QCD Isospin Breaking in Meson Masses, Decay Constants and Quark Mass Ratios

Abstract

The procedure to calculate masses and matrix-elements in the presence of mixing of the basis states is explained in detail. We then apply this procedure to the two-loop calculation in Chiral Perturbation Theory of pseudoscalar masses and decay constants including quark mass isospin breaking. These results are used to update our analysis of $K_{\ell 4}$ done previously and obtain a value of $m_u/m_d$ in addition to values for the low-energy-constants $L_i^r$.

22 pages, uses axodraw.sty

Cited by in corpus (146)

• FLAG Review 2019
• FLAG Review 2021
• QCD and strongly coupled gauge theories: challenges and perspectives
• 2+1 Flavor Lattice QCD toward the Physical Point
• Review of lattice results concerning low energy particle physics
• From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance
• Kaon Decays in the Standard Model
• Light pseudoscalar decay constants, quark masses, and low energy constants from three-flavor lattice QCD
• Meson-meson scattering within one loop Chiral Perturbation Theory and its unitarization
• Flavor Physics in the Quark Sector
• Finite volume effects for meson masses and decay constants
• Octet baryon masses and sigma terms from an SU(3) chiral extrapolation
• Mesonic low-energy constants
• $\pi \pi$ Scattering in Three Flavour ChPT
• Vus from pi and K decay constants in full lattice QCD with physical u, d, s and c quarks
• Flavour-symmetry breaking of the quark condensate and chiral corrections to the Gell-Mann-Oakes-Renner relation
• Strangeness-changing scalar form factors
• A new measurement of K+(e4) decay and the s-wave pi-pi-scattering length a00
• $K_{\ell 3}$ decays in Chiral Perturbation Theory
• Pion and Kaon Electromagnetic Form Factors
• f_B and f_B_s from QCD sum rules
• Chiral Perturbation Theory Beyond One Loop
• Electromagnetic mass splittings of the low lying hadrons and quark masses from 2+1 flavor lattice QCD+QED
• The < S P P > Green function and SU(3) breaking in K_{l3} decays
• Chiral perturbation theory
• $\eta \to 3\pi$ at Two Loops In Chiral Perturbation Theory
• Non-perturbative quark mass renormalization in two-flavor QCD
• High statistics measurement of Ke4 decay properties
• First determination of the strange and light quark masses from full lattice QCD
• Octet baryon masses in next-to-next-to-next-to-leading order covariant baryon chiral perturbation theory
• Strange and non-strange quark mass dependence of elastic light resonances from SU(3) Unitarized Chiral Perturbation Theory to one loop
• Meson resonances, large N_c and chiral symmetry
• Varying the light quark mass: impact on the nuclear force and Big Bang nucleosynthesis
• A note on isospin violation in Pl2(gamma) decays
• Isospin Breaking in K -> Pi Pi Decays
• QCD Short-distance Constraints and Hadronic Approximations
• FLAG Review 2024
• Isospin breaking effects due to the up-down mass difference in Lattice QCD
• Chiral extrapolation of light resonances from one and two-loop unitarized Chiral Perturbation Theory versus lattice results
• Electromagnetic corrections in eta --> 3 pi decays
• Charmonium properties from lattice QCD + QED: hyperfine splitting, $J/\psi$ leptonic width, charm quark mass and $a_{\mu }^c$
• Low-energy interactions of Nambu-Goldstone bosons with $D$ mesons in covariant chiral perturbation theory
• $\pi K$ Scattering in Three Flavour ChPT
• Dispersion Relation Bounds for pi pi Scattering
• Baryon mass splittings and strong CP violation in SU(3) Chiral Perturbation Theory
• A new determination of α_s from hadronic τ decays
• Analytical dispersive construction of $\eta \to 3\pi$ amplitude: First order in isospin breaking
