Delta I=1/2 and epsilon'/epsilon in Large-Nc QCD

Abstract

We present new results for the matrix elements of the Q_6 and Q_4 penguin operators, evaluated in a large-Nc approach which incorporates important O(N_c^2\frac{n_f}{N_c}) unfactorized contributions. Our approach shows analytic matching between short- and long-distance scale dependences within dimensional renormalization schemes, such as MS-bar. Numerically, we find that there is a large positive contribution to the Delta I =1/2 matrix element of Q_6 and hence to the direct CP-violation parameter epsilon'/epsilon. We also present results for the Delta I = 1/2 rule in K -> pi pi amplitudes, which incorporate the related and important ``eye-diagram'' contributions of O(N_c^2\frac{1}{N_c}) from the Q_2 operator (i.e. the penguin-like contraction). The results lead to an enhancement of the Delta I = 1/2 effective coupling. The origin of the large unfactorized contributions which we find is discussed in terms of the relevant scales of the problem.

25 pages, 8 figures, LaTeX file. Couple of references added

References in corpus (4)

• Light quark masses, chiral condensate and quark-gluon condensate in quenched lattice QCD with exact chiral symmetry
• Long-distance dimension-eight operators in B_K
• Chiral Effective Lagrangian and Quark Masses
• Electroweak Penguins and Large Nc

Cited by in corpus (49)

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• SU(N) gauge theories at large N
• Anatomy of Prominent B and K Decays and Signatures of CP-Violating New Physics in the Electroweak Penguin Sector
• The Impact of Universal Extra Dimensions on B -> X_s gamma, B -> X_s gluon, B -> X_s mu^+ mu^-, K_L -> pi^0 e^ +e^-, and epsilon'/epsilon
• Flavor Physics in the Randall-Sundrum Model: II. Tree-Level Weak-Interaction Processes
• Isospin violation in epsilon'
• Rare Kaon Decays Revisited
• A Rational Approach to Resonance Saturation in large-Nc QCD
• Lepton flavor (universality) violation in rare kaon decays
• Direct CP violation in $K^0\to \pi \pi$: Standard Model Status
• Gluino-mediated electroweak penguin with flavor-violating trilinear couplings
• Four-point correlator constraints on electromagnetic chiral parameters and resonance effective Lagrangians
• Four-point functions and kaon decays in a minimal AdS/QCD model
• Radiative Kaon Decays and the Penguin Contribution to the Delta I = 1/2 Rule
• epsilon'/epsilon at the NLO: 10 Years Later
• Twisted mass QCD and lattice approaches to the $\Delta I=1/2$ rule
• On the Delta I = 1/2 Rule in Holographic QCD
• New Physics Patterns in ${\epsilon }^{\prime }/\epsilon$ and ${\epsilon }_K$ with Implications for Rare Kaon Decays and $\Delta M_K$
• Novel patterns for vector mesons from the large-Nc limit
• Isospin-Violating Contributions to ${\epsilon }^{\prime }/\epsilon$
• Upper Bounds on epsilon'/epsilon Parameters B_6^{(1/2)} and B_8^{(3/2)} from Large N QCD and other News
• Correlations between epsilon'/epsilon and Rare K Decays in the Littlest Higgs Model with T-Parity
• Charged Kaon K \to 3 pi CP Violating Asymmetries at NLO in CHPT
• Large $N_c$ scaling of meson masses and decay constants
• Towards Lagrangian construction for infinite half-integer spin field
• K-->pipi amplitudes from lattice QCD with a light charm quark
• Mixed-symmetry continuous-spin fields in flat and AdS spaces
• Non-leptonic kaon decays at large $N_c$
• SU(3) analysis of four-quark operators: $K\to \pi \pi$ and vacuum matrix elements
• The value of B_K from the experimental data on CP-violation in K-mesons and up-to-date values of CKM matrix parameters
• Analytic estimates for penguin operators in quenched QCD
• Theoretical status of ${\epsilon }^{\prime }/\epsilon$
• Probing the chiral weak Hamiltonian at finite volumes
• $K\to \pi {\ell }^{+}{\ell }^{-}$ form factor in the Large-N${}_c$ and cut-off regularization method
• Probing SUSY effects in $K_S^0\to {\mu }^{+}{\mu }^{-}$
• Kaon mixing and the charm mass
• Dissecting the $\Delta I=1/2$ rule at large $N_c$
• Charm mass dependence of the weak Hamiltonian in chiral perturbation theory
• Hadronic Matrix Elements for Kaons
• Analytic estimates of quenched penguins
• Study of Kaon Decay to Two Pions
• Kaon weak interactions in powers of 1/Nc
• Recent progress on CP violation in $K\to \pi \pi$ decays in the SM and a supersymmetric solution
• Non-leptonic kaon decays at large $N_c$
• Unfactorizing Polychromatic Penguins
• Kaon Decays from AdS/QCD
• Chiral loop corrections and isospin violation effects in epsilon'/epsilon
• Vector Meson Contributions in epsilon'/epsilon