The $B_K$ Parameter in the $1/N_c$ Expansion

Abstract

We calculate the $B_K$ parameter within the framework of the $1/N_c$ expansion. We essentially use the technique presented by Bardeen, Buras and Gérard but calculate an off-shell Green function in order to disentangle different contributions. We study this Green function in pure Chiral Perturbation Theory (CHPT) first and afterwards in the $1/N_c$ expansion in the presence of an explicit cut-off to determine $B_K$ and the counterterms appearing in CHPT. The high energy part is done using the renormalization group. For the low-energy contributions we use both CHPT and an Extended Nambu--Jona-Lasinio model. This model has the right properties to match with the high energy QCD behaviour. We then study explicit chiral symmetry breaking effects by calculating with both massless and degenerate quarks together with the real case. A detailed analysis and comparison with the results found within other approaches is done. Consequences for present lattice calculations of this parameter are then obtained. As final result we get $0.60<{\hat{B}}_K<0.80$. If $m_s=m_d=0$ we get $0.25<{\hat{B}}_K^{\chi }<0.55$.

44 pages, uses epsf.sty, 9 figures included (8 postscript, 1 LaTeX)

References in corpus (10)

• QCD Phenomenology based on a Chiral Effective Lagrangian
• Enhancement of the $K_L$ -- $K_S$ Mass Difference by Short Distance QCD Corrections Beyond Leading Logarithms
• Chiral Lagrangians and Nambu-Jona-Lasinio like models
• Calculation of the K^0-\bar{K}^0 mixing parameter via the QCD sum rules at finite energies
• QCD Predictions for the Tau Hadronic Width: Determination of alpha_s(M_τ^2)
• Two- and Three-Point Functions in the Extended NJL Model
• Anomalies, VMD and the Enjl Model
• $B_K$ and Explicit Chiral Symmetry Breaking
• A Study of the Nambu--Jona-Lasinio Model on the Lattice
• The Nambu--Jona-Lasinio Model of QCD on the Lattice

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