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En-Hung Chao

Publications and source records attributed to En-Hung Chao.

18 recordsLinked to original sources
arXiv2026

Vacuum polarization in QED with an electromagnetic background from the lattice

We propose a framework to determine the vacuum polarization functions in QED in the presence of an electromagnetic background field in the spacelike region on the lattice. This method consists in reweighting lattice Monte Carlo data generated without the background with the fermion determinant ratio evaluated in the continuous spacetime using worldline formalism. This proposal can be further extended to other applications in lattice gauge theory, such as QCD in finite chemical potential.

hep-lat↗
arXiv2026

Renormalizing a three-flavor lattice calculation of the two-photon contribution to $K_L\to\mu^+\mu^-$

The Standard Model prediction for the rare $K_L\to\mu^+\mu^-$ decay depends critically on the long-distance contribution coming from the exchange of two photons. Such a contribution can be computed using lattice QCD and an effective three-flavor theory including only the $u$, $d$ and $s$ quarks, provided terms falling as the inverse square of the omitted charm quark mass, $1/m_c^2$ are neglected. Because of the missing Glashow-Iliopoulos-Maiani cancelation, this three-flavor theory contains additional low-energy constants that depend on $m_c$. Here we show how these constants can be determined from a practical four-flavor lattice QCD calculation performed on a small volume with $u$ and $d$ quark masses that are heavier than physical.

hep-lat↗
arXiv2025

Long-distance contributions to kaon decays on the lattice

In the past decades, significant improvements have been made on standard-model predictions on kaon decays using lattice quantum chromodynamics. In these proceedings, I review selected works on long-distance contributions to kaon decays and developments on QED corrections to those.

hep-lat↗
arXiv2025

An exploratory calculation of $K_{\rm L}\toμ^+μ^-$ decay from Lattice QCD at physical pion mass

We compute the complex, long-distance two-photon-exchange amplitude which contributes to the rare $K_{\rm L}\rightarrowμ^+μ^-$ decay from lattice QCD. We use a $24^3\times 64$ physical-pion-mass gauge field ensemble at an inverse lattice spacing of $1.023$ GeV and a QED${}_\infty$-based formalism. Our implementation strategies for all five non-SU$(3)$-flavor-suppressed diagram topologies are given in detail. We achieve a 25% statistical precision on the dispersive part of this long-distance amplitude. This calculation is carried out with 2+1 quark flavors and therefore requires the addition of counter terms to compensate for the absence of the Glashow-Iliopoulos-Maiani mechanism. These counter terms are not included in the current calculation and will be the subject of a second paper. The precision of our results is limited by the reconstruction of the physical contribution of the $η$ intermediate state, for which various strategies are tested and compared.

hep-lat↗
arXiv2025

Computing the UV-finite electromagnetic corrections to the hadronic vacuum polarization in the muon $(g-2)$ from lattice QCD

In order to reach a precision of $0.2\%$ on the hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon, $(g-2)_μ$, such that the full Standard-Model prediction matches in precision the direct experimental measurement, it is crucial to include the leading, O($α$) electromagnetic corrections to HVP. In this work, we determine an important contribution to the latter from a diagram comprised of two two-point quark-loops, connected by the internal photon and gluons. This ultraviolet-finite correction is calculated from lattice QCD using a coordinate-space formalism, where photons are treated in the continuum and infinite volume. Our result amounts to a $(-0.89\pm 0.18)\%$ correction to the leading-order HVP contribution to $(g-2)_μ$. To overcome the worsening statistical noise at large distances, our analysis is combined with phenomenological models featuring light pseudoscalar mesons with masses below 1 GeV. In particular, our data show a very steep mass dependence as dictated by the charged pion loop. Similarly, the other diagrams appearing in the O$(α)$-corrections to the HVP with the internal photon connecting two separate quark loops are also ultraviolet-finite and can be computed with the same formalism.

hep-lat↗
arXiv2025

Kaon Physics: A Cornerstone for Future Discoveries

The kaon physics programme, long heralded as a cutting-edge frontier by the European Strategy for Particle Physics, continues to stand at the intersection of discovery and innovation in high-energy physics (HEP). With its unparalleled capacity to explore new physics at the multi-TeV scale, kaon research is poised to unveil phenomena that could reshape our understanding of the Universe. This document highlights the compelling physics case, with emphasis on exciting new opportunities for advancing kaon physics not only in Europe but also on a global stage. As an important player in the future of HEP, the kaon programme promises to drive transformative breakthroughs, inviting exploration at the forefront of scientific discovery.

