Chiral perturbation theory: Expansions in the mass of the strange quark

“…These are the coupling L 10 of the O(p 4 ) chiral Lagrangian [14] and the electromagnetic pion-mass difference. They are expressed in terms of Π V,A (Q 2 ) as 14) and…”

Section: The Modelmentioning

confidence: 99%

Large-N_c QCD meets Regge theory: the example of spin-one two-point functions

Golterman

Peris

2001

“…2. Let us try to understand the allowed values of a + and b + with the help of the amplitude (11). The real part of the two-pion contribution, Re W ππ + (z), is a monotonically decreasing function of z in the physical region.…”

Section: 3mentioning

confidence: 99%

“…The main assumption underlying the form factor (11) is that all other contributions to the dispersion integral except the two-pion intermediate state can be well approximated by a linear polynomial for small values of z.…”

Section: 2mentioning

confidence: 99%

The decays K→πl⁺l⁻ beyond leading order in the chiral expansion

D’Ambrosio¹,

Ecker²,

Isidori³

et al. 1998

161

245

We present a model-independent analysis of K + → π + ℓ + ℓ − and K S → π 0 ℓ + ℓ − decays, including K → 3π unitarity corrections and a general decomposition of the dispersive amplitude. From the existing data on K + → π + e + e − we predict the ratio R = B(K + → π + µ + µ − )/B(K + → π + e + e − ) to be larger than 0.23, in slight disagreement with the recent measurement R = 0.167 ± 0.036. Consequences for the K ± → π ± e + e − charge asymmetries and for the K L → π 0 e + e − mode are also discussed.

“…The Goldstone nature of the pseudoscalar bosons implies strong constraints on their interactions, which can be most easily analyzed on the basis of an effective Lagrangian organized as an expansion in powers of momenta (derivatives) and quark masses over the chiral symmetry breaking scale Λ χ ≃ 4πF π ≃ 1.2 GeV. The resulting Goldstone effective field theory, Chiral Perturbation Theory (χPT) [3][4][5], has achieved a remarkable success describing the low-energy dynamics of QCD [6,7].…”

Section: Introductionmentioning

confidence: 99%

Quantum Loops in the Resonance Chiral Theory: The Vector Form-Factor

Rosell

Sanz-Cillero

Pich

2004

172

We present a calculation of the Vector Form Factor at the next-to-leading order in the 1/N C expansion, within the framework of Resonance Chiral Theory. The calculation is performed in the chiral limit, and with two dynamical quark flavours. The ultraviolet behaviour of quantum loops involving virtual resonance propagators is analyzed, together with the kind of counterterms needed in the renormalization procedure. Using the lowest-order equations of motion, we show that only a few combinations of local couplings appear in the final result. The low-energy limit of our calculation reproduces the standard Chiral Perturbation Theory formula, allowing us to determine the resonance contribution to the chiral low-energy couplings, at the next-to-leading order in 1/N C , keeping a full control of their renormalization scale dependence.