Lattice QCD and the anomalous magnetic moment of the muon

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. Second, we have implemented the on-shell 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 → γγ at NLO. With additional input from experiment and theory, we reproduce recent estimates for the decay width Γ(π 0 → 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 HLbL;π 0 µ = (59.7 ± 3.6) × 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 HLbL;π 0 µ = (62.3 ± 2.3) × 10 −11 .

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“…i and q [6] i with i = 1, 2. In the pion rest frame, both photons have back-to-back spatial momenta and q 1 = − q 2 .…”

Section: Hypercubic Effectsmentioning

confidence: 99%

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

2019

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“…Furthermore, we expect a large correlation between propagators with similar quark masses which means that the estimate eq. ( 5.4) will have a reduced variance to the single quark loop [15]. Indeed, the variance of the estimator for the difference is reduced with respect to the variance on a single trace, as can be observed in figure 3 (green open squares), where a second flavour with a large quark mass m 1 0 has been introduced, see tab.…”

Section: Variance-reduction For Disconnected Diagramsmentioning

confidence: 69%

Multi-level integration for meson propagators

Giusti¹,

Harris²,

Nada³

et al. 2018

Preprint

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The computation of many correlation functions in lattice QCD is severely hindered by a signal-tonoise problem. Recent developments in the factorization of both the fermion propagator and determinant pave the way for the implementation of multi-level Monte Carlo integration techniques for lattice QCD. In these proceedings we introduce new strategies for the estimation of the factorized contribution to the connected and disconnected diagrams for meson two-point functions. An estimator for the factorized connected diagram is constructed sequentially for a two-level integration scheme. For the disconnected diagram, we introduce an improved estimator by performing a frequency-splitting of traces, applicable with or without multi-level integration. Preliminary results in the quenched theory with a two-level integration scheme are presented.

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“…Fortunately, lattice QCD is making big progress and begins to help to settle hadronic issues. For both of the critical contributions HVP and HLbL lattice QCD will be the answer one day (see [8] and references therein), I expect. But a lot remains to be done while a new a exp µ is on the way!…”

Section: Discussionmentioning

confidence: 95%

“…Lattice QCD ab initio calculations come closer in precision and already have provided important constraints and information (see e.g. [8]).…”

Section: To Be Improved: Leading Hadronic=mesonic Effectsmentioning

confidence: 99%

The Role of Mesons in Muon g-2

Jegerlehner

2018

Preprint

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The muon anomaly a µ = (g µ − 2)/2 showing a persisting 3 to 4 σ deviation between the SM prediction and the experiment is one of the most promising signals for physics beyond the SM. As is well known, the hadronic uncertainties are limiting the accuracy of the Standard Model prediction. Therefore a big effort is going on to improve the evaluations of hadronic effects in order to keep up with the 4fold improved precision expected from the new Fermilab measurement in the near future. A novel complementary type experiment planned at J-PARC in Japan, operating with ultra cold muons, is expected to be able to achieve the same accuracy but with completely different systematics. So exciting times in searching for New Physics are under way. I discuss the role of meson physics in calculations of the hadronic part of the muon g-2. The improvement is expected to substantiate the present deviation ∆a New Physics µ

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Lattice QCD and the anomalous magnetic moment of the muon

Cited by 7 publications

References 231 publications

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

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

Multi-level integration for meson propagators

The Role of Mesons in Muon g-2

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