The Modern Description of Semileptonic Meson Form Factors

Semileptonic transitions of one meson into another yield important measurements of both weak and strong dynamics. By comparing the experimentally determined decay rate to a theoretical normalization of the relevant hadron transition amplitude at one or more kinematic points, elements of the CabibboKobayashi-Maskawa (CKM) matrix are determined. Independent of the overall normalization, the shape of the semileptonic spectrum provides a quantitative probe of underlying hadron dynamics. Of the six CKM elements that can be probed directly using stable hadrons, determinations from exclusive semileptonic transitions are the most precise (|Vus|); competitive with other determinations (|Vub|, |Vcb| from inclusive semileptonic B decays; |Vcd| from deep-inelastic neutrino scattering; |Vcs| from charmtagged W decays); or complementary to existing determinations (|Vud|, from nuclear beta decay) [1]. In all cases, the theoretical normalization gives a dominant error. The experimentally determined spectrum can be used both to test the nonperturbative methods used in determining this normalization, and to optimize the merger of theory with experiment. For the study of hadron dynamics, the use of a virtual W boson probe in semileptonic transitions can be viewed in analogy with the use of a virtual photon in deep-inelastic scattering. The “known” and theoretically “clean” weak (electromagnetic) physics is used to probe the “unknown” and theoretically “messy” strong physics of the meson (proton). For the case of semileptonic transitions, in addition to the virtuality of the exchanged boson, we can envision “dialing the knobs” of the initialand final-state meson masses. To be precise, consider the situation pictured in Fig. 1. A Qq̄ pair with quantum numbers of the “heavy” meson H is created at spacetime point x, interacts with a flavor-changing current at y, and the q′q̄ pair with quantum numbers of the “light” meson L is annihilated at z. By suitable manipulations ,