Du, Menglin: Topics in chiral perturbation theory for charmed mesons. - Bonn, 2017. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-48436
@phdthesis{handle:20.500.11811/7266,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-48436,
author = {{Menglin Du}},
title = {Topics in chiral perturbation theory for charmed mesons},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2017,
month = oct,

note = {This thesis is concerned with topics in chiral perturbation theory for pseudoscalar charmed mesons in a manifestly Lorentz-invariant way. After constructing the chiral effective Lagrangian describing spinless matter fields living in the fundamental representation of $SU(N)$, we systematically study the effective generating functional using the background field method up to leading one-loop order, i.e. $mathcal{O}(p^3)$, where $p$ denotes a small momentum or Goldstone boson mass. In general, when matter fields are included, loop diagrams are both UV divergent and spoil the power counting rules. To obtain a well defined effective generating functional, both free of UV divergences and power counting breaking (PCB) terms, we renormalize it within the extended-on-mass-shell (EOMS) scheme on the Lagrangian level. Using heat kernel expansion techniques, the divergences of the one-loop effective generating functional are extracted. The divergences are absorbed by counterterms not only from the third order but also from the second order chiral Lagrangian. Likewise, PCB terms are polynomials in chiral quantities, and thus can be absorbed by conterterms. The PCB terms and the counterterms are calculated using the external field expansion. The theory can be applied to any theory with a spontaneous symmetry breaking of $SU(N)_Ltimes SU(N)_R$ to $SU(N)_V$ and spinless matter fields in the fundamental representation.
The theory is then applied to the scattering of the Goldstone bosons of chiral symmetry off the pseudoscalar charmed mesons. To investigate the nonperturbative effects and describe the scattering lengths at unphysically high pion masses, we unitarize the scattering amplitudes to fit the available lattice data of the $S$-wave scattering lengths. The lattice data are well described. However, most of the low-energy constants (LECs) determined from the fit bear large uncertainties. Lattice simulations in more channels are necessary to pin down these values which can then be used to make predictions in other processes related by chiral and heavy quark symmetries. Furthermore, we search for dynamically generated open-charm states with $J^P=0^+$ as poles of the $S$-matrix on various Riemann sheets. The trajectories of those poles for varying pion masses are presented as well.
To assess the contribution from the heavy quark spin partner, vector charmed mesons are included explicitly in order to quantify their influences on the $S$-wave scattering lengths. The obtained results are compared to the ones without an explicit contribution of the vector charmed mesons. It is found that the difference is negligible for $S$-wave scattering in the threshold region. This validates the use of $D^ast$-less one-loop potentials in the study of the pertinent scattering lengths.
At last, we investigate the numerical values of the LECs of ChPT for charmed mesons. This thesis is tackled from two sides: estimates using the resonance exchange model, and positivity constraints from the general properties of the $S$-matrix including analyticity, crossing symmetry and unitarity. These estimates and constraints are compared with the values of the scattering length determined by fitting to lattice datas. Tensions are found, and possible reasons are discussed. We conclude that more data from lattice calculations and experiments are necessary to fix these constants better. As a by-product, we also estimate the coupling constant $g_{DDa_2}$, with $a_2$ the light tensor meson, via the QCD sum rule approach.},

url = {http://hdl.handle.net/20.500.11811/7266}
}

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