StrongCPproblem, up-quark mass, and the Randall-Sundrum microscope

In the Randall-Sundrum model, setting the ratio of up- and down-quark masses $m_u/m_d\ll 1$, relevant to the strong $CP$ problem, does not require chiral symmetry or fine-tuning, due to exponential bulk fermion profiles. We point out that such geometric suppression of the mass of a fermion magnifies the masses of its corresponding Kaluza-Klein (KK) states. In this sense, these KK states act as “microscopes” for probing light quark and lepton masses. In simple realizations, this hypothesis can be testable at future colliders, like the LHC, by measuring the spectrum of level-1 KK fermions. The microscope can then provide an experimental test for the vanishing of $m_u$ in the ultraviolet, independently of nonperturbative determinations, by lattice simulations or other means, at hadronic scales. We also briefly comment on application of our microscope idea to other fermions, such as the electron and neutrinos.