Chiral Perturbation Theory and the f2(1270) resonance

Within Chiral Perturbation Theory, we study elastic pion scattering in the I=0, J=2, channel, whose main features are the f2(1270) resonance and the vanishing of the lowest order. By means of a chiral model that includes an explicit resonance coupled to pions, we describe the data and calculate the resonance contribution to the O(p^4) and O(p^6) chiral parameters. We also generalize the Inverse Amplitude Method to higher orders, which allows us to study channels with vanishing lowest order. In particular, we apply it to the I=0,J=2 case, finding a good description of the f2(1270) resonance, as a pole in the second Riemann sheet.Comment: 4 pages,1 figur

On the precision of the theoretical predictions for pi pi scattering

In a recent paper, Pelaez and Yndurain evaluate some of the low energy observables of pi pi scattering and obtain flat disagreement with our earlier results. The authors work with unsubtracted dispersion relations, so that their results are very sensitive to the poorly known high energy behaviour of the scattering amplitude. They claim that the asymptotic representation we used is incorrect and propose an alternative one. We repeat their calculations on the basis of the standard, subtracted fixed-t dispersion relations, using their asymptotics. The outcome fully confirms our earlier findings. Moreover, we show that the Regge parametrization proposed by these authors for the region above 1.4 GeV violates crossing symmetry: Their ansatz is not consistent with the behaviour observed at low energies.Comment: Added more material, mostly in Sects. 7, 8 and 9, in support of the same conclusions. Latex, 28 pages, 3 figure

Simultaneous Softening of sigma and rho Mesons associated with Chiral Restoration

Complex poles of the unitarized pi-pi scattering amplitude in nuclear matter are studied. Partial restoration of chiral symmetry is modeled by the decrease of in-medium pion decay constant f*_{pi}. For large chiral restoration (f*_{pi}/f_{pi} << 1), 2nd sheet poles in the scalar (sigma) and the vector (rho) mesons are both dictated by the Lambert W function and show universal softening as f*_{pi} decreases. In-medium pi-pi cross section receives substantial contribution from the soft mode and exhibits a large enhancement in low-energy region. Fate of this universality for small chiral restoration (f*_{pi}/f_{pi} ~ 1) is also discussed.Comment: 5 pages, 4-eps figures, version accepted by Phys. Rev. C (R) with minor modification

ππ\pi\pi scattering S wave from the data on the reaction π−p→π0π0n\pi^-p\to\pi^0\pi^0n

The results of the recent experiments on the reaction $\pi^-p\to\pi^0\pi^0n$ performed at KEK, BNL, IHEP, and CERN are analyzed in detail. For the I=0 $\pi\pi$ S wave phase shift $\delta^0_0$ and inelasticity $\eta^0_0$ a new set of data is obtained. Difficulties emerging when using the physical solutions for the $\pi^0\pi^0$ S and D wave amplitudes extracted with the partial wave analyses are discussed. Attention is drawn to the fact that, for the $\pi^0\pi^0$ invariant mass, m, above 1 GeV, the other solutions, in principle, are found to be more preferred. For clarifying the situation and further studying the $f_0(980)$ resonance thorough experimental investigations of the reaction $\pi^-p\to\pi^0\pi^0n$ in the m region near the $K\bar K$ threshold are required.Comment: 17 pages, 5 figure

Evidence for two-quark content of f0(980)f_{0}(980) in exclusive b→cb\to c decays

Inspired by a large decay branching ratio (BR) of $B^{+}\to f_{0}(980)K^{+}$ measured by Belle recently, we propose that a significant evidence of the component of $n\bar{n}=(u\bar{u}+d\bar{d})/\sqrt{2}$ in $f_{0}(980)$ could be demonstrated in exclusive $b\to c$ decays by the observation of $f_{0}(980)$ in the final states $\bar{B}\to D^{0(*)} \pi^{+} \pi^{-}(KK)$ and $\bar{B}\to J/\Psi \pi^{+} \pi^{-}(KK)$. We predict the BRs of $\bar{B}\to D^{0(*)} (J/\Psi) f_{0}(980)$ to be ${\cal {O}}(10^{-4})$ (${\cal {O}}(10^{-5})$) while the unknown wave functions of $D^{(*)0}$ ($J/\Psi$) are chosen to fit the observed decays of $\bar{B}\to D^{(*)0} \pi^{0} (J/\Psi K^{0(*)})$.Comment: 4 pages, 2 figures, Revtex4, version to appear in PR

The light sigma meson

In the framework of the dispersion relation N/D-approach, we restore the low-energy pi-pi (IJ^{PC}=00^{++})-wave amplitude sewing it with the previously obtained K-matrix solution for the region 450-1900 MeV. The restored N/D-amplitude has a pole on the second sheet of the complex-s plane near the pi-pi threshold, that is the light sigma meson.Comment: 5 pages, LaTeX, 3 EPS figures, epsfig.st

