arXiv subjects

Harvey B. Meyer

Publications and source records attributed to Harvey B. Meyer.

At least 55 records · Page 3Linked 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.

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arXiv2023

Window observable for the hadronic vacuum polarization contribution to the muon $g-2$ from lattice QCD

Euclidean time windows in the integral representation of the hadronic vacuum polarization contribution to the muon $g-2$ serve to test the consistency of lattice calculations and may help in tracing the origins of a potential tension between lattice and data-driven evaluations. In this paper, we present results for the intermediate time window observable computed using O($a$) improved Wilson fermions at six values of the lattice spacings below 0.1\,fm and pion masses down to the physical value. Using two different sets of improvement coefficients in the definitions of the local and conserved vector currents, we perform a detailed scaling study which results in a fully controlled extrapolation to the continuum limit without any additional treatment of the data, except for the inclusion of finite-volume corrections. To determine the latter, we use a combination of the method of Hansen and Patella and the Meyer-Lellouch-Lüscher procedure employing the Gounaris-Sakurai parameterization for the pion form factor. We correct our results for isospin-breaking effects via the perturbative expansion of QCD+QED around the isosymmetric theory. Our result at the physical point is $a_μ^{\mathrm{win}}=(237.30\pm0.79_{\rm stat}\pm1.22_{\rm syst})\times10^{-10}$, where the systematic error includes an estimate of the uncertainty due to the quenched charm quark in our calculation. Our result displays a tension of 3.9$σ$ with a recent evaluation of $a_μ^{\mathrm{win}}$ based on the data-driven method.

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arXiv2022

The pion-nucleon sigma term with $N_f=2+1$ $\mathcal{O}(a)$-improved Wilson fermions

We present an analysis of the pion-nucleon sigma term on the CLS ensembles with $N_f=2+1$ flavors of $\mathcal{O}(a)$-improved Wilson fermions. We perform a chiral interpolation based on ensembles with pion masses ranging from 130 MeV to roughly 350 MeV. The analysis covers four lattice spacings between $a\approx [0.05 \, \rm{fm}\ldots 0.09\, \rm{fm}]$, allowing for an estimate of systematics associated with lattice artefacts.

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arXiv2022

Mass and isovector matrix elements of the nucleon at zero-momentum transfer

We present the current status of our analysis of nucleon structure observables including isovector charges and twist-2 matrix elements as well as the nucleon mass. Results are computed on a large set of CLS $N_f=2+1$ gauge ensembles with $M_π\approx0.130\mathrm{MeV}\ldots 350\mathrm{MeV}$, four values of the lattice spacing $a=0.05\mathrm{fm}\ldots 0.09\mathrm{fm}$ and covering a large range of physical volumes. Compared to the results presented at last year's conference we have added data on a very fine and large box at small light quark mass ($T\times L^3=192 \times 96^3$, $M_π=172\mathrm{MeV}$, $a=0.05\mathrm{fm}$). Additional (intermediate) source-sink separations have been computed on the coarser ensembles, further increasing effective statistics and allowing for a more fine-grained control in the treatment of the excited-state contamination. Excited states in the nucleon matrix elements are tamed by a simultaneous, two-state fit ansatz using the summation method.

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arXiv2022

The hadronic running of the electroweak couplings from lattice QCD

The energy dependency (running) of the strength of electromagnetic interactions $α$ plays an important role in precision tests of the Standard Model. The running of the former to the $Z$ pole is an input quantity for global electroweak fits, while the running of the mixing angle is susceptible to the effects of Beyond Standard Model physics, particularly at low energies. We present a computation of the hadronic vacuum polarization (HVP) contribution to the running of these electroweak couplings at the non-perturbative level in lattice QCD, in the space-like regime up to $Q^2$ momentum transfers of $7\,\mathrm{GeV}^2$. This quantity is also closely related to the HVP contribution to the muon $g-2$. We observe a tension of up to $3.5$ standard deviation between our lattice results for $Δα^{(5)}_{\mathrm{had}}(-Q^2)$ and estimates based on the $R$-ratio for $Q^2$ in the $3$ to $7\,\mathrm{GeV}^2$ range. The tension is, however, strongly diminished when translating our result to the $Z$ pole, by employing the Euclidean split technique and perturbative QCD, which yields $Δα^{(5)}_{\mathrm{had}}(M_Z^2)=0.027\,73(15)$. This value agrees with results based on the $R$-ratio within the quoted uncertainties, and can be used as an alternative to the latter in global electroweak fits.