• Scalar strangeness content of the nucleon and baryon sigma terms
• Magnetic form factors of the octet baryons from lattice QCD and chiral extrapolation
• Three-body Final State Interaction in $\eta \to 3\pi$
• Improved Determination of the Electroweak Penguin Contribution to epsilon'/epsilon in the Chiral Limit
• A new global fit of the $L_i^r$ at next-to-next-to-leading order in Chiral Perturbation Theory
• $K\to 3\pi$ Decays in Chiral Perturbation Theory
• Thermal rho and sigma mesons from chiral symmetry and unitarity
• Integrating out strange quarks in ChPT
• Determination of <2pi_{I=2}|Q_{7,8}|K0> in the Chiral Limit
• Precise Measurement of the Pion Axial Form Factor in the Pi+ -> e+ nu gamma Decay
• Meson-meson Scattering in QCD-like Theories
• Electric form factors of the octet baryons from lattice QCD and chiral extrapolation
• Strange Quark Mass from Pseudoscalar Sum Rule with O(alpha_s^4) Accuracy
• Towards a determination of the chiral couplings at NLO in 1/N(C): L_8(mu) and C_38(mu)
• On the Radiative Pion Decay
• Axial-vector Form Factors for $K_{\ell 2\gamma }$ and ${\pi }_{\ell 2\gamma }$ at $O(p^6)$ in Chiral Perturbation Theory
• Matching Chiral Perturbation Theory and the Dispersive Representation of the Scalar Kpi Form Factor
• Improved Analysis of J/psi Decays into a Vector Meson and Two Pseudoscalars
• Partial waves and large $N_C$ resonance sum rules
• α_S from $F_{\pi }$ and Renormalization Group Optimized Perturbation
• Three-body final state interaction in $\eta \to 3\pi$ updated
• Tests of non-standard electroweak couplings of right-handed quarks
• The Kl3 scalar form factors in the standard model
• Scalar Form Factors in SU(3) Chiral Perturbation Theory
• Electromagnetic Corrections in Partially Quenched Chiral Perturbation Theory
• Kaon semileptonic vector form factor and determination of |V_{us}| using staggered fermions
• Three-Flavor Partially Quenched Chiral Perturbation Theory at NNLO for Meson Masses and Decay Constants
• Isospin Breaking in $K\to 3\pi$ Decays III: Bremsstrahlung and Fit to Experiment
• Scalar susceptibilities and four-quark condensates in the meson gas within Chiral Perturbation Theory
• Chiral extrapolation of pion-pion scattering phase shifts within standard and unitarized Chiral Perturbation Theory
• Interactions of $\pi K$, $\pi \pi K$ and $KK\pi$ systems at maximal isospin from lattice QCD
• Low Energy Chiral Lagrangian in Curved Space-Time from the Spectral Quark Model
• Chiral Extrapolation of the Strangeness Changing K pi Form Factor
• Chiral perturbation theory in a theta vacuum
• Light hadron and diquark spectroscopy in quenched QCD with overlap quarks on a large lattice
• Isospin breaking corrections to low-energy pi-K scattering
• Strong contribution to octet baryon mass splittings
• Decay Constants of Pseudoscalar Mesons to Two Loops in Three-Flavor Partially Quenched $\chi$PT
• Non-factorization of four-quark condensates at low energies within Chiral Perturbation Theory
• The SU(2) and SU(3) chiral phase transitions within Chiral Perturbation Theory
• The Pseudoscalar Meson Mass to Two Loops in Three-Flavor Partially Quenched $\chi$PT
• Isospin Breaking in the Relation Between the tau-->nu_tau pi pi and e^+e^- -->pi^+ pi^- Versions of |F_π(s)|^2$ and Implications for (g-2)_mu
• Masses and Decay Constants of Pseudoscalar Mesons to Two Loops in Two-Flavor Partially Quenched Chiral Perturbation Theory
• Strange quark condensate from QCD sum rules to five loops
• Electromagnetic low-energy constants in ChPT
• Finite Volume Dependence of the Quark-Antiquark Vacuum Expectation Value
• Isospin Breaking in $K\to 3\pi$ Decays II: Radiative Corrections
• Chiral extrapolation and determination of low-energy constants from lattice data
