Models Nucleon

1 models

1.1 skyrmion models
1.2 mit bag model
1.3 chiral bag model

models

although known nucleon made 3 quarks, of 2006, not known how solve equations of motion quantum chromodynamics. thus, study of low-energy properties of nucleon performed means of models. first-principles approach available attempt solve equations of qcd numerically, using lattice qcd. requires complicated algorithms , powerful supercomputers. however, several analytic models exist:

skyrmion models

the skyrmion models nucleon topological soliton in non-linear su(2) pion field. topological stability of skyrmion interpreted conservation of baryon number, is, non-decay of nucleon. local topological winding number density identified local baryon number density of nucleon. pion isospin vector field oriented in shape of hedgehog space, model readily solvable, , called hedgehog model. hedgehog model able predict low-energy parameters, such nucleon mass, radius , axial coupling constant, approximately 30% of experimental values.

mit bag model

the mit bag model confines 3 non-interacting quarks spherical cavity, boundary condition quark vector current vanish on boundary. non-interacting treatment of quarks justified appealing idea of asymptotic freedom, whereas hard boundary condition justified quark confinement.

mathematically, model vaguely resembles of radar cavity, solutions dirac equation standing in solutions maxwell equations , vanishing vector current boundary condition standing conducting metal walls of radar cavity. if radius of bag set radius of nucleon, bag model predicts nucleon mass within 30% of actual mass.

although basic bag model not provide pion-mediated interaction, describes excellently nucleon-nucleon forces through 6 quark bag s-channel mechanism using p matrix.

chiral bag model

the chiral bag model merges mit bag model , skyrmion model. in model, hole punched out of middle of skyrmion, , replaced bag model. boundary condition provided requirement of continuity of axial vector current across bag boundary.

very curiously, missing part of topological winding number (the baryon number) of hole punched skyrmion made non-zero vacuum expectation value (or spectral asymmetry) of quark fields inside bag. of 2017, remarkable trade-off between topology , spectrum of operator not have grounding or explanation in mathematical theory of hilbert spaces , relationship geometry. several other properties of chiral bag notable: provides better fit low energy nucleon properties, within 5–10%, , these independent of chiral bag radius (as long radius less nucleon radius). independence of radius referred cheshire cat principle, after fading smile of lewis carroll s cheshire cat. expected first-principles solution of equations of qcd demonstrate similar duality of quark-pion descriptions.