We present two-loop calculations on the axial-vector form factors F A of semileptonic radiative kaon and pion decays in chiral perturbation theory. The relevant dimension-6 terms of the lagrangian are evaluated from the resonance contribution and the results of the irreducible two-loop graphs of the sunset topology are given in detail. We also explicitly show that the divergent parts in F A are cancelled exactly as required.

We study the forward-backward asymmetries in the decays of K + → π + ℓ + ℓ − (ℓ = e and µ) in the presence of scalar or tensor terms. We find that with the scalar (tensor) type interaction the asymmetry can be up to O(10 −3 ) (O(10 −1 )) and arbitrary large for the electron and muon modes, respectively, without conflict with the experimental data. We also discuss the cases in the minimal supersymmetric standard model where the scalar terms can be induced. In particular we show that the asymmetry in K + → π + µ + µ − can be as large as O(10 −3 ) in the large tan β limit, which can be tested in future experiments such as CKM at Fermilab.

We investigate the constraint on the split fermions in extra dimensions by considering the universality of W leptonic decays W → l i ν i , the lepton decays l i → l j ν iνj , the lepton flavor violating process l i →l j l k l h and the l i → l j γ transition where l i = e, µ or τ . For the Standard Model (SM) background of W → l i ν i , we extended the one loop quantum correction to include effects of order m 2 l /M 2 W and the Higgs mass dependence. We find that in general the split fermion scenarios the 4D effective Yukawa matrix of the Kaluza-Klein Higgs bosons is misaligned with respect to the fermion mass matrix. This leads to decays of l i →l j l k l h at tree level and l i → l j γ transition at one loop level. Interestingly the leptonic universality of W boson decays are not affected.