QCD Short-distance Constraints and Hadronic Approximations

Abstract

This paper discusses a general class of ladder resummation inspired hadronic approximations. It is found that this approach naturally reproduces many successes of single meson per channel saturation models (e.g. VMD) and NJL based models. In particular the existence of a constituent quark mass and a gap equation follows naturally. We construct an approximation that satisfies a large set of QCD short-distance and large $N_c$ constraints and reproduces many hadronic observables. We show how there exists in general a problem between QCD short-distance constraints for Green Functions and those for form factors and cross-sections following from the quark-counting rule. This problem while expected for Green functions that do not vanish in purely perturbative QCD also persists for many Green functions that are order parameters.

27 pages

Cited by in corpus (65)

• The anomalous magnetic moment of the muon in the Standard Model
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• Longitudinal short-distance constraints for the hadronic light-by-light contribution to $(g-2{)}_{\mu }$ with large-$N_c$ Regge models
• Towards a consistent estimate of the chiral low-energy constants
• Mesonic low-energy constants
• $\pi \pi$ Scattering in Three Flavour ChPT
• Axial-vector exchange contribution to the hadronic light-by-light piece of the muon anomalous magnetic moment
• Chiral Perturbation Theory Beyond One Loop
• The < S P P > Green function and SU(3) breaking in K_{l3} decays
• Odd-intrinsic-parity processes within the Resonance Effective Theory of QCD
• $\eta \to 3\pi$ at Two Loops In Chiral Perturbation Theory
• Hadronic light-by-light scattering in the muon g-2: a new short-distance constraint on pion exchange
• Revisiting γγ->π^+π^- at low energies
• Form Factors in the radiative pion decay
• Resonance saturation in the odd-intrinsic parity sector of low-energy QCD
• <VAP> Green Function in the Resonance Region
• Chiral dynamics in form factors, spectral-function sum rules, meson-meson scattering and semilocal duality
• A Rational Approach to Resonance Saturation in large-Nc QCD
• Short-distance constraints on hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• $\pi K$ Scattering in Three Flavour ChPT
• Low-energy photon-photon collisions to two loops revisited
• Four-point correlator constraints on electromagnetic chiral parameters and resonance effective Lagrangians
• Radiative corrections in weak semi-leptoni processes at low energy: a two-step matching determination
• Quantum Loops in the Resonance Chiral Theory: The Vector Form Factor
• Short-distance constraints for the longitudinal component of the hadronic light-by-light amplitude: an update
• Meson dominance of hadron form factors and large-Nc phenomenology
• New $\tau$-based evaluation of the hadronic contribution to the vacuum polarization piece of the muon anomalous magnetic moment
• Determination of the Chiral Couplings L_10 and C_87 from Semileptonic Tau Decays
• Integrating out strange quarks in ChPT
• Large-Nc Properties of the rho and f0(600) Mesons from Unitary Resonance Chiral Dynamics
• Towards a determination of the chiral couplings at NLO in 1/N(C): L_8(mu) and C_38(mu)
• Large-$N_c$ naturalness in coupled-channel meson-meson scattering
• Effects of Longitudinal Short-Distance Constraints on the Hadronic Light-by-Light Contribution to the Muon $g-2$
• Chiral dynamics predictions for eta' -> eta pi pi
• Semileptonic tau decays beyond the Standard Model
• The vector form factor at the next-to-leading order in 1/N(C): chiral couplings L9(mu) and C88(mu) - C90(mu)
• Scalar Form Factors in SU(3) Chiral Perturbation Theory
• Modeling interactions of photons with pseudoscalar and vector mesons
• Pion light-by-light contributions to the muon $g-2$
• One-loop Renormalization of Resonance Chiral Theory: Scalar and Pseudoscalar Resonances
• Tests of the naturalness of the coupling constants in ChPT at order p^6
• Study of η-η' mixing from radiative decay processes
• Low Energy Chiral Lagrangian in Curved Space-Time from the Spectral Quark Model
• Spin-1 Correlators at Large NC: Matching OPE and Resonance Theory up to O(alpha_s)
• Three pseudoscalar meson production in $e^{+}{e}^{-}$ annihilation
• Lepton-flavour violation in hadronic tau decays and $\mu -\tau$ conversion in nuclei
• Charged Kaon K \to 3 pi CP Violating Asymmetries at NLO in CHPT
• Two and Three Pseudoscalar Production in $e^{+}{e}^{-}$ annihilation and their contributions to $(g-2{)}_{\mu }$
• Scalar-involved three-point Green functions and their phenomenology
• Vanishing chiral couplings in the large-N_C resonance theory
• Hadronic decays of the tau lepton: Theoretical outlook
• The $B_K$ Kaon Parameter in the Chiral Limit
• OPE-RchiT matching at order alpha_s: hard gluonic corrections to three-point Green functions
• High energy constraints in the octet SS-PP correlator and resonance saturation at NLO in 1/Nc
• Resonance saturation of the chiral couplings at NLO in 1/Nc
• Resonance effects in pion and kaon decay constants
• Hadronic Matrix Elements for Kaons
• Hadronic Light by Light Corrections to the Muon Anomalous Magnetic Moment
• Phenomenology of the <VVP> Green's function within the Resonance Chiral Theory
• Hadronic Light-by-Light Contribution to Muon g-2: Status and Prospects
• On the three-point order parameters of chiral symmetry breaking
• From hadronic tau decays to the chiral couplings L_10 and C_87
• Calculations of $\mathcal{O}(p^6)$ Resonance Coupling Constants in the Scalar Sector of the ENJL Model
• Scalar and pseudoscalar correlators in Resonance Chiral Theory