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Register a new userm_u + m_d from QCD-Hadron Duality
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Authors
Joaquim Prades
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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.
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The MILC Collaboration has completed production running of electromagnetic effects on light mesons using asqtad improved staggered quarks. In these calculations, we use quenched photons in the noncompact formalism. We study four lattice spacings from $approx!0.12:$fm to $approx!0.045:$fm. To study finite-volume effects, we used six spatial lattice sizes $L/a=12$, 16, 20, 28, 40, and 48, at $a!approx!0.12:$fm. We update our preliminary values for the correction to Dashens theorem ($epsilon$) and the quark-mass ratio $m_u/m_d$.
We investigate the origin of the quark-hadron duality-violating terms in the expansion of the QCD two-point vector correlation function at large energies in the complex $q^2$ plane. Starting from the dispersive representation for the associated polarization, the analytic continuation of the operator product expansion from the Euclidean to the Minkowski region is performed by means of a generalized Borel-Laplace transform, borrowing techniques from hyperasymptotics. We establish a connection between singularities in the Borel plane and quark-hadron duality violating contributions. Starting with the assumption that for QCD at $N_c=infty$ the spectrum approaches a Regge trajectory at large energy, we obtain an expression for quark-hadron duality violations at large, but finite $N_c$.
The claim that the light quark mass ratio (m_d - m_u)/m_s can be extracted from the decay width ratio Gamma(eta -> pi^0 pi^+ pi^-)/Gamma(eta -> eta pi^+ pi^-) is critically investigated within a U(3) chiral unitary framework. The influence of the recent VES data on the eta -> eta pi^+ pi^- decay is also discussed.
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.
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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