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Andreas Nyffeler

Publications and source records attributed to Andreas Nyffeler.

At least 19 recordsLinked to original sources
arXiv2023

Hadronic light-by-light scattering contribution to the muon $g-2$ from lattice QCD: semi-analytical calculation of the QED kernel

Hadronic light-by-light scattering is one of the virtual processes that causes the gyromagnetic factor $g$ of the muon to deviate from the value of two predicted by Dirac's theory. This process makes one of the largest contributions to the uncertainty of the Standard Model prediction for the muon $(g-2)$. Lattice QCD allows for a first-principles approach to computing this non-perturbative effect. In order to avoid power-law finite-size artifacts generated by virtual photons in lattice simulations, we follow a coordinate-space approach involving a weighted integral over the vertices of the QCD four-point function of the electromagnetic current carried by the quarks. Here we present in detail the semi-analytical calculation of the QED part of the amplitude, employing position-space perturbation theory in continuous, infinite four-dimensional Euclidean space. We also provide some useful information about a computer code for the numerical implementation of our approach that has been made public at https://github.com/RJHudspith/KQED.

hep-lat↗
arXiv2019

Developments in the position-space approach to the HLbL contribution to the muon $g-2$ on the lattice

The measurement of the anomalous magnetic moment of the muon and its prediction allow for a high-precision test of the Standard Model (SM). In this proceedings article we present ongoing work combining lattice QCD and continuum QED in order to determine an important SM contribution to the magnetic moment, the hadronic light-by-light contribution. We compute the quark-connected contribution in the Mainz position-space approach and investigate the long-distance part of our data using calculations of the $π^0$-pole and charged pion loop contributions.

hep-lat↗
arXiv2019

Lattice calculation of the pion transition form factor with $N_f=2+1$ Wilson quarks

We present a lattice QCD calculation of the double-virtual neutral pion transition form factor, with the goal to cover the kinematic range relevant to hadronic light-by-light scattering in the muon $g-2$. Several improvements have been made compared to our previous work. First, we take into account the effects of the strange quark by using the $N_f=2+1$ CLS gauge ensembles. Secondly, we have implemented the on-shell $\mathcal{O}(a)$-improvement of the vector current to reduce the discretization effects associated with Wilson quarks. Finally, in order to have access to a wider range of photon virtualities, we have computed the transition form factor in a moving frame as well as in the pion rest-frame. After extrapolating the form factor to the continuum and to physical quark masses, we compare our results with phenomenology. We extract the normalization of the form factor with a precision of 3.5\% and confirm within our uncertainty previous somewhat conflicting estimates for a low-energy constant that appears in chiral perturbation theory for the decay $π^0 \to γγ$ at NLO. With additional input from experiment and theory, we reproduce recent estimates for the decay width $Γ(π^0 \to γγ)$. We also study the asymptotic large-$Q^2$ behavior of the transition form factor in the double-virtual case. Finally, we provide as our main result a more precise model-independent lattice estimate of the pion-pole contribution to hadronic light-by-light scattering in the muon $g-2$: $a_μ^{\mathrm{HLbL}; π^0} = (59.7 \pm 3.6) \times 10^{-11}$. Using in addition the normalization of the form factor obtained by the PrimEx experiment, we get the lattice and data-driven estimate $a_μ^{\mathrm{HLbL}; π^0} = (62.3 \pm 2.3) \times 10^{-11}$.

hep-lat↗
arXiv2018

Hadronic light-by-light scattering in the anomalous magnetic moment of the muon

Hadronic light-by-light scattering in the anomalous magnetic moment of the muon $a_μ$ is one of two hadronic effects limiting the precision of the Standard Model prediction for this precision observable, and hence the new-physics discovery potential of direct experimental determinations of $a_μ$. In this contribution, we report on recent progress in the calculation of this effect achieved both via dispersive and lattice QCD methods.

hep-lat↗
arXiv2018

Hadronic light-by-light scattering contribution to the muon g-2 on the lattice

We briefly review several activities at Mainz related to hadronic light-by-light scattering (HLbL) using lattice QCD. First we present a position-space approach to the HLbL contribution in the muon g-2, where we focus on exploratory studies of the pion-pole contribution in a simple model and the lepton loop in QED in the continuum and in infinite volume. The second part describes a lattice calculation of the double-virtual pion transition form factor F_{pi^0 gamma^* gamma^*}(q_1^2, q_2^2) in the spacelike region with photon virtualities up to 1.5 GeV^2 which paves the way for a lattice calculation of the pion-pole contribution to HLbL. The third topic involves HLbL forward scattering amplitudes calculated in lattice QCD which can be described, using dispersion relations (HLbL sum rules), by gamma^* gamma^* -> hadrons fusion cross sections and then compared with phenomenological models.

hep-lat↗
arXiv2017

Exploratory studies for the position-space approach to hadronic light-by-light scattering in the muon $g-2$

