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

• Published in: The journal of high energy physics 2022-08, Vol.2022 (8), p.220-76, Article 220
• Main Authors: Cè, Marco, Gérardin, Antoine, von Hippel, Georg, Meyer, Harvey B., Miura, Kohtaroh, Ottnad, Konstantin, Risch, Andreas, José, Teseo San, Wilhelm, Jonas, Wittig, Hartmut
• Format: Article
• Language: English
• Subjects: Classical and Quantum Gravitation; Continuity (mathematics); Couplings; Decomposition; Electromagnetic coupling; Elementary Particles; Fermions; Flavor (particle physics); Hadronic Spectroscopy; High energy physics; Physics; Physics and Astronomy; Pions; Quantum chromodynamics; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quarks; Rational functions; Regular Article - Theoretical Physics; Relativity Theory; Standard Model Parameters; String Theory; Structure and Interactions; Vector currents
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP08(2022)220

A bstract We compute the hadronic running of the electromagnetic and weak couplings in lattice QCD with N f = 2 + 1 flavors of 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 Π ¯ γγ and Π ¯ γZ for Euclidean squared momenta Q 2 ≤ 7 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 SU(3)-flavor-suppressed HVP function Π ¯ 08 that enters the running of sin 2 θ W . Our results for Π ¯ γγ , Π ¯ γZ and Π ¯ 08 are presented in terms of rational functions for continuous values of Q 2 below 7 GeV 2 . We observe a tension of up to 3 . 5 standard deviation between our lattice results for ∆ α had 5 (− Q 2 ) and estimates based on the R -ratio for space-like momenta in the range 3–7 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 ∆ α had 5 M Z 2 = 0 . 02773(15) and agrees with results based on the R -ratio within the quoted uncertainties.