Kpi form factors and final state interactions in D+ --> K- pi+ pi+ decays

We present a model for the decay D+ --> K- pi+ pi+. The weak interaction part of this reaction is described using the effective weak Hamiltonian in the factorisation approach. Hadronic final state interactions are taken into account through the Kpi scalar and vector form factors fulfilling analyticity, unitarity and chiral symmetry constraints. The model has only two free parameters that are fixed from experimental branching ratios. We show that the modulus and phase of the S wave thus obtained agree nicely with experiment up to 1.55 GeV. We perform Monte Carlo simulations to compare the predicted Dalitz plot with experimental analyses. Allowing for a global phase difference between the S and P waves of -65 degrees, the Dalitz plot of the D+ --> K- pi+ pi+ decay, the Kpi invariant mass spectra and the total branching ratio due to S-wave interactions are well reproduced.Comment: 24 pages, 4 figures, REVTeX style. A discussion on the isospin 2 component has been included. Two references added. Published in Phys. Rev.

Generalized companion matrix for approximate GCD

We study a variant of the univariate approximate GCD problem, where the coefficients of one polynomial f(x)are known exactly, whereas the coefficients of the second polynomial g(x)may be perturbed. Our approach relies on the properties of the matrix which describes the operator of multiplication by gin the quotient ring C[x]=(f). In particular, the structure of the null space of the multiplication matrix contains all the essential information about GCD(f; g). Moreover, the multiplication matrix exhibits a displacement structure that allows us to design a fast algorithm for approximate GCD computation with quadratic complexity w.r.t. polynomial degrees.Comment: Submitted to MEGA 201

Constraining the Kpi vector form factor by tau---> K pi nu_tau and K_l3 decay data

A subtracted dispersive representation of the $K\pi$ vector form factor, $F_+^{K\pi}$, is used to fit the Belle spectrum of \tauKpi decays incorporating constraints from results on $K_{l3}$ decays. Through the use of three subtractions, the slope and curvature of $F_+^{K\pi}$ are obtained directly from the data yielding $\lambda_+'=(25.49 \pm 0.31) \times 10^{-3}$ and $\lambda_+"= (12.22 \pm 0.14) \times 10^{-4}$. The phase-space integrals relevant for $K_{l3}$ analyses are calculated. Additionally, from the pole position on the second Riemann sheet the mass and width of the $K^*(892)^\pm$ are found to be $m_{K^*(892)^\pm}= 892.0\pm 0.5$ MeV and $\Gamma_{K^*(892)^\pm}= 46.5 \pm 1.1$ MeV. Finally, we study the $P$-wave isospin-1/2 $K\pi$ phase-shift and its threshold parameters.Comment: Talk presented at 15th International QCD Conference, Montpellier, France. Submitted to Nuc. Phys. (Proc. Suppl.), 4 pages, 1 figur

Anomalous dimensions of four-quark operators and renormalon structure of mesonic two-point correlators

In this work, we calculate leading-order anomalous dimension matrices for dimension-6 four-quark operators which appear in the operator product expansion of flavour non-diagonal and diagonal vector and axial-vector two-point correlation functions. The infrared renormalon structure corresponding to four-quark operators is reviewed and it is investigated how the eigenvalues of the anomalous dimension matrices influence the singular behaviour of the $u=3$ infrared renormalon pole. It is found that compared to the large-$\beta_0$ approximation where at most quadratic poles are present, in full QCD at $N_f=3$ the most singular pole is more than cubic with an exponent $\kappa\approx 3.2$.Comment: 19 pages, 1 figure; version to appear in JHE