The well-known discrepancy in the muon $g-2$ between experiment and theory demands further theory investigations in view of the upcoming new experiments. One of the leading uncertainties lies in the hadronic light-by-light scattering contribution (HLbL), that we address with our position-space approach. We focus on exploratory studies of the pion-pole contribution in a simple model and the fermion loop without gluon exchanges in the continuum and in infinite volume. These studies provide us with useful information for our planned computation of HLbL in the muon $g-2$ using full QCD.

hep-lat↗
arXiv2017

Hadronic light-by-light scattering in the muon g-2

We briefly review the current status of the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon. Based on various model calculations in the literature, we obtain the estimate a_{mu}^{HLbL} = (102 \pm 39) x 10^{-11}. Recent developments including more model-independent approaches using dispersion relations and lattice QCD, that could lead to a more reliable estimate, are also discussed.

hep-ph↗
arXiv2016

Lattice calculation of the pion transition form factor $π^0 \to γ^* γ^*$

We calculate the $π^0\to γ^*γ^*$ transition form factor ${\cal F}_{π^0γ^*γ^*}(q_1^2,q_2^2)$ in lattice QCD with two flavors of quarks. Our main motivation is to provide the input to calculate the $π^0$-pole contribution to hadronic light-by-light scattering in the muon $(g-2)$, $a_μ^{\rm HLbL;π^0}$. We therefore focus on the region where both photons are spacelike up to virtualities of about $1.5~$GeV$^2$, which has so far not been experimentally accessible. Results are obtained in the continuum at the physical pion mass by a combined extrapolation. We reproduce the prediction of the chiral anomaly for real photons with an accuracy of about $8-9\%$. We also compare to various recently proposed models and find reasonable agreement for the parameters of some of these models with their phenomenological values. Finally, we use the parametrization of our lattice data by these models to calculate $a_μ^{\rm HLbL;π^0}$.

hep-lat↗
arXiv2016

Lattice calculation of the pion transition form factor $π^0 \to γ^* γ^*$

We calculate the pion transition form factor ${\cal F}_{π^0γ^*γ^*}(q_1^2,q_2^2)$, which describe the interaction of an on-shell pion with two off-shell photons, using lattice QCD simulations with two degenerate flavors of dynamical quarks. This form factor is the main ingredient in the calculation of the pion-pole contribution to hadronic light-by-light scattering in the muon $g-2$, $a_μ^{\mathrm{HLbL}; π^0}$. We focus our study on the spacelike region with photon virtualities up to $1.5~\mathrm{GeV}^2$, not yet measured experimentally. Several lattice spacings and pion masses are used to extrapolate the results to the physical point and a comparison with different phenomenological models is performed. Finally, we use our extrapolated form factor to provide a lattice determinaiton of $a_μ^{\mathrm{HLbL}; π^0}$.

hep-lat↗
arXiv2016

Position-space approach to hadronic light-by-light scattering in the muon $g-2$ on the lattice

The anomalous magnetic moment of the muon currently exhibits a discrepancy of about three standard deviations between the experimental value and recent Standard Model predictions. The theoretical uncertainty is dominated by the hadronic vacuum polarization and the hadronic light-by-light (HLbL) scattering contributions, where the latter has so far only been fully evaluated using different models. To pave the way for a lattice calculation of HLbL, we present an expression for the HLbL contribution to $g-2$ that involves a multidimensional integral over a position-space QED kernel function in the continuum and a lattice QCD four-point correlator. We describe our semi-analytic calculation of the kernel and test the approach by evaluating the $π^0$-pole contribution in the continuum.

hep-lat↗
arXiv2016

On the precision of a data-driven estimate of the pseudoscalar-pole contribution to hadronic light-by-light scattering in the muon g-2

The evaluation of the numerically dominant pseudoscalar-pole contribution to hadronic light-by-light scattering in the muon g-2 involves the pseudoscalar-photon transition form factor F_{P gamma^* gamma^*}(-Q_1^2, -Q_2^2) with P = pi^0, eta, eta^\prime and, in general, two off-shell photons with spacelike momenta Q_{1,2}^2. We determine which regions of photon momenta give the main contribution for hadronic light-by-light scattering. Furthermore, we analyze how the precision of future measurements of the single- and double-virtual form factor impacts the precision of a data-driven estimate of this contribution to hadronic light-by-light scattering.

hep-ph↗
arXiv2016

On the precision of a data-driven estimate of hadronic light-by-light scattering in the muon g-2: pseudoscalar-pole contribution

