The muon anomalous magnetic moment a μ and the hadronic vacuum polarization are examined using data analyzed within the framework of a suitably broken HLS model. The analysis relies on all available scan data samples and leaves provisionally aside the existing ISR data. Our HLS model based global fit approach allows for a better check of consistency between data sets and we investigate how results depend on different strategies which may be followed. Relying on global fit qualities, we find several acceptable solutions leading to ambiguities in the reconstructed value for (a μ ) th . Among these, the most conservative solution is a had,LO μ [HLS improved] = 687.72(4.63) × 10 −10 and (a μ ) th = 11 659 175.37(5.31) × 10 −10 corresponding to a 4.1σ significance for the difference a μ = (a μ ) exp − (a μ ) th . It is also shown that the various contributions accessible through the model yield uniformly a factor 2 improvement of their uncertainty. The breaking procedure implemented in the HLS model is an extension of the former procedure based on a mechanism defined by Bando, Kugo and Yamawaki (BKY). This yields a quite satisfactory simultaneous description of most e + e − annihilation channels up to and including the φ meson (and of a set of 10 (mostly radiative) decay widths of light mesons. It also allows to achieve the proof of consistency between the e + e − → π + π − annihilation and the τ ± → π ± π 0 ν decay and gives a solution to the reported problem concerning the measured partial width ratio Γ (φ → K + K − )/Γ (φ → K 0 K 0 ). Prospects for improving the VMD based estimates of a μ are emphasized. a

A global fit of parameters allows us to pin down the Hidden Local Symmetry (HLS) effective Lagrangian, which we apply for the prediction of the leading hadronic vacuum polarization contribution to the muon g − 2. The latter is dominated by the annihilation channel e + e − → π + π − , for which data are available by scan (CMD-2 & SND) and ISR (KLOE-2008, KLOE-2010 experiments. It is well known that the different data sets are not in satisfactory agreement. In fact it is possible to fix the model parameters without using the π + π − data, by using instead the dipion spectra measured in the τ -decays together with experimental spectra for the π 0 γ , ηγ , π + π − π 0 , K + K − , K 0 K 0 final states, supplemented by specific meson decay properties. Among these, the accepted decay width for ρ 0 → e + e − and the partial widths and phase information for the ω/φ → π + π − transitions, are considered. It is then shown that, relying on this global data set, the HLS model, appropriately broken, allows to predict accurately the pion form factor below 1.05 GeV. It is shown that the data samples provided by CMD-2, SND and KLOE-2010 behave consistently with each other and with the other considered data. Consistency problems with the KLOE-2008 and BaBar data samples are substantiated. "All data" global fits are investigated by applying reweighting the conflicting data sets. Constraining to our best fit, the broken HLS model yields a th μ = (11 659 169.55 + +1.26 −0.59 φ + +0.00 −2.00 τ ± 5.21 th ) 10 −10 associated with a very good global fit probability. Correspondingly, we find that a μ = a exp μ − a th μ exhibits a significance ranging between 4.7 and 4.9σ .

We reexamine the problem of simultaneously describing in a consistent way all radiative and leptonic decays of light mesons (V→ P␥, P→V␥, P→␥␥, V→e ϩ e Ϫ ). For this purpose, we rely on the hidden local symmetry model in both its anomalous and non-anomalous sectors. We show that the SU͑3͒ symmetry breaking scheme proposed by Bando, Kugo and Yamawaki, supplemented with nonet symmetry breaking in the pseudoscalar sector, allows one to reach a nice agreement with all data, except for the K* Ϯ radiative decay. An extension of this breaking pattern allows one to account for this particular decay mode too. Considered together, the whole set of radiative decays provides a pseudoscalar mixing angle P ӍϪ11°and a value for V which is Ӎ3°from that of ideal mixing. We also show that it is impossible, in a practical sense, to disentangle the effects of nonet symmetry breaking and those of glue inside the Ј, using only light meson decays.

We show that the Hidden Local Symmetry Model, supplemented with well-known procedures for breaking flavor SU(3) and nonet symmetry, provides all the information contained in the standard Chiral Perturbation Theory (ChPT) Lagrangian L (0) + L (1) . This allows to rely on radiative decays of light mesons (V P γ and P γγ) in order to extract some numerical information of relevance to ChPT: a value for Λ 1 = 0.20 ± 0.04, a quark mass ratio of ≃ 21.2 ± 2.4, and a negligible departure from the Gell-Mann-Okubo mass formula. The mixing angles are θ 8 = −20.40 • ± 0.96 • and θ 0 = −0.05 • ± 0.99 • . We also give the values of all decay constants. It is shown that the common mixing pattern with one mixing angle θ P is actually quite appropriate and algebraically related to the η/η ′ mixing pattern presently preferred by the ChPT community. For instance the traditional θ P is functionally related to the ChPT θ 8 and fulfills θ P ≃ θ 8 /2. The vanishing of θ 0 , supported by all data on radiative decays, gives a novel relation between mixing angles and the violation of nonet symmetry in the pseudoscalar sector. Finally, it is shown that the interplay of nonet symmetry breaking through U(3) → SU(3)× U(1) satisfies all requirements of the physics of radiative decays without any need for additional glueballs.