hep-ph↗
arXiv2024

Two-photon contribution to the $K_L\toμ^+μ^-$ decay amplitude from a $1/a\approx 1 $ GeV lattice

We present a lattice-QCD calculation of the long-distance two-photon contribution to the decay amplitude of a long-lived kaon to a pair of muons on a $24^3\times 64$ physical-pion-mass ensemble. In these proceedings, the theoretical foundation of this calculation will be reviewed and preliminary numerical results will be presented for all diagrams with the exception of those that are quark-line disconnected SU(3)-flavor-suppressed. At this stage, the intermediate $η$ contribution appears to be the largest source of statistical uncertainty. Our proposed strategies to reduce these statistical errors are discussed in great detail.

hep-lat↗
arXiv2024

Calculating the two-photon exchange contribution to $K_L\rightarrowμ^+μ^-$ decay

We present a theoretical framework within which both the real and imaginary parts of the complex, two-photon exchange amplitude contributing to $K_L\rightarrowμ^+μ^-$ decay can be calculated using lattice QCD. The real part of this two-photon amplitude is of approximately the same size as that coming from a second-order weak strangeness-changing neutral-current process. Thus a test of the standard model prediction for this second-order weak process depends on an accurate result of this two-photon amplitude. A limiting factor of our proposed method comes from low-energy three-particle $ππγ$ states. The contribution from these states will be significantly distorted by the finite volume of our calculation -- a distortion for which there is no available correction. However, a simple estimate of the contribution of these three-particle states suggests their contribution to be at most a few percent allowing their neglect in a lattice calculation with a 10% target accuracy.

hep-ph↗
arXiv2023

$K_{\rm L}\rightarrowμ^+μ^-$ from lattice QCD

We propose a lattice-QCD-suitable framework for computing the two-photon long-distance contribution to the complex $K_{\rm L}\rightarrowμ^+μ^-$ decay amplitude, where QED is treated perturbatively in the continuum and infinite-volume. We provide preliminary numerical results on the quark-connected diagrams on one ensemble at physical pion mass from this method, with well-controlled systematic errors. The successful application of this method will allow the determination of the dispersive part of the aforementioned contribution from first-principles and enable a meaningful comparison between the Standard-Model prediction and experiment.

hep-lat↗
arXiv2023

Coordinate-space calculation of QED corrections to the hadronic vacuum polarization contribution to $(g-2)_μ$

As several lattice collaborations agree on the result for the window quantity of the hadronic vacuum polarization (HVP) contribution to $(g-2)_μ$, whilst being in tension with the calculation using the dispersive approach, further effort is needed in order to pin down the cause for this difference. Here we want to focus on the isospin breaking corrections to the leading order HVP. In many lattice applications, the photon propagator is treated stochastically; however, by analogy with the hadronic light-by-light contribution (HLbL) to $(g-2)_μ$, we suggest a coordinate-space approach to the HVP at next-to-leading order. We present a calculation of the two diagrams of the (2+2) topology at unphysical pion mass, where we apply a Pauli-Villars regularization for the extra photon propagator in the diagram that is UV-divergent. We compare the UV-finite diagram to the pseudoscalar exchange contributions calculated from a vector-meson dominance model.

hep-lat↗
arXiv2023

Forward light-by-light scattering and electromagnetic correction to hadronic vacuum polarization

Lattice QCD calculations of the hadronic vacuum polarization (HVP) have reached a precision where the electromagnetic (e.m.) correction can no longer be neglected. This correction is both computationally challenging and hard to validate, as it leads to ultraviolet (UV) divergences and to sizeable infrared (IR) effects associated with the massless photon. While we precisely determine the UV divergence using the operator-product expansion, we propose to introduce a separation scale $Λ\sim400\;$MeV into the internal photon propagator, whereby the calculation splits into a short-distance part, regulated in the UV by the lattice and in the IR by the scale $Λ$, and a UV-finite long-distance part to be treated with coordinate-space methods, thereby avoiding power-law finite-size effects altogether. In order to predict the long-distance part, we express the UV-regulated e.m. correction to the HVP via the forward hadronic light-by-light (HLbL) scattering amplitude and relate the latter via a dispersive sum rule to $γ^*γ^*$ fusion cross-sections. Having tested the relation by reproducing the two-loop QED vacuum polarization (VP) from the tree-level $γ^*γ^*\to e^+e^-$ cross-section, we predict the expected lattice-QCD integrand resulting from the $γ^*γ^*\toπ^0$ process.

