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The generic unparticle propagator may be modified in two ways. Breaking the conformal symmetry effectively adds a mass term to the propagator, while considering vacuum polarization corrections adds a width-like term. Both of these modifications result naturally from the coupling of the unparticle to standard model (SM) fields. We explore how these modifications to the propagator affect the calculation of the lepton anomalous magnetic moment using an integral approximation of the propagator that is accurate for $dlesssim1.5$, where $d$ is the unparticle dimension. We find that for this range of $d$ and various values of the conformal breaking scale $mu$, the value of $g-2$ calculated when allowing various SM fermions to run in the unparticle self-energy loops does not significantly deviate from the value of $g-2$ when the width term is ignored. We also investigate the limits on a characteristic mass scale for the unparticle sector as a function of $mu$ and $d$.
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This article reports an automated approach to the evaluation of higher-order terms of QED perturbation to anomalous magnetic moments of charged leptons by numerical means. We apply this approach to tenth-order correction due to a particular subcollection of Feynman diagrams, which have no virtual lepton loops. This set of diagrams is distinctive in that it grows factorially in number as the order increases, and also each of the diagrams holds quite a large number of subtraction terms to be treated along renormalization procedure. Thus some automated scheme has long been required to evaluate correctly this class of diagrams. We developed a fast algorithm and an implementation which automates necessary steps to generate from the representation of each Feynman diagram the FORTRAN codes for numerical integration. Currently those diagrams of tenth order are being evaluated.
We reanalyze the two-loop electroweak hadronic contributions to the muon g-2 that may be enhanced by large logarithms. The present evaluation is improved over those already existing in the literature by the implementation of the current algebra Ward identities and the inclusion of the correct short-distance QCD behaviour of the relevant hadronic Greens function.
Among 12672 Feynman diagrams contributing to the electron anomalous magnetic moment at the tenth order, 6354 are the diagrams having no lepton loops, i.e., those of quenched type. Because the renormalization structure of these diagrams is very complicated, some automation scheme is inevitable to calculate them. We developed an algorithm to write down FORTRAN programs for numerical evaluation of these diagrams, where the necessary counterterms to subtract out ultraviolet subdivergence are generated according to Zimmermanns forest formula. Thus far we have evaluated crudely integrals of 2232 tenth-order vertex diagrams which require vertex renormalization only. Remaining 4122 diagrams, which have ultraviolet-divergent self-energy subdiagrams and infrared-divergent subdiagrams, are being evaluated by giving small mass lambda to photons to control the infrared problem.
The current $3.7sigma$ discrepancy between the Standard Model prediction and the experimental value of the muon anomalous magnetic moment could be a hint for the existence of new physics. The hadronic light-by-light contribution is one of the pieces requiring improved precision on the theory side, and an important step is to derive short-distance constraints for this quantity containing four electromagnetic currents. Here, we derive such short-distance constraints for three large photon loop virtualities and the external fourth photon in the static limit. The static photon is considered as a background field and we construct a systematic operator product expansion in the presence of this field. We show that the massless quark loop, i.e. the leading term, is numerically dominant over non-perturbative contributions up to next-to-next-to leading order, both those suppressed by quark masses and those that are not.
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.
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