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

Stephan Narison

doi:10.1016/j.nuclphysa.2022.122393

Article Dans Une Revue Nuclear Physics A Année : 2022

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

(1)

Stephan Narison

Fonction : Auteur

Laboratoire Univers et Particules de Montpellier

Résumé

In 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

\sqrt{χ^{'} (0)} (Q^{2} = 2 {GeV}^{2}) = 24.3 (3.4)

MeV from low degree moments which imply

\int_{0}^{1} d x g_{1}^{P} (x) = 0.144 (5) [data : 0.145 (14)]

for the first moment of the polarized proton structure function (proton spin) and

G_{A}^{(0)} (10 {GeV}^{2}) \equiv Δ u + Δ d + Δ s = 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 light

η_{1}

[singlet gluon component of the

η^{'} (958)

] with

[M_{η_{1}}, f_{η_{1}}] = [825 (45), 905 (72)]

MeV which is important for understanding the

U {(1)}_{A}

anomaly; The two new medium gluonia with

M_{P_{1 a}} = 1338 (112)

MeV and

[M_{P_{1 b}} = 1462 (117)

MeV or their mean

[M_{P_{1}}, f_{P_{1}}] = [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:

M_{P_{1 a}^{'}} = 1508 (226)

MeV and

M_{P_{1 b}^{'}} = 1553 (139)

MeV with their mean:

[M_{P_{1}^{'}}, f_{P_{1}^{'}}] = [1541 (118), 205 (282)]

MeV which may be identified (up to some eventual mixings with

\bar{q} q

states) with the observed

η (1475, 1700)

states; The heavy gluonium with the mean mass:

[M_{P_{2}}, f_{P_{2}}] = [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) \to η_{1}; G_{1} (1.55) \to P_{1}; [σ^{'} (1.1), G^{'} (1.56)] \to P_{1 a, 1 b}^{'}; G_{2} (3) \to P_{2}

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.

Mots clés

QCD spectral sum rules Perturbative and non-perturbative QCD Exotic hadrons Masses and decay constants charge topological p spin hadron exotic mass quantum chromodynamics nonperturbative sum rule spectral form factor axial structure function gluon singlet current pseudoscalar slope GeV duality excited state 4/3 glueball lattice moment instanton spectral representation mixing anomaly chiral

Domaines

Physique des Hautes Energies - Phénoménologie [hep-ph] Physique Nucléaire Théorique [nucl-th]

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https://hal.science/hal-03554635

Soumis le : lundi 22 juillet 2024-11:03:35

Dernière modification le : lundi 22 juillet 2024-11:03:36

Dates et versions

hal-03554635 , version 1 (22-07-2024)

Licence

Paternité - Pas d'utilisation commerciale

Identifiants

HAL Id : hal-03554635 , version 1
DOI : 10.1016/j.nuclphysa.2022.122393
INSPIRE : 2021983
PII : S0375-9474(22)00013-6

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Stephan Narison. Slope of the topological charge, proton spin and the $0^{-+}$ pseudoscalar di-gluonia spectra. Nuclear Physics A, 2022, 1020, pp.122393. ⟨10.1016/j.nuclphysa.2022.122393⟩. ⟨hal-03554635⟩

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

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