arXiv subjects

Maarten Golterman

Publications and source records attributed to Maarten Golterman.

At least 37 records · Page 2Linked to original sources

arXiv2022

Data-based determination of the isospin-limit light-quark-connected contribution to the anomalous magnetic moment of the muon

We describe how recent determinations of exclusive-mode contributions to $a_μ^{\rm LO,HVP}$, the leading-order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon, can be used to provide, up to small electromagnetic (EM) corrections accessible from the lattice, a data-based dispersive determination of $a_μ^{\rm lqc;\, IL}$, the isospin-limit, light-quark-connected contribution to $a_μ^{\rm LO,HVP}$. Such a determination is of interest in view of the existence of a number of lattice results for this quantity, emerging evidence for a tension between lattice and dispersive determinations of $a_μ^{\rm LO,HVP}$, and the desire to clarify the source of this tension. Taking as input for the small EM correction that must be applied to the purely data-driven dispersive determination the result $-0.93(58)\times 10^{-10}$ obtained in a recent BMW lattice study, we find $a_μ^{\rm lqc;\, IL}$ to be $635.0(2.7)\times 10^{-10}$ if the results of Keshavarzi, Nomura and Teubner are used for the exclusive-mode contributions and $638.4(4.1)\times 10^{-10}$ if instead those of Davier, Höcker, Malaescu and Zhang are used.

hep-ph↗

arXiv2022

$α_s$ from an improved $τ$ vector isovector spectral function

After discussing difficulties in determining $α_s$ from tau decay due to the existence of Duality Violations and the associated asymptotic nature of the OPE, we describe a new determination based on an improved vector isovector spectral function, now based solely on experimental input, obtained by (i) combining ALEPH and OPAL results for $2π+4π$ and (ii) replacing $K^-K^0$ and higher-multiplicity exclusive-mode contributions, both previously estimated using Monte Carlo, with new experimental BaBar results for $K^-K^0$ and results implied by $e^+ e^-$ cross sections and CVC for the higher-multiplicity modes. We find $α_s(m_τ)=0.3077\pm 0.0075$, which corresponds to $α_s(m_Z)=0.1171\pm 0.0010$. Finally, we comment on some of the shortcomings in the criticism of our approach by Pich and Rodriguez-Sanchez.

hep-ph↗

arXiv2022

Theory review for hadronic corrections to $g-2$

We review Standard-Model evaluations of hadronic contributions to the muon anomalous magnetic moment $g-2$. Most space is devoted to the hadronic vacuum polarization contribution, in view of the discrepancy between the data-based dispersive evaluation and the lattice evaluation by the BMW collaboration.

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arXiv2022

The muon anomalous magnetic moment with staggered fermions: is the lattice spacing small enough?

We extend our previous work on the light-quark connected part, $a_μ^{\rm HVP,lqc}$, of the leading order hadronic-vacuum-polarization (HVP) contribution to the muon anomalous magnetic moment $a_μ$, using staggered fermions, in several directions. We have collected more statistics on ensembles with lattice spacings of $0.06$, $0.09$ and $0.12$ fm, and we added two new ensembles, both with lattice spacing $0.15$ fm, but with different volumes. The increased statistics allow us to reduce statistical errors on $a_μ^{\rm HVP,lqc}$ and related window quantities significantly. We also calculate the current-current correlator from which $a_μ^{\rm HVP,lqc}$ is obtained to next-to-next-to-leading order (NNLO) in staggered chiral perturbation theory, so that we can correct lattice values for $a_μ^{\rm HVP,lqc}$ to NNLO for finite-volume, pion-mass mistuning and taste-breaking effects. We discuss the applicability of NNLO chiral perturbation theory to $a_μ^{\rm HVP,lqc}$ and to the window quantities, emphasizing that it provides a systematic EFT approach to $a_μ^{\rm HVP,lqc}$, but not to short- or intermediate-distance window quantities. This makes it difficult to assess systematic errors on the standard intermediate-distance window quantity that is now widely considered in the literature. In view of this, we investigate a longer-distance window, for which EFT methods should be more reliable. Our most important conclusion is that, especially for staggered fermions, new high-statistics computations at lattice spacings smaller than $0.06$ fm are indispensable.

