[Paper Review] Lattice calculation of the short and intermediate time-distance hadronic vacuum polarization contributions to the muon magnetic moment using twisted-mass fermions

C. Alexandrou, Simone Bacchio+15 more|arXiv (Cornell University)|Jun 30, 2022

Particle physics theoretical and experimental studies19 citations

TL;DR

This lattice QCD study computes the short- and intermediate-distance hadronic vacuum polarization (HVP) contributions to the muon anomalous magnetic moment using twisted-mass fermions on physical-point ensembles with Nf = 2+1+1 dynamical quarks. The ETMC collaboration finds aSDμ = 69.27(34)×10⁻¹⁰ and aWμ = 236.3(1.3)×10⁻¹⁰, showing tension with dispersive e⁺e⁻ data in the intermediate window, suggesting possible discrepancies in hadronic cross-section data below 2 GeV.

ABSTRACT

We present a lattice determination of the leading-order hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment, $a_μ^{ m HVP}$, in the so-called short and intermediate time-distance windows, $a_μ^{ m SD}$ and $a_μ^{ m W}$, defined by the RBC/UKQCD Collaboration [1]. We employ gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with $N_f = 2 + 1 + 1$ flavors of Wilson-clover twisted-mass quarks with masses of all the dynamical quark flavors tuned close to their physical values. The simulations are carried out at three values of the lattice spacing equal to $\simeq 0.057, 0.068$ and $0.080$ fm with spatial lattice sizes up to $L \simeq 7.6$~fm. For the short distance window we obtain $a_μ^{ m SD}({ m ETMC}) = 69.27\,(34) \cdot 10^{-10}$, which is consistent with the recent dispersive value of $a_μ^{ m SD}(e^+ e^-) = 68.4\,(5) \cdot 10^{-10}$ [2]. In the case of the intermediate window we get the value $a_μ^{ m W}({ m ETMC}) = 236.3\,(1.3) \cdot 10^{-10}$, which is consistent with the result $a_μ^{ m W}({ m BMW}) = 236.7\,(1.4) \cdot 10^{-10}$ [3] by the BMW collaboration as well as with the recent determination by the CLS/Mainz group of $a_μ^{ m W}({ m CLS}) = 237.30\,(1.46) \cdot 10^{-10}$ [4]. However, it is larger than the dispersive result of $a_μ^{ m W}(e^+ e^-) = 229.4\,(1.4) \cdot 10^{-10}$ [2] by approximately $3.6$ standard deviations. The tension increases to approximately $4.5$ standard deviations if we average our ETMC result with those by BMW and CLS/Mainz. Our accurate lattice results in the short and intermediate windows point to a possible deviation of the $e^+ e^-$ cross section data with respect to Standard Model predictions in the low and intermediate energy regions, but not in the high energy region.

Motivation & Objective

• To compute the short- and intermediate-distance hadronic vacuum polarization (HVP) contributions to the muon anomalous magnetic moment using lattice QCD with physical-point ensembles.
• To test the consistency of lattice QCD results with dispersive determinations based on e⁺e⁻ annihilation data.
• To assess potential deviations in the e⁺e⁻ cross-section data from Standard Model predictions in low- and intermediate-energy regions.
• To reduce systematic uncertainties by using Nf = 2+1+1 twisted-mass fermions with quark masses tuned near physical values.
• To enable cross-validation between lattice QCD and dispersive approaches by isolating short- and intermediate-distance contributions.

Proposed method

• Utilizes gauge ensembles from the Extended Twisted Mass Collaboration (ETMC) with Nf = 2+1+1 Wilson-clover twisted-mass fermions at three lattice spacings (a ≈ 0.057, 0.068, 0.080 fm) and spatial sizes up to L ≈ 7.6 fm.
• Applies the Euclidean time-momentum representation to extract aHVPμ from the zero-momentum correlation function of electromagnetic currents.
• Employs smooth step-functions to decompose the full HVP into short (aSDμ), intermediate (aWμ), and long-distance (aLDμ) components.
• Performs continuum and infinite-volume extrapolations using physical-point ensembles to minimize chiral extrapolation errors.
• Uses Bayesian model averaging and information criteria to optimize fit functions for the correlator and extract uncertainties.
• Applies finite-size effect corrections and controls discretization errors via multiple lattice spacings and improved fermion actions.

Experimental results

Research questions

• RQ1 How do lattice QCD results for the short- and intermediate-distance HVP contributions compare with dispersive determinations based on e⁺e⁻ data?
• RQ2 Is there a discrepancy between lattice QCD results and dispersive e⁺e⁻ data in the intermediate energy region (1–2 GeV)?
• RQ3 What is the level of consistency between independent lattice calculations (ETMC, BMW, CLS/Mainz) in the intermediate window?
• RQ4 Can the observed tension in the intermediate window be attributed to systematic errors or potential deviations in e⁺e⁻ cross-section data?
• RQ5 To what extent do lattice results support the hypothesis that the e⁺e⁻ cross-section data may underestimate hadronic contributions in the low- and intermediate-energy regions?

Key findings

• The ETMC result for the short-distance contribution is aSDμ(ETMC) = 69.27(34)×10⁻¹⁰, consistent with the dispersive value of 68.4(5)×10⁻¹⁰.
• The intermediate-window result is aWμ(ETMC) = 236.3(1.3)×10⁻¹⁰, which is consistent with the BMW collaboration’s result of 236.7(1.4)×10⁻¹⁰ and the CLS/Mainz result of 237.30(1.46)×10⁻¹⁰.
• However, the ETMC result exceeds the dispersive e⁺e⁻ determination of aWμ(e⁺e⁻) = 229.4(1.4)×10⁻¹⁰ by approximately 3.6 standard deviations.
• When averaged with BMW and CLS/Mainz results, the tension increases to about 4.5 standard deviations.
• The observed discrepancy suggests a possible deviation of e⁺e⁻ cross-section data from Standard Model predictions in the low- and intermediate-energy regions.
• The results indicate that the tension is not due to lattice artifacts in the short- and intermediate-distance regions, but may instead stem from the e⁺e⁻ data itself in the 1–2 GeV range.