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Register a new userQED Corrections to Hadronic Processes in Lattice QCD
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In this paper, for the first time a method is proposed to compute electromagnetic effects in hadronic processes using lattice simulations. The method can be applied, for example, to the leptonic and semileptonic decays of light or heavy pseudoscalar mesons. For these quantities the presence of infrared divergences in intermediate stages of the calculation makes the procedure much more complicated than is the case for the hadronic spectrum, for which calculations already exist. In order to compute the physical widths, diagrams with virtual photons must be combined with those corresponding to the emission of real photons. Only in this way do the infrared divergences cancel as first understood by Bloch and Nordsieck in 1937. We present a detailed analysis of the method for the leptonic decays of a pseudoscalar meson. The implementation of our method, although challenging, is within reach of the present lattice technology.
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After a brief self-contained introduction to the muon anomalous magnetic moment, (g-2), we review the status of lattice calculations of the hadronic vacuum polarization contribution and present first results from lattice QCD for the hadronic light-by-light scattering contribution. The signal for the latter is consistent with model calculations. While encouraging, the statistical error is large and systematic errors are mostly uncontrolled. The method is applied first to pure QED as a check.
We demonstrate that the leading and next-to-leading finite-volume effects in the evaluation of leptonic decay widths of pseudoscalar mesons at $O(alpha)$ are universal, i.e. they are independent of the structure of the meson. This is analogous to a similar result for the spectrum but with some fundamental differences, most notably the presence of infrared divergences in decay amplitudes. The leading non-universal, structure-dependent terms are of $O(1/L^2)$ (compared to the $O(1/L^3)$ leading non-universal corrections in the spectrum). We calculate the universal finite-volume effects, which requires an extension of previously developed techniques to include a dependence on an external three-momentum (in our case, the momentum of the final state lepton). The result can be included in the strategy proposed in Ref.,cite{Carrasco:2015xwa} for using lattice simulations to compute the decay widths at $O(alpha)$, with the remaining finite-volume effects starting at order $O(1/L^2)$. The methods developed in this paper can be generalised to other decay processes, most notably to semileptonic decays, and hence open the possibility of a new era in precision flavour physics.
In a previous letter (arXiv:1306.2287) we determined the isospin mass splittings of the baryon octet from a lattice calculation based on quenched QED and $N_f{=}2{+}1$ QCD simulations with 5 lattice spacings down to $0.054~mathrm{fm}$, lattice sizes up to $6~mathrm{fm}$ and average up-down quark masses all the way down to their physical value. Using the same data we determine here the corrections to Dashens theorem and the individual up and down quark masses. For the parameter which quantifies violations to Dashenss theorem, we obtain $epsilon=0.73(2)(5)(17)$, where the first error is statistical, the second is systematic, and the third is an estimate of the QED quenching error. For the light quark masses we obtain, $m_u=2.27(6)(5)(4)~mathrm{MeV}$ and $m_d=4.67(6)(5)(4)~mathrm{MeV}$ in the $bar{mathrm{MS}}$ scheme at $2~mathrm{GeV}$ and the isospin breaking ratios $m_u/m_d=0.485(11)(8)(14)$, $R=38.2(1.1)(0.8)(1.4)$ and $Q=23.4(0.4)(0.3)(0.4)$. Our results exclude the $m_u=0$ solution to the strong CP problem by more than $24$ standard deviations.
The ratios among the leading-order (LO) hadronic vacuum polarization (HVP) contributions to the anomalous magnetic moments of electron, muon and tau-lepton, $a_{ell=e,mu tau}^{HVP,LO}$, are computed using lattice QCD+QED simulations. The results include the effects at order $O(alpha_{em}^2)$ as well as the electromagnetic and strong isospin-breaking corrections at orders $O(alpha_{em}^3)$ and $O(alpha_{em}^2(m_u-m_d))$, respectively, where $(m_u-m_d)$ is the $u$- and $d$-quark mass difference. We employ the gauge configurations generated by the Extended Twisted Mass Collaboration with $N_f=2+1+1$ dynamical quarks at three values of the lattice spacing ($a simeq 0.062, 0.082, 0.089$ fm) with pion masses in the range 210 - 450 MeV. We show that in the case of the electron-muon ratio the hadronic uncertainties in the numerator and in the denominator largely cancel out, while in the cases of the electron-tau and muon-tau ratios such a cancellation does not occur. For the electron-muon ratio we get $R_{e/mu } equiv (m_mu/m_e)^2 (a_e^{HVP,LO} / a_mu^{HVP,LO}) = 1.1456~(83)$ with an uncertainty of $simeq 0.7 %$. Our result, which represents an accurate Standard Model (SM) prediction, agrees very well with the estimate obtained using the results of dispersive analyses of the experimental $e^+ e^- to$ hadrons data. Instead, it differs by $simeq 2.7$ standard deviations from the value expected from present electron and muon (g - 2) experiments after subtraction of the current estimates of the QED, electro-weak, hadronic light-by-light and higher-order HVP contributions, namely $R_{e/mu} = 0.575~(213)$. An improvement of the precision of both the experiment and the QED contribution to the electron (g - 2) by a factor of $simeq 2$ could be sufficient to reach a tension with our SM value of the ratio $R_{e/mu }$ at a significance level of $simeq 5$ standard deviations.
Mixing in the $Sigma^0$-$Lambda^0$ system is a direct consequence of broken isospin symmetry and is a measure of both isospin-symmetry breaking as well as general SU(3)-flavour symmetry breaking. In this work we present a new scheme for calculating the extent of $Sigma^0$-$Lambda^0$ mixing using simulations in lattice QCD+QED and perform several extrapolations that compare well with various past determinations. Our scheme allows us to easily contrast the QCD-only mixing case with the full QCD+QED mixing.
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