Slope of the topological charge, proton spin and the $0^{-+}$ pseudoscalar di-gluonia spectra

International audienceIn this paper, we attempt to discuss the topics mentioned in the title by scrutinizing and improving the 0−+ pseudoscalar di-gluonia/glueballs sum rules within the standard SVZ-expansion at N2LO without instantons. First, we reconsider the estimate of the slope of the topological charge χ′(0)(Q2=2GeV2)=24.3(3.4) MeV from low degree moments which imply ∫01dxg1P(x)=0.144(5)[data:0.145(14)] for the first moment of the polarized proton structure function (proton spin) and GA(0)(10GeV2)≡Δu+Δd+Δs=0.340(50)[data=0.330(39)] for the singlet form factor of the axial current. Second, we work with high degree moments and parametrize the spectral function beyond the minimal duality ansatz: “One resonance ⊕ QCD continuum” to get the 0−+ pseudoscalar di-gluonia spectra. Then, we obtain three groups of gluonia: The familiar lightη1 [singlet gluon component of the η′(958)] with [Mη1,fη1]=[825(45),905(72)] MeV which is important for understanding the U(1)A anomaly; The two new medium gluonia with MP1a=1338(112) MeV and [MP1b=1462(117) MeV or their mean [MP1,fP1]=[1397(81),594(144)] MeV which support the gluonium nature of the excellent experimental candidate η(1405) and may bring a small gluon piece to the η(1295); their corresponding 1st radial excitations: MP1a′=1508(226) MeV and MP1b′=1553(139) MeV with their mean: [MP1′,fP1′]=[1541(118),205(282)] MeV which may be identified (up to some eventual mixings with q¯q states) with the observed η(1475,1700) states; The heavy gluonium with the mean mass: [MP2,fP2]=[2751(140),500(43)] MeV which can be compared with the lattice results. One can remark the (natural) one to one correspondence between the pseudoscalar gluonia and their chiral scalar analogue from Ref. [1]: σ(1)→η1;G1(1.55)→P1;[σ′(1.1),G′(1.56)]→P1a,1b′;G2(3)→P2 which is mainly due to the importance of the QCD PT contributions in the sum rule analysis that are almost equal in these two channels