Abstract
The self-energies of the full set of flavor SU(3) octet and decuplet baryons are computed within a relativistic chiral effective theory framework. The leading nonanalytic chiral behavior is derived for the octet and decuplet masses, and a finite-range regularization consistent with Lorentz and gauge invariance is applied to account for the finite size of the baryons. Using a four-dimensional dipole form factor, the relative importance of various meson-baryon loop contributions to the self-energies is studied numerically as a function of the dipole range parameter and meson mass, and comparison is made between the relativistic results and earlier approximations within the heavy baryon limit.
Highlights
Understanding the structure and interactions of atomic nuclei and their constituents from the fundamental theory of quantum chromodynamics (QCD) poses one of the greatest challenges of modern subatomic physics
The use of the fourdimensional regulator ensures that the calculation preserves the necessary Lorentz, gauge and chiral symmetries of the fundamental QCD theory
We studied the dependence of the baryon self-energies numerically as a function of the regulator mass, Λ, and identified the most important channels for each baryon external state
Summary
Understanding the structure and interactions of atomic nuclei and their constituents from the fundamental theory of quantum chromodynamics (QCD) poses one of the greatest challenges of modern subatomic physics. Expanding the masses in terms of powers of mπ, the low-mπ behavior is characterized by model-independent nonanalytic terms that involve odd powers of mπ or logarithms of mπ [8] Such behavior can only arise from pseudoscalar meson loops, and must be present in any effective treatment of QCD near the chiral limit [9]. Other approaches have emphasized the importance of taking the finite size of baryons into account, regularizing the ultraviolet behavior via form factors or finite-range regulators [16] The latter have been argued to lead to better convergence of the chiral expansion, through a resummation of nominally higher-order terms as relativistic corrections to the leading nonanalytic (LNA) terms [3]. We summarize our coupling constants, integral relations and example of decay rate derivation in Appendixes A, B and C, respectively
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