Effective hadron dynamics: From meson masses to the proton spin puzzle

BHLS 2 upgrade: τ spectra, muon HVP and the [ π 0 , η , η ' ] system

The generic hidden local symmetry (HLS) model has recently given rise to its BHLS 2 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 τ dipion spectra, especially the Belle one, is not fully satisfactory, whereas the simultaneous dealing with its annihilation sector (e + e - → π + π - / π + π - π 0 / π 0 γ / η γ / K + K - / K L K S ) 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 [ π 0 , η , η ' ] system within this extended BHLS 2 ( EBHLS 2 ) scope. This mechanism, an extension of the usual 't Hooft determinant term, only affects the kinetic energy part of the BHLS 2 Lagrangian. One thus obtains a fair account for the τ 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 τ lepton decay; this evidence is enforced by imposing the conditions< 0 | J μ q | [ q ' q ' ¯ ] ( p ) > = i p μ f q δ q q ' , { [ q q ¯ ] , q = u , d , s } on EBHLS 2 axial current matrix elements. EBHLS 2 is found to recover the usual (completed) formulae for the [π 0 , η , η ' ] 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, namelya μ H V P - L O ( KLOE ) = 687.48 ± 2.93 anda μ H V P - L O ( BaBar ) = 692.53 ± 2.95 , in units of 10 - 10 , rather than some combination of these. Taking into account common systematics, their differences from the experimental BNL-FNAL average value exhibit significance > 5.4 σ (KLOE) and > 4.1 σ (BaBar), with fit probabilities favoring the former.

Chiral anomaly and strange-nonstrange mixing

As a first step, a simple and pedagogical recall of the η-η′ system is presented, in which the role of the axial anomaly, related to the heterochiral nature of the multiplet of (pseudo)scalar states, is underlined. As a consequence, η is close to the octet and η′ to the singlet configuration. On the contrary, for vector and tensor states, which belong to homochiral multiplets, no anomalous contribution to masses and mixing is present. Then, the isoscalar physical states are to a very good approximation nonstrange and strange, respectively. Finally, for pseudotensor states, which are part of an heterochiral multiplet (just as pseudoscalar ones), a sizable anomalous term is expected: η2(1645) roughly corresponds to the octet and η2(1870) to the singlet.

η and η' mixing from lattice QCD

We present a lattice QCD computation of η and η' masses and mixing angles, for the first time controlling continuum and quark mass extrapolations. The results for M(η) = 551(8)(stat) (6)(yst) MeV and M(η') = 1006(54)(stat)(38)(syst)(+61)(ex) MeV are in excellent agreement with experiment. Our data show that the mixing in the quark flavor basis can be described by a single mixing angle of Ø = 46(1)(stat)(3)(syst)° indicating that the η' is mainly a flavor singlet state.