Anatomy of ${\epsilon }^{\prime }/\epsilon$ beyond the Standard Model

Abstract

We present for the first time a model-independent anatomy of the ratio ${\epsilon }^{\prime }/\epsilon$ in the context of the $\Delta S=1$ effective theory with operators invariant under QCD and QED and in the context of the Standard Model Effective Field Theory (SMEFT) with the operators invariant under the full SM gauge group. Our goal is to identify the new physics scenarios that are probed by this ratio and which could help to explain a possible deviation from the SM that is hinted by the data. To this end we derive a master formula for ${\epsilon }^{\prime }/\epsilon$, which can be applied to any theory beyond the Standard Model (BSM) in which the Wilson coefficients of all contributing operators have been calculated at the electroweak scale. The relevant hadronic matrix elements of BSM operators are from the Dual QCD approach and the SM ones from lattice QCD. Within SMEFT, the constraints from $K^0$ and $D^0$ mixing as well as electric dipole moments limit significantly potential new physics contributions to ${\epsilon }^{\prime }/\epsilon$. Correlations of ${\epsilon }^{\prime }/\epsilon$ with $K\to \pi \nu \bar{\nu }$ decays are briefly discussed. Building on our EFT analysis and the model-independent constraints, we discuss implications of a possible deviation from the SM in ${\epsilon }^{\prime }/\epsilon$ for model building, highlighting the role of the new scalar and tensor matrix elements in models with scalar mediators.

arXiv comment47 pages, 4 figures. v3: signs in tables 6-10 corrected, numerical results and conclusions unchanged

References in corpus (77)

• Weak Decays Beyond Leading Logarithms
• Dimension-Six Terms in the Standard Model Lagrangian
• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of summer 2016
• Renormalization Group Evolution of the Standard Model Dimension Six Operators III: Gauge Coupling Dependence and Phenomenology
• Renormalization Group Evolution of the Standard Model Dimension Six Operators II: Yukawa Dependence
• Renormalization Group Evolution of the Standard Model Dimension Six Operators I: Formalism and lambda Dependence
• A Revised Experimental Upper Limit on the Electric Dipole Moment of the Neutron
• The $\Delta S=1$ Effective Hamiltonian Including Next-to-Leading Order QCD and QED Corrections
• Photonic penguins at two loops and m_t-dependence of BR[ B -> X_s l^+ l^-]
• Low-Energy Effective Field Theory below the Electroweak Scale: Operators and Matching
• Kaon Decays in the Standard Model
• Effective description of general extensions of the Standard Model: the complete tree-level dictionary
• The Anatomy of ${\epsilon }^{\prime }/\epsilon$ Beyond Leading Logarithms with Improved Hadronic Matrix Elements
• Two-Loop QCD Anomalous Dimensions of Flavour-Changing Four-Quark Operators Within and Beyond the Standard Model
• Low-Energy Effective Field Theory below the Electroweak Scale: Anomalous Dimensions
• The Two-Loop Anomalous Dimension Matrix for $\Delta S=1$ Weak Non-Leptonic Decays I: $\mathcal{O}({\alpha }_s^2)$
• Effective Hamiltonian for Non-Leptonic |Delta F| = 1 Decays at NNLO in QCD
• Baryon Number and Lepton Universality Violation in Leptoquark and Diquark Models
• Two--Loop Anomalous Dimension Matrix for $\Delta S=1$ Weak Non-Leptonic Decays II: $\mathcal{O}({\alpha }_e{\alpha }_s)$
• A precision measurement of direct CP violation in the decay of neutral kaons into two pions
• Wilson: a Python package for the running and matching of Wilson coefficients above and below the electroweak scale
• 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
• Beta Decays and Non-Standard Interactions in the LHC Era
• DsixTools: The Standard Model Effective Field Theory Toolkit
• Matching of gauge invariant dimension 6 operators for $b\to s$ and $b\to c$ transitions
• Standard-model prediction for direct CP violation in $K\to \pi \pi$ decay
• ${\epsilon }^{\prime }/\epsilon$ at the next-to-leading order in QCD and QED
• Neutron EDM from Electric and Chromoelectric Dipole Moments of Quarks
• Precise Measurements of Direct CP Violation, CPT Symmetry, and Other Parameters in the Neutral Kaon System
• Right-handed charged currents in the era of the Large Hadron Collider
• B physics Beyond the Standard Model at One Loop: Complete Renormalization Group Evolution below the Electroweak Scale
• Epsilon_K at Next-to-Next-to-Leading Order: The Charm-Top-Quark Contribution
• $K\to \pi \pi$ $\Delta I=3/2$ decay amplitude in the continuum limit
• WCxf: an exchange format for Wilson coefficients beyond the Standard Model
• Iso-vector and Iso-scalar Tensor Charges of the Nucleon from Lattice QCD
• Simplified models with baryon number violation but no proton decay
• Patterns of Flavour Violation in Models with Vector-Like Quarks
• Implications of the LHCb Evidence for Charm CP Violation
• Quark flavour observables in the Littlest Higgs model with T-parity after LHC Run 1
• $K_L-K_S$ mass difference from lattice QCD
• Flavor Violation Tests of Warped/Composite SM in the Two-Site Approach
• Flavor diagonal tensor charges of the nucleon from 2+1+1 flavor lattice QCD
• Improved anatomy of epsilon'/epsilon in the Standard Model
• Isospin violation in epsilon'
• Nucleon charges with dynamical overlap fermions
• Combining K-\bar K mixing and D-\bar D mixing to constrain the flavor structure of new physics
• Effects of finite volume on the $K_L$-$K_S$ mass difference
• Combining Direct & Indirect Kaon CP Violation to Constrain the Warped KK Scale
• Isospin Breaking in B -> K^* gamma Decays
• ΔS=2 and ΔC=2 bag parameters in the SM and beyond from Nf=2+1+1 twisted-mass LQCD
• Global Effective-Field-Theory analysis of New-Physics effects in (semi)leptonic kaon decays
• Yukawa enhancement of $Z$-mediated New Physics in $\Delta S=2$ and $\Delta B=2$ Processes
• An ${\epsilon }^{\prime }$ improvement from right-handed currents
• Isospin Breaking in K -> Pi Pi Decays
• Supersymmetric Explanation of CP Violation in $K\to \pi \pi$ Decays
• How large can the SM contribution to CP violation in $D^0-{\bar{D}}^0$ mixing be?
• Neutral Kaon Mixing Beyond the Standard Model with $n_f=2+1$ Chiral Fermions Part 1: Bare Matrix Elements and Physical Results
• Revisiting Kaon Physics in General $Z$ Scenario
• Studying ${\epsilon }^{\prime }/\epsilon$ in the Chiral Quark Model: ${\gamma }_5$-Scheme Independence and NLO Hadronic Matrix Elements
• Chargino contributions in light of recent ${\epsilon }^{\prime }/\epsilon$
• Gluino-mediated electroweak penguin with flavor-violating trilinear couplings
• Electroweak Penguin Contributions to Non-Leptonic Delta F = 1 Decays at NNLO
• Singularity-free Next-to-leading Order $\Delta S=1$ Renormalization Group Evolution and ${\epsilon }_K^{\prime }/{\epsilon }_K$ in the Standard Model and Beyond
• flavio: a Python package for flavour and precision phenomenology in the Standard Model and beyond
• Charming CP Violation and Dipole Operators from RS Flavor Anarchy
• ${\epsilon }^{\prime }/\epsilon$ from charged-Higgs-induced gluonic dipole operators
• Neutral kaon mixing beyond the standard model with nf=2+1 chiral fermions
• QCD Corrections to Quark (Chromo)Electric Dipole Moments in High-scale Supersymmetry
• $\Delta F=1$ constraints on composite Higgs models with LR parity
• New Physics Patterns in ${\epsilon }^{\prime }/\epsilon$ and ${\epsilon }_K$ with Implications for Rare Kaon Decays and $\Delta M_K$
• Dipole operator constraints on composite Higgs models
• BSM Hadronic Matrix Elements for ${\epsilon }^{\prime }/\epsilon$ and $K\to \pi \pi$ Decays in the Dual QCD Approach
• Towards NNLO accuracy for ${\epsilon }^{\prime }/\epsilon$
• Anomalous triple gauge couplings from $B$-meson and kaon observables
• $K\to \pi$ matrix elements of the chromomagnetic operator on the lattice

