Gilberto Colangelo

The mesonic chiral lagrangean of order p6

We construct the effective chiral lagrangean for chiral perturbation theory in the mesonic even-intrinsic-parity sector at order p6. The lagrangean contains 112 in principle measurable + 3 contact terms for the general case of n light flavours, 90+4 for three and 53+4 for two flavours. The equivalence between equations of motion and field redefinitions to remove spurious terms in the lagrangeans is shown to all orders in the chiral expansion. We also discuss and implement other methods for reducing the number of terms to a minimal set.

Renormalization of Chiral Perturbation Theory to Order p 6

The renormalization of chiral perturbation theory is carried out to next-to-next-to-leading order in the meson sector. We calculate the divergent part of the generating functional of Green functions of quark currents to O(p6) for chiral SU(n), involving one- and two-loop diagrams. The renormalization group equations for the renormalized low-energy constants of O(p6) are derived. We compare our results with previous two-loop calculations in chiral perturbation theory.

The ππ S-wave scattering lengths

Abstract We match the known chiral perturbation theory representation of the ππ scattering amplitude to two loops with a phenomenological description that relies on the Roy equations. On this basis, the corrections to Weinbergs low energy theorems for the S-wave scattering lengths are worked out to second order in the expansion in powers of the quark masses. The resulting predictions, a00=0.220±0.005, a02=−0.0444±0.0010, contain remarkably small uncertainties and thus allow a very sensitive experimental test of the hypothesis that the quark condensate is the leading order parameter of the spontaneously broken chiral symmetry.

The quark condensate from K(e(4)) decays.

We show that, independently of the size of the quark condensate, chiral symmetry correlates the two S-wave pipi scattering lengths. In view of this constraint, the new precision data on K(e(4)) decay allow a remarkably accurate determination of these quantities. The result confirms the hypothesis that the quark condensate is the leading order parameter.

Double Chiral Logs

Abstract We determine the full structure of the leading (double-pole) divergences of O ( p 6 ) in the meson sector of chiral perturbation theory. The field theoretic basis for this calculation is described. We then use an extension of this result to determine the p 6 contributions containing double chiral logarithms ( L 2 ), single logarithms times p 4 constants ( L × L i r ) and products of two p 4 constants ( L i r × L j r ) for F π , F K / F π , K l 3 and K e 4 form factors. Numerical results are presented for these quantities.

Dispersion relations and soft pion theorems for K→ππ

Abstract We propose a new method to obtain the K → ππ amplitude from K → π which allows one to fully account for the effects of final state interactions. The method is based on a set of dispersion relations for the K → ππ amplitude in which the weak Hamiltonian carries momentum. The soft pion theorem, which relates this amplitude to the K → π amplitude, can be used to determine one of the two subtraction constants—the second constant is at present known only to leading order in chiral perturbation theory. We solve the dispersion relations numerically and express the result in terms of the unknown higher order corrections to this subtraction constant.

Supersymmetric contributions to direct CP violation in K→ππγ decays

Abstract We analyze the supersymmetric contributions to direct– CP –violating observables in K → ππγ decays induced by gluino–mediated magnetic–penguin operators. We find that ϵ ′ +− γ and the differential width asymmetry of K ± → π ± π 0 γ decays could be substantially enhanced with respect to their Standard Model values, especially in the scenario where ϵ ′/ ϵ is dominated by supersymmetric contributions. These observables could therefore provide a useful tool to search for New Physics effects in |Δ S |=1 transitions, complementary to ϵ ′/ ϵ and rare decays.

A note on the dispersive treatment of K→ππ with the kaon off-shell

Abstract It has been recently suggested that it is possible to calculate the effect of final state interactions in K → ππ amplitudes by applying dispersive methods to the amplitude with the kaon off-shell. We critically reexamine the procedure, and point out the effects of the arbitrariness in the choice of the off-shell field for the kaon.

Supersymmetric contributions to direct CP violation in K ---> pi pi gamma decays

Abstract We analyze the supersymmetric contributions to direct– CP –violating observables in K → ππγ decays induced by gluino–mediated magnetic–penguin operators. We find that ϵ ′ +− γ and the differential width asymmetry of K ± → π ± π 0 γ decays could be substantially enhanced with respect to their Standard Model values, especially in the scenario where ϵ ′/ ϵ is dominated by supersymmetric contributions. These observables could therefore provide a useful tool to search for New Physics effects in |Δ S |=1 transitions, complementary to ϵ ′/ ϵ and rare decays.

Chiral perturbation theory, dispersion relations and final state interactions in K → ππ

We discuss the recent literature on the treatment of final state interactions in K → ππ. Various approaches are compared and particular emphasis is given to the possibility of combining dispersive methods with lattice input. Recent results on the dependence of various quantities on the quark masses at order p6 in the chiral expansion are presented and the relevance for the lattice calculations is discussed.