The Complete |Delta S|=2 Hamiltonian in the Next-To-Leading Order

Abstract

We present the complete next-to-leading order short-distance QCD corrections to the effective \dstwo -hamiltonian in the Standard Model. The calculation of the coefficient ${\eta }_3$ is described in great detail. It involves the two-loop mixing of bilocal structures composed of two \dsone\ operators into \dstwo\ operators. The next-to-leading order corrections enhance ${\eta }_3$ by 27\% to $η_3=0.47 \errorpm{+0.03}{-0.04}$ thereby affecting the phenomenology of ${\epsilon }_K$ sizeably. ${\eta }_3$ depends on the physical input parameters $m_t$, $m_c$ and $\laMSb$ only weakly. The quoted error stems from renormalization scale dependences, which have reduced compared to the old leading log result. The known calculation of ${\eta }_1$ and ${\eta }_2$ is repeated in order to compare the structure of the three QCD coefficients. We further discuss some field theoretical aspects of the calculation such as the renormalization group equation for Green's functions with two operator insertions and the renormalization scheme dependence caused by the presence of evanescent operators.

68 pages, requires LaTeX2e and the standard LaTeX-packages epsf.sty, rotate.sty, a4.sty, subeqn.sty, cite.sty, array.sty, dcolumn.sty; Figures are submitted as a seperate tar.gz-file. A complete PostScript version may be obtained from ftp://feynman.t30.physik.tu-muenchen.de/pub/preprints/tum-86-96.ps.gz or ftp://feynman.t30.physik.tu-muenchen.de/pub/preprints/tum-86-96.ps2.gz (scaled down and rotated version to print two pages on one sheet of paper). Source available at ftp://feynman.t30.physik.tu-muenchen.de/pub/preprints/tum-86-96.tar.gz

References in corpus (11)

• Heavy Quark Effective Theory beyond Perturbation Theory: Renormalons, the Pole Mass and the Residual Mass Term
• The Pole Mass of The Heavy Quark. Perturbation Theory and Beyond
• The Two-Loop Anomalous Dimension Matrix for $\Delta S=1$ Weak Non-Leptonic Decays I: $\mathcal{O}({\alpha }_s^2)$
• Waiting for the Top Quark Mass, K^+ --> π^+ ν\barν, B_s^0-\bar{B}_s^0 Mixing and CP Asymmetries in B-Decays
• Reduced Effective Lagrangians
• Enhancement of the $K_L$ -- $K_S$ Mass Difference by Short Distance QCD Corrections Beyond Leading Logarithms
• The Rare Decays $K^{+}\to {\pi }^{+}\nu \bar{\nu }$\ and $K_L\to {\mu }^{+}{\mu }^{-}$\ Beyond Leading Logarithms
• Evanescent Operators, Scheme Dependences and Double Insertions
• Indirect CP-Violation in the Neutral Kaon System Beyond Leading Logarithms
• Equations of Motion for Effective Lagrangians and Penguins in Rare B-Decays
• Indirect CP-Violation in the Neutral Kaon System Beyond Leading Logarithms and Related Topics

Cited by in corpus (120)

