R. Kaminski

Pion-pion scattering amplitude. IV. Improved analysis with once subtracted Roy-like equations up to 1100 MeV

We improve our description of π π scattering data by imposing additional requirements on our previous fits, in the form of once-subtracted Roy-like equations, while extending our analysis up to 1100 MeV. We provide simple and ready to use parametrizations of the amplitude. In addition, we present a detailed description and derivation of these once-subtracted dispersion relations that, in the 450 to 1100 MeV region, provide an additional constraint which is much stronger than our previous requirements of forward dispersion relations and standard Roy equations. The ensuing constrained amplitudes describe the existing data with rather small uncertainties in the whole region from threshold up to 1100 MeV, while satisfying very stringent dispersive constraints. For the S0 wave, this requires an improved matching of the low and high energy parametrizations. Also for this wave we have considered the latest low energy K_(l4) decay results, including their isospin violation correction, and we have removed some controversial data points. These changes on the data translate into better determinations of threshold and subthreshold parameters which remove almost alldisagreement with previous chiral perturbation theory and Roy equation calculations below 800 MeV. Finally, our results favor the dip structure of the S0 inelasticity around the controversial 1000 MeV region.

Precise determination of the f0(600) and f0(980) pole parameters from a dispersive data analysis

We use our latest dispersive analysis of ππ scattering data and the very recent K(ℓ4) experimental results to obtain the mass, width, and couplings of the two lightest scalar-isoscalar resonances. These parameters are defined from their associated poles in the complex plane. The analytic continuation to the complex plane is made in a model-independent way by means of once- and twice-subtracted dispersion relations for the partial waves, without any other theoretical assumption. We find the f(0)(600) pole at (457(-13))+14))-i(279(-7)(+11)) MeV and that of the f(0)(980) at (996 ± 7)-i(25(-6)(+10)) MeV, whereas their respective couplings to two pions are 3.59(-0.13)(+0.11) and 2.3 ± 0.2 GeV.

Separation of S-wave pseudoscalar and pseudovector amplitudes in π−P↑ → π+π−n reaction on polarized target

A new analysis of S-wave production amplitudes for the reaction π−p↑ → π+π−n on a transversely polarized target is performed. It is based on the results obtained by the CERN-Cracow-Munich collaboration in the ππ energy range from 600 MeV to 1600 MeV at 17.2 GeV/c π− momentum. Energy-independent separation of the S-wave pseudoscalar amplitude (π exchange) from the pseudovector amplitude (a1 exchange) is carried out using assumptions much weaker than those in all previous analyses. We show that, especially around 1000 MeV and around 1500 MeV, the a1 exchange amplitude cannot be neglected. The scalarisoscalar ππ phase shifts are calculated using fairly weak assumptions. Below the KK̅ threshold we find two solutions for the π — π phase shifts, for which the phases increase slower with the effective π — π mass than the P-wave phases. Both solutions are consistent with a broad f0(500) but only one is similar to the well-known “down” solution. We find also the third solution (with a somewhat puzzling behavior of inelasticity) which exhibits a narrow f0(750) claimed by Svec. All the solutions undergo a rapid change at the KK̅ threshold. Above 1420 MeV the phase shifts increase with energy faster than those obtained without the polarized-target data. This phase behavior as well as an increase of the modulus of the a1-exchange amplitude can be due to the presence of the f0(1500).

Three channel model of meson-meson scattering and scalar meson spectroscopy

Abstract New solutions on the scalar-isoscalar ππ phase shifts are analysed together with previous K K results using a separable potential model of three coupled channels (ππ, K K and an effective 2π2π system). Model parameters are fitted to two sets of solutions obtained in a recent analysis of the CERN-Cracow-Munich measurements of the π−p↑ → π+π−n reaction on a polarized target. A relatively narrow (90–180 MeV) scalar resonance f0(1400–1460) is found, in contrast to a much broader (Γ ≈ 500 MeV) state emerging from the analysis of previous unpolarized target data.

Gluonium nature of the σ/f0(600) from its coupling to KK¯

Abstract We extract the K + K − couplings of the isoscalar scalar mesons σ / f 0 ( 600 ) and f 0 ( 980 ) from π π → π π / K K ¯ scatterings. We find respectively about 0.6(2) and 2.0(3) for the ratios of the K + K − over π + π − couplings of the σ and f 0 ( 980 ) , which we compare with some other determinations. The (relative) strong coupling of the σ → K ¯ K , together with its tiny “direct” γγ and its large hadronic widths, are in favour of a large gluonium/glueball component of the σ-meson, as predicted by QCD spectral sum rules (QSSR) ⊕ some low-energy theorems (LET). These properties then suggest that the σ can be (up to some mixing) a scalar meson associated to the U ( 1 ) V conformal anomaly like the η ′ -meson to the U ( 1 ) A anomaly.

Gluonium nature of the sigma/f(0)(600) from its coupling to K anti-K

Abstract We extract the K + K − couplings of the isoscalar scalar mesons σ / f 0 ( 600 ) and f 0 ( 980 ) from π π → π π / K K ¯ scatterings. We find respectively about 0.6(2) and 2.0(3) for the ratios of the K + K − over π + π − couplings of the σ and f 0 ( 980 ) , which we compare with some other determinations. The (relative) strong coupling of the σ → K ¯ K , together with its tiny “direct” γγ and its large hadronic widths, are in favour of a large gluonium/glueball component of the σ-meson, as predicted by QCD spectral sum rules (QSSR) ⊕ some low-energy theorems (LET). These properties then suggest that the σ can be (up to some mixing) a scalar meson associated to the U ( 1 ) V conformal anomaly like the η ′ -meson to the U ( 1 ) A anomaly.

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{-}}