A. Furman

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.

Long-distance effects and final state interactions in B→ππK and B→KK¯K decays

Abstract B decays into π π K and K K ¯ K , where the ππ and K ¯ K pairs interact in isospin zero S-wave, are studied in the ππ effective mass range from threshold to 1.2 GeV. The interplay of strong and weak decay amplitudes is analyzed using an unitary ππ and K K ¯ coupled channel model. Final state interactions are described in terms of four scalar form factors constrained by unitarity and chiral perturbation theory. Branching ratios for the B → f 0 ( 980 ) K decay, calculated in the factorization approximation with some QCD corrections, are too low as compared to recent data. In order to improve agreement with experiment, we introduce long-distance contributions called charming penguins. Effective mass distributions, branching ratios and asymmetries are compared with the existing data from BaBar and Belle Collaborations. A particularly large negative asymmetry in charged B decays is predicted for one set of the charming penguin amplitudes.

Final state interactions in B±→K+K−K± decays

Charged B decays to three charged kaons are analysed in the framework of the QCD factorization approach. The strong final state K+K-interactions are described using the kaon scalar and vector form factors. The scalar non-strange and strange form factors at low K+K- effective masses are constrained by chiral perturbation theory and satisfy the two-body unitarity conditions. The latter stem from the properties of the meson-meson amplitudes which describe all possible S-wave transitions between three coupled channels consisting of two kaons, two pions and four pions. The vector form factors are fitted to the data on the electromagnetic kaon interactions. The model results are compared with the Belle and BaBar data. Away from phi(1020) resonance, in the S-wave dominated K+K- mass spectra, a possibility for a large CP asymmetry is identified.

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

Abstract B decays into π π K and K K ¯ K , where the ππ and K ¯ K pairs interact in isospin zero S-wave, are studied in the ππ effective mass range from threshold to 1.2 GeV. The interplay of strong and weak decay amplitudes is analyzed using an unitary ππ and K K ¯ coupled channel model. Final state interactions are described in terms of four scalar form factors constrained by unitarity and chiral perturbation theory. Branching ratios for the B → f 0 ( 980 ) K decay, calculated in the factorization approximation with some QCD corrections, are too low as compared to recent data. In order to improve agreement with experiment, we introduce long-distance contributions called charming penguins. Effective mass distributions, branching ratios and asymmetries are compared with the existing data from BaBar and Belle Collaborations. A particularly large negative asymmetry in charged B decays is predicted for one set of the charming penguin amplitudes.

Properties of the a0 resonances

Abstract We present results following from the coupled channel model of two ao resonances decaying into the πη and K K mesons. The a0(980) resonance can be described by two distinct poles. It is shown that the discrepancy in the a0(980) mass position between the Crystal Barrel Collaboration and the E852 Group can be explained and removed. In our model with parameters fixed by the present experimental data the a0(980) cannot be interpreted as a bound K K state although the K K forces in the S-wave isovector channel are attractive.

Dalitz plot studies of D0 to K0S pi+ pi- decays

The availaible data on the D0 to K0S pi+ pi- decays are analysed in the framework of the quasi two-body QCD factorization approximation. The annihilation, via W-exchange, amplitudes are added to the weak-decay tree amplitudes. The doubly Cabibbo suppressed parts of the amplitudes are also considered. The strong interactions between the kaon-pion and pion-pion pairs in the S-, P- and D-final states are described in terms of the corresponding form factors. The kaon-pion or pion-pion scalar and vector form factors are constrained by other experimental data. Unitarity, analyticity and chiral symmetry are also used to obtain their functional forms. We go through a minimization procedure to reproduce the K0S pi-, K0S pi+ and pi+ pi- effective mass projections of the Dalitz plot distributions. The large number (27) of non-zero amplitudes leads to a large number of parameters. The resulting model distributions and branching fractions are compared to the accurate Belle Collaboration data.

ANALYSIS OF B± → K+K-K± DECAYS

Rare B decays to three charged kaons are analysed. The weak decay amplitudes are derived in the QCD factorization approach. The strong final state interactions between pairs of kaons are described using the kaon scalar and vector form factors. The scalar form factors at low K+K- effective mass distributions are constrained by chiral symmetry and are related to the coupled channel meson-meson amplitudes describing all the transitions between three channels consisting of two kaons, two pions and four pions. The vector form factors are fitted to the data on e+e- collisions. The model results are compared with the Belle and BaBar data.

Analysis of B+- to K+ K- K+- decays

Rare B decays to three charged kaons are analysed. The weak decay amplitudes are derived in the QCD factorization approach. The strong final state interactions between pairs of kaons are described using the kaon scalar and vector form factors. The scalar form factors at low K+K- effective mass distributions are constrained by chiral symmetry and are related to the coupled channel meson-meson amplitudes describing all the transitions between three channels consisting of two kaons, two pions and four pions. The vector form factors are fitted to the data on e+e- collisions. The model results are compared with the Belle and BaBar data.

CP violation and final state interactions in B → Kππ decays

Effects of CP violation and of final state interactions between pairs of pseudoscalar mesons are studied in three-body B+,B−,B0 and 0 decays into Kππ. An alternative approach to the isobar model for three-body B decays is proposed. It is based on the QCD factorization approximation and the knowledge of the meson-meson form factors. Some phenomenological charming penguin amplitudes are needed to describe the branching fractions, direct CP asymmetries of the quasi-two-body B → K* (892)π and B → K0* (1430)π decays as well as the Kπ effective mass and the helicity angle distributions. The experimental branching fractions for the B → K0* (1430)π decay, obtained by the Belle and BaBar collaborations using the isobar model, are larger than our predictions by about 52 per cent.

CP violation and strong pion-pion interactions in the weak B charged decays into three charged pions

An analysis of charged B decay data in a quasi two-body decay into a charged pion plus a S, P,or D state of two charged pions is performed in the QCD factorization framework. The short distance amplitudes are calculated including next-to-leading order corrections in the strong coupling constant for vertex and penguin contributions. The long distance amplitudes due to the two charged pion final state interactions are described by the pion non-strange scalar and vector form factors for the two-pion S- and P-wave states, respectively and by a relativistic Breit-Wigner formula for the D-wave state. We achieve a good fit of the data with only three parameters for the S wave, one for the P wave and one for the D wave. Our model gives a unified unitary description of the three scalar resonances, f_0(600), f_0(980) and f_0(1400) in terms of the pion scalar form factor. We predict for the B to f_2(1270) transition form factor a value of 0.098+-0.007 at a momentum transfer square equal to the pion-mass square.