QCD sum rules with spectral densities solved in inverse problems

Li, Hsiang-nan; Umeeda, Hiroyuki

doi:10.1103/physrevd.102.114014

Cited by 13 publications

(7 citation statements)

References 53 publications

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“…The nonperturbative approach based on dispersion relations for physical observables was proposed in [17], and then applied to the constraint on the hadronic vacuum polarization contribution to the muon anomalous magnetic moment [25], to the reformulation of QCD sum rules for extracting properties of the series of ρ resonances [26], glueball masses [19] and the pion light-cone distribution amplitude [27], and to the explanation of the large observed D meson mixing parameters [15]. Here we will extend it to the analysis of heavy quark decay widths and demonstrate that the involved fermion masses can be constrained, as the hadronic thresholds are introduced into the relevant dispersion relations.…”

Section: Dispersive Constraintsmentioning

confidence: 99%

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Dispersive constraints on fermion masses

Li¹

2023

Preprint

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We demonstrate that fermion masses in the Standard Model (SM) can be constrained by the dispersion relations obeyed by hadronic and semileptonic decay widths of a fictitious heavy quark Q with an arbitrary mass. These relations, imposing stringent connections between the high-mass and low-mass behaviors of decay widths, correlate a heavy quark mass and the chiral symmetry breaking scale. Given the known input from leading-order heavy quark expansion and a hadronic threshold for decay products, we solve for a physical heavy quark decay width. It is shown that the charm (bottom) quark mass mc = 1.35 GeV (m b = 4.0 GeV) can be determined by the dispersion relation for the Q → du d (Q → cūd) decay with the threshold 2mπ (mπ + mD), where mπ (mD) denotes the pion (D meson) mass. Requiring that the dispersion relation for the Q → su d (Q → dµ + νµ, Q → uτ − ντ ) decay with the threshold mπ + mK (mπ + mµ, mπ + mτ ) yields the same heavy quark mass, mK being the kaon mass, we constrain the strange quark (muon, τ lepton) mass to be ms = 0.12 GeV (mµ = 0.11 GeV, mτ = 2.0 GeV). Moreover, all the predicted decay widths corresponding to the above masses agree with data. It is pointed out that our formalism is similar to QCD sum rules for probing resonance properties, and that the Pauli interference (weak annihilation) provides the higher-power effect necessary for establishing the solutions of the hadronic (semilaptonic) decay widths. This work suggests that the parameters in the SM may not be free, but arranged properly to achieve internal dynamical consistency.

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Section: Dispersive Constraintsmentioning

confidence: 99%

“…The functions M (m Q ) and Γ(m Q ) represent the dispersive and absorptive pieces, respectively. It has been observed that power corrections are crucial for establishing a resonance solution in QCD sum rules [26]. Hence, we rely on those heavy meson decays, which contain sizable higher-power corrections.…”

Section: Dispersive Constraintsmentioning

confidence: 99%

Dispersive constraints on fermion masses

Li¹

2023

Preprint

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“…We proposed to handle QCD sum rules [36] for nonpertrbative observables, such as the ρ meson mass, as an inverse problem in [37]. The spectral density on the hadron side of a dispersion relation, derived from a correlation function, is regarded as an unknown.…”

Section: Introductionmentioning

confidence: 99%

“…The long-existing concern on the rigorousness and predictive power of QCD sum rules [40,41] 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 [37]. We then developed an inverse matrix method to solve for scalar and pseudoscalar glueball masses from the corresponding dispersion relations [42].…”

Section: Introductionmentioning

confidence: 99%

“…We then developed an inverse matrix method to solve for scalar and pseudoscalar glueball masses from the corresponding dispersion relations [42]. This new viewpoint, based only on the analyticity of physical observables, has been extended to the explanation of the D meson mixing parameters [43] and to the constraint on the hadronic vacuum polarization contribution to the muon anomalous magnetic moment [44].…”

Section: Introductionmentioning

confidence: 99%

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Dispersive derivation of the pion distribution amplitude

2022

Preprint

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We derive the dependence of the leading-twist pion light-cone distribution amplitude (LCDA) on a parton momentum fraction x by directly solving the dispersion relations for the moments with inputs from the operator product expansion (OPE) of the corresponding correlation function. It is noticed that these dispersion relations must be organized into those for the Gegenbauer coefficients first in order to avoid the ill-posed problem appearing in the conversion from the moments to the Gegenbauer coefficients. Given the values of various condensates in the OPE, we find that a solution for the pion LCDA, which is stable in the Gegenbauer expansion, exists. Moreover, the solution from summing contributions up to 18 Gegenbauer polynomials is smooth, and can be well approximated by a function proportional to x p (1−x) p with p ≈ 0.45 at the scale µ = 2 GeV. Turning off the condensates, we get the asymptotic form, independent of the scale µ, for the pion LCDA as expected. We then solve for the pion LCDA at a different scale µ = 1.5 GeV with the condensate inputs at this µ, and demonstrate that the result is consistent with the one obtained by evolving the Gegenbauer coefficients from µ = 2 GeV to 1.5 GeV. That is, our formalism is compatible with the QCD evolution. The strength of the above approach that goes beyond analyses limited to only the first few moments of a LCDA in conventional QCD sum rules is highlighted. The precision of our results can be improved systematically by including higher-order and higher-power terms in the OPE.

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Hyperon semileptonic decays in QCD sum rules

Zhang,

Qiao

2024

J. High Energ. Phys.

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We investigate the hyperon semileptonic decays within the framework of QCD sum rules. The flavor SU(3) symmetry breaking effects are analyzed via the relevant form factors and corresponding branching fractions. Employing the z-series parameterization to capture the q2 dependence of form factors, we calculate the hyperon semileptonic decay rates and confront them with the recent experimental measurements. Moreover, we calculate as well the non-standard tensor form factors, which involve certain new physics beyond the standard model.

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QCD sum rules with spectral densities solved in inverse problems

Cited by 13 publications

References 53 publications

Dispersive constraints on fermion masses

Dispersive constraints on fermion masses

Dispersive derivation of the pion distribution amplitude

Hyperon semileptonic decays in QCD sum rules

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