Explore the vast range of titles available.

Abstract We study the transition form factors (TFFs) of axial-vector mesons in the context of currently available experimental data, including new constraints from e + e − → f 1(1285)π + π − that imply stringent limits on the high-energy behavior and, for the first time, allow us to provide an unambiguous determination of the couplings corresponding to the two antisymmetric TFFs. We discuss how these constraints can be implemented in a vector-meson-dominance picture, and, in combination with contributions from the light-cone expansion, construct TFFs as input for the evaluation of axial-vector contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon.

Abstract Estimating the contribution from axial-vector intermediate states to hadronic light-by-light scattering requires input on their transition form factors (TFFs). Due to the Landau–Yang theorem, any experiment sensitive to these TFFs needs to involve at least one virtual photon, which complicates their measurement. Phenomenologically, the situation is best for the f 1(1285) resonance, for which information is available from e + e − → e + e − f 1, f 1 → 4π, f 1 → ργ, f 1 → ϕγ, and f 1 → e + e − . We provide a comprehensive analysis of the f 1 TFFs in the framework of vector meson dominance, including short-distance constraints, to determine to which extent the three independent TFFs can be constrained from the available experimental input — a prerequisite for improved calculations of the axial-vector contribution to hadronic light-by-light scattering. In particular, we focus on the process f 1 → e + e − , evidence for which has been reported recently by SND for the first time, and discuss the impact that future improved measurements will have on the determination of the f 1 TFFs.

Abstract Based on explicitly gauge invariant interpolating operators we compute complete next-leading order QED-corrections for leptonic decays. These are sizeable since the helicity-suppression in V-A interactions allows for structure-dependent collinear logs. We have explicitly checked that these logs are absent for helicity-unsuppressed Yukawa-type transitions. Based on B → γ form factors we present the rates for B − → μ − τ − ν ¯ γ$$ {B}^{-}\\to \\left({\\mu}^{-},{\\tau}^{-}\\right)\\overline{\\nu}\\left(\\gamma \\right) $$in differential and integrated form as a function of the photon energy cut-off E γ cut$$ {E}_{\\gamma}^{\\textrm{cut}} $$. The effect of the virtual structure-dependent corrections are approximately +5% and +3% for the μ- and τ-channel respectively. The structure dependence of the real radiation exceeds that of the virtual one for E γ cut μ$$ {\\left.{E}_{\\gamma}^{\\textrm{cut}}\\right|}_{\\mu } $$> 0.18(3) GeV and is subdominant for the tau channel even when fully inclusive.

A bstract We present a detailed analysis of QED corrections to B ¯ → K ¯ ℓ + ℓ − decays at the double-differential level. Cancellations of soft and collinear divergences are demonstrated analytically using the phase space slicing method. Whereas soft divergences are found to cancel at the differential level, the cancellation of the hard-collinear logs ln m ℓ require, besides photon-inclusiveness, a specific choice of kinematic variables. In particular, hard-collinear logs in the lepton-pair invariant mass distribution ( q 2 ), are sizeable and need to be treated with care when comparing with experiment. Virtual and real amplitudes are evaluated using an effective mesonic Lagrangian. Crucially, we show that going beyond this approximation does not introduce any further infrared sensitive terms. All analytic computations are performed for generic charges and are therefore adaptable to semileptonic decays such as B ¯ → D ℓ ν ¯ .

A bstract We address the contribution of the 3 π channel to hadronic vacuum polarization (HVP) using a dispersive representation of the e + e − → 3 π amplitude. This channel gives the second-largest individual contribution to the total HVP integral in the anomalous magnetic moment of the muon ( g − 2) μ , both to its absolute value and uncertainty. It is largely dominated by the narrow resonances ω and ϕ , but not to the extent that the off-peak regions were negligible, so that at the level of accuracy relevant for ( g − 2) μ an analysis of the available data as model independent as possible becomes critical. Here, we provide such an analysis based on a global fit function using analyticity and unitarity of the underlying γ ∗ → 3 π amplitude and its normalization from a chiral low-energy theorem, which, in particular, allows us to check the internal consistency of the various e + e − → 3 π data sets. Overall, we obtain a μ 3 π | ≤1.8 GeV = 46 . 2(6)(6) × 10 −10 as our best estimate for the total 3 π contribution consistent with all (low-energy) constraints from QCD. In combination with a recent dispersive analysis imposing the same constraints on the 2 π channel below 1 GeV, this covers nearly 80% of the total HVP contribution, leading to a μ HVP = 692 . 3(3 . 3) × 10 −10 when the remainder is taken from the literature, and thus reaffirming the ( g −2) μ anomaly at the level of at least 3 . 4 σ . As side products, we find for the vacuum-polarization-subtracted masses M ω = 782 . 63(3)(1) MeV and M ϕ = 1019 . 20(2)(1) MeV, confirming the tension to the ω mass as extracted from the 2 π channel.

