Phenomenology of the <VVP> Green's function within the Resonance Chiral Theory

We analyse the odd-intrinsic-parity effective Lagrangian of QCD valid for processes involving one pseudoscalar with two vector mesons described in terms of antisymmetric tensor fields. Substantial information on the odd-intrinsic-parity couplings is obtained by constructing the vector-vector-pseudoscalar Green's three-point function, at leading order in 1/N_C, and demanding that its short-distance behaviour matches the corresponding OPE result. The QCD constraints thus enforced allow us to predict the decay amplitude omega -> pi gamma, the O(p^6) corrections to pi -> gamma gamma and the slope parameter in pi -> gamma gamma^*.Comment: 4 pages, 1 figure. Talk given at QCD 03: High-Energy Physics International Conference in Quantum Chromodynamics, Montpellier, France, 2-8 Jul 200

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

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.Comment: 27+1 pages, 9 figure

Towards a determination of the chiral couplings at NLO in 1/N(C): L_8(mu) and C_38(mu)

We present a dispersive method which allows to investigate the low-energy couplings of chiral perturbation theory at the next-to-leading order (NLO) in the 1/N(C) expansion, keeping full control of their renormalization scale dependence. Using the resonance chiral theory Lagrangian, we perform a NLO calculation of the scalar and pseudoscalar two-point functions, within the single-resonance approximation. Imposing the correct QCD short-distance constraints, one determines their difference Pi(t)=Pi_S(t)-Pi_P(t) in terms of the pion decay constant and resonance masses. Its low momentum expansion fixes then the low-energy chiral couplings L_8 and C_38. At mu_0=0.77 GeV, we obtain L_8(mu_0)^{SU(3)} = (0.6+-0.4)10^{-3} and C_{38}(mu_0)^{SU(3)}=(2+-6)10^{-6}.Comment: Extended version published at JHEP01(2007)039. A NLO prediction for the O(p6) chiral coupling C_38 has been added. The original L_8 results remain unchange

The BKB_K Kaon Parameter in the Chiral Limit

We introduce four-point functions in the hadronic ladder resummation approach to large $N_c$ QCD Green functions. We determine the relevant one to calculate the $B_K$ kaon parameter in the chiral limit. This four-point function contains both the large momenta QCD OPE and the small momenta ChPT at NLO limits, analytically. We get $\hat B_K^\chi = 0.38 \pm 0.15$. We also give the ChPT result at NLO for the relevant four-point function to calculate $B_K$ outside the chiral limit, while the leading QCD OPE is the same as the chiral limit one.Comment: 17 page

Form Factors in the radiative pion decay

We perform an analysis of the form factors that rule the structure-dependent amplitude in the radiative pion decay. The resonance contributions to pion -> e nu_e gamma decays are computed through the proper construction of the vector and axial-vector form factors by setting the QCD driven asymptotic properties of the three-point Green functions VVP and VAP, and by demanding the smoothing of the form factors at high transfer of momentum. A comparison between theoretical and experimental determinations of the form factors is also carried out. We also consider and evaluate the role played by a non-standard tensor form factor. We conclude that, at present and due to the hadronic incertitudes, the search for New Physics in this process is not feasible.Comment: 14 pages, no figures. Typos corrected. Accepted for publication in The European Physical Journal