Nucleon axial structure from lattice QCD
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Springer
Received: January Revised: March Accepted: April Published: May
10, 13, 24, 26,
2020 2020 2020 2020
Nucleon axial structure from lattice QCD
Gunnar S. Bali,a,b Lorenzo Barca,a Sara Collins,a Michael Gruber,a Marius L¨ offler,a a a a a Andreas Sch¨ afer, Wolfgang S¨ oldner, Philipp Wein, Simon Weish¨ aupl and a Thomas Wurm a
Institut f¨ ur Theoretische Physik, Universit¨ at Regensburg, Universit¨ atsstraße 31, D-93040 Regensburg, Germany b Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: We present a new analysis method that allows one to understand and model excited state contributions in observables that are dominated by a pion pole. We apply this method to extract axial and (induced) pseudoscalar nucleon isovector form factors, which satisfy the constraints due to the partial conservation of the axial current up to expected discretization effects. Effective field theory predicts that the leading contribution to the (induced) pseudoscalar form factor originates from an exchange of a virtual pion, and thus exhibits pion pole dominance. Using our new method, we can recover this behavior directly from lattice data. The numerical analysis is based on a large set of ensembles generated by the CLS effort, including physical pion masses, large volumes (with up to 96 3 × 192 sites and Lmπ = 6.4), and lattice spacings down to 0.039 fm, which allows us to take all the relevant limits. We find that some observables are much more sensitive to the choice of parametrization of the form factors than others. On the one hand, the z-expansion leads to significantly smaller values for the axial dipole mass than the dipole ansatz (MAz-exp = 1.02(10) GeV versus MAdipole = 1.31(8) GeV). On the other hand, we find that the result for the induced pseudoscalar coupling at the muon capture point is almost independent of the choice of parametrization (gP? z-exp = 8.68(45) and gP? dipole = 8.30(24)), and is in good agreement with both, chiral perturbation theory predictions and experimental measurement via ordinary muon capture. We also determine the axial coupling constant gA . Keywords: Lattice QCD, Neutrino Physics, Nonperturbative Effects ArXiv ePrint: 1911.13150
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2020)126
JHEP05(2020)126
The RQCD collaboration
Contents 1 Introduction
1 3 3 5 12
3 Data analysis 3.1 Lattice setup 3.2 Fits to the correlation functions 3.3 Excited state energies
14 14 19 26
4 Form factors 4.1 Approximate restoration of PCAC and PPD 4.2 Parametrization and extrapolation 4.2.1 Dipole ansatz 4.2.2 z-expansion 4.2.3 Consistency with PCAC in the continuum 4.2.4 Continuum, quark mass, and volume extrapolation 4.3 Results 4.4 Discussion
27 27 28 28 29 30 32 3
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