Enhancement of the $K_L$ -- $K_S$ Mass Difference by Short Distance QCD Corrections Beyond Leading Logarithms

Abstract

We calculate the next-to-leading order short distance QCD corrections to the coefficient ${\eta }_1$ of the effective $\Delta S=2$ hamiltonian in the standard model. This part dominates the short distance contribution $(\Delta m_K{)}^{\mathrm{SD}}$ to the $K_L$ -- $K_S$ mass difference. The next-to-leading order result enhances ${\eta }_1$ and $(\Delta m_K{)}^{\mathrm{SD}}$ by 20\% compared to the leading order estimate. Taking $0.200 \gev \le \laMSb \le 0.350 \gev$ and $1.35 \gev \le m_c(m_c) \le 1.45 \gev$ we obtain $0.922\le {\eta }_1^{\mathrm{NLO}}\le 1.419$ compared to $0.834\le {\eta }_1^{\mathrm{LO}}\le 1.138$. For $B_K=0.7$ this corresponds to 48 -- 75 \% of the experimentally observed mass difference. The inclusion of next-to- leading order corrections to ${\eta }_1$ reduces considerably the theoretical uncertainty related to the choice of renormalization scales.

30 pages and 9 figures (available as uuencoded tarred postscript files), LaTeX, TUM-T31-40/93

References in corpus (1)

• The Rare Decays $K^{+}\to {\pi }^{+}\nu \bar{\nu }$\ and $K_L\to {\mu }^{+}{\mu }^{-}$\ Beyond Leading Logarithms

Cited by in corpus (140)

