Isospin-Violating Contributions to ${\epsilon }^{\prime }/\epsilon$

Abstract

The known isospin-breaking contributions to the $K\to \pi \pi$ amplitudes are reanalyzed, taking into account our current understanding of the quark masses and the relevant non-perturbative inputs. We present a complete numerical reappraisal of the direct CP-violating ratio ${\epsilon }^{\prime }/\epsilon$, where these corrections play a quite significant role. We obtain the Standard Model prediction $\text{Re}\left({\epsilon }^{\prime }/\epsilon \right)=\left(14\pm 5\right)\cdot 10^{-4}$, which is in very good agreement with the measured ratio. The uncertainty, which has been estimated conservatively, is dominated by our current ignorance about $1/N_C$-suppressed contributions to some relevant chiral-perturbation-theory low-energy constants.

49 pages, 4 figures

References in corpus (100)

• Weak Decays Beyond Leading Logarithms
• ππscattering
• Mass and width of the lowest resonance in QCD
• The $\Delta S=1$ Effective Hamiltonian Including Next-to-Leading Order QCD and QED Corrections
• Kaon Decays in the Standard Model
• The Anatomy of ${\epsilon }^{\prime }/\epsilon$ Beyond Leading Logarithms with Improved Hadronic Matrix Elements
• The Mesonic Chiral Lagrangian of Order $p^6$
• Version 3 of {\tt RunDec} and {\tt CRunDec}
• Effective Hamiltonian for Non-Leptonic |Delta F| = 1 Decays at NNLO in QCD
• An evaluation of |Vus| and precise tests of the Standard Model from world data on leptonic and semileptonic kaon decays
• Two--Loop Anomalous Dimension Matrix for $\Delta S=1$ Weak Non-Leptonic Decays II: $\mathcal{O}({\alpha }_e{\alpha }_s)$
• Virtual Photons in Chiral Perturbation Theory
• Towards a consistent estimate of the chiral low-energy constants
• Mesonic low-energy constants
• S-wave Kpi scattering in chiral perturbation theory with resonances
• Extension of the Chiral Perturbation Theory Meson Lagrangian to Order $P^6$
• Vus from pi and K decay constants in full lattice QCD with physical u, d, s and c quarks
• ${\epsilon }^{\prime }/\epsilon$ at the next-to-leading order in QCD and QED
• A sum rule approach to the violation of Dashen's theorem
• Right-handed charged currents in the era of the Large Hadron Collider
• Radiative corrections to K_{l3} decays
• $K\to \pi \pi$ $\Delta I=3/2$ decay amplitude in the continuum limit
• Electromagnetic Corrections for Pions and Kaons : Masses and Polarizabilities
• The < S P P > Green function and SU(3) breaking in K_{l3} decays
• Odd-intrinsic-parity processes within the Resonance Effective Theory of QCD
• Patterns of Flavour Violation in Models with Vector-Like Quarks
• Light-meson leptonic decay rates in lattice QCD+QED
• A precise measurement of the direct CP violation parameter Re(epsilon'/epsilon)
• Quark flavour observables in the Littlest Higgs model with T-parity after LHC Run 1
• epsilon'/epsilon and Rare K and B Decays in the MSSM
• An Upgraded Analysis of $\epsilon \prime /\epsilon$ at the Next-to-Leading Order
• $K\to \pi \nu \bar{\nu }$ and ${\epsilon }^{\prime }/\epsilon$ in Simplified New Physics Models
• Improved anatomy of epsilon'/epsilon in the Standard Model
• Order p^6 chiral couplings from the scalar K Pi form factor
• Chiral Perturbation Theory with Virtual Photons and Leptons
• The Standard Model Prediction for epsilon'/epsilon
• Isospin violation in epsilon'
• Meson resonances, large N_c and chiral symmetry
• Weak $K$--Amplitudes in the Chiral and $1/N_c$--Expansions
• Matching the Electroweak Penguins $Q_7$, $Q_8$ and Spectral Correlators
• Yukawa enhancement of $Z$-mediated New Physics in $\Delta S=2$ and $\Delta B=2$ Processes
• The Mixing Angle of the Lightest Scalar Nonet
• An ${\epsilon }^{\prime }$ improvement from right-handed currents
• Isospin Breaking in K -> Pi Pi Decays
• Standard Model Confronting New Results for epsilon'/epsilon
• Supersymmetric Explanation of CP Violation in $K\to \pi \pi$ Decays
• Colourless Mesons in a Polychromatic World
• Revisiting Kaon Physics in General $Z$ Scenario
• Direct CP violation in $K^0\to \pi \pi$: Standard Model Status
• Leptoquarks meet ${\epsilon }^{\prime }/\epsilon$ and rare Kaon processes
• The $\Delta I=1/2$ Rule in the Chiral Limit
