Theoretical aspects of Chiral Dynamics

Abstract

Many of the quantities of interest at the precision frontier in particle physics require a good understanding of the strong interaction at low energies. The present talk reviews the theoretical framework used in this context. In particular, I draw attention to the fact that applications of effective field theory methods in the low energy domain involve two different aspects: dependence of the quantities of interest on the quark masses and dependence on the momenta. While the lattice approach gives an excellent handle on the low energy constants that govern the quark mass dependence, the most efficient tool to pin down the momentum dependence is dispersion theory. At the same time, the dispersive analysis enlarges the energy range where the effective theory applies. In the meson sector, the interplay of the various sources of information has led to a coherent framework that describes the low energy structure at remarkably high resolution. The understanding of the low energy properties in the baryon sector is less well developed. There is significant progress in the dispersive analysis of $\pi N$ scattering, for example, but it leads to puzzling conclusions concerning the pattern of SU(3) symmetry breaking in the baryon octet, which yet remain to be understood. Finally, I critically examine recent papers dealing with the Cottingham formula for the electromagnetic contribution to the mass difference between proton and neutron.

Contribution to the proceedings of the Workshop on Chiral Dynamics, Pisa 2015. Extended the discussion of the sigma-term, to account for a new lattice result that appeared only after the closing of the workshop

References in corpus (25)

• Parton distributions for the LHC
• Ab initio calculation of the neutron-proton mass difference
• Dispersion relation for hadronic light-by-light scattering: theoretical foundations
• Matching pion-nucleon Roy-Steiner equations to chiral perturbation theory
• Standard-model prediction for direct CP violation in $K\to \pi \pi$ decay
• Lattice computation of the nucleon scalar quark contents at the physical point
• $\eta \to 3\pi$ at Two Loops In Chiral Perturbation Theory
• The Electromagnetic Self-Energy Contribution to M_p - M_n and the Isovector Nucleon Magnetic Polarizability
• Scalar strangeness content of the nucleon and baryon sigma terms
• Isospin breaking in Kl4 decays
• Isospin breaking in the pion-nucleon scattering lengths
• Dispersive estimate of the electromagnetic charge symmetry violation in the octet baryon masses
• Electromagnetic Contribution to the Proton-Neutron Mass Splitting
• $J=0$ fixed pole and $D$-term form factor in deeply virtual Compton scattering
• First $\pi K$ atom lifetime and $\pi K$ scattering length measurements
• Chiral extrapolation and determination of low-energy constants from lattice data
• On the two-loop contributions to the pion mass
• Cottingham formula and nucleon polarizabilities
• Improving the phenomenology of K_{l3} form factors with analyticity and unitarity
• Status of chiral perturbation theory for light mesons
• Effective Field Theories and Lattice QCD
• Pions: Experimental Tests of Chiral Symmetry Breaking
• Nucleon PDF separation with the collider and fixed-target data
• Leading logarithms for mesons and nucleons
• Testing the consistency of the $\omega \pi$ transition form factor with unitarity and analyticity

Cited by in corpus (7)

• Lattice computation of the nucleon scalar quark contents at the physical point
• Remarks on the pion-nucleon sigma-term
• Consistency between SU(3) and SU(2) chiral perturbation theory for the nucleon mass
• Chiral Effective Theory Methods and their Application to the Structure of Hadrons from Lattice QCD
• Chiral Extrapolation of the Sigma Resonance
• Finite volume corrections to forward Compton scattering off the nucleon
• Chiral dynamics with confinement versus the standard chiral theory