Flavor-violation tests of the warped/composite standard model in the two-site approach

Abstract

We study flavor violation in the quark sector in a purely 4D, two-site effective field theory description of the Standard Model and just their first Kaluza-Klein excitations from a warped extra dimension. The warped 5D framework can provide solutions to both the Planck-weak and flavor hierarchies of the SM. It is also related (via the AdS/CFT correspondence) to partial compositeness of the SM. We focus on the dominant contributions in the two-site model to two observables which we argue provide the strongest constraints from flavor violation, namely, ǫ K and BR (b → sγ), where contributions in the two-site model occur at tree and loop-level, respectively. In particular, we demonstrate that a "tension" exists between these two observables in the sense that they have opposite dependence on composite site Yukawa couplings, making it difficult to decouple flavor-violating effects using this parameter. We choose the size of the composite site QCD coupling based on the relation of the two-site model to the 5D model (addressing the Planck-weak hierarchy), where we match the 5D QCD coupling to the 4D coupling at the loop-level and assuming negligible tree-level brane-localized kinetic terms. We estimate that a larger size of the 5D gauge coupling is constrained by the requirement of 5D perturbativity. We find that ∼ O(5) TeV mass scale for the new particles in the two-site model can then be consistent with both observables. We also compare our analysis of ǫ K in the two-site model to that in 5D models, including both the cases of a brane-localized and bulk Higgs.

Combining direct & indirect kaon CP violation to constrain the warped KK scale

“…The β = 0 case describes a Higgs maximally-spread into the bulk (saturating the stability bound), while β = 1 corresponds to the two-site model considered in [9]. For a concrete comparison we take β = 1, and add the case of the weakest expected bound on the KK scale, which is obtained for β = 0.…”

“…The KK decomposition for the Higgs is H(x, z) =ṽ(β, z) + n H (n) (x)φ n (z) [9], whereṽ(β, z) is the Higgs VEV profile, which is very close to the physical Higgs profile when m h M KK (here β = 4 + µ 2 , with µ being the bulk Higgs mass in units of k). This profile can be chosen to peak near the IR brane:ṽ…”

“…We use y d to denote a generic entry in Y d (in units of √ k). Note that in comparison to the notation of [9],…”

“…In [9] it was pointed out that when the Higgs is in the bulk, the light fermions can be made less composite while still keeping their masses constant, and also the overall Yukawa scale can be increased without violating the corresponding perturbative bound. Both effects allow to ameliorate the RS K problem.…”

“…Recently in [9] it was pointed out, based on matching the full RS set-up onto a two site model (originally suggested in [10]), that if the Higgs is in the bulk and one-loop matching of the gauge coupling is included, the KK scale can be lowered down to O(5) TeV. An important ingredient in that paper's analysis is the ability to raise the overall size of the 5D down-type Yukawa coupling, y d .…”