• The Delta I = 1/2 Rule and B_K at O(p^4) in the Chiral Expansion
• Dispersive calculation of B_7^{3/2} and B_8^{3/2} in the chiral limit
• Master formula for ${\epsilon }^{\prime }/\epsilon$ beyond the Standard Model
• Chargino contributions in light of recent ${\epsilon }^{\prime }/\epsilon$
• epsilon'/epsilon in the Chiral Limit
• Gluino-mediated electroweak penguin with flavor-violating trilinear couplings
• Improved Determination of the Electroweak Penguin Contribution to epsilon'/epsilon in the Chiral Limit
• Delta I=1/2 and epsilon'/epsilon in Large-Nc QCD
• Four-point correlator constraints on electromagnetic chiral parameters and resonance effective Lagrangians
• Electroweak Penguin Contributions to Non-Leptonic Delta F = 1 Decays at NNLO
• Quantum Loops in the Resonance Chiral Theory: The Vector Form Factor
• Obtaining K to pi pi from Off-Shell K to pi Amplitudes
• Singularity-free Next-to-leading Order $\Delta S=1$ Renormalization Group Evolution and ${\epsilon }_K^{\prime }/{\epsilon }_K$ in the Standard Model and Beyond
• pi^0-eta Mixing and CP Violation
• Matrix Elements of Electroweak Penguin Operators in the 1/Nc Expansion
• The $\Delta I=1/2$ Selection Rule
• Determination of <2pi_{I=2}|Q_{7,8}|K0> in the Chiral Limit
• ${\epsilon }^{\prime }/\epsilon$ in 331 Models
• 1/N_c Corrections to the Hadronic Matrix Elements of Q_6 and Q_8 in K --> pi pi Decays
• The $\Delta S=1$ Weak Chiral Lagrangian as the Effective Theory of the Chiral Quark Model
• Extended chiral Khuri-Treiman formalism for $\eta \to 3\pi$ and the role of the $a_0(980)$, $f_0(980)$ resonances
• ${\epsilon }^{\prime }/\epsilon$ from charged-Higgs-induced gluonic dipole operators
• Towards a determination of the chiral couplings at NLO in 1/N(C): L_8(mu) and C_38(mu)
• Large-$N_c$ naturalness in coupled-channel meson-meson scattering
• Form-factors and current correlators: chiral couplings L_10(mu) and C_87(mu) at NLO in 1/N(C)
• Correlating ${\epsilon }^{\prime }/\epsilon$ to hadronic $B$ decays via $U(2{)}^3$ flavour symmetry
• New QCD estimate of the kaon penguin matrix elements and epsilon'/epsilon
• QCD corrections to inclusive $\Delta S=1,2$ transitions at the next-to-leading order
• An updated analysis of eps'/eps in the standard model with hadronic matrix elements from the chiral quark model
• The vector form factor at the next-to-leading order in 1/N(C): chiral couplings L9(mu) and C88(mu) - C90(mu)
• Electromagnetism in nonleptonic weak interactions
• Final State Interactions in $K\to \pi \pi$ Decays: $\Delta I=1/2$ Rule vs. ${\epsilon }^{\prime }/\epsilon$
• A Critical Reassessment of Q7 and Q8 Matrix Elements
• Updated determination of chiral couplings and vacuum condensates from hadronic tau decay data
• New Physics Patterns in ${\epsilon }^{\prime }/\epsilon$ and ${\epsilon }_K$ with Implications for Rare Kaon Decays and $\Delta M_K$
• Upper Bounds on epsilon'/epsilon Parameters B_6^{(1/2)} and B_8^{(3/2)} from Large N QCD and other News
• Isospin Breaking in $K\to 3\pi$ Decays III: Bremsstrahlung and Fit to Experiment
• $K\to \pi \nu \overline{\nu }$ in the MSSM in Light of the ${\epsilon }_K^{\prime }/{\epsilon }_K$ Anomaly
• The order $p^8$ mesonic chiral Lagrangian
• BSM Hadronic Matrix Elements for ${\epsilon }^{\prime }/\epsilon$ and $K\to \pi \pi$ Decays in the Dual QCD Approach
• Towards NNLO accuracy for ${\epsilon }^{\prime }/\epsilon$
• Simultaneous interpretation of $K$ and $B$ anomalies in terms of chiral-flavorful vectors
• ${\epsilon }_K^{\prime }/{\epsilon }_K$ and $K\to \pi \nu \bar{\nu }$ in a two-Higgs doublet model
• ${\epsilon }^{\prime }/\epsilon$ Anomaly and Neutron EDM in $SU(2{)}_L\times SU(2{)}_R\times U(1{)}_{B-L}$ model with Charge Symmetry
• Analytic representation of $F_K/F_{\pi }$ in two loop chiral perturbation theory
• The Strong Isospin-Breaking Correction for the Gluonic Penguin Contribution to epsilon'/epsilon at Next-to-Leading Order in the Chiral Expansion
• ${\epsilon }_K$ and ${\epsilon }^{\prime }/\epsilon$ in a diquark model
• Direct CP Violation in Cabibbo-Favored Charmed Meson Decays and ${\epsilon }^{\prime }/\epsilon$ in $SU(2{)}_L\times SU(2{)}_R\times U(1{)}_{B-L}$ Model
• Anatomy of a Weak Matrix Element

