Quark mass dependence of baryon properties

Abstract

I discuss the quark mass dependence of various baryon properties derived from chiral perturbation theory. Such representations can eventually be used as chiral extrapolation functions when lattice data at sufficiently small quark masses become available. The quark mass dependence is encoded in loop and contact term contributions, the latter given in terms of low-energy constants. I stress the importance of utilizing phenomenological input to constrain a certain class of low-energy constants and discuss the ensuing theoretical uncertainty for various baryon observables, like the nucleon and the baryon octet masses, the nucleon isovector anomalous magnetic moment and the axial-vector coupling of the nucleon. I stress the role of resonance decoupling and present first results for the delta mass based on an effective field theory in which the nucleon-delta mass splitting is counted as a small parameter. I also discuss briefly the pion mass dependence of the nuclear force as derived from chiral nuclear effective field theory.

Neutron-proton mass difference in isospin-asymmetric nuclear matter

“…These values are consistent with the most recent pion-nuclei scattering data as it was summarized in Ref. [47] and lead to the threshold values b 0 (m π ) ≈ 0 and b 1 (m π ) ≈ −0.0883m…”

The hadron spectrum from lattice QCD

“…The effective Lagrangian introduces parameters, which can be determined by comparing with experiment (or lattice results) [40,41]. Expansion of the nucleon mass involves terms O(m), O(m 2 ) ∝ m π , and so on, (the exact form depending on whether one uses quenched ChPT [42] or not).…”

Nuclear central force in the chiral limit

“…Finally, in Sec. IX, I briefly summarize the results and discuss the relation of this work to previous treatments of the nuclear force in the chiral limit [4][5][6].…”

“…The beauty of the IAM representation is that this simple rearrangement allows the amplitude to satisfy unitarity exactly. While the method necessarily differs from the full answer beyond the order to which it has been matched, 6 studies have shown that this representation provides a good description of the scattering amplitudes up to reasonably large energies. For example, the scalar-isoscalar IAM amplitude is compared to the physical result of CGL in Fig.…”