A New Estimate of ${\epsilon }^{\prime }/\epsilon$

Abstract

We discuss direct $CP$ violation in the standard model by giving a new estimate of ${\epsilon }^{\prime }/\epsilon$ in kaon decays. Our analysis is based on the evaluation of the hadronic matrix elements of the \mbox{$\Delta S=1$} effective quark lagrangian by means of the chiral quark model, with the inclusion of meson one-loop renormalization and NLO Wilson coefficients. Our estimate is fully consistent with the $\Delta I=1/2$ selection rule in $K\to \pi \pi$ decays which is well reproduced within the same framework. By varying all parameters in the allowed ranges and, in particular, taking the quark condensate---which is the major source of uncertainty---between $(-200\mathrm{MeV}{)}^3$ and $(-280\mathrm{MeV}{)}^3$ we find $$-5.0\times 10^{-3}<{\epsilon }^{\prime }/\epsilon <1.4\times 10^{-3}.$$ Assuming for the quark condensate the improved PCAC result \mbox{$\vev{\bar qq} = -(221\: \pm 17\ {\rm MeV})^3$} and fixing ${\Lambda }_{\mathrm{QCD}}^{(4)}$ to its central value, we find the more restrictive prediction $${\epsilon }^{\prime }/\epsilon =(4\pm 5)\times 10^{-4},$$ where the central value is defined as the average over the allowed values of Im ${\lambda }_t$ in the first and second quadrants. In these estimates the relevant mixing parameter Im ${\lambda }_t$ is self-consistently obtained from $\epsilon$ and we take $m_t^{\mathrm{pole}}=180\pm 12$ GeV. Our result is, to a very good approximation, renormalization-scale and ${\gamma }_5$-scheme independent.

40 pages, uuencoded LATEX2e file including 13 eps figures, revised version to appear in Nucl. Phys. B

References in corpus (15)

• The $\Delta S=1$ Effective Hamiltonian Including Next-to-Leading Order QCD and QED Corrections
• The Anatomy of ${\epsilon }^{\prime }/\epsilon$ Beyond Leading Logarithms with Improved Hadronic Matrix Elements
• Enhancement of the $K_L$ -- $K_S$ Mass Difference by Short Distance QCD Corrections Beyond Leading Logarithms
• Nambu Jona-Lasinio Like Models and the Low Energy Effective Action of QCD
• ${\epsilon }^{\prime }/\epsilon$ at the next-to-leading order in QCD and QED
• QCD tests from $e^+e^- \rar I=1~$ hadrons data and implication on the value of ${\alpha }_s$ from $\tau$-decays
• Light Quark Masses from QCD
• The Strange Quark Mass from QCD Sum Rules
• An Upgraded Analysis of $\epsilon \prime /\epsilon$ at the Next-to-Leading Order
• Quark Masses from Lattice QCD at the Next-to-Leading Order
• Studying ${\epsilon }^{\prime }/\epsilon$ in the Chiral Quark Model: ${\gamma }_5$-Scheme Independence and NLO Hadronic Matrix Elements
• The $\Delta I=1/2$ Selection Rule
• The $\Delta S=1$ Weak Chiral Lagrangian as the Effective Theory of the Chiral Quark Model
• Phenomenology with Wilson fermions using smeared sources
• Updating the Unitarity Triangle: Top Quark Mass Versus Nonperturbative Uncertainties

Cited by in corpus (30)

• 50 Years of Quantum Chromodynamics
• Patterns of Flavour Violation in Models with Vector-Like Quarks
• Estimating epsilon'/epsilon. A Review
• The Standard Model Prediction for epsilon'/epsilon
• ${\epsilon }^{\prime }/\epsilon$ at $O(p^4)$ in the Chiral Expansion
• Standard Model Confronting New Results for epsilon'/epsilon
• Direct CP violation in $K^0\to \pi \pi$: Standard Model Status
• The Delta I = 1/2 Rule and B_K at O(p^4) in the Chiral Expansion
• Renormalization Group Invariant Matrix Elements of DS = 2 and DI = 3/2 Four-Fermion Operators without Quark Masses
• Final State Interactions in Kaon Decays
• 1/N_c Corrections to the Hadronic Matrix Elements of Q_6 and Q_8 in K --> pi pi Decays
• Kaon CP violation and neutron EDM in the minimal left-right symmetric model
• The $\Delta S=1$ Weak Chiral Lagrangian as the Effective Theory of the Chiral Quark Model
• ${\epsilon }^{\prime }/\epsilon$: three years later
• Final State Interactions in $K\to \pi \pi$ Decays: $\Delta I=1/2$ Rule vs. ${\epsilon }^{\prime }/\epsilon$
• Combined analysis of the unitarity triangle and CP violation in the Standard Model
• A Heavy-Light Chiral Quark Model
• Constraints on the Mass and Mixing of the 4th Generation Quark From Direct CP Violation${\epsilon }^{\prime }/\epsilon$ and Rare K Decays
• Comment on `Analysis of O(p^2) Corrections to <2pi|Q_{7,8}|K>'
• A joint analysis of the S-wave in the pi+pi- and pi0pi0 data
• The Physics of $K^0-{\bar{K}}^0$ Mixing: ${\hat{B}}_K$ and $\Delta M_{LS}$ in the Chiral Quark Model
• epsilon'/epsilon in the Standard Model
• Chiral Limit Prediction for epsilon'/epsilon at NLO in 1/N_c
• The Isgur-Wise Function within a Modified Heavy-Light Chiral Quark Model
• Theoretical status of epsilon'/epsilon
• Final State Interactions and eps'/eps
• Theoretical status of epsilon'/epsilon
• The Revival of Kaon Flavour Physics
• 1/N_c and epsilon'/epsilon
• CP conserved nonleptonic $K\to \pi \pi \pi$ decays in the Chiral Quark Model