Integrating out strange quarks in ChPT

Abstract

We study three flavour chiral perturbation theory in a limit where the strange quark mass is much larger than the external momenta and the up and down quark masses, and where the external fields are those of two-flavour chiral perturbation theory. In this case, the theory reduces to the one of SU(2)_L x SU(2)_R. Through this reduction, one can work out the strange quark mass dependence of the LECs in the two-flavour case. We present the pertinent relations at two-loop order for F,B and l_i.

14 pages, 3 figures, References added. Due to a typo in a form program, we missed a finite, scale independent part in l_7. Is now included. Version to appear in Phys.Lett.B

References in corpus (27)

• ππscattering
• The Mesonic Chiral Lagrangian of Order $p^6$
• Towards a consistent estimate of the chiral low-energy constants
• Renormalization of chiral perturbation theory to order p^6
• $\pi \pi$ Scattering in Three Flavour ChPT
• Resonance estimates of O(p^6) low-energy constants and QCD short-distance constraints
• QCD Isospin Breaking in Meson Masses, Decay Constants and Quark Mass Ratios
• $K_{\ell 3}$ decays in Chiral Perturbation Theory
• A sum rule approach to the violation of Dashen's theorem
• Pion and Kaon Electromagnetic Form Factors
• Two-point Functions at Two Loops in Three Flavour Chiral Perturbation Theory
• Chiral Perturbation Theory Beyond One Loop
• The < S P P > Green function and SU(3) breaking in K_{l3} decays
• Order p^6 chiral couplings from the scalar K Pi form factor
• <VAP> Green Function in the Resonance Region
• Chiral extrapolations of baryon masses for unquenched three-flavor lattice simulations
• Decays of the pi+ pi- atom
• Paramagnetic effect of light quark loops on Chiral Symmetry Breaking
• QCD Short-distance Constraints and Hadronic Approximations
• Resumming QCD vacuum fluctuations in three-flavour Chiral Perturbation Theory
• Relativistic effects in the pionium lifetime
• Scalar Form Factors in SU(3) Chiral Perturbation Theory
• Tests of the naturalness of the coupling constants in ChPT at order p^6
• Flavour Stability of the Chiral Vacuum and Scalar Meson Dynamics
• Chiral order and fluctuations in multi-flavour QCD
• Finite Volume Dependence of the Quark-Antiquark Vacuum Expectation Value
• The expansion by regions in pi K scattering

Cited by in corpus (42)

• FLAG Review 2019
• Review of lattice results concerning low energy particle physics
• Physical Results from 2+1 Flavor Domain Wall QCD and SU(2) Chiral Perturbation Theory
• Mesonic low-energy constants
• $\Delta I=1/2$ rule for kaon decays derived from QCD infrared fixed point
• Chiral expansions of the pi0 lifetime
• New insights into the neutron electric dipole moment
• Singular values of the Dirac operator in dense QCD-like theories
• A new global fit of the $L_i^r$ at next-to-next-to-leading order in Chiral Perturbation Theory
• Aspects of meson-baryon scattering in three- and two-flavor chiral perturbation theory
• Determination of the Chiral Couplings L_10 and C_87 from Semileptonic Tau Decays
• Results for light pseudoscalar mesons
• Two-loop analysis of the pion-mass dependence of the $\rho$ meson
• Chiral Extrapolation of the Strangeness Changing K pi Form Factor
• Non-factorization of four-quark condensates at low energies within Chiral Perturbation Theory
• Integrating out strange quarks in ChPT: terms at order p^6
• $O(p^6)$ extension of the large--$N_C$ partial wave dispersion relations
• Electromagnetic low-energy constants in ChPT
• A Combined NNLO Lattice-Continuum Determination of $L_{10}^r$
• Determining the chiral condensate from the distribution of the winding number beyond topological susceptibility
• NNLO low-energy constants from flavor-breaking chiral sum rules based on hadronic tau-decay data
• On the two-loop contributions to the pion mass
• An Analytic Analysis of the Pion Decay Constant in Three-Flavoured Chiral Perturbation Theory
• Finite-size scaling for the left-current correlator with non-degenerate quark masses
• Quark Mass dependence at Two Loops for Meson Properties
• Approximating chiral SU(3) amplitudes
• Status of Strong ChPT
• Status of chiral perturbation theory for light mesons
• Relations between SU(2)- and SU(3)-LECs in chiral perturbation theory
• Chiral Limit and Light Quark Masses in 2+1 Flavor Domain Wall QCD
• On the low energy end of the QCD spectrum
• New method for fitting the low-energy constants in chiral perturbation theory
• Chiral low-energy constants L_10 and C_87 from hadronic tau decays
• Chiral perturbation theory in the meson sector
• Lattice Kaon Physics
• Integrating out the heaviest quark in N--flavour ChPT
• Bayesian method for fitting the low-energy constants in chiral perturbation theory
• From hadronic tau decays to the chiral couplings L_10 and C_87
• Status of chiral perturbation theory
• Odd sector of QCD
• Reducing Hadronic Uncertainty in Low-Energy Neutral-Current Processes
• Chiral Low-Energy Constants: Status and Prospects