• Weak Decays Beyond Leading Logarithms
• CP Violation and the CKM Matrix: Assessing the Impact of the Asymmetric B Factories
• Universal Unitarity Triangle and Physics Beyond the Standard Model
• Theoretical Uncertainties and Phenomenological Aspects of $B\to X_s\gamma$ Decay
• Phenomenology of Two Higgs Doublet Models with Flavor Changing Neutral Currents
• Left-Right Symmetry at LHC
• Waiting for the Top Quark Mass, K^+ --> π^+ ν\barν, B_s^0-\bar{B}_s^0 Mixing and CP Asymmetries in B-Decays
• Anatomy and Phenomenology of FCNC and CPV Effects in SUSY Theories
• Flavor Physics in the Quark Sector
• Delta F=2 Observables and Fine-Tuning in a Warped Extra Dimension with Custodial Protection
• Next-to-Leading Order QCD Corrections to $\Delta F=2$ effective Hamiltonians
• Higgs-mediated FCNCs: Natural Flavour Conservation vs. Minimal Flavour Violation
• Master Formulae for Delta F=2 NLO-QCD Factors in the Standard Model and Beyond
• Anatomy of New Physics in B-Bbar mixing
• On epsilon_K beyond lowest order in the Operator Product Expansion
• Next-to-Next-to-Leading-Order Charm-Quark Contribution to the CP Violation Parameter epsilon_K and Delta M_K
• Correlations among new CP violating effects in Delta F = 2 observables
• Lattice QCD inputs to the CKM unitarity triangle analysis
• The Impact of Universal Extra Dimensions on the Unitarity Triangle and Rare K and B Decays
• Leptonic and Semileptonic Decays of Charm and Bottom Hadrons
• The Complete |Delta S|=2 Hamiltonian in the Next-To-Leading Order
• Rare K and B Decays in a Warped Extra Dimension with Custodial Protection
• Evanescent Operators, Scheme Dependences and Double Insertions
• Possible Indications of New Physics in Bd-mixing and in sin(2 beta) Determinations
• The flavor of a little Higgs with T-parity
• Charm Quark Contribution to K+ -> pi+ nu anti-nu at Next-to-Next-to-Leading Order
• Epsilon_K at Next-to-Next-to-Leading Order: The Charm-Top-Quark Contribution
• Present and Future K and B Meson Mixing Constraints on TeV Scale Left-Right Symmetry
• Indirect CP-Violation in the Neutral Kaon System Beyond Leading Logarithms
• Flavor Physics in the Randall-Sundrum Model: II. Tree-Level Weak-Interaction Processes
• Less space for a new family of fermions
• The Anatomy of Quark Flavour Observables in 331 Models in the Flavour Precision Era
• Direct CP Violation in K_L --> π^0 e^+e^- Beyond Leading Logarithms
• How much space is left for a new family?
• epsilon'/epsilon and Rare K and B Decays in the MSSM
• The fourth family: a simple explanation for the observed pattern of anomalies in B-CP asymmetries
• QCD Corrections to Flavor-Changing Neutral Currents in the Supersymmetric Standard Model
• Estimating epsilon'/epsilon. A Review
• The Standard Model Prediction for epsilon'/epsilon
• Possible evidence for the breakdown of the CKM-paradigm of CP-violation
• SM with four generations: Selected implications for rare B and K decays
• CP Violation in the B System and Relations to $K\to \pi \nu \bar{\nu }$ Decays
• Waiting for Precise Measurements of K^+->pi^+ nu nu and K_L->pi^0 nu nu
• The Anatomy of Z' and Z with Flavour Changing Neutral Currents in the Flavour Precision Era
• Flavor changing neutral current processes in $B$ and $K$ decays in the supergravity model
• ${\epsilon }^{\prime }/\epsilon$ at $O(p^4)$ in the Chiral Expansion
• SUSY_FLAVOR: a computational tool for FCNC and CP-violating processes in the MSSM
• $\Delta M_s/\Delta M_d$, $\sin 2\beta$ and the angle $\gamma$ in the Presence of New $\Delta F=2$ Operators
• Muon anomalous magnetic moment, lepton flavor violation, and flavor changing neutral current processes in SUSY GUT with right-handed neutrino
• K0-anti-K0 mixing in the 1/Nc expansion
• Patterns of Flavour Violation in the Presence of a Fourth Generation of Quarks and Leptons
• Standard Model Confronting New Results for epsilon'/epsilon
• CP violation in kaon decays
• Supersymmetric Explanation of CP Violation in $K\to \pi \pi$ Decays
• Standard-model prediction of ${\epsilon }_K$ with manifest CKM unitarity
• The Delta I = 1/2 Rule and B_K at O(p^4) in the Chiral Expansion
• Long distance contribution to the $K_L-K_S$ mass difference
• Four-point functions and kaon decays in a minimal AdS/QCD model
• Limits on scalar leptoquark interactions and consequences for GUTs
• The CP violating phase $\gamma$ from global fit of rare charmless hadronic B decays
• The $B_K$ Parameter in the $1/N_c$ Expansion
• Bounds on the Unitarity Triangle, $\sin 2\beta$ and $K\to \pi \nu \bar{\nu }$ Decays in Models with Minimal Flavour Violation
• SUSY_FLAVOR v2.5: a computational tool for FCNC and CP-violating processes in the MSSM
• Constraints on the Four-Generation Quark Mixing Matrix from a Fit to Flavor-Physics Data
• CP violation and the CKM matrix
• Standard Model Predictions for Rare K and B Decays without New Physics Infection
• Particle-Antiparticle Mixing, epsilon_K, Delta Gamma_q, A_SL^q, A_CP(B_d -> psi K_S), A_CP(B_s -> psi phi) and B -> X_{s,d} gamma in the Littlest Higgs Model with T-Parity
• ${\epsilon }^{\prime }/\epsilon$: three years later
• A Lower Bound on sin 2βfrom Minimal Flavour Violation
• Implications of the Top Quark Mass Measurement for the CKM Parameters, $x_s$ and CP Asymmetries