No abstract

We readdress the problem of finding a simultaneous description of the pion form factor data in e + e − annihilations and in τ decays. For this purpose, we work in the framework of the Hidden Local Symmetry (HLS) Lagrangian and modify the vector meson mass term by including the pion and kaon loop contributions. This leads us to define the physical ρ, ω and φ fields as linear combinations of their ideal partners, with coefficients being meromorphic functions of s, the square of the 4-momentum flowing into the vector meson lines. This allows us to define a dynamical, i.e. s-dependent, vector meson mixing scheme. The model is overconstrained by extending the framework in order to include the description of all meson radiative (V P γ and P γγ couplings) and leptonic (V e + e − couplings) decays and also the isospin breaking (ω/φ → π + π − ) decay modes. The model provides a simultaneous, consistent and good description of the e + e − and τ dipion spectra. The expression for pion form factor in the latter case is derived from those in the former case by switching off the isospin breaking effects specific to e + e − and switching on those for τ decays. Besides, the model also provides a good account of all decay modes of the form V P γ, P γγ as well as the isospin breaking decay modes. It leads us to propose new reference values for the ρ 0 → e + e − and ω → π + π − partial widths which are part of our description of the pion form factor. Other topics (φ → KK, the ρ meson mass and width parameters) are briefly discussed. As the e + e − data are found perfectly consistent with τ data up to identified isospin breaking effects, one finds no reason to cast any doubt on them and, therefore, on the theoretical estimate of the muon anomalous moment a µ derived from them. Therefore, our work turns out to confirm the relevance of the reported 3.3 σ discrepancy between this theoretical estimate of a µ and its direct BNL measurement. 1 1 Of course, in the SU(2) symmetry limit, we have ǫ = 0 and q π = Q π . 7

We examine the mechanisms producing departures from ideal mixing for vector mesons within the context of the Hidden Local Symmetry (HLS) model. We show that kaon loop transitions between the ideal combinations of the ω and φ mesons necessitate a field transformation in order to get the mass eigenstates. It is shown that this transformation is close to a rotation for processes involving, like meson decays, on-shell ω and φ mesons. The HLS model predicts a momentum dependent, slowly varying mixing angle between the ideal states. We examine numerically the consequences of this for radiative and leptonic decays of light mesons. The mean ω − φ mixing angle is found smaller than its ideal value; this is exhibited separately in radiative and in leptonic decays. Effects of nonet symmetry breaking in the vector sector are compared to those produced by the field rotation implied by the HLS model. * Supported by the US Department of Energy under contract DE-AC03-76SF00515The Hidden Local Symmetry (HLS) Model in both its non-anomalous [2] and anomalous (FKTUY) sectors [3] is a powerful tool for analyzing experimental data, by providing a clear framework with the fewest possible number of free parameters. For instance, it allows a 3-parameter description of the I = 1 pion form factor; this gives a statistically optimal description in an energy interval running from threshold to the φ mass. This has been shown by Ref. [4] in analyzing the world data set for e + e − → π + π − annihilation collected in Ref. [5]. The exercise has been repeated as successfully with the data set recently collected by the CMD-2 Collaboration on the VEPP-2M collider at Novosibirsk [6].However, in order to go beyond while staying within the framework defined by the HLS model and its anomalous sector, one needs to define a consistent scheme of symmetry breakings. Without SU(3) breaking, the HLS model cannot successfully describe the kaon form factors; without nonet symmetry breaking in the pseudoscalar (PS) sector, it cannot be used reliably to describe radiative decays of light mesons. The BKY mechanism [7,8] is a consistent way to introduce SU(3) breaking in both the vector (V) and PS sectors. It has been shown recently [9] that the BKY SU(3) breaking in the PS sector is in perfect agreement with all accessible predictions of Chiral Perturbation Theory [10-12] at first order in the breaking parameters. In order to reach this conclusion, the needed ingredients were only the BKY breaking in the PS sector (referred to hereafter as X A breaking), the kinetic energy term of the non-anomalous HLS Lagrangian and the P γγ Lagrangian of Wess, Zumino and Witten [13]. Thus, this part is on secure grounds.When dealing with PS mesons, the question of nonet symmetry breaking (NSB) cannot be avoided, as clear from Refs. [14,15] for instance. It was already introduced in the physics of single photon radiative decays (12 modes) by O'Donnell long ago [16], relying basically only on group theoretical considerations, but outside the context of effective Lagrangians. Th...

Previous studies have shown that the Hidden Local Symmetry (HLS) model, supplied with appropriate symmetry breaking mechanisms, provides an effective Lagrangian (Broken Hidden Local Symmetry, BHLS) which encompasses a large number of processes within a unified framework. Based on it, a global fit procedure allows for a simultaneous description of the e + e − annihilation into six final states-and includes the dipion spectrum in the τ decay and some more light meson decay partial widths. The contribution to the muon anomalous magnetic moment a th μ of these annihilation channels over the range of validity of the HLS model (up to 1.05 GeV) is found much improved in comparison to the standard approach of integrating the measured spectra directly. However, because most spectra for the annihilation process e + e − → π + π − undergo overall scale uncertainties which dominate the other sources, one may suspect some bias in the dipion contribution to a th μ , which could question the reliability of the global fit method. However, an iterated global fit algorithm, shown to lead to unbiased results by a Monte Carlo study, is defined and applied successfully to the e + e − → π + π − data samples from CMD2, SND, KLOE, BaBar, and BESSIII. The iterated fit solution is shown to further improve the prediction for a μ , which we find to deviate from its experimental value above the 4σ level. The contribution to a μ of the π + π − intermediate state up to 1.05 GeV has an uncertainty about 3 times smaller than the corresponding usual estimate. Therefore, global fit techniques are shown to work and lead to improved unbiased results.a