hep-lat↗

arXiv2022

Evaluation of the three-flavor quark-disconnected contribution to the muon anomalous magnetic moment from experimental data

We point out that the sum of the strange-quark-connected and full, three-flavor quark-disconnected contributions to the leading-order hadronic vacuum polarization contribution, $a_μ^{\mathrm{LO,HVP}}$, to the anomalous magnetic moment of the muon, is a physical observable, and provide a data-based determination of this quantity in the isospin limit. The result, $40.1(1.5)\times 10^{-10}$, or $38.7(2.0)\times 10^{-10}$, depending on which data compilation is used, serves as a target of comparison for lattice calculations of the same isospin-limit combination. Subtracting from this result the average of lattice determinations of the strange-quark-connected contribution, one obtains also an alternate determination of the isospin-limit three-flavor disconnected contribution to $a_μ^{\mathrm{LO,HVP}}$. The result of this determination, $-13.3(1.5)\times 10^{-10}$, or $-14.6(2.0)\times 10^{-10}$, depending on which data compilation is used, agrees well and is competitive with the most precise current lattice determination.

hep-ph↗

arXiv2022

Pion electric polarizabilities from lattice QCD

We report a first principle lattice calculation of the pion electric polarizability $α_π$ at the physical pion mass. First, we derive the master formula, which relates the pion polarizabilities with the position space hadronic Compton tensor, $\langle π| J_μ(x) J_ν(0) | π\rangle$. The finite volume error of the master formula is exponentially suppressed by the spatial extent of the lattice. Then, the hadronic tensor is calculated using domain wall fermions (DWF) directly at physical pion mass. The gauge ensembles are generated by the RBC-UKQCD collaborations.

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arXiv2021

On the use of the Operator Product Expansion in finite-energy sum rules for light-quark correlators

Tau-based finite-energy sum-rule (FESR) analyses often assume that scales $s_0\sim m_τ^2$ are large enough that (i) integrated duality violations (DVs) can be neglected, and (ii) contributions from non-perturbative OPE condensates of dimension $D$ scale as $(Λ_{\rm QCD}/m_τ)^D$, allowing the OPE series to be truncated at low dimension. The latter assumption is not necessarily valid since the OPE series is not convergent, while the former is open to question given experimental results for the electromagnetic, $I=1$ vector ($V$), $I=1$ axial vector ($A$) and $I=1$ $V+A$ current spectral functions, which show DV oscillations with amplitudes comparable in size to the corresponding $α_s$-dependent perturbative contributions at $s\sim2-3$ GeV$^2$. Here, we discuss recently introduced new tools for assessing the numerical relevance of omitted higher-$D$ OPE contributions. Applying these to the ``truncated OPE'' strategy used in Refs.[1,2] and earlier work by the same authors, we find that this strategy fails to yield reliable results for the strong coupling from hadronic $τ$ decays.

hep-ph↗

arXiv2021

Strong coupling at the $τ$-mass scale from an improved vector isovector spectral function

We perform a precise extraction of the QCD coupling at the $τ$-mass scale, $α_s(m_τ)$, from a new vector isovector spectral function which combines ALEPH and OPAL distributions for the dominant channels, $τ\toππ^0ν_τ$, $τ\to 3ππ^0ν_τ$ and $τ\to π3π^0ν_τ$, with estimates of sub-leading contributions obtained from electroproduction cross-sections using CVC, as well as BaBar results for $τ\to K^-K^0ν_τ$. The fully inclusive spectral function thus obtained is entirely based on experimental data, without Monte Carlo input. From this new data set, we obtain $α_s(m_τ)=0.3077\pm0.0075$, which corresponds to $α_s(m_Z)=0.1171\pm0.0010$. This analysis can be improved on the experimental side with new measurements of the dominant $ππ^0$, $π3π^0$, and $3ππ^0$ $τ$ decay modes.

