Effective Field Theories of Heavy-Quark Mesons

Abstract

We study the masses of the low-lying charm and bottom mesons within the framework of heavy-hadron chiral perturbation theory. We work to third order in the chiral expansion, where meson loops contribute. In contrast to previous approaches, we use physical meson masses in evaluating these loops. This ensures that their imaginary parts are consistent with the observed widths of the D-mesons. The lowest odd- and even-parity, strange and nonstrange mesons provide enough constraints to determine onlycertain linear combinations of the low-energy constants (LECs) in the effective Lagrangian. We comment on how lattice QCD could provide further information to disentangle these constants.Then we use the results from the charm sector to predict the spectrum of odd- and even-parity of the bottom mesons.The predicted masses from our theory arein good agreement with experimentally measured massesfor the case of the odd-parity sector.For the even-parity sector, the $B$-meson states have not yet been observed; thus,our results provide usefulinformation for experimentalists investigating such states. The near degeneracy of nonstrange and strange scalar $B$ mesonsis confirmed in our predictions using $\mathrm{HHChPT}$.Finally,we show why previous approachesof using$\mathrm{HHChPT}$ in studying the mass degeneracy in the scalar statesof charm and bottom meson sectorsgave unsatisfactory results.Interactions between these heavy mesons are treated using effectivetheories similar to those used to study nuclear forces.We first look at astrongly-interacting channel which produces a bound or virtual state anda dimer state which couples weakly to a weakly-interacting channel to produce a narrow resonance.We also look at theshort-range interactions intwo channels. We consider two cases:two channels where one has a strong $s$-wave interactionwhich produces bound or virtual states,and a dimer state which couples weakly to weakly-coupled channels which in turn can produce narrow resonances.For each of these systems, we use well-defined power-counting schemes.The results can be used to investigateresonances in the charmonium and bottomonium systems. We demonstrate howthe method can be applied to the $X(3872)$.The widths of the $X(3872)$for decay processes to $\bar{D}^0 D^{*0}$ and $\bar{D}^0D^0\pi$are calculated.We use these results to obtain the line shapes of the $X(3872)$ under different assumptions about the nature of this state.

Date of Award	1 Aug 2015
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Michael Birse (Supervisor)