Abstract: We study theoretically the effects of finite volume for pi pi scattering in order to extract physical observables for infinite volume from lattice QCD. We compare three different approaches for pi pi scattering (lowest order Bethe-Salpeter approach, N/D and inverse amplitude methods) with the aim of studying the effects of the finite size of the box in the potential of the different theories, specially the left-hand cut contribution through loops in the crossed t, u-channels. We quantify the error made by neglecting these effects in usual extractions of physical observables from lattice ()CD spectrum. We conclude that for pi pi phase-shifts in the scalar-isoscalar channel up to 800 MeV this effect is negligible for box sizes bigger than 2,5m(pi)(-1) and of the order of 5% at around 1.5 – 2m(pi)(-1). For isospin 2 the finite size effects can reach up to 10% for that energy. We also quantify the error made when using the standard Luscher method to extract physical observables from lattice QCD, which is widely used in the literature but is an approximation of the one used in the present work.

Abstract: We present a one-loop calculation of the oblique S parameter within Higgsless models of electroweak symmetry breaking and analyze the phenomenological implications of the available electroweak precision data. We use the most general effective Lagrangian with at most two derivatives, implementing the chiral symmetry breaking SU(2)(L) circle times SU(2)(R) -> SU(2)(L+R) with Goldstones, gauge bosons and one multiplet of vector and axial-vector massive resonance states. Using the dispersive representation of Peskin and Takeuchi and imposing the short-distance constraints dictated by the operator product expansion, we obtain S at the NLO in terms of a few resonance parameters. In asymptotically-free gauge theories, the final result only depends on the vector-resonance mass and requires M-V > 1.8TeV (3.8TeV) to satisfy the experimental limits at the 3 sigma (1 sigma) level; the axial state is always heavier, we obtain M-A > 2.5TeV (6.6TeV) at 3 sigma (1 sigma). In strongly-coupled models, such as walking or conformal technicolour, where the second Weinberg sum rule does not apply, the vector and axial couplings are not determined by the short-distance constraints; but one can still derive a lower bound on S, provided the hierarchy M-V < M-A remains valid. Even in this less constrained situation, we find that in order to satisfy the experimental limits at 3 sigma one needs M-V,M-A > 1.8TeV.

Abstract: 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) circle times 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.

Abstract: We perform a chiral extrapolation of lattice data on the scalar K pi form factor and the ratio of the kaon and pion decay constants within Chiral Perturbation Theory to two loops. We determine the value of the scalar form factor at zero momentum transfer, at the Callan-Treiman point and at its soft kaon analog as well as its slope. Results are in good agreement with their determination from experiment using the standard couplings of quarks to the W boson. The slope is however rather large. A study of the convergence of the chiral expansion is also performed.

Abstract: Using the Resonance Chiral Theory Lagrangian, we perform a calculation of the vector form factor of the pion at the next-to-leading order (NLO) in the 1/N-C expansion. Imposing the correct QCD short-distance constraints, one fixes the amplitude in terms of the pion decay constant F and resonance masses. Its low momentum expansion determines then the corresponding O(p(4)) and O(p(6)) low-energy chiral couplings at NLO, keeping control of their renormalization scale dependence. At mu(0) = 0.77 GeV, we obtain L-9(mu(0)) = (7.9 +/- 0.4).10(-3) and C-88(mu(0)) – C-90(mu(0)) = (-4.6 +/- 0.4).10(-5).