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Nazario Tantalo
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Isospin symmetry is not exact and the corrections to the isosymmetric limit are, in general, at the percent level. For gold plated quantities, such as pseudoscalar meson masses or the kaon leptonic and semileptonic decay rates, these effects are of the same order of magnitude of the errors quoted in nowadays lattice calculations and cannot be neglected any longer. In this talk I discuss the methods that have been developed in the last few years to calculate isospin breaking corrections by starting from first principles lattice simulations. In particular, I discuss how to perform a combined QCD+QED lattice simulation and a renormalization prescription to be used in order to separate QCD from QED isospin breaking effects. A brief review of recent lattice results of isospin breaking effects on the hadron spectrum is also included.
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Isospin symmetry is explicitly broken in the Standard Model by the non-zero differences of mass and electric charge between the up and down quarks. Both of these corrections are expected to have a comparable size of the order of one percent relatively to hadronic energies. Although these contributions are small, they play a crucial role in hadronic and nuclear physics. In this review we explain how to properly define QCD and QED on a finite and discrete space-time so that isospin corrections to hadronic observables can be computed ab-initio. We then consider the different approaches to compute lattice correlation functions of QCD and QED observables. Finally we summarise the actual lattice results concerning the isospin corrections to the light hadron spectrum.
We present a new method to evaluate with high precision the isospin breaking effects due to the mass difference between the up and down quarks using lattice QCD. Our proposal is applicable in principle to any hadronic observable which can be computed on the lattice. It is based on the expansion of the path-integral in powers of the small parameter $m_d - m_u$. In this talk we discuss how to apply this method to compute the leading isospin breaking effects for several physical quantities of interest: the kaon masses, the kaon decay constants and the neutron-proton mass splitting.
We present a study of the isospin-breaking (IB) corrections to pseudoscalar (PS) meson masses using the gauge configurations produced by the ETM Collaboration with $N_f=2+1+1$ dynamical quarks at three lattice spacings varying from 0.089 to 0.062 fm. Our method is based on a combined expansion of the path integral in powers of the small parameters $(widehat{m}_d - widehat{m}_u)/Lambda_{QCD}$ and $alpha_{em}$, where $widehat{m}_f$ is the renormalized quark mass and $alpha_{em}$ the renormalized fine structure constant. We obtain results for the pion, kaon and $D$-meson mass splitting; for the Dashens theorem violation parameters $epsilon_gamma(overline{mathrm{MS}}, 2~mbox{GeV})$, $epsilon_{pi^0}$, $epsilon_{K^0}(overline{mathrm{MS}}, 2~mbox{GeV})$; for the light quark masses $(widehat{m}_d - widehat{m}_u)(overline{mathrm{MS}}, 2~mbox{GeV})$, $(widehat{m}_u / widehat{m}_d)(overline{mathrm{MS}}, 2~mbox{GeV})$; for the flavour symmetry breaking parameters $R(overline{mathrm{MS}}, 2~mbox{GeV})$ and $Q(overline{mathrm{MS}}, 2~mbox{GeV})$ and for the strong IB effects on the kaon decay constants.
We present a new method to evaluate with high precision isospin breaking effects due to the small mass difference between the up and down quarks using lattice QCD. Our proposal is applicable in principle to any hadronic observable which can be computed on the lattice. It is based on the expansion of the path-integral in powers of the small parameter md-mu. In this paper, we apply this method to compute the leading isospin breaking effects for several physical quantities of interest: the kaon meson masses, the kaon decay constant, the form factors of semileptonic Kl3 decays and the neutron-proton mass splitting.
The remarkable recent progress in the precision of Lattice QCD computations for a number of physical quantities relevant for flavour physics has motivated the introduction of isospin-breaking effects, including in particular electromagnetic corrections, to the computations. The isospin breaking corrections are necessary to fully exploit this improved precision for the determination of the fundamental parameters of the Standard Model, including the CKM matrix elements, and to look for deviations from experimental measurements which might signal the presence of new physics. Together with colleagues from Rome, we have developed and implemented a framework for including isospin-breaking corrections in leptonic decays $Ptoellbar u_ell(gamma)$, where $P$ is a pseudoscalar meson and $ell$ a charged lepton, and the theoretical framework and numerical results are reviewed below. The status of our studies to extend this framework to semileptonic decays $P_1to P_2ellbar u_ell(gamma)$, where $P_{1,2}$ are pseudoscalar mesons, is also presented.
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