Strong isospin breaking of the nucleon and delta masses on the lattice |
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| Institution: | 1. Helsinki Institute of Sustainability Science (HELSUS), University of Helsinki, Helsinki, Finland;2. Global Change and Conservation (GCC), Organismal and Evolutionary Biology Research Programme, Faculty of Biological and Environmental Sciences, University of Helsinki, Helsinki, Finland;3. Department of Human Dimensions of Natural Resources, Colorado State University, Fort Collins, CO, USA;4. Department of Linguistic and Cultural Evolution, Max Planck Institute for the Science of Human History, Jena, Germany;5. Development Studies, Faculty of Social Sciences, University of Helsinki, Helsinki, Finland;6. Department of Geography, Indiana University Bloomington, Bloomington, IN, USA;7. Department of Anthropology, Indiana University Bloomington, Bloomington, IN, USA |
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| Abstract: | Strong isospin breaking in the spectrum of the nucleons and deltas can be studied in lattice QCD with the help of chiral perturbation theory. At leading order in the chiral expansion, the mass splittings between the proton and neutron and between the deltas are linear in the quark mass difference. The next-to-leading order contributions to these splittings vanish even away from the strong-isospin limit. Therefore, any non-linear quark mass dependence of these mass splittings is a signal of the next-to-next-to-leading order mass contributions, thus providing access to low energy constants at this order. We determine the mass splittings of the nucleons and deltas in two-flavor, heavy baryon chiral perturbation theory to next-to-next-to-leading order. We also derive expressions for the nucleon and delta masses in partially quenched chiral perturbation theory to the same order. The resulting mass expressions will be useful both for the extrapolation of lattice data on baryon masses, and for the study of strong isospin breaking. |
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