A bstract We present a detailed analysis of e + e − → π + π − data up to s = 1 GeV in the framework of dispersion relations. Starting from a family of ππ P -wave phase shifts, as derived from a previous Roy-equation analysis of ππ scattering, we write down an extended Omnès representation of the pion vector form factor in terms of a few free parameters and study to which extent the modern high-statistics data sets can be described by the resulting fit function that follows from general principles of QCD. We find that statistically acceptable fits do become possible as soon as potential uncertainties in the energy calibration are taken into account, providing a strong cross check on the internal consistency of the data sets, but preferring a mass of the ω meson significantly lower than the current PDG average. In addition to a complete treatment of statistical and systematic errors propagated from the data, we perform a comprehensive analysis of the systematic errors in the dispersive representation and derive the consequences for the two-pion contribution to hadronic vacuum polarization. In a global fit to both time- and space-like data sets we find a μ ππ | ≤ 1 GeV  = 495.0(1.5)(2.1) × 10 − 10 and a μ ππ | ≤ 0.63 GeV  = 132.8(0.4)(1.0) × 10 − 10 . While the constraints are thus most stringent for low energies, we obtain uncertainty estimates throughout the whole energy range that should prove valuable in corroborating the corresponding contribution to the anomalous magnetic moment of the muon. As side products, we obtain improved constraints on the ππ P -wave, valuable input for future global analyses of low-energy ππ scattering, as well as a determination of the pion charge radius, 〈 r π 2 〉 = 0 . 429(1)(4) fm 2 .

A bstract The pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon ( g − 2) μ is fully determined by the doubly-virtual pion transition form factor. Although this crucial input quantity is, in principle, directly accessible in experiment, a complete measurement covering all kinematic regions relevant for ( g −2) μ is not realistic in the foreseeable future. Here, we report in detail on a reconstruction from available data, both space- and time-like, using a dispersive representation that accounts for all the low-lying singularities, reproduces the correct high- and low-energy limits, and proves convenient for the evaluation of the ( g − 2) μ loop integral. We concentrate on the systematics of the fit to e + e − → 3 π data, which are key in constraining the isoscalar dependence, as well as the matching to the asymptotic limits. In particular, we provide a detailed account of the pion transition form factor at low energies in the time- and space-like region, including the error estimates underlying our final result for the pion-pole contribution, a μ π 0 − pole = 62.6 − 2.5 + 3.0 × 10 − 11 , and demonstrate how forthcoming singly-virtual measurements will further reduce its uncertainty.

A bstract While the low-energy part of the hadronic light-by-light (HLbL) tensor can be constrained from data using dispersion relations, for a full evaluation of its contribution to the anomalous magnetic moment of the muon ( g − 2) μ also mixed- and high-energy regions need to be estimated. Both can be addressed within the operator product expansion (OPE), either for configurations where all photon virtualities become large or one of them remains finite. Imposing such short-distance constraints (SDCs) on the HLbL tensor is thus a major aspect of a model-independent approach towards HLbL scattering. Here, we focus on longitudinal SDCs, which concern the amplitudes containing the pseudoscalar-pole contributions from π 0 , η , η′ . Since these conditions cannot be fulfilled by a finite number of pseudoscalar poles, we consider a tower of excited pseudoscalars, constraining their masses and transition form factors from Regge theory, the OPE, and phenomenology. Implementing a matching of the resulting expressions for the HLbL tensor onto the perturbative QCD quark loop, we are able to further constrain our calculation and significantly reduce its model dependence. We find that especially for the π 0 the corresponding increase of the HLbL contribution is much smaller than previous prescriptions in the literature would imply. Overall, we estimate that longitudinal SDCs increase the HLbL contribution by Δ a μ LSDC = 13 6 × 10 -11 . This number does not include the contribution from the charm quark, for which we find a μ c − quark = 3(1) × 10 − 11 .

A bstract We provide a systematic treatment of the previously discovered power- enhanced QED corrections to the leptonic decay B q → μ + μ − ( q = d, s ) in the frame- work of soft-collinear effective theory (SCET). Employing two-step matching on SCETI and SCET II , and the respective renormalization group equations, we sum the leading- logarithmic QED corrections and the mixed QED-QCD corrections to all orders in the couplings for the matrix element of the semileptonic weak effective operator Q 9 . We pro- pose a treatment of the B -meson decay constant and light-cone distribution amplitude in the presence of process-specific QED corrections. Finally we include ultrasoft photon radiation and provide updated values of the non-radiative and radiative branching fractions of B q → μ + μ − decay that include the double-logarithmic QED and QCD corrections.

We compute$$ \\mathcal{O}\\left({\\alpha}^2Z\\right) $$O α 2 Z radiative corrections to superallowed β decays with a heavy-particle effective field theory that systematically describes the interactions of low-energy ultrasoft photons with nuclei. We calculate two-loop virtual and one-loop real-virtual amplitudes by reducing the Feynman integrals to a set of master integrals, which we solve analytically using a variety of techniques. These techniques can be applied to other phenomenologically interesting observables. The ultrasoft corrections can then be combined with contributions arising from the exchange of potential photons to obtain the complete$$ \\mathcal{O}\\left({\\alpha}^2Z\\right) $$O α 2 Z correction to the decay rate, with resummation of large logarithms of the electron energy times the nuclear radius. We find that$$ \\mathcal{O}\\left({\\alpha}^2Z\\right) $$O α 2 Z ultrasoft loops induce a relative correction to the decay rate that ranges from 0.7 ∙ 10 − 3 in the decay of 10 C to 3.6 ∙ 10 − 3 in the decay of 54 Co, and will thus impact the extraction of V ud at the permille level. We show that the inclusion of these corrections reduces the residual renormalization scale dependence of the decay rate to a negligible level, making missing ultrasoft perturbative corrections a subdominant source of theoretical uncertainty.