New results in $\rho^0$ meson physics

Abstract

We compare the predictions of a range of existing models based on the Vector Meson Dominance hypothesis with data on e + e − → π + π − and e + e − → µ + µ − 1 Permanent address. 2 Present address.cross-sections and the phase and near-threshold behavior of the timelike pion form factor, with the aim of determining which (if any) of these models is capable of providing an accurate representation of the full range of experimental data. We find that, of the models considered, only that proposed by Bando et al. is able to consistently account for all information, provided one allows its parameter a to vary from the usual value of 2 to 2.4. Our fit with this model gives a point-like coupling γπ + π − of magnitude −e/6, while the common formulation of VMD excludes such a term. The resulting values for the ρ mass and π + π − and e + e − partial widths as well as the branching ratio for the decay ω → π + π − obtained within the context of this model are consistent with previous results.

An update of the HLS estimate of the muon g−2

“…Using NSK data or any of both KLOE samples, instead of the PDG information, does not lead to predicted curves substantially different from their analogue already shown and commented upon in the previous subsection. Interesting parameter values have been extracted from global fits using only the (0.75-0.82) GeV region from the NSK and KLOE spectra for e + e − → π + π − and are reported in Table 1; they are in reasonable agreement with the reported branching ratio product F ω [29] and the Orsay phase [70,71] as well. Indeed, taking the RPP F ω value as reference, our estimates using the 70 MeV in- terval surrounding the interference region are at 0.1σ , 1.8σ and 3.0σ for respectively the NSK [27,29], KLOE08 [31] and KLOE10 [32] data samples.…”

“…The probabilities are those of the global fit; the last data column shows the contribution of each π + π − data set to the total χ 2 Using the RPP recommended value for Br(ω → π + π − ) and the Orsay phase information from [70] yields a value for F ω in good correspondence with expectations, as clear from the entry τ + PDG in Table 1. Using NSK data or any of both KLOE samples, instead of the PDG information, does not lead to predicted curves substantially different from their analogue already shown and commented upon in the previous subsection.…”

“…For the missing phase information we adopt the result from the fit [70] for the Orsay phase of the ω → π + π − amplitude and the result from SND [72] for the phase of the φ → π + π − amplitude. 25 Following the discussion in the preceding sub- 24 By abusively, we mean, first that the "Orsay" phases for both the ω and φ mesons have no entry in the RPP and, second, that the benchmark represented by the processes listed in Sect.…”

“…(1.53 ± 0.13) % [24] and the Orsay phase from [70] as input values for the "τ + PDG" fit. The probabilities are those of the global fit; the last data column shows the contribution of each π + π − data set to the total χ 2 Using the RPP recommended value for Br(ω → π + π − ) and the Orsay phase information from [70] yields a value for F ω in good correspondence with expectations, as clear from the entry τ + PDG in Table 1.…”

The pion form factor within the hidden local symmetry model

“…Recently, it has been remarked [16] that the Hidden Local Symmetry (HLS) Model [17] provides another consistent framework for data analysis and a new expression for F π (s) at low energies. Indeed, besides the usual vector meson exchanges, this model predicts that some departure from standard VMD could show up as a residual direct coupling γπ + π − .…”