• Universal Unitarity Triangle and Physics Beyond the Standard Model
• Kaon Decays in the Standard Model
• Left-Right Symmetry at LHC
• 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
• 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
• Correlations among new CP violating effects in Delta F = 2 observables
• The Impact of Universal Extra Dimensions on the Unitarity Triangle and Rare K and B Decays
• Effects of mixing with quark singlets
• Rare K and B Decays in a Warped Extra Dimension with Custodial Protection
• Charged-Higgs phenomenology in the Aligned two-Higgs-doublet model
• Low-energy effective field theory below the electroweak scale: matching at one loop
• 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
• Flavor Physics in the Randall-Sundrum Model: II. Tree-Level Weak-Interaction Processes
• Electroweak Corrections to the Charm Quark Contribution to K+ -> pi+ nu nu-bar
• Less space for a new family of fermions
• The Anatomy of Quark Flavour Observables in 331 Models in the Flavour Precision Era
• How much space is left for a new family?
• Kaon Matrix Elements and CP-violation from Quenched Lattice QCD: (I) the 3-flavor case
• epsilon'/epsilon and Rare K and B Decays in the MSSM
• QCD Corrections to Flavor-Changing Neutral Currents in the Supersymmetric Standard Model
• Estimating epsilon'/epsilon. A Review
• Two-loop matching of the dipole operators for $b\to s\gamma$ and $b\to sgluon$
• Elementary derivation of a recently proposed integral representation for permanents
• The ultimate theoretical error on gamma from B -> D K decays
• The Standard Model Prediction for epsilon'/epsilon
• 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
• $\Delta M_s/\Delta M_d$, $\sin 2\beta$ 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
• Supersymmetric Explanation of CP Violation in $K\to \pi \pi$ Decays
• Standard Model Confronting New Results for epsilon'/epsilon
• Neutral kaon mixing from 2+1 flavor Domain Wall QCD
• Standard-model prediction of ${\epsilon }_K$ with manifest CKM unitarity
• Delta F = 2 observables and B -> X_q gamma decays in the Left-Right Model: Higgs particles striking back
• The Delta I = 1/2 Rule and B_K at O(p^4) in the Chiral Expansion
• Phenomenological consequences of radiative flavor violation in the MSSM
• Four-point functions and kaon decays in a minimal AdS/QCD model
• Bounds on the Unitarity Triangle, $\sin 2\beta$ and $K\to \pi \nu \bar{\nu }$ Decays in Models with Minimal Flavour Violation
• The supersymmetric Higgs sector and B-Bbar mixing for large tan beta
• The Gold-plated mode revisited: sin(2 beta) and B^0 to J/Psi K_S in the Standard Model
• Constraints on the Four-Generation Quark Mixing Matrix from a Fit to Flavor-Physics Data
• Standard Model Predictions for Rare K and B Decays without New Physics Infection
• ${\epsilon }^{\prime }/\epsilon$: three years later
• 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
• Particle-Antiparticle Mixing, ε_K and the Unitarity Triangle in the Littlest Higgs Model
• A Lower Bound on sin 2βfrom Minimal Flavour Violation
• Particle-Antiparticle Mixing, CP Violation and Rare K and B Decays in a Minimal Theory of Fermion Masses
• 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
• On the consistency between the observed amount of CP violation in the K- and Bd-systems within minimal flavor violation
• FCNC Processes in the Littlest Higgs Model with T-Parity: an Update
• An updated analysis of eps'/eps in the standard model with hadronic matrix elements from the chiral quark model
• 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-
• Measurements of the $\rho$ and $\eta$ parameters of the $V_{CKM}$ matrix and perspectives
• Determining the Sign of the Z-Penguin Amplitude
• Correlators of left charges and weak operators in finite volume chiral perturbation theory
• Correlations between epsilon'/epsilon and Rare K Decays in the Littlest Higgs Model with T-Parity
• The Anatomy of Neutral Scalars with FCNCs in the Flavour Precision Era
• Determination of the CKM angle gamma and |V_{ub}/V_{cb}| from inclusive direct CP asymmetries and branching ratios in charmless B decays
• Combined analysis of the unitarity triangle and CP violation in the Standard Model
• Novel CP-violating Effects in B decays from Charged-Higgs in a Two-Higgs Doublet Model for the Top Quark
• Leptonic Decays of Heavy Quarks on the Lattice
• Flavour Theory: 2009
• Flavor signatures of isosinglet vector-like down quark model
• Constraints on $Z^{\prime }$ Boson within Minimal Flavor Violation
• On the Correlations between Flavour Observables in Minimal U(2)^3 Models
• Standard Model evaluation of ${\epsilon }_K$ using lattice QCD inputs for ${\hat{B}}_K$ and $V_{cb}$
• Towards a Next-to-Next-to-Leading Order analysis of matching in $B^0$-${\bar{B}}^0$ mixing
• Exact Chiral Symmetry on the Lattice: QCD Applications
• Dispersive analysis of neutral meson mixing
• General squark flavour mixing: constraints, phenomenology and benchmarks
• FCNC, CP violation and implications for some rare decays in an SU(4)_L X U(1)_X extension of the standard model
• Electroweak Corrections to the Charm-Top-Quark Contribution to ${\epsilon }_K$
• Two Higgs Bi-doublet Left-Right Model With Spontaneous P and CP Violation
• Difference of \tilde εand εin fitting the parameters of CKM matrix
• Constraints on R-Parity violating stop couplings from flavor physics
• SU(3) analysis of four-quark operators: $K\to \pi \pi$ and vacuum matrix elements
• The $B_K$ Kaon Parameter in the Chiral Limit
• The Physics of $K^0-{\bar{K}}^0$ Mixing: ${\hat{B}}_K$ and $\Delta M_{LS}$ in the Chiral Quark Model
• Prospects and Constraints for Vector-like MFV Matter at LHC
• Updated evaluation of ${\epsilon }_K$ in the Standard Model with lattice QCD inputs
• Probing Yukawa Unification with K and B Mixing
• Short-distance QCD corrections to $K^0{\bar{K}}^0$ mixing at next-to-leading order in Left-Right models
• Next-to-Leading Order QCD corrections to $B\bar{B}$-mixing and ${\epsilon }_K$ within the MSSM
• Global CKM Fits with the Scan Method
• Weak mixing below the weak scale in dark-matter direct detection
• Dimension 7 operators in the b to s transition
• Predictions for b -> ssdbar, ddsbar decays in the SM and with new physics
• Effective Weak Chiral Lagrangian to $\mathcal{O}(p^4)$ in the Chiral Quark Model
• Kaon mixing and the charm mass
• Power corrections to the CP-violation parameter ${\epsilon }_K$
• One-loop matching of Delta S=2 four-quark operators with improved staggered fermions
• $\Delta S=1,2$ Effective Weak Chiral Lagrangian from the Instanton Vacuum
• B_K in the chiral limit within the 1/Nc expansion
• Estimating eps'/eps in the standard model independently of Im λ_t
• Theoretical status of epsilon'/epsilon
• Unitarity Triangle from CP invariant quantities
• On the QCD corrections to Delta F=2 FCNC in the Supersymmetric SM with hierarchical squark masses
• 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
• Semi-aligned two Higgs doublet model
• $b\to ss\bar{d}$ decay in Randall-Sundrum models
• Challenges for New Physics in the Flavour Sector
• K0-K0bar on the Lattice
• b \to ss\bar{d}$ in a Vector Quark Model
• Testing spin-2 mediator by angular observables in $b\to s{\mu }^{+}{\mu }^{-}$
• Kaon physics overview
• Theoretical uncertainties for weak decays: higher dimension operators
• Phenomenology of epsilon_K in the top era
• The charm-quark contribution to epsilon_K and Delta M_K