Limitations of the heavy-baryon expansion as revealed by a pion-mass dispersion relation
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The dependence of hadron properties on the quark masses—the chiral behaviour—is crucial for interpreting the modern lattice QCD calculations, which usually require an extrapolation in the quark mass. It is also important for determining the quark-mass values, as well as for any quantitative description of chiral symmetry breaking. Chiral perturbation theory (χPT) [1, 2], a low-energy effective field theory (EFT) of QCD, should in principle describe the nonanalytic dependencies on the light-quark masses in a systematic fashion. The analytic (series-like) dependencies are more arbitrary in χPT, and are specified in terms of low-energy constants (LECs). They are to be fixed by matching to the underlying theory, which is usually achieved by fitting to lattice QCD results.
In the baryon sector of χPT one often invokes an additional expansion in the inverse baryon masses called the heavy-baryon expansion, or HBχPT [3, 4]. The baryon χPT without the heavy-baryon expansion will...
KeywordsAnomalous Magnetic Moment Chiral Symmetry Breaking Pion Mass Loop Momentum Nucleon Mass
V.P. is thankful to Dr. Nikolai Kivel for stimulating discussions of the heavy-quark and heavy-baryon expansions. This work has been supported by the Deutsche Forschungsgemeinschaft through the Collaborative Research Centre SFB1044, and by the Australian Research Council through grant DP110101265.