Cited by in corpus (28)

• B-decay discrepancies after Moriond 2019
• On the Importance of NNLO QCD and Isospin-breaking Corrections in ${\epsilon }^{\prime }/\epsilon$
• $b\to s{\ell }^{+}{\ell }^{-}$ Transitions in Two-Higgs-Doublet Models
• Effective field theory interpretation of lepton magnetic and electric dipole moments
• Model-independent bounds on new physics effects in non-leptonic tree-level decays of B-mesons
• Master formula for ${\epsilon }^{\prime }/\epsilon$ beyond the Standard Model
• flavio: a Python package for flavour and precision phenomenology in the Standard Model and beyond
• Correlating ${\epsilon }^{\prime }/\epsilon$ to hadronic $B$ decays via $U(2{)}^3$ flavour symmetry
• Quantum tops at circular lepton colliders
• Left-handed color-sextet diquark in the Kaon system
• Beyond Jarlskog: 699 invariants for CP violation in SMEFT
• ${\epsilon }^{\prime }/\epsilon$ in the Standard Model at the Dawn of the 2020s
• Quark-Lepton Connections in $Z^{\prime }$ Mediated FCNC Processes: Gauge Anomaly Cancellations at Work
• The direct CP violation in a general two Higgs doublet model
• Opportunistic CP Violation
• Rank-One Flavor Violation and B-meson anomalies
• BSM Master Formula for ${\epsilon }^{\prime }/\epsilon$ in the WET Basis at NLO in QCD
• Effect of the Pauli exclusion principle in the electric dipole moment of ${}^9$Be with $|\Delta S|=1$ interactions
• Flavour Violating Effects of Yukawa Running in SMEFT
• Kaon Physics Without New Physics in ${\epsilon }_K$
• Another SMEFT Story: $Z^{\prime }$ Facing New Results on ${\epsilon }^{\prime }/\epsilon$, $\Delta M_K$ and $K\to \pi \nu \bar{\nu }$
• Master formula for one-loop renormalization of bosonic SMEFT operators
• Doubling down on down-type diquarks
• Nuclear EDM from SMEFT flavor-changing operator
• Kaon physics overview
• ${\epsilon }^{\prime }/\epsilon$ in and beyond the Standard Model
• General non-leptonic $\Delta F=1$ WET at the NLO in QCD
• The Optimal Strategy for ${\epsilon }^{\prime }/\epsilon$ in the SM: 2019