Regular Article - Theoretical Physics
BHLS upgrade: spectra, muon HVP and the  system
LPNHE des Universités Paris VI et Paris VII, IN2P3/CNRS, 75252, Paris, France
2 Institut für Physik, Humboldt-Universität zu Berlin, Newtonstrasse 15, 12489, Berlin, Germany
3 Deutsches Elektronen-Synchrotron (DESY), Platanenallee 6, 15738, Zeuthen, Germany
Accepted: 7 February 2022
Published online: 28 February 2022
The generic hidden local symmetry (HLS) model has recently given rise to its variant, defined by introducing symmetry breaking mostly in the vector meson sector; the central mechanism is a modification of the covariant derivative at the root of the HLS approach. However, the description of the dipion spectra, especially the Belle one, is not fully satisfactory, whereas the simultaneous dealing with its annihilation sector () is optimum. We show that this issue is solved by means of an additional breaking term which also allows us to consistently include the mixing properties of the system within this extended () scope. This mechanism, an extension of the usual ’t Hooft determinant term, only affects the kinetic energy part of the Lagrangian. One thus obtains a fair account for the dipion spectra which complements the fair account of the annihilation channels already reached. The Belle dipion spectrum is found to provide evidence in favor of a violation of the conserved vector current (CVC) in the lepton decay; this evidence is enforced by imposing the conditions on axial current matrix elements. is found to recover the usual (completed) formulae for the  mixing parameters, and the global fits return mixing parameter values in agreement with expectations and better uncertainties. Updating the muon hadronic vacuum polarization (HVP), one also argues that the strong tension between the KLOE and BaBar pion form factors imposes to provide two solutions, namely and , in units of , rather than some combination of these. Taking into account common systematics, their differences from the experimental BNL-FNAL average value exhibit significance (KLOE) and (BaBar), with fit probabilities favoring the former.
© The Author(s) 2022
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3