Determination of the a0-a2 pion scattering length from K->pi+ pi0 pi0 decay

We present a new method for the determination of the pion-pion scattering lenght combination a0-a2, based on the study of the pi0-pi0 spectrum in K->pi+ pi0 pi0 in the vicinity of the pi+ pi- threshold. The method requires a minimum of theoretical input, and is potentially very accurate.Comment: 8 pages, 2 figures -- corrected two typo

Pion-pion scattering and the K->3pi decay amplitudes

We revisit the recently proposed method for the determination of the pi-pi scattering length combination a_{0}-a_{2}, based on the study of the pi0 pi0 spectrum in K+ -> pi+ pi0 pi0. In view of a precision measurement, we discuss here the effects due to smaller absorptive contributions to the K+ -> pi+ pi0 pi0 and K+ -> pi+ pi+ pi- amplitudes. We outline a method of analysis that can lead to a precision determination of a_{0}-a_{2} and is based on very general properties of the S matrix. The discussion of final-state rescattering and cusp effects is also extended to the two K_L -> 3pi coupled channels. Thanks to the present work, the theoretical error on the a_{0}-a_{2} combination extracted from the K+ -> pi+ pi0 pi0 spectrum is reduced to about 5%. A further reduction requires the evaluation of the effects arising from radiative corrections.Comment: 32 pages, 6 figure

The Determination of the CKM Matrix

A general discussion of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is given and the importance stressed of determining the matrix elements as an essential part of understanding CP violation in and beyond the Standard Model. The status of knowledge of the matrix elements connecting the first and second generation quarks is reviewed. A perspective on determinations of the full CKM matrix is presented as an introduction to the separate contributions to the panel discussion that follows.Comment: Invited talk at Beauty 2000, Kibbutz Maagan, Israel, September 13-18, 2000; 6 pages; no figure

Comment on evidence for new interference phenomena in the decay D+ -> K- pi+ mu+ nu

The experimental determination of low energy pi K scattering phase shifts would assist in determining scattering lengths as well as low energy constants of chiral perturbation theory for which sum rules have been constructed. The FOCUS collaboration has presented evidence for interference pheomena from their analysis of D_l4 decays based on decay amplitudes suitable for a cascade decay D -> K* -> K pi. We point out that if the well-known full five body kinematics are taken into account, pi K scattering phases may be extracted. We also point out that other distributions considered in the context of K_l4 decays can be applied to charm meson decays to provide constraints on violation of |Delta I|=1/2 rule and T-violation.Comment: 9 pages, plain latex; version with minor changes compared to v1 on lepton masses effects, sign error eliminated, clarifying remarks added, one additional ref.; version to appear in Phys. Lett.

Tests of Factorization and SU(3) Relations in B Decays into Heavy-Light Final States

Using data from the B factories and the Tevatron, we perform tests of how well non-leptonic B decays of the kind B -> D^{(*)}_{(s)} P, where P is a pion or kaon, are described within the factorization framework. We find that factorization works well - as is theoretically expected - for color-allowed, tree-diagram-like topologies. Moreover, also exchange topologies, which have a non-factorizable character, do not show any anomalous behavior. We discuss also isospin triangles between the B -> D^{(*)} pi decay amplitudes, and determine the corresponding amplitudes in the complex plane, which show a significant enhancement of the color-suppressed tree contribution with respect to the factorization picture. Using data for B -> D^{(*)} K decays, we determine SU(3)-breaking effects and cannot resolve any non-factorizable SU(3)-breaking corrections larger than \sim 5%. In view of these results, we point out that a comparison between the \bar B^0_d -> D^+\pi^- and \bar B^0_s -> D_s^+\pi^- decays offers an interesting new determination of f_d/f_s. Using CDF data, we obtain the most precise value of this ratio at CDF, and discuss the prospects for a corresponding measurement at LHCb.Comment: 12 pages, 6 figures, matches published version in Physical Review

Drell-Hearn-Gerasimov Sum Rule for the Nucleon in the Large-N_c Limit

We show that the Drell-Hearn-Gerasimov sum rule for the nucleon is entirely saturated by the \Delta resonance in the limit of a large number of colors, N_c \to \infty. Corrections are at relative order 1/N_c^2.Comment: 6 pages, latex, no figure

Semileptonic Hyperon Decays and CKM Unitarity

Using a technique that is not subject to first-order SU(3) symmetry breaking effects, we determine the $V_{us}$ element of the CKM matrix from data on semileptonic hyperon decays. We obtain $V_{us}$ =0.2250(27). This value is of similar precision to the one derived from $K_{l3}$, but higher and in better agreement with the unitarity requirement, $|V_{ud}|^2+|V_{us}|^2+|V_{ub}|^2=1$.Comment: 3 pages, 1 tabl

V_{us} from hyperon semileptonic decays

A model-independent determination of the CKM matrix element V_{us} from five measured strangeness-changing hyperon semileptonic decays is performed. Flavor SU(3) symmetry breaking effects in the leading vector and axial-vector form factors are analyzed in the framework of the 1/N_c expansion of QCD. A fit to experimental data allows one to extract the value V_{us}=0.2199\pm 0.0026, which is comparable to the one from K_{e3} decays. This reconciliation is achieved through second-order symmetry breaking effects of a few percent in the form factors f_1, which increase their magnitudes over their SU(3) predictions.Comment: 23 pages, Revtex4, 12 tables, no figure