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 non-strange mesons provide enough constraints to determine only certain 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 are in good agreement with experimentally measured masses for 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 useful information for experimentalists investigating such states. The near degeneracy of nonstrange and strange scalar $B$ mesons is confirmed in our predictions using $\mathrm{HHChPT}$. Finally,we show why previous approaches of using $\mathrm{HHChPT}$ in studying the mass degeneracy in the scalar states of charm and bottom meson sectors gave unsatisfactory results. Interactions between these heavy mesons are treated using effective theories similar to those used to study nuclear forces. We first look at a strongly-interacting channel which produces a bound or virtual state and a dimer state which couples weakly to a weakly-interacting channel to produce a narrow resonance. We also look at the short-range interactions in two channels. We consider two cases: two channels where one has a strong $s$-wave interaction which 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 investigate resonances in the charmonium and bottomonium systems. We demonstrate how the 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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:634951 |
| Date | January 2015 |
| Creators | Alhakami, Mohammad Hasan M. |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/effective-field-theories-of-heavyquark-mesons(826c18ee-f14b-44e1-aa8d-dba588971048).html |
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