J. J. Sanz-Cillero

One-loop

A bstractIn this work we study the γγxa0→u2009WL+WL− and γγ → ZLZL scattering processes within the effective chiral Lagrangian approach, including a light Higgs-like scalar as a dynamical field together with the would-be-Goldstone bosons w± and z associated to the electroweak symmetry breaking. This approach is inspired by the possibility that the Higgs-like boson be a composite particle behaving as another Goldstone boson, and assumes the existence of a mass gap between mh, mW , mZ and the potential new emergent resonances, setting an intermediate energy region (above mh,W,Z and below the resonance masses) where the use of these effective chiral Lagrangians are the most appropriate tools to compute the relevant observables. We analyse in detail the proper chiral counting rules for the present case of photon-photon scattering and provide the computation of the one-loop γγxa0→u2009WL+WL− and γγ → ZLZL scattering amplitudes within this Effective Chiral Lagrangian approach and the Equivalence Theorem, including a discussion on the involved renormalization procedure. We also propose here a joint analysis of our results for the twophoton scattering amplitudes together with other photonic processes and electroweak (EW) precision observables for a future comparison with data. This could help to disentangle the nature of the light Higgs-like particle.

\gamma\gamma \to

A bstractThe 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 JP = 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.

W

A bstractWe have studied the P → γ⋆γ⋆ transition form-factors (P = π0, η, η′) within a chiral invariant framework that allows us to relate the three form-factors and evaluate the corresponding contributions to the muon anomalous magnetic moment aμ = (gμ−2)/2, through pseudoscalar pole contributions. We use a chiral invariant Lagrangian to describe the interactions between the pseudo-Goldstones from the spontaneous chiral symmetry breaking and the massive meson resonances. We will consider just the lightest vector and pseudoscalar resonance multiplets. Photon interactions and U(3) flavor breaking effects are accounted for in this covariant framework. This article studies the most general corrections of order mP2 within this setting. Requiring short-distance constraints fixes most of the parameters entering the form-factors, consistent with previous determinations. The remaining ones are obtained from a fit of these form-factors to experimental measurements in the space-like (q2 ≤ 0) region of photon momenta. No time-like observable is included in our fits. The combination of data, chiral symmetry relations between form-factors and high-energy constraints allows us to determine with improved precision the on-shell P -pole contribution to the Hadronic Light-by-Light scattering of the muon anomalous magnetic moment: we obtain aμP,HLbL=8.47±0.16·10−10

W

{a}_{mu}^{{}^{P, HLbL}}=left(8.47 pm 0.16right) cdotp {10}^{-10}

and

for our best fit. This result was obtained excluding BaBar π0 data, which our analysis finds in conflict with the remaining experimental inputs. This study also allows us to determine the parameters describing the η−η′ system in the two-mixing angle scheme and their correlations. Finally, a preliminary rough estimate of the impact of loop corrections (1/NC ) and higher vector multiplets (asym) enlarges the uncertainty up to aμP,HLbL=8.47±0.16sta±0.091/NC−0+0.5asym·10−10

Z

{a}_{mu}^{P, HLbL}=left(8.47pm {0.16}_{mathrm{sta}} pm {0.09}_{1/{mathrm{N}}_{mathrm{C}}}{{}_{-0}^{+0.5}}_{asym}right)cdotp {10}^{-10}