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Register a new userFrom continuum QCD to hadron observables
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Authors
D. Binosi
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We show that the form of the renormalization group invariant quark-gluon interaction predicted by a refined nonperturbative analysis of the QCD gauge sector is in quantitative agreement with the one required for describing a wide range of hadron observables using sophisticated truncation schemes of the Schwinger-Dyson equations relevant in the matter sector.
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We sketch the basic ideas of the lattice regularization in Quantum Field Theory, the corresponding Monte Carlo simulations, and applications to Quantum Chromodynamics (QCD). This approach enables the numerical measurement of observables at the non-perturbative level. We comment on selected results, with a focus on hadron masses and the link to Chiral Perturbation Theory. At last we address two outstanding issues: topological freezing and the sign problem.
The value of the light quark masses combination $m_u + m_d$ is analized using QCD-Hadron Duality. A detailed analysis of both the perturbative QCD [to four-loops] and the hadronic parametrization needed is done. The result we get is $[m_u + m_d] (1 GeV^2) = (12.8 pm 2.5)$ MeV ($[m_u + m_d] (4 GeV^2) = (9.8 pm 1.9)$ MeV) in the $barMS$ scheme.
We review the status of lattice calculations of the deep-inelastic structure functions of the nucleon. In addition, we present some results on the pion and rho structure functions.
Nonperturbative QCD corrections are important to many low-energy electroweak observables, for example the muon magnetic moment. However, hadronic corrections also play a significant role at much higher energies due to their impact on the running of standard model parameters, such as the electromagnetic coupling. Currently, these hadronic contributions are accounted for by a combination of experimental measurements, effective field theory techniques and phenomenological modeling but ideally should be calculated from first principles. Recent developments indicate that many of the most important hadronic corrections may be feasibly calculated using lattice QCD methods. To illustrate this, we will examine the lattice computation of the leading-order QCD corrections to the muon magnetic moment, paying particular attention to a recently developed method but also reviewing the results from other calculations. We will then continue with several examples that demonstrate the potential impact of the new approach: the leading-order corrections to the electron and tau magnetic moments, the running of the electromagnetic coupling, and a class of the next-to-leading-order corrections for the muon magnetic moment. Along the way, we will mention applications to the Adler function, which can be used to determine the strong coupling constant, and QCD corrections to muonic-hydrogen.
Recent progress in lattice QCD calculations of nucleon structure will be presented. Calculations of nucleon matrix elements and form factors have long been difficult to reconcile with experiment, but with advances in both methodology and computing resources, this situation is improving. Some calculations have produced agreement with experiment for key observables such as the axial charge and electromagnetic form factors, and the improved understanding of systematic errors will help to increase confidence in predictions of unmeasured quantities. The long-omitted disconnected contributions are now seeing considerable attention and some recent calculations of them will be discussed.
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