3 the s uppression factor goes as a square of the largest U(2)(F)-non-invariant Yuk awa coupling, which implies the lower bound M-Pf > 10 TeV or so from the K- o- (K) over bar(o) system. Situation is different in the scenarios when fla vor Higgs fields (and thus familons) live on a (3 + N')-brane of lower dime nsionality than the gauge fields. The further suppression of gauge-mediated operators can be achieved by an explicit construction: for instance, if U( 2), is broken by a vacuum expectation value of the doublet. the troublesome operators are suppressed in the leading order, due to custodial SO(4) symm etry of the Higgs-gauge quartic coupling. (C) 1999 published by Elsevier Sc ience B.V. All rights reserved.