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arXiv2022

Estimation of the photon production rate using imaginary momentum correlators

The thermal photon emission rate is determined by the spatially transverse, in-medium spectral function of the electromagnetic current. Accessing the spectral function using Euclidean data is, however, a challenging problem due to the ill-posed nature of inverting the Laplace transform. In this contribution, we present the first results on implementing the proposal of directly computing the analytic continuation of the retarded correlator at fixed, vanishing virtuality of the photon via the calculation of the appropriate Euclidean correlator at imaginary spatial momentum. We employ two dynamical O(a)-improved Wilson fermions at a temperature of 250 MeV.

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arXiv2022

Electromagnetic form factors of the proton and neutron from $N_f = 2 + 1$ lattice QCD

We present results for the electromagnetic form factors of the proton and neutron computed on the Coordinated Lattice Simulations (CLS) ensembles with $N_f = 2 + 1$ flavors of $\mathcal{O}(a)$-improved Wilson fermions and an $\mathcal{O}(a)$-improved conserved vector current. In order to estimate the excited-state contamination, we employ several source-sink separations and apply the summation method. The quark-disconnected diagrams entering the isoscalar quantities are computed explicitly. For this purpose, a stochastic estimation based on the one-end trick is performed, in combination with a frequency-splitting technique and the hopping-parameter expansion. By these means, we obtain a clear signal for the form factors including the quark-disconnected contributions, which have a statistically significant effect on our results. From the $Q^2$-dependence of the form factors, we determine the electric and magnetic charge radii and the magnetic moments of the proton and neutron. The chiral interpolation is carried out by simultaneously fitting the pion mass and $Q^2$-dependence of our form factor data directly to the expressions resulting from covariant chiral perturbation theory including vector mesons. To assess the influence of systematic effects, we average over various cuts in the pion mass and the momentum transfer, as well as over different models for the lattice spacing and finite volume dependence.

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arXiv2022

The hadronic running of the electromagnetic coupling and electroweak mixing angle

We present results for the hadronic running of the electromagnetic coupling and the weak mixing angle from simulations of lattice QCD with $N_f=2+1$ flavours of $O(a)$-improved Wilson fermions. Using two different discretisations of the vector current, we compute the quark-connected and -disconnected contributions to the hadronic vacuum polarisation (HVP) functions $\barΠ^{γγ}$ and $\barΠ^{Zγ}$ for spacelike squared momenta $Q^2\leq 7$ $\mathrm{GeV}^2$. Our results are extrapolated to the physical point using ensembles at four lattice spacings, with pion masses ranging from 130 to 420 MeV. We observe a tension of up to 3.5 standard deviations between our lattice results for $Δα_{\rm had}^{(5)}(-Q^2)$ and estimates based on the $\textit{R}$-ratio for space-like momenta in the range $Q^2=3-7\,\rm GeV^2$. To obtain an estimate for $Δα_\mathrm{had}^{(5)}(M_Z^2)$, we employ the Euclidean split technique. The implications for comparison with global electroweak fits are assessed.

