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Article Dans Une Revue Journal of High Energy Physics Année : 2022

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

Marco Cè
  • Fonction : Auteur
Georg von Hippel
  • Fonction : Auteur
Harvey B. Meyer
  • Fonction : Auteur
Kohtaroh Miura
  • Fonction : Auteur
Konstantin Ottnad
  • Fonction : Auteur
Andreas Risch
  • Fonction : Auteur
Teseo San José
  • Fonction : Auteur
Jonas Wilhelm
  • Fonction : Auteur
Hartmut Wittig
  • Fonction : Auteur

Résumé

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 $\bar{\Pi}^{\gamma\gamma}$ and $\bar{\Pi}^{\gamma Z}$ 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 $\bar{\Pi}^{08}$ that enters the running of $\sin^2\theta_{\mathrm{W}}$. Our results for $\bar{\Pi}^{\gamma\gamma}$, $\bar{\Pi}^{\gamma Z}$ and $\bar{\Pi}^{08}$ 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 $\Delta\alpha^{(5)}_{\mathrm{had}}(-Q^2)$ 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 $\Delta\alpha^{(5)}_{\mathrm{had}}(M_Z^2)=0.027\,73(15)$ and agrees with results based on the $R$-ratio within the quoted uncertainties.
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Dates et versions

hal-03625829 , version 1 (12-09-2023)

Identifiants

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Marco Cè, Antoine Gérardin, Georg von Hippel, Harvey B. Meyer, Kohtaroh Miura, et al.. The hadronic running of the electromagnetic coupling and the electroweak mixing angle from lattice QCD. Journal of High Energy Physics, 2022, 2022 (08), pp.220. ⟨10.1007/JHEP08(2022)220⟩. ⟨hal-03625829⟩
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