Phenomenology of Heavy Meson Chiral Lagrangians

Abstract

The approximate symmetries of Quantum ChromoDynamics in the infinite heavy quark ($Q=c,b$) mass limit ($m_Q \to \infty$) and in the chiral limit for the light quarks ($m_q \to 0,\;q=\,u,\,d,\,s$) can be used together to build up an effective chiral lagrangian for heavy and light mesons describing strong interactions among effective meson fields as well as their couplings to electromagnetic and weak currents, including the relevant symmetry breaking terms. The effective theory includes heavy ($Q \bar q$) mesons of both negative and positive parity, light pseudoscalars, as well as light vector mesons. We summarize the estimates for the parameters entering the effective lagrangian and discuss in particular some phenomenologically important couplings, such as $g_{B^* B π}$. The hyperfine splitting of heavy mesons is discussed in detail. The effective lagrangian allows for the possibility to describe consistently weak couplings of heavy ($B,\, D$) to light ($π,\, ρ, \, K^*,\,$ etc.) mesons. The method has however its own limitations, due to the requirement that the light meson momenta should be small, and we discuss how such limitations can be circumvented through reasonable ansatz on the form factors. Flavour conserving (e. g. $B^* \to B\, γ$) and flavour changing (e. g. $B \to K^* \, γ$) radiative decays provide another field of applications of effective lagrangians; they are discussed together with their phenomenological implications. Finally we analyze effective lagrangians describing heavy charmonium- like ($\bar Q Q$) mesons and their strong and electromagnetic interactions. The role of approximate heavy quark symmetries for this case and the phenomenological tests of these models are also discussed.