Four-point functions and kaon decays in a minimal AdS/QCD model

Abstract

We study the predictions of holographic QCD for various observable four-point quark flavour current-current correlators. The dual 5-dimensional bulk theory we consider is a $SU(3{)}_L\times SU(3{)}_R$ Yang Mills theory in a slice of $Ad{S}_5$ spacetime with boundaries. Particular UV and IR boundary conditions encode the spontaneous breaking of the dual 4D global chiral symmetry down to the $SU(3{)}_V$ subgroup. We explain in detail how to calculate the 4D four-point quark flavour current-current correlators using the 5D holographic theory, including interactions. We use these results to investigate predictions of holographic QCD for the $\Delta I=1/2$ rule for kaon decays and the $B_K$ parameter. The results agree well in comparison with experimental data, with an accuracy of 25% or better. The holographic theory automatically includes the contributions of the meson resonances to the four-point correlators. The correlators agree well in the low-momentum and high-momentum limit, in comparison with chiral perturbation theory and perturbative QCD results, respectively.

Published version, title changed to conform with Journal format, references and clarifying remarks added, 40 pages, 5 figures

References in corpus (68)

• Gauge Theory Correlators from Non-Critical String Theory
• Large N Field Theories, String Theory and Gravity
• Weak Decays Beyond Leading Logarithms
• Low energy hadron physics in holographic QCD
• QCD and a Holographic Model of Hadrons
• Linear Confinement and AdS/QCD
• Hard Scattering and Gauge/String Duality
• Chiral symmetry breaking from five dimensional spaces
• More on a holographic dual of QCD
• Chiral Symmetry Breaking and Pions in Non-Supersymmetric Gauge/Gravity Duals
• Towards a holographic dual of large-N_c QCD
• The Pomeron and Gauge/String Duality
• Deep Inelastic Scattering and Gauge/String Duality
• Meson Spectroscopy in AdS/CFT with Flavour
• Hadronic Spectrum of a Holographic Dual of QCD
• Supersymmetric Gauge Theories and the AdS/CFT Correspondence
• The Anatomy of ${\epsilon }^{\prime }/\epsilon$ Beyond Leading Logarithms with Improved Hadronic Matrix Elements
• The Two-Loop Anomalous Dimension Matrix for $\Delta S=1$ Weak Non-Leptonic Decays I: $\mathcal{O}({\alpha }_s^2)$
• Two--Loop Anomalous Dimension Matrix for $\Delta S=1$ Weak Non-Leptonic Decays II: $\mathcal{O}({\alpha }_e{\alpha }_s)$
• Enhancement of the $K_L$ -- $K_S$ Mass Difference by Short Distance QCD Corrections Beyond Leading Logarithms
• QCD and dimensional deconstruction
• Light-Front Hadron Dynamics and AdS/CFT Correspondence
• Quantum Field Theory and Unification in AdS5
• The Complete |Delta S|=2 Hamiltonian in the Next-To-Leading Order
• Interpolating between low and high energy QCD via a 5D Yang-Mills model
• ${\epsilon }^{\prime }/\epsilon$ at the next-to-leading order in QCD and QED
• The scalar and pseudoscalar sector in a five-dimensional approach to chiral symmetry breaking
• Indirect CP-Violation in the Neutral Kaon System Beyond Leading Logarithms
• Holographic Model for Hadrons in Deformed AdS5 Background
• The Standard Model Prediction for epsilon'/epsilon
• Weak $K$--Amplitudes in the Chiral and $1/N_c$--Expansions
• Tensors Mesons in AdS/QCD
• K0-anti-K0 mixing in the 1/Nc expansion
• Lattice QCD with two dynamical flavors of domain wall quarks
• Kaon B parameter from quenched domain-wall QCD
• The Delta I = 1/2 Rule and B_K at O(p^4) in the Chiral Expansion
• The $\Delta I=1/2$ Rule in the Chiral Limit
• epsilon'/epsilon in the Chiral Limit
• Delta I=1/2 and epsilon'/epsilon in Large-Nc QCD
• Perfecting the Ultra-violet of Holographic Descriptions of QCD
• Holographic decays of large-spin mesons
• $K\to 3\pi$ Decays in Chiral Perturbation Theory
• The $B_K$ Parameter in the $1/N_c$ Expansion
• Analysis of ε'/εin the 1/N_c Expansion
• Hard Scattering in the M-Theory Dual for the QCD String
• The Gross-Neveu Model from String Theory
• 1/N_c Corrections to the Hadronic Matrix Elements of Q_6 and Q_8 in K --> pi pi Decays
• Heavy-Light Mesons from the AdS/CFT Correspondence
• On the Delta I = 1/2 Rule in Holographic QCD
• Long-distance dimension-eight operators in B_K
• Scheme Dependence of Weak Matrix Elements in the $1/N_c$ Expansion
• Improving the Infra-red of Holographic Descriptions of QCD
• A precise determination of $B_K$ in quenched QCD
• Three Flavour QCD from the Holographic Principle
• New Analysis of the Delta I = 1/2 Rule in Kaon Decays and the B_K Parameter
• Scalar effective potential for D7 brane probes which break chiral symmetry
• QCD and String Theory
• On the Couplings of the Rho Meson in AdS/QCD
• $B_K$ and Explicit Chiral Symmetry Breaking
• Sea quark effects in B_K from N_f=2 clover-improved Wilson fermions
• A Gravity Dual of Chiral Symmetry Breaking
• Testing improved staggered fermions with $m_s$ and $B_K$
• BK from the lattice with Wilson quarks
• The $B_K$ Kaon Parameter in the Chiral Limit
• Building a "holographic dual" to QCD in the AdS${}_5$: instantons and confinement
• Hadron Spectroscopy and Wavefunctions in QCD and the AdS/CFT Correspondence
• Kaon B-parameter with NF=2 dynamical Wilson fermions
• Calculating $B_K$ using a mixed action

Cited by in corpus (24)

• Light-Front Dynamics and AdS/QCD Correspondence: The Pion Form Factor in the Space- and Time-Like Regions
• Meson wave function from holographic models
• Pion Form Factor in Improved Holographic QCD Backgrounds
• Hadrons in AdS / QCD correspondence
• Anomalous Form Factor of the Neutral Pion in Extended AdS/QCD Model with Chern-Simons Term
• Pion in the Holographic Model with 5D Yang-Mills Fields
• Strange mesons and kaon-to-pion transition form factors from holography
• Holographic Nuclear Matter in AdS/QCD
• Confront Holographic QCD with Regge Trajectories of vectors and axial-vectors
• Meson-Nucleon Coupling from AdS/QCD
• Hadron structure functions at small $x$ from string theory
• Deep inelastic scattering from polarized spin-$1/2$ hadrons at low $x$ from string theory
• Deep inelastic scattering cross sections from the gauge/string duality
• Quark Wigner Distributions and GTMDs of Pion in the Light-Front Holographic Model
• Weak-Interacting Holographic QCD
• Holographic QCD beyond the leading order
• Deep inelastic scattering off scalar mesons in the 1/N expansion from the D3D7-brane system
• A holographic approach to low-energy weak interactions of hadrons
• Strange meson form factors in holographic QCD
• Four-point vector correlators and AdS/QCD correspondence
• Charmonium sum rules applied to a holographic model
• Four-point correlator of vector currents and electric current susceptibility in holographic QCD
• Kaon Decays from AdS/QCD
• ADS/CFT Applied To Vector Meson Emission From A Heavy Accelerated Nucleus