hep-ph↗

arXiv2021

Dilaton chiral perturbation theory and applications

We review dilaton chiral perturbation theory (dChPT), the effective low-energy theory for the light sector of near-conformal, confining theories. dChPT provides a systematic expansion in both the fermion mass and the distance to the conformal window. It accounts for the pions and the light scalar, the approximate Nambu-Goldstone bosons for chiral and scale symmetry, respectively. A unique feature of dChPT is the existence of a large-mass regime in which the theory exhibits approximate hyperscaling, while the expansion nevertheless remains systematic. We discuss applications to lattice data, presenting successes as well as directions for future work.

hep-lat↗

arXiv2021

$S$ parameter from a prototype composite-Higgs model

We have calculated the low-energy constant $L_{10}$ in a prototype composite Higgs model with dynamical fermions in two different representations of the gauge group. The resulting contribution of the new strong sector to the $S$ parameter is consistent with current bounds on the vacuum misalignment parameter. We end with a brief discussion of future directions.

hep-lat↗

arXiv2021

The muon $g-2$ with four flavors of staggered quarks

We present updated results for the light-quark connected part of the leading hadronic contribution to the muon $g-2$ from configurations with 2+1+1 flavors of HISQ quarks using the time-momentum representation of the electromagnetic current correlator. We have added statistics on two ensembles as well as a fourth lattice spacing using configurations that have been generated by the MILC collaboration at the physical pion mass. Additionally we account for the leading finite-volume and taste-breaking effects using Staggered Chiral Perturbation Theory at NNLO.

hep-lat↗

arXiv2021

Low-energy constant $L_{10}$ in a two-representation lattice theory

We calculate the low-energy constant $L_{10}$ in a two-representation SU(4) lattice gauge theory that is close to a composite-Higgs model. From this we obtain the contribution of the new strong sector to the $S$ parameter. This leads to an upper bound on the vacuum misalignment parameter $ξ$ which is similar to current estimates of this bound. Our result agrees with large-$N_c$ scaling expectations, within large systematic uncertainties.

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arXiv2021

The strong coupling from an improved $τ$ vector isovector spectral function

We combine ALEPH and OPAL results for the spectral distributions measured in $τ\toπ^-π^0ν_τ$, $τ\to 2π^-π^+π^0ν_τ$ and $τ\toπ^-3π^0ν_τ$ decays with (i) recent BaBar results for the analogous $τ\to K^- K^0ν_τ$ distribution and (ii) estimates of the contributions from other hadronic $τ$-decay modes obtained using CVC and electroproduction data, to obtain a new and more precise non-strange, inclusive vector, isovector spectral function. The BaBar $K^- K^0$ and CVC/electroproduction results provide us with alternate, entirely data-based input for the contributions of all exclusive modes for which ALEPH and OPAL employed Monte-Carlo-based estimates. We use the resulting spectral function to determine $α_s(m_τ)$, the strong coupling at the $τ$ mass scale, employing finite energy sum rules. Using the fixed-order perturbation theory (FOPT) prescription, we find $α_s(m_τ)=0.3077\pm 0.0075$, which corresponds to the five-flavor result $α_s(M_Z)=0.1171\pm 0.0010$ at the $Z$ mass. While we also provide an estimate using contour-improved perturbation theory (CIPT), we point out that the FOPT prescription is to be preferred for comparison with other $α_s$ determinations employing the $\overline{\rm MS}$ scheme, especially given the inconsistency between CIPT and the standard operator product expansion recently pointed out in the literature. Additional experimental input on the dominant $2π$ and $4π$ modes would allow for further improvements to the current analysis.

