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

Article · Constantia Alexandrou, Simone Bacchio, P. Dimopoulos, Jacob Finkenrath, R. Frezzotti, G. Gagliardi, Marco Garofalo, Kyriakos Hadjiyiannakou, Bartosz Kostrzewa, Karl Jansen, Vittorio Lubicz B, Marcus Petschlies, Francesco Sanfilippo, Silvano Simula, Carsten Urbach, Urs Wenger

- Archive id: doi:10.1103/physrevd.107.074506
- Published: 2023-04-19
- Venue: Physical review. D/Physical review. D.
- DOI: https://doi.org/10.1103/physrevd.107.074506
- Citations: 179
- Source URL: https://doi.org/10.1103/physrevd.107.074506
- PDF: http://link.aps.org/pdf/10.1103/PhysRevD.107.074506
- Provenance: openalex

## Abstract

We present a lattice determination of the leading-order hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment, ${a}\_{\\ensuremath{\\mu}}^{\\mathrm{HVP}}$, in the so-called short and intermediate time-distance windows, ${a}\_{\\ensuremath{\\mu}}^{\\mathrm{SD}}$ and ${a}\_{\\ensuremath{\\mu}}^{\\mathrm{W}}$, defined by the RBC/UKQCD Collaboration \[Phys. Rev. Lett. 121, 022003 (2018)\]. 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 $\\ensuremath{\\simeq}0.057$, 0.068 and 0.080 fm with spatial lattice sizes up to $L\\ensuremath{\\simeq}7.6\\text{ }\\text{ }\\mathrm{fm}$. For the short-distance window we obtain ${a}\_{\\ensuremath{\\mu}}^{\\mathrm{SD}}(\\mathrm{ETMC})=69.27(34)\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{\\ensuremath{-}10}$, which is consistent with the recent dispersive value of ${a}\_{\\ensuremath{\\mu}}^{\\mathrm{SD}}({e}^{+}{e}^{\\ensuremath{-}})=68.4(5)\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{\\ensuremath{-}10}$ \[, Phys. Lett. B 833, 137313 (2022)\]. In the case of the intermediate window we get the value ${a}\_{\\ensuremath{\\mu}}^{\\mathrm{W}}(\\mathrm{ETMC})=236.3(1.3)\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{\\ensuremath{-}10}$, which is consistent with the result ${a}\_{\\ensuremath{\\mu}}^{\\mathrm{W}}(\\mathrm{BMW})=236.7(1.4)\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{\\ensuremath{-}10}$ \[, Nature (London) 593, 51 (2021)\] by the BMW Collaboration as well as with the recent determination by the CLS/Mainz group of ${a}\_{\\ensuremath{\\mu}}^{\\mathrm{W}}(\\mathrm{CLS})=237.30(1.46)\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{\\ensuremath{-}10}$ \[, Phys. Rev. D 106, 114502 (2022)\]. However, it is larger than the dispersive result of ${a}\_{\\ensuremath{\\mu}}^{\\mathrm{W}}({e}^{+}{e}^{\\ensuremath{-}})=229.4(1.4)\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{\\ensuremath{-}10}$ 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 ${e}^{+}{e}^{\\ensuremath{-}}$ cross section data with respect to Standard Model predictions in the low- and intermediate-energy regions but not in the high-energy region.

_Abstract reproduced under CC-BY (publisher license, via OpenAlex)._

Topics: [Particle Physics & Beyond the Standard Model](https://space-kitty.com/topics/particle-physics-bsm)

Cited in dossiers:
- [Particle Physics & Beyond the Standard Model: State of the Field (October 2026)](https://space-kitty.com/dossiers/particle-physics-bsm)

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