2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/45850In the context of the Calabi-Yau string model we discuss the origin of characteristic pattern of quark-lepton masses and the CKM matrix. The discrete $R$-symmetry $Z_{2k+1} \times Z_2$ is introduced and the $Z_2$ is assigned to the $R$-parity. The gauge symmetry at the string scale is broken into the standard model gauge group at an intermediate energy scale. At energies below the intermediate scale down-type quarks and also leptons are mixed with unobserved heavy states, respectively. On the other hand, there are no such mixings for up-type quarks. The large mixings between light states and heavy ones cause different mass pattern of leptons and down-type quarks from that of up-type quarks and yield a nontrivial CKM matrix for quarks but a trivial one for leptons. The mixing mechanism is illustrated using a two-generation toy model.High Energy Physics - Phenomenologytext