L. Lesniak

S-, P- and D-wave final state interactions and CP violation in B+- --> pi+- pi-+ pi+- decays

We study CP violation and the contribution of the strong pion-pion interactions in the three-body B+- --> pi+- pi-+ pi+- decays within a quasi two-body QCD factorization approach. The short distance interaction amplitude is calculated in the next-to-leading order in the strong coupling constant with vertex and penguin corrections. The meson-meson final state interactions are described by pion non-strange scalar and vector form factors for the S and P waves and by a relativistic Breit-Wigner formula for the D wave. The pion scalar form factor is calculated from a unitary relativistic coupled-channel model including pi pi, Kbar K and effective (2pi)(2pi) interactions. The pion vector form factor results from a Belle Collaboration analysis of tau- --> pi- pi0 nu_tau data. The recent B+- --> pi+- pi-+ pi+- BABAR Collaboration data are fitted with our model using only three parameters for the S wave, one for the P wave and one for the D wave. We find not only a sizable contribution of the S wave just above the pi pi threshold but also under the rho(770) peak a significant interference, mainly between the S and P waves. For the B to f_2(1270) transition form factor, we predict F^{Bf_2}(m_\pi^2)=0.098+-0.007. Our model yields a unified unitary description of the contribution of the three scalar resonances f_0(600), f_0(980) and f_0(1400) in terms of the pion non-strange scalar form factor.

Interference between f(0)(980) and rho(770)0 resonances in B ---> pi+ pi- K decays

We study the contribution of the strong interaction between the two pions in S- and P-waves to the weak B --> pion pion kaon decay amplitudes. The interference between these two waves is analyzed in the pion-pion effective mass range of the rho(770) and f0(980) resonances. We use a unitary pion-pion and antikaon-kaon coupled-channel model to describe the S-wave interactions and a Breit-Wigner function for the P-wave amplitude. The weak B-decay amplitudes, obtained from QCD factorization, are supplemented with charming penguin contributions in both waves. The four complex parameters of these long distance terms are determined by fitting the model to the BaBar and Belle data on B^{+,-,0} --> pi+ pi- K^{+,-,0} branching fractions, CP asymmetries, pion-pion effective mass and helicity-angle distributions. This set of data, and in particular the large direct CP-asymmetry for B^{+,-} --> rho0(770) K^{+,-} decays, is well reproduced. The interplay of charming penguin amplitudes and the interference of S- and P-waves describes rather successfully the experimental S and A values of the CP-violating asymmetry for both B0 --> f0(980) K0S and B0 --> rho0(770) K0S decays.

Dalitz plot studies of

The presently available high-statistics data of the

D^0 \to K_S^0 \pi^+ \pi^-

{D}^{0}\ensuremath{\rightarrow}{K}_{S}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}

decays in a factorization approach

processes measured by the Belle and BABAR collaborations are analyzed within a quasi-two-body factorization framework. Starting from the weak effective Hamiltonian, tree and annihilation amplitudes build up the

Long-distance effects and final state interactions in B to pion pion K and B to K anti-K K decays

{D}^{0}\ensuremath{\rightarrow}{K}_{S}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}

Parametrizations of three-body hadronic

decay amplitude. Two of the three final-state mesons are assumed to form a single scalar, vector or tensor state originating from a quark-antiquark pair so that the factorization hypothesis can be applied. The meson-meson final state interactions are described by

B

K\ensuremath{\pi}

- and

and

D

\ensuremath{\pi}\ensuremath{\pi}