Soft and Hard Mesons in Chiral Perturbation Theory

Abstract: This thesis deals with Chiral Perturbation Theory (ChPT), an effective field theory for the strong force used to describe meson interactions. The work done can be split in two parts. The first one is on ChPT in its standard formulation. This theory has been very successful so far in describing low energetic processes. However, it is still not entirely clear how much it can be trusted for precision determinations of hadronic observables. Paper I and II explore this aspect. Paper I shows the results of a search for relations between several observables calculated with ChPT at order $p^{6}$. The relations are built up such that the couplings of the theory cancel out. These combinations can then be used to test the convergence of the perturbative expansion in a way that is almost independent from the unknown couplings. Paper II presents the results for a new global fit at order $p^{6}$ of the couplings of the $p^{4}$ ChPT Lagrangian. The fit includes the most recent phenomenological information. Furthermore, a new way to deal with the $p^{6}$ couplings, based on a random walk algorithm, is considered. This method allows to study correlations between the couplings. The second part, paper III and IV, focuses on an extension of ChPT out of its usual energy range. This approach is called hard pion ChPT and it is expected to be useful for the analysis of lattice data. Paper III provides arguments that further support the use of hard pion ChPT to calculate chiral logarithms when hard external pions arise. The hard pion ChPT approach is applied in this paper to semileptonic decays of $B$ and $D$ mesons to pions. In Paper IV hard pion ChPT is extended to the three-flavour case, thereby describing the $B$ and $D$ meson transitions to all the light pseudoscalar mesons ($\pi$, $K$ and $\eta$). A comparison with data is also presented and it shows that the corrections are sizable. Moreover, the procedure is applied to scalar and vector formfactors of the pions and kaons and to $B\rightarrow D$ decay.