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arXiv2022

Isovector Axial Form Factor of the Nucleon from Lattice QCD

The isovector axial form factor of the nucleon plays a key role in interpreting data from long-baseline neutrino oscillation experiments. We present a lattice QCD calculation of this form factor, introducing a new method to directly extract its z-expansion from lattice correlators. Our final parameterization of the form factor, which extends up to spacelike virtualities of 0.7 GeV^2 with fully quantified uncertainties, agrees with previous lattice calculations but is significantly less steep than neutrino-deuterium scattering data suggests.

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arXiv2022

Intermediate window observable for the hadronic vacuum polarization contribution to the muon $g-2$ from O$(a)$ improved Wilson quarks

Following the publication of the new measurement of the anomalous magnetic moment of the muon, the discrepancy between experiment and the theory prediction from the $g-2$ theory initiative has increased to $4.2\,σ$. Recent lattice QCD calculations predict values for the hadronic vacuum polarization contribution that are larger than the data-driven estimates, bringing the Standard Model prediction closer to the experimental measurement. Euclidean time windows in the time-momentum representation of the hadronic vacuum polarization contribution to the muon $g-2$ can help clarify the discrepancy between the phenomenological and lattice predictions. We present our calculation of the intermediate distance window contribution using $N_\mathrm{f}=2+1$ flavors of O$(a)$ improved Wilson quarks. We employ ensembles at six lattice spacings below $0.1\,$fm and pion masses down to the physical value. We present a detailed study of the continuum limit, using two discretizations of the vector current and two independent sets of improvement coefficients. Our result at the physical point displays a tension of $3.9\,σ$ with a recent evaluation of the intermediate window based on the data-driven method.

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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.

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arXiv2022

Aspects of chiral symmetry in QCD at T = 128 MeV

We investigate several aspects of chiral symmetry in QCD at a temperature of $T = 128\,\text{MeV}$. The study is based on a $24\times 96^3$ lattice-QCD ensemble with O($a$)-improved Wilson quarks and physical up, down and strange quark masses. The pion quasiparticle turns out to be significantly lighter than the zero-temperature pion mass, even though the corresponding static correlation length is shorter. We perform a quantitative comparison of our findings to predictions of chiral perturbation theory. Among several order parameters for chiral symmetry restoration, we compute the difference of the vector- and axial-vector time-dependent correlators and find it to be reduced by a factor $\sim2/3$ as compared to its vacuum counterpart.

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arXiv2022

The hadronic running of the electromagnetic coupling and the electroweak mixing angle from lattice QCD

We compute the hadronic running of the electromagnetic and weak couplings in lattice QCD with $N_{\mathrm{f}}=2+1$ flavors of $\mathcal{O}(a)$ improved Wilson fermions. Using two different discretizations of the vector current, we compute the quark-connected and -disconnected contributions to the hadronic vacuum polarization (HVP) functions $\barΠ^{γγ}$ and $\barΠ^{γZ}$ for Euclidean squared momenta $Q^2\leq 7\,\mathrm{GeV}^2$. Gauge field ensembles at four values of the lattice spacing and several values of the pion mass, including its physical value, are used to extrapolate the results to the physical point. The ability to perform an exact flavor decomposition allows us to present the most precise determination to date of the $\mathrm{SU}(3)$-flavor-suppressed HVP function $\barΠ^{08}$ that enters the running of $\sin^2θ_{\mathrm{W}}$. Our results for $\barΠ^{γγ}$, $\barΠ^{γZ}$ and $\barΠ^{08}$ are presented in terms of rational functions for continuous values of $Q^2$ below $7 \,\mathrm{GeV}^2$. We observe a tension of up to $3.5$ standard deviation between our lattice results for $Δα^{(5)}_{\mathrm{had}}(-Q^2)$ and estimates based on the $R$-ratio for space-like momenta in the range $3$--$7\,\mathrm{GeV}^2$. The tension is, however, strongly diminished when translating our result to the $Z$ pole, by employing the Euclidean split technique and perturbative QCD, which yields $Δα^{(5)}_{\mathrm{had}}(M_Z^2)=0.027\,73(15)$ and agrees with results based on the $R$-ratio within the quoted uncertainties.

