Dispersion relations for hadronic light-by-light and the muon g − 2

The largest uncertainties in the Standard Model calculation of the anomalous magnetic moment of the muon (g−2)µ come from hadronic effects, namely hadronic vacuum polarization (HVP) and hadronic lightby-light (HLbL) contributions. Especially the latter is emerging as a potential roadblock for a more accurate determination of (g−2)µ. The main focus here is on a novel dispersive description of the HLbL tensor, which is based on unitarity, analyticity, crossing symmetry, and gauge invariance. This opens up the possibility of a data-driven determination of the HLbL contribution to (g−2)µ with the aim of reducing model dependence and achieving a reliable error estimate. Our dispersive approach defines unambiguously the pion-pole and the pion-box contribution to the HLbL tensor. Using Mandelstam double-spectral representation, we have proven that the pion-box contribution coincides exactly with the one-loop scalar-QED amplitude, multiplied by the appropriate pion vector form factors. Using dispersive fits to high-statistics data for the pion vector form factor, we obtain $ \alpha _\mu ^{\pi {\rm{ - box}}} = - 15.9(2) \times {10^{ - 11}} $. A first model-independent calculation of effects of ππ intermediate states that go beyond the scalar-QED pion loop is also presented. We combine our dispersive description of the HLbL tensor with a partial-wave expansion and demonstrate that the known scalar-QED result is recovered after partial-wave resummation. After constructing suitable input for the γ*γ* → ππ helicity partial waves based on a pion-pole left-hand cut (LHC), we find that for the dominant charged-pion contribution this representation is consistent with the two-loop chiral prediction and the COMPASS measurement for the pion polarizability. This allows us to reliably estimate S-wave rescattering effects to the full pion box and leads to $ \alpha _\mu ^{\pi {\rm{ - box}}} + \alpha _{\mu ,J = 0}^{\pi \pi ,\pi {\rm{ - pole}}\,{\rm{LHC}}} = - 24(1) \times {10^{ - 11}} $.

Dispersion relations for hadronic light-by-light scattering and the muon g – 2

The largest uncertainties in the Standard Model calculation of the anomalous magnetic moment of the muon (g – 2)μ come from hadronic effects, and in a few years the subleading hadronic light-by-light (HLbL) contribution might dominate the theory error. We present a dispersive description of the HLbL tensor, which is based on unitarity, analyticity, crossing symmetry, and gauge invariance. This opens up the possibility of a data-driven determination of the HLbL contribution to (g – 2)μ with the aim of reducing model dependence and achieving a reliable error estimate. Our dispersive approach defines unambiguously the pion-pole and the pion-box contribution to the HLbL tensor. Using Mandelstam double-spectral representation, we have proven that the pion-box contribution coincides exactly with the one-loop scalar-QED amplitude, multiplied by the appropriate pion vector form factors. Using dispersive fits to high-statistics data for the pion vector form factor, we obtain [see formula in PDF]. A first model-independent calculation of effects of ππ intermediate states that go beyond the scalar-QED pion loop is also presented. We combine our dispersive description of the HLbL tensor with a partial-wave expansion and demonstrate that the known scalar-QED result is recovered after partial-wave resummation. After constructing suitable input for the γ*γ* → ππ helicity partial waves based on a pion-pole left-hand cut (LHC), we find that for the dominant charged-pion contribution this representation is consistent with the two-loop chiral prediction and the COMPASS measurement for the pion polarizability. This allows us to reliably estimate S-wave rescattering effects to the full pion box and leads to [see formula in PDF].

On the Hadronic light-by-light contribution to the muon g – 2

This talk is about the hadronic light-by-light contribution to the muon anomalous magnetic moment, mainly our old work but including some newer results as well. It concentrates on the model calculations. Most attention is paid to pseudo-scalar exchange and the pion loop contribution. Scalar, a1-exchange and other contributions are shortly discussed as well. For the π0-exchange a possible large cancellation between connected and disconnected diagrams is expected.

Fine structure of the diffraction cone: From the ISR to the LHC

Following earlier findings, we argue that the low-[Formula: see text] structure in the elastic diffractive cone, recently reported by the TOTEM Collaboration at [Formula: see text] TeV, is a consequence of the threshold singularity required by [Formula: see text]channel unitarity, such as revealed earlier at the ISR. By using simple Regge-pole models, we analyze the available data on the [Formula: see text] elastic differential cross section in a wide range of c.m. energies, namely those from ISR to LHC8, obtaining good fits of all datasets. This study hints at the fact that the non-exponential behavior observed at LHC8 is a recurrence of the low-[Formula: see text] “break” phenomenon, observed in the seventies at ISR, being induced by the presence of a two-pion loop singularity in the Pomeron trajectory.

PION LOOP CONTRIBUTION TO THE ELECTROMAGNETIC PION CHARGE RADIUS

A phenomenological Dyson-Schwinger equation approach to QCD, formalized in terms of a QCD-based model field theory, is used to calculate the electromagnetic charge radius of the pion. The contributions from the core of dressed quarks and the pion loop are identified and compared. It is shown explicitly that the divergence of the charge radius in the chiral limit is due to the pion loop but that at mπ=0.14 GeV this loop contributes less than 15% to [Formula: see text], i.e. the dressed quark core is the dominant determining characteristic for the pion.