Theoretical Aspects of the Pion-Pion Interaction

We give a brief review of the theoretical description of low energy pion-pion scattering by the combined use of Chiral Perturbation Theory and Roy equations, an update of the Regge parametrization of $\pi\pi$ cross sections at high energies, and a short discussion of the scalar radius of the pion.Comment: 4 pages, talk presented by I. Caprini at the International Conference on QCD and Hadronic Physics, June 16-20 2005, Beijin

Mass and width of the lowest resonance in QCD

We demonstrate that near the threshold, the pi pi scattering amplitude contains a pole with the quantum numbers of the vacuum - commonly referred to as the sigma - and determine its mass and width within small uncertainties. Our derivation does not involve models or parametrizations, but relies on a straightforward calculation based on the Roy equation for the isoscalar S-wave.Comment: Revtex, 4 pages, 2 figures, two refences added, minor text changes, version appeared in Phys. Rev. Let

Regge analysis of the pi pi scattering amplitude

The theoretical predictions for the subtraction constants lead to a very accurate dispersive representation of the pi pi scattering amplitude below 0.8 GeV. The extension of this representation up to the maximum energy of validity of the Roy equations (1.15 GeV) requires a more precise input at high energies. In this paper we determine the trajectories and residues of the leading Regge contributions to the pi pi amplitude (Pomeron, f and rho), using factorization, phenomenological parametrizations of the pi N and NN total cross sections at high energy and a set of sum rules which connect the high and low energy properties of pi pi scattering. We find that nonleading Regge terms are necessary in order to achieve a smooth transition from the partial waves to the Regge representation at or below 2 GeV. We obtain thus a Regge representation consistent both with the experimental information at high energies and the Roy equations for the partial waves with l =< 4. The uncertainties in our result for the Regge parameters are sizable but in the solutions of the Roy equations, these only manifest themselves above K-Kbar threshold.Comment: 27 pages, 16 figures - v2 coincides with the published version apart from a footnote on p. 14 which has been added after publication, in August 201

Mass and width of the sigma

I report on recent work done in collaboration with Irinel Caprini and Gilberto Colangelo. We observe that the Roy equations lead to a representation of the pion pion scattering amplitude that exclusively involves observable quantities, but is valid for complex values of s. At low energies, this representation is dominated by the contributions from the two subtraction constants, which are known to remarkable precision from the low energy theorems of chiral perturbation theory. Evaluating the remaining contributions on the basis of the available data, we demonstrate that the lowest resonance carries the quantum numbers of the vacuum and occurs in the vicinity of the threshold. Although the uncertainties in the data are substantial, the pole position can be calculated quite accurately, because it occurs in the region where the amplitude is dominated by the subtractions. The calculation neatly illustrates the fact that the dynamics of the Goldstone bosons is governed by the symmetries of QCD.Comment: Contribution to the proceedings of MESON 2006 (Krakow

Erratum to: Cottingham formula and nucleon polarisabilities

This erratum corrects some misprints appearing in the article. They do not affect any of the results

Cottingham formula and nucleon polarisabilities

The difference between the electromagnetic selfenergies of proton and neutron can be calculated with the Cottingham formula, which expresses the self-energies as an integral over the electroproduction cross sections – provided the nucleon matrix elements of the current commutator do not contain a fixed pole. We show that, under the same proviso, the subtraction function occurring in the dispersive representation of the virtual Compton forward scattering amplitude is determined by the cross sections. The representation in particular leads to a parameter-free sum rule for the nucleon polarisabilities. We evaluate the sum rule for the difference between the electric polarisabilities of proton and neutron by means of the available parameterisations of the data and compare the result with experiment

1/N_c Corrections to the Hadronic Matrix Elements of Q_6 and Q_8 in K --> pi pi Decays

We calculate long-distance contributions to the amplitudes A(K^0 --> pi pi, I) induced by the gluon and the electroweak penguin operators Q_6 and Q_8, respectively. We use the 1/N_c expansion within the effective chiral lagrangian for pseudoscalar mesons. In addition, we adopt a modified prescription for the identification of meson momenta in the chiral loop corrections in order to achieve a consistent matching to the short-distance part. Our approach leads to an explicit classification of the loop diagrams into non-factorizable and factorizable, the scale dependence of the latter being absorbed in the low-energy coefficients of the effective theory. Along these lines we calculate the one-loop corrections to the O(p^0) term in the chiral expansion of both operators. In the numerical results, we obtain moderate corrections to B_6^(1/2) and a substantial reduction of B_8^(3/2).Comment: 32 pages, LaTeX, 8 eps figures. One reference added, to appear in Phys. Rev.

The Strong Isospin-Breaking Correction for the Gluonic Penguin Contribution to epsilon'/epsilon at Next-to-Leading Order in the Chiral Expansion

The strong isospin-breaking correction, Omega_{st}, which appears in estimates of the Standard Model value for the direct CP-violating ratio epsilon'/epsilon, is evaluated to next-to-leading order (NLO) in the chiral expansion using Chiral Perturbation Theory. The relevant linear combinations of the unknown NLO CP-odd weak low-energy constants (LEC's) which, in combination with 1-loop and strong LEC contributions, are required for a complete determination at this order, are estimated using two different models. It is found that, to NLO, Omega_{st}=0.08 +/- 0.05, significantly reduced from the ``standard'' value, 0.25 +/- 0.08, employed in recent analyses. The potentially significant numerical impact of this decrease on Standard Model predictions for epsilon'/epsilon, associated with the decreased cancellation between gluonic penguin and electroweak penguin contributions, is also discussed.Comment: 12 pages, 1 figur