hep-ph↗

arXiv2020

Explorations beyond dilaton chiral perturbation theory in the eight-flavor SU(3) gauge theory

We continue our study of spectroscopy data for the SU(3) gauge theory with eight fundamental fermions, motivated by the effective field theory framework of dilaton chiral perturbation theory (dChPT). At leading order dChPT predicts a constant mass anomalous dimension $γ_m$, consistent with the assumed proximity of an infrared fixed point. For the relatively large fermion masses simulated by the LatKMI collaboration, the influence of the infrared fixed point diminishes, and our fits suggest that $γ_m$ starts running. Since a complete higher-order analysis is not feasible with presently available data, we adopt a more phenomenological approach. We propose a partial extension to higher orders, which incorporates the running of $γ_m$ into the tree-level lagrangian. We find that this extension successfully describes the full fermion-mass range of the LatKMI data, including the pion taste splittings which arise from using staggered fermions in the lattice simulations. We also investigate a more general class of dilaton potentials proposed in the literature, using both the LSD and LatKMI data sets, concluding that these data favor the form predicted by dChPT.

hep-lat↗

arXiv2020

Application of dilaton chiral perturbation theory to $N_f=8$, ${\rm SU}(3)$ spectral data

We extend dilaton chiral perturbation theory (dChPT) to include the taste splittings in the Nambu--Goldstone sector observed in lattice simulations of near-conformal theories with staggered fermions. We then apply dChPT to a recent simulation by the LSD collaboration of the SU(3) gauge theory with 8 fermions in the fundamental representation, which is believed to exhibit near-conformal behavior in the infrared, and in which a light singlet scalar state, nearly degenerate with the pions, has been found. We find that the mesonic sector of this theory can be successfully described by dChPT, including, in particular, the mesonic taste splittings found in the simulation. We confirm that current simulations of this theory are in the "large-mass" regime.

hep-ph↗

arXiv2020

On the application of Effective Field Theory to finite-volume effects in $a_μ^{\rm HVP}$

One of the more important systematic effects affecting lattice computations of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon, $a_μ^{\rm HVP}$, is the distortion due to a finite spatial volume. In order to reach sub-percent precision, these effects need to be reliably estimated and corrected for, and one of the methods that has been employed for doing this is finite-volume chiral perturbation theory. In this paper, we argue that finite-volume corrections to $a_μ^{\rm HVP}$ can, in principle, be calculated at any given order in chiral perturbation theory. More precisely, once all low-energy constants needed to define the Effective Field Theory representation of $a_μ^{\rm HVP}$ in infinite volume are known to a given order, also the finite-volume corrections can be predicted to that order in the chiral expansion.

hep-lat↗

arXiv2020

Light quark vacuum polarization at the physical point and contribution to the muon $g-2$

We report on the computation of the connected light quark vacuum polarization with 2+1+1 flavors of HISQ fermions at the physical point and its contribution to the muon anomalous magnetic moment. Three ensembles, generated by the MILC collaboration, are used to take the continuum limit. The finite volume correction to this result is computed in the (Euclidean) time-momentum representation to NNLO in chiral perturbation theory. We find $a_μ^{ll}({\rm HVP})=(659\pm 20\pm 5\pm 5\pm 4)\times 10^{-10}$, where the errors are statistical and estimates of residual uncertainties from taking the continuum limit, scale setting, and truncation of chiral perturbation theory at NNLO. We compare our results with recent ones in the literature.

hep-lat↗

arXiv2019

Fits of $SU(3)$ $N_f=8$ data to dilaton-pion effective field theory

We report on fits of the $SU(3)$ $N_f=8$ LSD spectral data to chiral perturbation theory with a dilatonic meson. These fits confirm that current simulations are in the "large-mass" regime, with approximate hyperscaling as the leading mass dependence. We find that the leading-order effective field theory describes the data well. In particular, the effective field theory allows us to understand the staggered taste splitting, explaining the pattern observed in the LSD data, which looks different from QCD.

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