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arXiv2022

The isovector axial form factor of the nucleon from lattice QCD

The isovector axial form factor of the nucleon plays a key role in interpreting data from long-baseline neutrino oscillation experiments. We perform a lattice-QCD based calculation of this form factor, introducing a new method to directly extract its $z$-expansion from lattice correlators. Our final parametrization of the form factor, which extends up to spacelike virtualities of $0.7\,{\rm GeV}^2$ with fully quantified uncertainties, agrees with previous lattice calculations but is significantly less steep than neutrino-deuterium scattering data suggests.

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arXiv2022

Isoscalar electromagnetic form factors of the nucleon in $N_\mathrm{f} = 2 + 1$ lattice QCD

We present results for the isoscalar electromagnetic form factors of the nucleon computed on the Coordinated Lattice Simulations (CLS) ensembles with $N_\mathrm{f} = 2 + 1$ flavors of $\mathcal{O}(a)$-improved Wilson fermions and an $\mathcal{O}(a)$-improved conserved vector current. In order to estimate the excited-state contamination, we employ several source-sink separations and apply the summation method. For the computation of the quark-disconnected diagrams, a stochastic estimation based on the one-end trick is performed, in combination with a frequency-splitting technique and the hopping parameter expansion. By these means, we obtain a clear signal for the form factors including the quark-disconnected contributions, which have a statistically significant effect on our results.

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arXiv2022

Photon emissivity of the quark-gluon plasma: a lattice QCD analysis of the transverse channel

We present results for the thermal photon emissivity of the quark-gluon plasma derived from spatially transverse vector correlators computed in lattice QCD at a temperature of 250 MeV. The analysis of the spectral functions, performed at fixed spatial momentum, is based on continuum-extrapolated correlators obtained with two flavours of dynamical Wilson fermions. We compare the next-to-leading order perturbative QCD correlators, as well as the ${\cal N}=4$ supersymmetric Yang-Mills correlators at infinite coupling, to the correlators from lattice QCD and find them to lie within $\sim10\%$ of each other. We then refine the comparison, performing it at the level of filtered spectral functions obtained model-independently via the Backus-Gilbert method. Motivated by these studies, for frequencies $ω\lesssim2.5\,$GeV we use fit ansätze to the spectral functions that perform well when applied to mock data generated from the NLO QCD or from the strongly-coupled SYM spectral functions, while the high-frequency part, $ω\gtrsim 2.5\,$GeV, is matched to NLO QCD. We compare our results for the photon emissivity to our previous analysis of a different vector channel at the same temperature. We obtain the most stringent constraint at photon momenta around $k\simeq0.8\,$GeV, for which we find a differential photon emission rate per unit volume of $dΓ_γ/d^3k = (α_{\rm em}/(\exp(k/T)-1))\times (2.2 \pm 0.8 ) \times 10^{-3}\,{\rm GeV}$.

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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.

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arXiv2022

The hadronic contribution to the running of the electromagnetic coupling and electroweak mixing angle

As present and future experiments, on both the energy and precision frontiers, look to identify new physics beyond the Standard Model, we require more precise determinations of fundamental quantities, like the QED and electroweak couplings at various momenta. These can be obtained either entirely from experimental measurements, or from one such measurement at a particular virtuality combined with the couplings' virtuality dependence computed within the SM. Thus, a precise, entirely theoretical determination of the running couplings is highly desirable, even more since the preliminary results of the E989 experiment in Fermilab were published. We give results for the hadronic contribution to the QED running coupling $α(Q^2)$ and weak mixing angle $\sin^2θ_W(Q^2)$ in the space-like energy region $(0, 7]~\text{GeV}^2$ with a total relative uncertainty of $2\%$ at energies $Q^2 \ll 1~\text{GeV}^2$, and $1\%$ at $Q^2 > 1~\text{GeV}^2$.

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