hep-lat↗
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↗
arXiv2022

Coordinate-space calculation of the window observable for the hadronic vacuum polarization contribution to $(g-2)_μ$

The `intermediate window quantity' of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon allows for a high-precision comparison between the data-driven approach and lattice QCD. The existing lattice results, which presently show good consistency among each other, are in strong tension with the data-driven determination. In order to check for a potentially common source of systematic error of the lattice calculations, which are all based on the time-momentum representation (TMR), we perform a calculation using a Lorentz-covariant coordinate-space (CCS) representation. We present results for the isovector and the connected strange-quark contributions to the intermediate window quantity at a reference point in the $(m_π,m_K)$ plane, in the continuum and infinite-volume limit, based on four different lattice spacings. Our results are in good agreement with those of the recent TMR-based Mainz-CLS publication.

hep-lat↗
arXiv2022

The charm-quark contribution to light-by-light scattering in the muon $(g-2)$ from lattice QCD

We compute the hadronic light-by-light scattering contribution to the muon $g-2$ from the charm quark using lattice QCD. The calculation is performed on ensembles generated with dynamical $(u,d,s)$ quarks at the SU(3)$_{\rm f}$ symmetric point with degenerate pion and kaon masses of around 415 MeV. It includes the connected charm contribution, as well as the leading disconnected Wick contraction, involving the correlation between a charm and a light-quark loop. Cutoff effects turn out to be sizeable, which leads us to use lighter-than-physical charm masses, to employ a broad range of lattice spacings reaching down to 0.039 fm and to perform a combined charm-mass and continuum extrapolation. We use the $η_c$ meson to define the physical charm-mass point and obtain a final value of $a_μ^{\rm HLbL,c} = (2.8\pm 0.5) \times 10^{-11}$, whose uncertainty is dominated by the systematics of the extrapolation. Our result is consistent with the estimate based on a simple charm-quark loop, whilst being free of any perturbative scheme dependence on the charm mass. The mixed charm-light disconnected contraction contributes a small negative amount to the final value.

hep-lat↗
arXiv2021

Hadronic light-by-light contribution to $(g-2)_μ$ from lattice QCD: a complete calculation

We compute the hadronic light-by-light scattering contribution to the muon $g-2$ from the up, down, and strange-quark sector directly using lattice QCD. Our calculation features evaluations of all possible Wick-contractions of the relevant hadronic four-point function and incorporates several different pion masses, volumes, and lattice-spacings. We obtain a value of $a_μ^{\text{Hlbl}} = 106.8(14.7) \times 10^{-11}$ (adding statistical and systematic errors in quadrature), which is consistent with current phenomenological estimates and a previous lattice determination. It now appears conclusive that the hadronic light-by-light contribution cannot explain the current tension between theory and experiment for the muon $g-2$.

hep-lat↗
arXiv2020

Hadronic light-by-light contribution to $(g-2)_μ$ from lattice QCD with SU(3) flavor symmetry

We perform a lattice QCD calculation of the hadronic light-by-light contribution to $(g-2)_μ$ at the SU(3) flavor-symmetric point $m_π=m_K\simeq 420\,$MeV. The representation used is based on coordinate-space perturbation theory, with all QED elements of the relevant Feynman diagrams implemented in continuum, infinite Euclidean space. As a consequence, the effect of using finite lattices to evaluate the QCD four-point function of the electromagnetic current is exponentially suppressed. Thanks to the SU(3)-flavor symmetry, only two topologies of diagrams contribute, the fully connected and the leading disconnected. We show the equivalence in the continuum limit of two methods of computing the connected contribution, and introduce a sparse-grid technique for computing the disconnected contribution. Thanks to our previous calculation of the pion transition form factor, we are able to correct for the residual finite-size effects and extend the tail of the integrand. We test our understanding of finite-size effects by using gauge ensembles differing only by their volume. After a continuum extrapolation based on four lattice spacings, we obtain $a_μ^{\rm hlbl} = (65.4\pm 4.9 \pm 6.6)\times 10^{-11}$, where the first error results from the uncertainties on the individual gauge ensembles and the second is the systematic error of the continuum extrapolation. Finally, we estimate how this value will change as the light-quark masses are lowered to their physical values.

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↗