The $B_K$ Kaon Parameter in the Chiral Limit

Abstract

We introduce four-point functions in the hadronic ladder resummation approach to large $N_c$ QCD Green functions. We determine the relevant one to calculate the $B_K$ kaon parameter in the chiral limit. This four-point function contains both the large momenta QCD OPE and the small momenta ChPT at NLO limits, analytically. We get ${\hat{B}}_K^{\chi }=0.38\pm 0.15$. We also give the ChPT result at NLO for the relevant four-point function to calculate $B_K$ outside the chiral limit, while the leading QCD OPE is the same as the chiral limit one.

17 pages

References in corpus (42)

• Weak Decays Beyond Leading Logarithms
• CP Violation and the CKM Matrix: Assessing the Impact of the Asymmetric B Factories
• The 2004 UTfit Collaboration Report on the Status of the Unitarity Triangle in the Standard Model
• Weak Hamiltonian, CP Violation and Rare Decays
• Enhancement of the $K_L$ -- $K_S$ Mass Difference by Short Distance QCD Corrections Beyond Leading Logarithms
• Next-to-Leading Order QCD Corrections to $\Delta F=2$ effective Hamiltonians
• Nambu Jona-Lasinio Like Models and the Low Energy Effective Action of QCD
• Resonance estimates of O(p^6) low-energy constants and QCD short-distance constraints
• The Complete |Delta S|=2 Hamiltonian in the Next-To-Leading Order
• QCD Isospin Breaking in Meson Masses, Decay Constants and Quark Mass Ratios
• Chiral Lagrangians and Nambu-Jona-Lasinio like models
• A sum rule approach to the violation of Dashen's theorem
• Pion and Kaon Electromagnetic Form Factors
• Indirect CP-Violation in the Neutral Kaon System Beyond Leading Logarithms
• Odd-intrinsic-parity processes within the Resonance Effective Theory of QCD
• The CKM Matrix and the Unitarity Triangle
• <VAP> Green Function in the Resonance Region
• $\pi \to l\nu \gamma$ Form Factors at Two-loop
• Meson resonances, large N_c and chiral symmetry
• Chiral Sum-Rules for ${\mathcal{L}}_{(6)}^{WZ}$ Parameters and Application to ${\pi }^0,\eta ,{\eta }^{\prime }$ Decays
• Matching the Electroweak Penguins $Q_7$, $Q_8$ and Spectral Correlators
• K0-anti-K0 mixing in the 1/Nc expansion
• QCD Short-distance Constraints and Hadronic Approximations
• Lattice QCD with two dynamical flavors of domain wall quarks
• Kaon B parameter from quenched domain-wall QCD
• Massive Spin-1 Field Chiral Lagrangian from an Extended Nambu-Jona-Lasinio Model of QCD
• The $B_K$ Parameter in the $1/N_c$ Expansion
• Calculation of the K^0-\bar{K}^0 mixing parameter via the QCD sum rules at finite energies
• Recent results from lattice calculations
• Low--Energy Behavior of Two--Point Functions of Quark Currents
• Long-distance dimension-eight operators in B_K
• Scheme Dependence of Weak Matrix Elements in the $1/N_c$ Expansion
• Extended Fermion Representation of Multi-Charge 1/2-BPS Operators in AdS/CFT -- Towards Field Theory of D-Branes --
• Two- and Three-Point Functions in the Extended NJL Model
• Anomalies, VMD and the Enjl Model
• $B_K$ and Explicit Chiral Symmetry Breaking
• Dimension-eight Operators in the Weak OPE
• Testing improved staggered fermions with $m_s$ and $B_K$
• Kaon B parameter from quenched domain-wall QCD
• Pi- Eta Mixing from QCD Sum Rules
• Chiral Symmetry Aspects of the Scalars
• The B_K Kaon Parameter in the 1/N_c Expansion

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• Kaon Decays in the Standard Model
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• Flavor Physics in the Quark Sector
• Chiral perturbation theory
• A Rational Approach to Resonance Saturation in large-Nc QCD
• Four-point functions and kaon decays in a minimal AdS/QCD model
• Novel patterns for vector mesons from the large-Nc limit
• SU(3) analysis of four-quark operators: $K\to \pi \pi$ and vacuum matrix elements
• Probing the chiral weak Hamiltonian at finite volumes
• An upper bound on the Kaon B-parameter and Re(epsilon_K)
• Theoretical overview of kaon decays