• The Energy Momentum Tensor of Chiral Quark Models at Low Energies
• Low-energy pi-pi and pi-K scatterings revisited in three-flavour resummed chiral perturbation theory
• Universal Bounds for SU(3) Low Energy Constants
• Isospin Breaking in $K\to 3\pi$ Decays I: Strong Isospin Breaking
• Patterns of CP violation from mirror symmetry breaking in the $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ Dalitz plot
• Isospin violation in pion-kaon scattering
• The expansion by regions in pi K scattering
• ${\tau }^{-}\to {\eta }^{(\prime )}{\pi }^{-}{\nu }_{\tau }\gamma$ decays as backgrounds in the search for second class currents
• SU(3) breaking in hyperon transition vector form factors
• Isospin Breaking and chiral symmetry restoration
• Corrections to the $\mathbf{SU}(3)\times \mathbf{SU}(3)$ Gell-Mann-Oakes-Renner relation and chiral couplings $L_8^r$ and $H_2^r$
• On the two-loop contributions to the pion mass
• Strong and Electromagnetic Mass Splittings in Heavy Mesons
• The $B_K$ Kaon Parameter in the Chiral Limit
• High energy constraints in the octet SS-PP correlator and resonance saturation at NLO in 1/Nc
• An Analytic Analysis of the Pion Decay Constant in Three-Flavoured Chiral Perturbation Theory
• Precision Test of Quark Mass Textures: A Model Independent Approach
• Isospin odd pi K scattering length
• Two-loop representations of low-energy pion form factors and pi-pi scattering phases in the presence of isospin breaking
• Consistency between SU(3) and SU(2) chiral perturbation theory for the nucleon mass
• Approximating chiral SU(3) amplitudes
• Analysis of $K^{+}\to e^{+}{\nu }_e\gamma$ in light-front quark model and chiral perturbation theory of order $p^6$
• $\sigma$ exchange in the one-boson exchange model involving the ground state octet baryons
• Properties of light resonances from unitarized Chiral perturbation theory: Nc behavior and quark mass dependence
• Masses, Decay Constants and Electromagnetic Form-factors with Twisted Boundary Conditions
• Kaon Thresholds and Two-Flavor Chiral Expansions for Hyperons
• Scalar meson dynamics in Chiral Perturbation Theory
• Scalar Kinetic Mixing and the Renormalization Group
• Study of the Radivative Pion Decay
• The chiral logs of the K -> pi pi amplitude
• Convergence properties of $\eta \to 3\pi$ decays in chiral perturbation theory
• Isospin-Breaking quark condensates in Chiral Perturbation Theory
• Relations at Order $p^6$ in Chiral Perturbation Theory
• Constraints on low energy QCD parameters from $\eta \to 3\pi$ and $\pi \pi$ scattering
• Hadronic string, conformal invariance and chiral symmetry
• The eta mass and NNLO Three-Flavor Partially Quenched Chiral Perturbation Theory
• Chiral expansion of moments of quark distributions
• Properties of the vector meson nonet at large N_c beyond the chiral limit
• Ratios of the light quark masses: Cubic curve vs ellipse
• The role of $U(1{)}_A$ symmetry breaking in the QCD corrections to the pion mass difference
• Analysis of discrepancies in Dalitz plot parameters in eta to 3 pion decay
• A Review of Rare Pion and Muon Decays
• Strongly interacting matter in extreme magnetic fields
• Pion mass dependence of the $K_{l3}$ semileptonic scalar form factor within finite volume
• Bounds on the Light Quark Masses: the scalar channel revisited
• Constraints on 3-flavor QCD order parameters from eta to pi+pi-pi0 decay width
• Chiral Lagrangians
• Chiral dynamics from the hadronic string: general formalism
• Electromagnetic and strong isospin breaking in light meson masses
• Quark Mass Ratios in ChPT with the Difference of Quark Condensates Considered
• Scalar and pseudoscalar correlators in Resonance Chiral Theory