On the use of Hadamard expansions in hyperasymptotic evaluation: differential equations of hypergeometric type

We describe how a modification of a common technique for developing asymptotic expansions of solutions of linear differential equations can be used to derive Hadamard expansions of solutions of differential equations. Hadamard expansions are convergent series that share some of the features of hyperasymptotic expansions, particularly that of having exponentially small remainders when truncated, and, as a consequence, provide a useful computational tool for evaluating special functions. The methods we discuss can be applied to linear differential equations of hypergeometric type and may have wider applicability

Roy's equations and the pion-pion experimental data

Roy's equations are used to check if the scalar-isoscalar pion-pion scattering amplitudes fitted to experimental data fulfill crossing symmetry conditions. It is shown that the amplitudes describing the ``down-flat'' phase shift solution satisfy crossing symmetry below 1 GeV while the amplitudes fitted to the "up-flat'' data do not. In this way the long standing "up-down" ambiguity in the phenomenological determination of the scalar-isoscalar pion-pion amplitudes has been resolved confirming the independent result of the recent joint analysis of the pi+pi- and pi0pi0 data.Comment: 6 pages, 2 figures, talk given at Tenth International Conference on Hadron Spectroscopy (Hadron'03), Aschaffenburg, Germany, August 31 - September 6 200

Peculiarities in multichannel interaction amplitudes for meson-meson scattering and scalar meson spectroscopy

Interactions in coupled channels pipi, KKbar and an effective 2pi2pi in scalar-isoscalar wave have been analysed. Influence of interchannel couplings on analytical structure of multichannel interaction amplitudes has been studied. Interplay of S-matrix zeroes and poles and their relation with parameters of scalar resonances has been investigated.Comment: presented by R. Kaminski at the Meson 2000 Conference, Cracow, Poland, May 19-23, 2000; 5 pages including 2 figures, to appear in Acta Physica Polonica

Analysis of New Results For Scalar-Isoscalar pi-pi Phase Shifts

The scalar -- isoscalar pi-pi phase shifts are analysed using a separable potential model of three coupled channels (pipi, KK and an effective 2pi2pi system). Model parameters are fitted to two sets of solutions obtained in a recent analysis of the CERN-Cracow-Munich measurements of the pi^- p --> pi^+ pi^- n reaction on a polarized target. A relatively narrow (90 -- 180 MeV) scalar resonance f_0(1400-1460) is found, together with a wide f_0(500) (Gamma = 500 MeV) and the narrow f_0(980) state.Comment: 4 pages, 3 figures. Talk given at 7th International Conference on Hadron Spectroscopy (Hadron 97), Upton, NY, 25-30 Aug 199

pi-pi scattering amplitudes constrained by Roy's equations

The scalar-isoscalar, scalar-isotensor and vector-isovector pi-pi amplitudes have been fitted simultaneously to experimental data and to to Roy's equations. Resulting pi-pi phase shifts up to 1600 MeV and near threshold observables have been analyzed. Only the amplitudes fitted to the "down-flat" set of phase shifts in scalar-isoscalar wave fulfill crossing symmetry conditions and can be regarded as physical.Comment: 4 pages, talk presented at 12th International QCD Conference (QCD05) 4-9th July 2005 Montpellier (France), to appear in Nucl. Phys. B (Proc. Suppl.

K* resonance effects on direct CP violation in B -> pi pi K

Charged and neutral B decays into two charged pions and a charged or a neutral kaon are analyzed within the QCD factorization scheme where final state interactions before and after hadronization are included. The K*(892) and K*(1430) resonance effects are taken into account using the presently known pion-Kaon strange vector and scalar form factors. The weak decay amplitudes, which are calculated at leading power in Lambda_QCD/m_b and at the next-to-leading order in the strong coupling constant, include the hard scattering and annihilation contributions. The end point divergences of these weak final state interactions are controlled by two complex parameters determined through a fit to the available effective mass and helicity angle distribution, CP asymmetry and K*(892) branching ratio data. The predicted K*(1430) branching ratios and the calculated direct CP violation asymmetries are compared to the Belle and BABAR Collaboration data.Comment: Comments: 22 pages, 2 figures and 3 tables. In this new version, the results are unchanged, but, the last paragraph of the Section "RESULTS AND SUMMARY" (now called "RESULTS AND DISCUSSION") has been replaced by a new Section "SUMMARY AND OUTLOOK". To appear in Physical Review

Towards a unitary Dalitz plot analysis of three-body hadronic B decays

A unitary model of the final state kaon pion interaction amplitudes in the B --> K pi pi decays is constructed. The weak decay penguin amplitudes, derived in QCD factorization, are supplemented by phenomenological contributions. The strange kaon- pion scalar and vector form factors are used to calculate the kaon pion effective mass and helicity angle distributions, branching ratios, CP asymmetries and the phase difference between the B0 and anti B0 decay amplitudes to K*(892) pi. The fit on the phenomenological parameters leads to a good agreement with the experimental data, particularly for the B --> K*(892) pi decays. However, our predicted B+- --> K*0(1430) pi+-, K*0(1430)--> K+-pi-+ branching fraction is smaller than the results of the Belle and BaBar collaborations, obtained from isobar model analyses. A new parameterization of the S-wave kaon- pion effective mass distribution, which can be used in future experimental Dalitz plot analyses, is proposed.Comment: 5 pages, 1 figure, contribution to Proc. Int. Europhysics Conference on High Energy Physics (HEP2009), July 16-22, 2009, Krakow, Poland, PoS(HEP2009)20

Final state interactions and CP violation in B decays to three pseudoscalars

We study CP violation and final state interactions between pions and kaons in B+, B-, B0 and bar B0 decays into K pi pi. The weak transition amplitudes consist of two terms: the first part is derived in QCD factorization approach and the second one is a phenomenological long-distance charming penguin contribution. The final state K pi interactions in S- and P-waves are described by strange scalar and vector form factors, respectively. These are determined using a unitary coupled channel model together with chiral symmetry and asymptotic QCD constraints. The final state interactions are dominated by presence of the scalar K*0(1430) and the vector K*(892) resonances. We show that additional charming penguin amplitudes are needed to reproduce the latest experimental K pi effective mass and helicity angle distributions, branching fractions and asymmetries obtained by Belle and BaBar collaborations.Comment: Talk given at XIII International Conference on Hadron Spectroscopy (Hadron 2009), Nov. 29 - Dec. 4 2009, Florida State Universit