The evaluation of the numerically dominant pseudoscalar-pole contribution to hadronic light-by-light scattering in the muon g-2 involves the pseudoscalar-photon transition form factor F_{P gamma^* gamma^*}(-Q_1^2, -Q_2^2) with P = pi^0, eta, eta^\prime and, in general, two off-shell photons with spacelike momenta Q_{1,2}^2. We show, in a largely model-independent way, that for pi^0 (eta, eta^\prime) the region of photon momenta below about 1 (1.5) GeV gives the main contribution to hadronic light-by-light scattering. We then discuss how the precision of current and future measurements of the single- and double-virtual transition form factor in different momentum regions impacts the precision of a data-driven estimate of this contribution to hadronic light-by-light scattering. Based on Monte Carlo simulations for a planned first measurement of the double-virtual form factor at BESIII, we find that for the pi^0, eta, eta^\prime-pole contributions a precision of 14\%, 23\%, 15\% seems feasible. Further improvements can be expected from other experimental data and also from the use of dispersion relations for the different form factors themselves.

hep-ph↗
arXiv2015

Direct calculation of hadronic light-by-light scattering

We report calculations of hadronic light-by-light scattering amplitudes via lattice QCD evaluation of Euclidean four-point functions of vector currents. These initial results include only the fully quark-connected contribution. Particular attention is given to the case of forward scattering, which can be related via dispersion relations to the $γ^* γ^* \to$ hadrons cross section, and thus allows lattice data to be compared with phenomenology. We also present a strategy for computing the hadronic light-by-light contribution to the muon anomalous magnetic moment.

hep-lat↗
arXiv2014

Remarks on higher-order hadronic corrections to the muon g-2

Recently, it was shown that insertions of hadronic vacuum polarization at O(alpha^4) generate non-negligible effects in the calculation of the anomalous magnetic moment of the muon. This result raises the question if other hadronic diagrams at this order might become relevant for the next round of g-2 measurements as well. In this note we show that a potentially enhanced such contribution, hadronic light-by-light scattering in combination with electron vacuum polarization, is already sufficiently suppressed.

hep-ph↗
arXiv2013

Status of hadronic light-by-light scattering in the muon g-2

We give an update on the status of the hadronic light-by-light scattering contribution to the muon g-2. We review recent work by various groups, list some of the open problems and give an outlook on how to better control the uncertainty of this contribution. This is necessary in order to fully profit from planned future muon g-2 experiments to test the Standard Model. Despite some recent developments, we think that the estimate a_{mu}^{HLbL} = (116 \pm 40) x 10^{-11} still gives a fair description of the current situation.

hep-ph↗
arXiv2013

Hadronic light-by-light scattering in the muon g-2: impact of proposed measurements of the (pi^0 -> gamma gamma) decay width and the (gamma^* gamma -> pi^0) transition form factor with the KLOE-2 experiment

The calculation of the hadronic light-by-light scattering contribution to the muon g-2 currently relies entirely on models. Measurements of the form factors which describe the interactions of hadrons with photons can help to constrain the models and reduce the uncertainty in a_{mu}(had. LbyL) = (116 \pm 40) x 10^{-11}. In the dominant pion-exchange contribution, the form factor F_{{pi^0}^*gamma^*gamma^*}((q_1 + q_2)^2, q_1^2, q_2^2) with an off-shell pion enters. In general, measurements of the transition form factor F(Q^2) = F_{{pi^0}^*gamma^*gamma^*}(m_{pi}^2, -Q^2, 0) are only sensitive to a subset of the model parameters. Thus, having a good description for F(Q^2) is only necessary, not sufficient, to determine a_{mu}(LbyL; pi^0). Simulations have shown that measurements at KLOE-2 should be able to determine the (pi^0 -> gamma gamma) decay width to 1% statistical precision and the transition form factor for small space-like momenta, 0.01 GeV^2 < Q^2 < 0.1 GeV^2, to 6% precision. In the two-loop integral for the pion-exchange contribution the relevant regions of momenta are in the range 0 - 1.5 GeV. With the (pi^0 -> gamma gamma) decay width from the PDG [PrimEx] and current data for the transition form factor, the error on a_{mu}(LbyL; pi^0) is (\pm 4 x 10^{-11}) [\pm 2 x 10^{-11}], not taking into account the uncertainty related to the off-shellness of the pion. Including the simulated KLOE-2 data reduces the error to (\pm (0.7 - 1.1) x 10^{-11}). For models like VMD, which have only few parameters that are completely determined by measurements of F(Q^2), this represents the total error. But maybe such models are too simplistic. In other models, e.g. those based on large-N_c QCD, parameters describing the off-shell pion dominate the uncertainty in a_{mu; large-N_c}(LbyL; pi^0) = (72 \pm 12) x 10^{-11}.

hep-ph↗
arXiv2012

Hadronic light-by-light scattering in the muon g-2: impact of proposed measurements of the (pi^0 -> gamma gamma) decay width and the (gamma^* gamma -> pi^0) transition form factor with the KLOE-2 experiment

We discuss, how planned measurements at KLOE-2 of the (pi^0 -> gamma gamma) decay width and the (gamma^* gamma -> pi^0) transition form factor can improve estimates for the numerically dominant pion-exchange contribution to hadronic light-by-light scattering in the muon g-2 and what are the limitations related to the modelling of the off-shellness of the pion.

hep-ph↗