Lepton Universality, Rare Decays and Split Fermions

We investigate the constraint on the split fermions in extra dimensions by considering the universality of $W$ leptonic decays $W\to l_i \nu_i$, the charged lepton decays $l_i \ra l_j\nu_i\bar{\nu}_j$, and the lepton flavor violating process $l_i\ra \bar{l}_j l_k l_h$ where $l_i= e,\mu$ or $\tau$. For the Standard Model (SM) background of $W\ra l_i \nu_i$, we extended the one loop quantum correction to include effects of order $m_l^2/M_W^2$ and the Higgs mass dependence. We find that in general the split fermion scenarios give rise to a 4D effective Yukawa matrix of the Kaluza-Klein Higgs bosons is misaligned with respect to the fermion mass matrix. This holds true also for gauge bosons as well. This leads to decays of $l_i\ra \bar{l_j}l_k l_h$ at tree level and muonium antimuonium conversion. Interestingly the leptonic universality of $W$ boson decays are not affected at this level.