η , η mixing angle and η (cid:2) gluonium content extraction from the KLOE R φ measurement (cid:4)

. In this report the extraction of the η , η (cid:2) mixing angle and of the η (cid:2) gluonium content from the R φ = Br ( φ (1020) → η (cid:2) γ ) /Br ( φ (1020) → ηγ ) is updated. The η (cid:2) gluonium content is estimated by ﬁtting R φ , together, with other decay branching ratios. The extracted parameters are: Z 2 G = 0 . 12 ± 0 . 04 and ϕ P = (40 . 4 ± 0 . 9) ◦ .


Introduction
The η -meson, being a pure SU (3) singlet, has been considered for years the meson within which a gluon condensate contribution can show up. In this paper we try to extract the gluon condensate and the η, η mixing angle in the constituent quark model using the approach from [1] and the wave function spatial overlapping parameters introduced by ref. [2]. In particular the same method of ref. [3] will be used but in addition the π 0 → γγ and η → γγ branching ratios are fitted according to the prescriptions from [4]. This method is chosen because it relates our measurement of Br(φ → η γ)/Br(φ → ηγ) [5] to the η gluonium content and the η, η mixing angle. The η and η mixing angle and the presence of a gluonium component in the η -meson have been mostly investigated in the past, but are still without a definitive conclusion [6]. Following the approach from [1,3] the η and η wave functions can be decomposed in three terms: the u, d quark wave function |qq = 1 √ 2 (|uū + |dd ), the strange component |ss and the |glue . The wave functions are written as follows: where ϕ P is the η, η mixing angle and Z 2 G = sin 2 φ G the gluon contribution. The ratio of the two branching ratios: R φ(1020) = Br(φ(1020) → η γ)/Br(φ(1020) → ηγ) is related to this decomposition by the formula In this formula p η and p η are the momenta of the η -and η-meson, respectively, m s /m = 2m s /(m u + m d ) is the constituent quark masses ratio, Z NS describes the spatial wave function overlapping between the qq component of the ω-meson and η-meson, and Z S the one between the ss component of the ηand φ(1020)-meson, φ V is the ω,

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The European Physical Journal A φ(1020) mixing angle. The parameters Z S , Z NS , φ V and m s /m are taken from [7] in which the Br(φ(1020) → η γ) and Br(φ(1020) → ηγ) are fitted together with other V → P γ decays (V indicates the vector mesons ρ, ω, φ(1020) and P the pseudoscalars π 0 , η, η ). As in the KLOE [8] paper [5] we fit the ratio R φ(1020) from the KLOE measurement together with the available data [9] on Γ (η → γγ)/Γ (π 0 → γγ), Γ (η → ργ)/Γ (ω → π 0 γ) and Γ (η → ωγ)/Γ (ω → π 0 γ). The dependence of these ratios on the mixing angle ϕ P and the gluonium content φ G is given by the following equations: Using the value of Z NS and Z S from [7], we obtain ϕ P = (39.7 ± 0.7) • and Z 2 G = sin 2 ϕ G = 0.14 ± 0.04, P (χ 2 ) = 49%. Imposing ϕ G = 0 the χ 2 probability of the fit decreases to 1%. The ratio of the Γ 's is obtained using the branching fractions of the decay and the total decay widths Γ ω , Γ π 0 from the PDG 2006 [9]. All the correlations amongst the measurements of the several branching ratios are taken into account. The correlations are due to the choice of normalising all decay widths to the Γ (ω → π 0 γ) and to the use of a constrained fit technique in the PDG 2006 in order to obtain more accurate estimates.
The parameter m s /m is determined mainly by K * + → K + γ while φ V is given by the V → π 0 γ transitions, giving negligible correlations to the ϕ P and Z 2 G parameters. On the other hand, the parameters Z S , Z NS are strongly correlated to the mixing angle parameter, ϕ P , in eq. (1). The constraint Γ (η → γγ)/Γ (π 0 → γγ) is, instead, independent of the parameters Z NS and Z S . In ref. [3] a similar procedure to the one of [7] was followed taking into account also the possibility of having a gluonium content. They find Z 2 G = 0.04 ± 0.09 that deviates of 1 σ from our result but with a larger error.
In [3] and [10] this difference was attributed to the use of overlapping parameters obtained by a fit which assumes no gluonium content. In order to check out this possibility, we have performed several tests on the fit procedure. We first performed a new fit using the overlapping parameter Z S and Z NS extracted by the fit in ref. [3], where the Table 1. Summary of the results obtained using new values for Z NS and ZS from [3].
gluonium content was left free, together with all the other parameters: Z NS = 0.86 ± 0.03, Z S = 0.79 ± 0.05, φ V = (3.2 ± 0.1) • , ms m = 1.24 ± 0.07. We obtained a result in perfect agreement with our previous determination: the errors remain unchanged while the central values move to ϕ P = 40.1, Z 2 G = 0.12. The value of the fit has been also repeated for different values of Z NS and Z S in the range 0.5-1.3, and the resulting Z 2 G varied between 0.07 and 0.18, showing small sensitivity to the used parameters Z NS and Z S that cannot cause the different result obtained by ref. [3]. Excluding the P → γγ constraint from the fit we obtain ϕ P = (40.4 ± 0.9) • and Z 2 G = 0.12 ± 0.05, showing that this constraint improves the sensitivity for the gluonium content. All results are summarized in table 1.
A global fit to all the V → P γ ratios of the branching fractions is in progress. This will allow the overlapping parameters to be left free as in the approach of ref. [3], that is quite different than ours in both fit procedure and input values.