Vacuum polarization contribution to muon 
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 as an inverse problem

Li, Hsiang-nan; Umeeda, Hiroyuki

doi:10.1103/physrevd.102.094003

Cited by 11 publications

(8 citation statements)

References 36 publications

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“…Distinct from the scalar and pseudoscalar glueball cases, only a single dimension-eight condensate is available for the OPE input. It has been verified [2] that at least two condensates of different dimensions are necessary for establishing the ρ meson state. We thus speculate that the absence of a resonance solution for the tensor glueball may be due to the insufficient nonperturbative input in the present setup.…”

Section: Introductionmentioning

confidence: 92%

“…After exploring the aspects of our approach, we apply it to the determination of the ρ meson mass from the corresponding dispersion relation. We first recapture and expand the idea of handling QCD sum rules as an inverse problem [2], starting with the two-point correlator…”

Section: B ρ Meson Massmentioning

confidence: 99%

“…The long-existing concern on the rigorousness and predictive power of QCD sum rules [5,6] is then resolved. As an example, we demonstrated how to extract the masses and decay constants of the series of ρ resonances from the dispersion relation obeyed by a two-current correlator [2]. This new viewpoint, based only on the analyticity of physical observables, has been extended to the explanation of the D meson mixing parameters [7] and to the constraint on the hadronic vacuum polarization contribution to the muon anomalous magnetic moment [8].…”

Section: Introductionmentioning

confidence: 98%

“…We proposed to handle QCD sum rules [1] for nonpertrbative observables, like the ρ meson mass, as an inverse problem recently [2]. The spectral density on the hadron side of a dispersion relation, including both resonance and continuum contributions, is regarded as an unknown.…”

Section: Introductionmentioning

confidence: 99%

“…The spectral density was parametrized as a sum of a pole contribution, which depends on the ρ meson mass and decay constant, and an arbitrary continuum contribution in [2]. The latter was expanded in terms of a set of orthogonal polynomials with unknown coefficients, which, together with the mass and decay constant, were deduced from the best fit of the hadron side to the OPE on the quark side.…”

Section: Introductionmentioning

confidence: 99%

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Dispersive analysis of glueball masses

2021

Preprint

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We develop an inverse matrix method to solve for resonance masses from a dispersion relation obeyed by a correlation function. Given the operator product expansion (OPE) of a correlation function in the deep Euclidean region, we obtain the nonperturbative spectral density, which exhibits resonance structures naturally. The value of the gluon condensate in the OPE is fixed by producing the ρ meson mass in the formalism, and then input into the dispersion relations for the scalar, pseudoscalar and tensor glueballs. It is shown that the low-energy limit of the correlation function for the scalar glueball, derived from the spectral density, discriminates the lattice estimate for the triple-gluon condensate from the single-instanton estimate. The spectral densities for the scalar and pseudoscalar glueballs reveal a double-peak structure: the peak located at lower mass implies that the f0(500) and f0(980) (η ad η ) mesons contain small amount of gluonium components, and should be included into scalar (pseudoscalar) mixing frameworks. Another peak determines the scalar (pseudoscalar) glueball mass around 1.50 (1.75) GeV with a broad width about 200 MeV, suggesting that the f0(1370), f0(1500) and f0(1710) (η( 1760)) mesons are the glue-rich states. We also predict the topological susceptability χ 1/4 t = 75-78 MeV, deduced from the correlation function for the pseudoscalar glueball at zero momentum. Our analysis gives no resonance solution for the tensor glueball, which may be attributed to the insufficient nonperturbative condensate information in the currently available OPE.

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Section: Introductionmentioning

confidence: 92%

Section: B ρ Meson Massmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dispersive analysis of glueball masses

2021

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Dispersive Analysis of Excited Glueball States

2024

Chinese Phys. Lett.

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Motivated by the determination for the spin-parity quantum numbers of the $X(2370)$ meson at BESIII, we extend our dispersive analysis on hadronic ground states to excited states. The idea is to start with the dispersion relation which a correlation function obeys, and subtract the known ground-state contribution from the involved spectral density. Solving the resultant dispersion relation as an inverse problem with available operator-product-expansion inputs, we extract excited-state masses from the subtracted spectral density. This formalism is verified by means of the application to the series of $\rho$ resonances, which establishes the $\rho(770)$, $\rho(1450)$ and $\rho(1700)$ mesons one by one under the sequential subtraction procedure. Our previous study has suggested the admixture of the $f_0(1370)$, $f_0(1500)$ and $f_0(1710)$ mesons (the $\eta(1760)$ meson) to be the lightest scalar (pseudoscalar) glueball. The present work predicts that the $f_0(2200)$ ($X(2370)$) meson is the first excited scalar (pseudoscalar) glueball.

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QCD sum rules with spectral densities solved in inverse problems

Umeeda

2020

Phys. Rev. D

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Vacuum polarization contribution to muon g−2 as an inverse problem

Cited by 11 publications

References 36 publications

Dispersive analysis of glueball masses

Dispersive analysis of glueball masses

Dispersive Analysis of Excited Glueball States

QCD sum rules with spectral densities solved in inverse problems

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