Chiral corrections to the $SU(2)\times SU(2)$ Gell-Mann-Oakes-Renner relation

Abstract

The next to leading order chiral corrections to the $SU(2)\times SU(2)$ Gell-Mann-Oakes-Renner (GMOR) relation are obtained using the pseudoscalar correlator to five-loop order in perturbative QCD, together with new finite energy sum rules (FESR) incorporating polynomial, Legendre type, integration kernels. The purpose of these kernels is to suppress hadronic contributions in the region where they are least known. This reduces considerably the systematic uncertainties arising from the lack of direct experimental information on the hadronic resonance spectral function. Three different methods are used to compute the FESR contour integral in the complex energy (squared) s-plane, i.e. Fixed Order Perturbation Theory, Contour Improved Perturbation Theory, and a fixed renormalization scale scheme. We obtain for the corrections to the GMOR relation, ${\delta }_{\pi }$, the value ${\delta }_{\pi }=(6.2,\pm 1.6)$. This result is substantially more accurate than previous determinations based on QCD sum rules; it is also more reliable as it is basically free of systematic uncertainties. It implies a light quark condensate $<0|\bar{u}u|0>\simeq <0|\bar{d}d|0>\equiv <0|\bar{q}q|0>{|}_{2\mathrm{GeV}}=(-267\pm 5MeV{)}^3$. As a byproduct, the chiral perturbation theory (unphysical) low energy constant $H_2^r$ is predicted to be $H_2^r({\nu }_{\chi }=M_{\rho })=-(5.1\pm 1.8)\times 10^{-3}$, or $H_2^r({\nu }_{\chi }=M_{\eta })=-(5.7\pm 2.0)\times 10^{-3}$.

arXiv commentA comment about the value of the strong coupling has been added at the end of Section 4. No change in results or conslusions

References in corpus (35)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)
• The four-loop beta-function in Quantum Chromodynamics
• The 4-loop quark mass anomalous dimension and the invariant quark mass
• Hadronic Z- and tau-Decays in Order alpha_s^4
• The 2009 World Average of ${\alpha }_s$
• Scalar Correlator at O(alpha_s^4), Higgs Decay into b-quarks and Bounds on the Light Quark Masses
• QCD Sum Rules, a Modern Perspective
• Flavour-symmetry breaking of the quark condensate and chiral corrections to the Gell-Mann-Oakes-Renner relation
• Renormalization group analysis of the tau-lepton decay within QCD
• The Determination of alpha_s from Tau Decays Revisited
• Light Quark Masses from QCD
• The Strange Quark Mass from QCD Sum Rules
• Leptonic Decays of Charged Pseudoscalar Mesons - 2013
• Constraints on Hadronic Spectral Functions From Continuous Families of Finite Energy Sum Rules
• $K_{\ell 4}$ Form-Factors and $\pi$-$\pi$ Scattering
• Leptonic decays of charged pseudoscalar mesons - 2012
• Introduction to Chiral Perturbation Theory
• ${\alpha }_s(m_Z)$ from tau decays with matching conditions at three loops
• Mass singularities in light quark correlators: the strange quark case
• Order-${\alpha }_s^3$ determination of the strange quark mass
• Finite energy chiral sum rules in QCD
• Chiral sum rules and duality in QCD
• Contour-improved versus fixed-order perturbation theory in hadronic tau decays
• Chiral condensates from tau decay: a critical reappraisal
• MILC results for light pseudoscalars
• D and D_{S} decay constants from QCD duality at three loops
• Strange quark mass from Finite Energy QCD sum rules to five loops
• QCD Duality and the Mass of the Charm Quark
• Up and down quark masses from Finite Energy QCD sum rules to five loops
• Strange quark condensate from QCD sum rules to five loops
• Bottom quark mass and QCD duality
• B and B_s decay constants from QCD Duality at three loops
• Ratio of strange to non-strange quark condensates in QCD
• B and B_S decay constants from moments of Finite Energy Sum Rules in QCD
• Global Fit of alpha_s(m_Z) to Thrust at NNNLL Order with Power Corrections

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