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 $H_2^r({\nu }_{\chi }=M_{\eta })=-(5.7\pm 2.0)\times 10^{-3}$.

A 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 (11)

• Hadronic Z- and tau-Decays in Order alpha_s^4
• The 2009 World Average of ${\alpha }_s$
• The Determination of alpha_s from Tau Decays Revisited
• Leptonic Decays of Charged Pseudoscalar Mesons - 2013
• Leptonic decays of charged pseudoscalar mesons - 2012
• Introduction to Chiral Perturbation Theory
• MILC results for light pseudoscalars
• Strange quark mass from Finite Energy QCD sum rules to five loops
• Up and down quark masses from Finite Energy QCD sum rules to five loops
• Strange quark condensate from QCD sum rules to five loops
• Global Fit of alpha_s(m_Z) to Thrust at NNNLL Order with Power Corrections

Cited by in corpus (21)

• Direct determination of the strange and light quark condensates from full lattice QCD
• Chiral properties of (2+1)-flavor QCD in strong magnetic fields at zero temperature
• $B$ Meson Decay Constants $f_{B_c}$, $f_{B_s}$ and $f_B$ from QCD Sum Rules
• QCD determination of the magnetic field dependence of QCD and hadronic parameters
• Chiral symmetry restoration and deconfinement in QCD at finite temperature
• What Does Low Energy Physics Tell Us About The Zero Momentum Gluon Propagator
• Charm-quark mass from weighted finite energy QCD sum rules
• Corrections to the $\mathbf{SU}(3)\times \mathbf{SU}(3)$ Gell-Mann-Oakes-Renner relation and chiral couplings $L_8^r$ and $H_2^r$
• Axial coupling constant in a magnetic background
• Analytical determination of the QCD quark masses
• New Sum Rule Determination of the Mass and Strangeness Content of the Nucleon
• Determination of the temperature dependence of the up- down-quark mass in QCD
• Sensitivity of predictions in an effective model -- application to the chiral critical end point position in the Nambu--Jona-Lasinio model
• Light-cone sum rules for proton decay
• Towards a unified treatment of $\Delta S=0$ parity violation in low-energy nuclear processes
• Chiral Properties of $(2+1)$-Flavor QCD in Magnetic Fields at Zero Temperature
• Magnetic effects of QCD parameters from finite energy sum rules
• The $a_1(1260)$ meson and chiral symmetry restoration and deconfinment at finite temperature QCD
• Semi-leptonic three-body proton decay modes from light-cone sum rules
• Hadronic and radiative decays of the tau lepton
• Chiral Corrections to the Gell-Mann-Oakes-Renner Relation from QCD Sum Rules