Constituent quarks and g1

Constituent quarks and g1

24 Feb 1999 | Steven D. Bass
The article reviews the theory and current status of the proton spin problem in QCD, focusing on the transition between current quarks and constituent quarks. It discusses the spin structure of the nucleon, particularly the flavour-singlet axial charge $ g_{A}^{(0)} $, which is extracted from the first moment of $ g_{1} $, the nucleon's spin-dependent structure function. Polarised deep inelastic scattering experiments have revealed a two-standard-deviation violation of OZI in $ g_{A}^{(0)} $, suggesting a complex interplay between quark and gluon contributions to the nucleon's spin. The spin decomposition of the proton is described by the equation $ \frac{1}{2} = \frac{1}{2}\Sigma + L_z + \Delta g $, where $ \frac{1}{2}\Sigma $ is the quark intrinsic spin, $ L_z $ is the orbital angular momentum, and $ \Delta g $ is the gluonic contribution. In deep inelastic processes, the nucleon's structure is described by the QCD parton model, where the structure functions are the sum of convolutions of parton distributions with hard scattering coefficients. At low energies, the nucleon behaves as a system of three constituent quarks interacting with a pion cloud. The transition between fundamental QCD quarks and constituent quarks is challenging, as the large mass of constituent quarks is due to dynamical chiral symmetry breaking and scalar confinement. The axial anomaly in QCD leads to gluonic contributions to $ g_{A}^{(0)} $, with the topological winding number being a global property of the theory. The topological contribution to the nucleon's spin has support only at $ x = 0 $, which is missed by polarised deep inelastic scattering experiments. The value of $ g_{A}^{(0)} $ extracted from these experiments is significantly less than semi-classical predictions, suggesting a role for gluon topology. The article discusses the relationship between chiral symmetry and the nucleon's spin structure, highlighting the Goldberger-Treiman relation and the role of the topological susceptibility. It also reviews the renormalisation group factor $ E(\alpha_s) $ and its impact on the scale dependence of $ g_{A}^{(0)} $. The axial anomaly and its role in the first moment of $ g_1 $ are explored, with the gluonic contribution to $ g_{A}^{(0)} $ being a key factor. The article also discusses the implications of the topological winding number and the role of instantons in breaking $ U_A(1) $ symmetry. The connection between the nucleon's spin structure and the dynamics of $ U_A(1) $ symmetry is emphasized, with experiments on $ \eta $ and $ \eta' $ meson production providing complementary insights into theThe article reviews the theory and current status of the proton spin problem in QCD, focusing on the transition between current quarks and constituent quarks. It discusses the spin structure of the nucleon, particularly the flavour-singlet axial charge $ g_{A}^{(0)} $, which is extracted from the first moment of $ g_{1} $, the nucleon's spin-dependent structure function. Polarised deep inelastic scattering experiments have revealed a two-standard-deviation violation of OZI in $ g_{A}^{(0)} $, suggesting a complex interplay between quark and gluon contributions to the nucleon's spin. The spin decomposition of the proton is described by the equation $ \frac{1}{2} = \frac{1}{2}\Sigma + L_z + \Delta g $, where $ \frac{1}{2}\Sigma $ is the quark intrinsic spin, $ L_z $ is the orbital angular momentum, and $ \Delta g $ is the gluonic contribution. In deep inelastic processes, the nucleon's structure is described by the QCD parton model, where the structure functions are the sum of convolutions of parton distributions with hard scattering coefficients. At low energies, the nucleon behaves as a system of three constituent quarks interacting with a pion cloud. The transition between fundamental QCD quarks and constituent quarks is challenging, as the large mass of constituent quarks is due to dynamical chiral symmetry breaking and scalar confinement. The axial anomaly in QCD leads to gluonic contributions to $ g_{A}^{(0)} $, with the topological winding number being a global property of the theory. The topological contribution to the nucleon's spin has support only at $ x = 0 $, which is missed by polarised deep inelastic scattering experiments. The value of $ g_{A}^{(0)} $ extracted from these experiments is significantly less than semi-classical predictions, suggesting a role for gluon topology. The article discusses the relationship between chiral symmetry and the nucleon's spin structure, highlighting the Goldberger-Treiman relation and the role of the topological susceptibility. It also reviews the renormalisation group factor $ E(\alpha_s) $ and its impact on the scale dependence of $ g_{A}^{(0)} $. The axial anomaly and its role in the first moment of $ g_1 $ are explored, with the gluonic contribution to $ g_{A}^{(0)} $ being a key factor. The article also discusses the implications of the topological winding number and the role of instantons in breaking $ U_A(1) $ symmetry. The connection between the nucleon's spin structure and the dynamics of $ U_A(1) $ symmetry is emphasized, with experiments on $ \eta $ and $ \eta' $ meson production providing complementary insights into the
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Understanding Constituent quarks and g1