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Register a new userNew results from the lattice on the theoretical inputs to the hadronic tau determination of V_us
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Recent sum rule determinations of |V_us|, employing flavor-breaking combinations of hadronic tau decay data, are significantly lower than either expectations based on 3-family unitarity or determinations from K_ell3 and Gamma[K_mu2]/Gamma[pi_mu2]. We use lattice data to investigate the accuracy/reliability of the OPE representation of the flavor-breaking correlator combination entering the tau decay analyses. The behavior of an alternate correlator combination, constructed to reduce problems associated with the slow convergence of the D = 2 OPE series, and entering an alternate sum rule requiring both electroproduction cross-section and hadronic tau decay data, is also investigated. Preliminary updates of both analyses, with the lessons learned from the lattice data in mind, are also presented.
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The actual limit of the unitarity condition of the first row of the CKM matrix |V_ud|^2+|V_us|^2+|V_ub|^2=1+Delta_CKM is Delta_CKM=-0.0001(6). In 2010 the same was Delta_CKM=+0.0001(6). Despite the only difference of a sign, and with an absolute change of the value of one third of the accuracy, a substantial amount of work has been done in the last two years to improve the knowledge of all the contributions to this stringent limit to CKM unitarity, and more is expected in the next years. In this paper we present an organized summary of all the important contributions presented during the WG1 sessions, referring as much as possible to the contribution papers prepared by the individual authors.
The leading order hadronic contribution to the muon magnetic moment anomaly, $a^{HAD}_mu$, is determined entirely in the framework of QCD. The result in the light-quark sector, in units of $10^{-10}$, is $a^{HAD}_mu|_{uds} =686 pm 26$, and in the heavy-quark sector $a^{HAD}_mu|_{c} =14.4 pm 0.1$, and $a^{HAD}_mu|_{b} =0.29 pm 0.01$, resulting in $a^{HAD}_mu = 701 pm 26$. The main uncertainty is due to the current lattice QCD value of the first and second derivative of the electromagnetic current correlator at the origin. Expected improvement in the precision of these derivatives may render this approach the most accurate and trustworthy determination of the leading order $a^{HAD}_mu$.
The Quantum Chromodynamics (QCD) coupling, $alpha_s$, is not a physical observable of the theory since it depends on conventions related to the renormalization procedure. We introduce a definition of the QCD coupling, denoted by $hatalpha_s$, whose running is explicitly renormalization scheme invariant. The scheme dependence of the new coupling $hatalpha_s$ is parameterized by a single parameter $C$, related to transformations of the QCD scale $Lambda$. It is demonstrated that appropriate choices of $C$ can lead to substantial improvements in the perturbative prediction of physical observables. As phenomenological applications, we study $e^+e^-$ scattering and decays of the $tau$ lepton into hadrons, both being governed by the QCD Adler function.
At low energies hadronic vacuum polarization (HVP) is strongly dominated by two-pion intermediate states, which are responsible for about $70%$ of the HVP contribution to the anomalous magnetic moment of the muon, $a_mu^text{HVP}$. Lattice-QCD evaluations of the latter indicate that it might be larger than calculated dispersively on the basis of $e^+e^-totext{hadrons}$ data, at a level which would contest the long-standing discrepancy with the $a_mu$ measurement. In this Letter we study to which extent this $2pi$ contribution can be modified without, at the same time, producing a conflict elsewhere in low-energy hadron phenomenology. To this end we consider a dispersive representation of the $e^+e^- to 2pi$ process and study the correlations which thereby emerge between $a_mu^text{HVP}$, the hadronic running of the fine-structure constant, the $P$-wave $pipi$ phase shift, and the charge radius of the pion. Inelastic effects play an important role, despite being constrained by the Eidelman-Lukaszuk bound. We identify scenarios in which $a_mu^text{HVP}$ can be altered substantially, driven by changes in the phase shift and/or the inelastic contribution, and illustrate the ensuing changes in the $e^+e^-to 2pi$ cross section. In the combined scenario, which minimizes the effect in the cross section, a uniform shift around $4%$ is required. At the same time both the analytic continuation into the space-like region and the pion charge radius are affected at a level that could be probed in future lattice-QCD calculations.
Evidence is presented for the necessity of including duality violations in a consistent description of spectral function moments employed in the precision determination of $alpha_s$ from $tau$ decay. A physically motivated ansatz for duality violations in the spectral functions enables us to perform fits to spectral moments employing both pinched and unpinched weights. We describe our analysis strategy and provide some preliminary findings. Final numerical results await completion of an ongoing re-determination of the ALEPH covariance matrices incorporating correlations due to the unfolding procedure which are absent from the currently post
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