• Particle-Antiparticle Mixing, ε_K and the Unitarity Triangle in the Littlest Higgs Model
• Particle-Antiparticle Mixing, CP Violation and Rare K and B Decays in a Minimal Theory of Fermion Masses
• QCD corrections to inclusive $\Delta S=1,2$ transitions at the next-to-leading order
• Indirect Measurement of the Vertex and Angles of the Unitarity Triangle
• Littlest Higgs Model with T-Parity Confronting the New Data on D^0-\bar D^0 Mixing
• An updated analysis of eps'/eps in the standard model with hadronic matrix elements from the chiral quark model
• FCNC Processes in the Littlest Higgs Model with T-Parity: an Update
• On the consistency between the observed amount of CP violation in the K- and Bd-systems within minimal flavor violation
• A New Estimate of ${\epsilon }^{\prime }/\epsilon$
• Minimal Flavour Violation Waiting for Precise Measurements of Delta M_s, S_{psi phi}, A^s_SL, |V_ub|, gamma and B^0_{s,d} -> mu+ mu-
• Hints for the scale of new CP-violating physics from B-CP anomalies
• Measurements of the $\rho$ and $\eta$ parameters of the $V_{CKM}$ matrix and perspectives
• Determining the Sign of the Z-Penguin Amplitude
• Theoretical Review of B-Physics
• CALCULATION OF THE D AND B MESON LIFETIMES AND THE UNITARITY TRIANGLE PARAMETERS
• Mass spectra and decay properties of $D$ Meson in a relativistic Dirac formalism
• Present knowledge of the Cabibbo-Kobayashi-Maskawa matrix
• The Anatomy of Neutral Scalars with FCNCs in the Flavour Precision Era
• Correlations between epsilon'/epsilon and Rare K Decays in the Littlest Higgs Model with T-Parity
• Combined analysis of the unitarity triangle and CP violation in the Standard Model
• Determination of the CKM angle gamma and |V_{ub}/V_{cb}| from inclusive direct CP asymmetries and branching ratios in charmless B decays
• CP Asymmetry Measurements in psi K0 and the CKM Paradigm
• Constraining the mixing matrix for Standard Model with four generations: time dependent and semi-leptonic CP asymmetries in $B_d^0$, $B_s$ and $D^0$
• Search for the signal of monotop production at the early LHC
• Flavour Theory: 2009
• The Impact of a 4th Generation on Mixing and CP Violation in the Charm System
• Constraints on $Z^{\prime }$ Boson within Minimal Flavor Violation
• Standard Model evaluation of ${\epsilon }_K$ using lattice QCD inputs for ${\hat{B}}_K$ and $V_{cb}$
• On the Correlations between Flavour Observables in Minimal U(2)^3 Models
• Complete analysis on the next-to-leading order supersymmetric QCD corrections to $B^0-{\bar{B}}^0$ mixing
• CP Violation and Flavour Mixing in the Standard Model -- 1996 Update
• A New Estimate of ${\epsilon }^{\prime }/\epsilon$
• ${\epsilon }_K^{\prime }/{\epsilon }_K$ and $K\to \pi \nu \bar{\nu }$ in a two-Higgs doublet model
• Precision Flavour Physics and Supersymmetry
• Electroweak Corrections to the Charm-Top-Quark Contribution to ${\epsilon }_K$
• Difference of \tilde εand εin fitting the parameters of CKM matrix
• Constraints on R-Parity violating stop couplings from flavor physics
• BK from the lattice with Wilson quarks
• The Physics of $K^0-{\bar{K}}^0$ Mixing: ${\hat{B}}_K$ and $\Delta M_{LS}$ in the Chiral Quark Model
• SU(3) analysis of four-quark operators: $K\to \pi \pi$ and vacuum matrix elements
• The $B_K$ Kaon Parameter in the Chiral Limit
• Updating the Unitarity Triangle: Top Quark Mass Versus Nonperturbative Uncertainties
• The value of B_K from the experimental data on CP-violation in K-mesons and up-to-date values of CKM matrix parameters
• Short-distance QCD corrections to $K^0{\bar{K}}^0$ mixing at next-to-leading order in Left-Right models
• Demise of CKM & its aftermath
• Global CKM Fits with the Scan Method
• CKM matrix and CP violation in B-mesons
• ${\epsilon }_K$ and ${\epsilon }^{\prime }/\epsilon$ in a diquark model
• Effective Weak Chiral Lagrangian to $\mathcal{O}(p^4)$ in the Chiral Quark Model
• Probing New Physics in Charm Couplings with FCNC
• Power corrections to the CP-violation parameter ${\epsilon }_K$
• $\Delta S=1,2$ Effective Weak Chiral Lagrangian from the Instanton Vacuum
• B_K in the chiral limit within the 1/Nc expansion
• CP Violation and Flavour Mixing in the Standard Model
• Theoretical status of epsilon'/epsilon
• Unitarity Triangle from CP invariant quantities
• CKM Matrix and Standard-Model CP Violation
• New constraints on R-parity violating couplings through the measurements of the $B_{s(d)}^0$-${\bar{B}}_{s(d)}^0$ and $K^0$-${\bar{K}}^0$ mixing
• Estimate of B(K -> pi nu nubar) from Standard Model fits to lambda_t
• $b\to ss\bar{d}$ decay in Randall-Sundrum models
• Semi-aligned two Higgs doublet model
• Long-distance contributions to weak amplitudes
• Challenges for New Physics in the Flavour Sector
• Impact of Delta mB_s on the determination of the unitary triangle and bounds on physics beyond the Standard Model
• K0-K0bar on the Lattice
• Two-loop Electroweak Corrections to the Top-Quark Contribution to ${\epsilon }_K$
• Probing CKM parameters through unitarity, ε_K and Δm_{B_{d,s}}
• Kaon Decays from AdS/QCD
• Quark-hadron duality for $K^0-\overline{K^0}$ mixing
• Next-to-leading order short distance QCD corrections to the effective $\Delta S=2$ Hamiltonian, implications for the $K_L$-$K_S$ mass difference