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.

We present a one-loop calculation of the oblique S and T parameters within strongly-coupled models of electroweak symmetry breaking with a light Higgs-like boson. We use a general effective Lagrangian, implementing the chiral symmetry breaking SU (2)L ⊗ SU (2)R → SU (2)L+R with Goldstones, gauge bosons, the Higgs-like scalar and one multiplet of vector and axial-vector massive resonance states. Using a dispersive representation and imposing a proper ultraviolet behaviour, we obtain S and T at the next-to-leading order in terms of a few resonance parameters. The experimentally allowed range forces the vector and axial-vector states to be heavy, with masses above the TeV scale, and suggests that the Higgs-like scalar should have a W W coupling close to the Standard Model one. Our conclusions are generic and apply to more specific scenarios such as the minimal SO(5)/SO(4) composite Higgs model.

Abstract:We study the η-η ′ mixing up to next-to-next-to-leading-order in U(3) chiral perturbation theory in the light of recent lattice simulations and phenomenological inputs. A general treatment for the η-η ′ mixing at higher orders, with the higher-derivative, kinematic and mass mixing terms, is addressed. The connections between the four mixing parameters in the two-mixing-angle scheme and the low energy constants in the U(3) chiral effective theory are provided both for the singlet-octet and the quark-flavor bases. The axial-vector decay constants of pion and kaon are studied in the same order and confronted with the lattice simulation data as well. The quark-mass dependences of m η , m η ′ and m K are found to be well described at next-to-leading order. Nonetheless, in order to simultaneously describe the lattice data and phenomenological determinations for the properties of light pseudoscalars π, K, η and η ′ , the next-to-next-to-leading order study is essential. Furthermore, the lattice and phenomenological inputs are well reproduced for reasonable values of low the energy constants, compatible with previous bibliography.

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 twopoint functions, within the single-resonance approximation. Imposing the correct QCD short-distance constraints, one determines their difference Π(t) ≡ Π S (t) − Π 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 µ 0 = 0.77 GeV, we obtain L r 8 (µ 0 ) SU (3) = (0.6 ± 0.4) · 10 −3 and C r 38 (µ 0 ) SU (3) = (2 ± 6) · 10 −6 .

Using 1/N C expansion and dispersion theory techniques, without relying on any explicit resonance lagrangian, we generalize the KSRF relation beyond the leading chiral order. Two sum rules for the low energy constants L 2 , L 3 and a new relation between resonance couplings are derived. A rather detailed examination to the new relation is also given.

The hadronic decays η ′ → ηππ are studied in the frameworks of large-N C Chiral Perturbation Theory, at lowest and next-to-leading orders, and Resonance Chiral Theory in the leading 1/N C approximation. Higher order effects such as ππ final state interactions are taken into account through a detailed unitarization procedure. The inclusion of finite-width effects in the case of RChT is also discussed. The Dalitz plot distribution and the differential branching ratio are computed in both approaches. The predicted Dalitz plot parameters obtained from the different treatments are compared with the most recent measured values. We find that the η ′ → ηππ branching ratios are easily understood, while the Dalitz plot parameters require the inclusion of ππ loops in order to achieve a reasonable agreement. Our final predictions agree with the experimental measurements. We hope our results to be of relevance for present and future experimental analyses of these decays.

The couplings of the electroweak effective theory contain information on the heavy-mass scales which are no-longer present in the low-energy Lagrangian. We build a general effective Lagrangian, implementing the electroweak chiral symmetry breaking SU(2) L ⊗ SU(2) R → SU(2) L+R , which couples the known particle fields to heavier states with bosonic quantum numbers J P = 0 ± and 1 ± . We consider colour-singlet heavy fields that are in singlet or triplet representations of the electroweak group. Integrating out these heavy scales, we analyze the pattern of low-energy couplings among the light fields which are generated by the massive states. We adopt a generic non-linear realization of the electroweak symmetry breaking with a singlet Higgs, without making any assumption about its possible doublet structure. Special attention is given to the different possible descriptions of massive spin-1 fields and the differences arising from naive implementations of these formalisms, showing their full equivalence once a proper short-distance behaviour is required.

Using the resonance chiral theory Lagrangian, we perform a calculation of the vector and axial-vector two-point functions at the next-to-leading order (NLO) in the 1/N C expansion. We have analyzed these correlators within the singleresonance approximation and have also investigated the corrections induced by a second multiplet of vector and axial-vector resonance states. Imposing the correct QCD short-distance constraints, one determines the difference of the two correlators Π(t) ≡ Π V V (t) − Π AA (t) in terms of the pion decay constant and resonance masses. Its low momentum expansion fixes then the low-energy chiral couplings L 10 and C 87 at NLO, keeping full control of their renormalization scale dependence. At µ 0 = 0.77 GeV, we obtain L r 10 (µ 0 ) = (−4.4±0.9)·10 −3 and C r 87 (µ 0 ) = (3.1±1.1)·10 −5 .