Cited by in corpus (21)

• FLAG Review 2021
• FLAG Review 2024
• Direct CP violation and the $\Delta I=1/2$ rule in $K\to \pi \pi$ decay from the Standard Model
• Study of CP violation in hyperon decays at Super Charm-Tau Factories with a polarized electron beam
• A low-energy perspective on the minimal left-right symmetric model
• Final-state interactions in the CP asymmetries of charm-meson two-body decays
• Axion-mediated forces, CP violation and left-right interactions
• ${\epsilon }^{\prime }/\epsilon$ in the Standard Model at the Dawn of the 2020s
• CP-violating axion interactions in effective field theory
• SU(3) analysis of four-quark operators: $K\to \pi \pi$ and vacuum matrix elements
• BSM Master Formula for ${\epsilon }^{\prime }/\epsilon$ in the WET Basis at NLO in QCD
• Flavor constraints for a Vector-like quark of Nelson-Barr type
• Isospin-breaking in ${\epsilon }^{\prime }/\epsilon$: Impact of ${\eta }_0$ at the Dawn of the 2020s
• Isospin 0 and 2 two-pion scattering at physical pion mass using all-to-all propagators with periodic boundary conditions in lattice QCD
• Dissecting the $\Delta I=1/2$ rule at large $N_c$
• $\Delta I=3/2$ and $\Delta I=1/2$ channels of $K\to \pi \pi$ decay at the physical point with periodic boundary conditions
• Strange processes in general two Higgs doublet model
• Workshop summary -- Kaons@CERN 2023
• CP violation in the hyperon decays $\Sigma \to N\pi$
• Vector-like quark doublets, weak-basis invariants and CP violation
• Kaon physics overview