Rescattering and chiral dynamics in B\to \rho\pi decay

We examine the role of B^0(\bar B^0) \to \sigma \pi^0 \to \pi^+\pi^- \pi^0 decay in the Dalitz plot analysis of B^0 (\bar B^0) \to \rho\pi \to \pi^+\pi^-\pi^0 decays, employed to extract the CKM parameter \alpha. The \sigma \pi channel is significant because it can break the relationship between the penguin contributions in B\to\rho^0\pi^0, B\to\rho^+\pi^-, and B\to\rho^-\pi^+ decays consequent to an assumption of isospin symmetry. Its presence thus mimics the effect of isospin violation. The \sigma\pi^0 state is of definite CP, however; we demonstrate that the B\to\rho\pi analysis can be generalized to include this channel without difficulty. The \sigma or f_0(400-1200) ``meson'' is a broad I=J=0 enhancement driven by strong \pi\pi rescattering; a suitable scalar form factor is constrained by the chiral dynamics of low-energy hadron-hadron interactions - it is rather different from the relativistic Breit-Wigner form adopted in earlier B\to\sigma\pi and D\to\sigma\pi analyses. We show that the use of this scalar form factor leads to an improved theoretical understanding of the measured ratio Br(\bar B^0 \to \rho^\mp \pi^\pm) / Br(B^-\to \rho^0 \pi^-).Comment: 26 pages, 8 figs, published version. typos fixed, minor change

The Dipion Mass Spectrum In e+e- Annihilation and tau Decay: A Dynamical (rho0, omega, phi) Mixing Approach

We readdress the problem of finding a simultaneous description of the pion form factor data in e+e- annihilations and in tau decays. For this purpose, we work in the framework of the Hidden Local Symmetry (HLS) Lagrangian and modify the vector meson mass term by including the pion and kaon loop contributions. This leads us to define the physical rho, omega and phi fields as linear combinations of their ideal partners, with coefficients being meromorphic functions of s, the square of the 4--momentum flowing into the vector meson lines. This allows us to define a dynamical, i.e. s-dependent, vector meson mixing scheme. The model is overconstrained by extending the framework in order to include the description of all meson radiative (V P gamma and P gamma gamma couplings) and leptonic (Ve+e- couplings) decays and also the isospin breaking (omega/ phi --> pi+ pi-) decay modes. The model provides a simultaneous, consistent and good description of the e+e- and tau dipion spectra. The expression for pion form factor in the latter case is derived from those in the former case by switching off the isospin breaking effects specific to e+e- and switching on those for tau decays. Besides, the model also provides a good account of all decay modes of the form V P gamma, Pgamma gamma as well as the isospin breaking decay modes. It leads us to propose new reference values for the rho^0 --> e+ e- and omega --> pi+ pi- partial widths which are part of our description of the pion form factor. Other topics (phi --> K anti K, the rho meson mass and width parameters) are briefly discussed. Therefore, we confirm the 3.3 sigma discrepancy between the theoretical estimate of a_mu based on e+e- and its direct BNL measurement.Comment: 71 pages, 8 figures. Accepted by EPJ C. Version 3: correct minor typos, minor changes spread out into the text. Extension of Sections 12.2 and 12.3.5 and introduction of the new Appendix

Couplings of light I=0 scalar mesons to simple operators in the complex plane

The flavour and glue structure of the light scalar mesons in QCD are probed by studying the couplings of the I=0 mesons $\sigma(600)$ and $f_0(980)$ to the operators $\bar{q}q$, $\alpha_s G^2$ and to two photons. The Roy dispersive representation for the $\pi\pi$ amplitude $t_0^0(s)$ is used to determine the pole positions as well as the residues in the complex plane. On the real axis, $t_0^0$ is constrained to solve the Roy equation together with elastic unitarity up to the K\Kbar threshold leading to an improved description of the $f_0(980)$. The problem of using a two-particle threshold as a matching point is discussed. A simple relation is established between the coupling of a scalar meson to an operator $j_S$ and the value of the related pion form-factor computed at the resonance pole. Pion scalar form-factors as well as two-photon partial-wave amplitudes are expressed as coupled-channel Omn\`es dispersive representations. Subtraction constants are constrained by chiral symmetry and experimental data. Comparison of our results for the $\bar{q}q$ couplings with earlier determinations of the analogous couplings of the lightest I=1 and $I=1/2$ scalar mesons are compatible with an assignment of the $\sigma$, $\kappa$, $a_0(980)$, $f_0(980)$ into a nonet. Concerning the gluonic operator $\alpha_s G^2$ we find a significant coupling to both the $\sigma$ and the $f_0(980)$.Comment: 31 pages, 5 figure

The pole structure of the unitary, crossing symmetric low energy ππ\pi\pi scattering amplitudes

The pole structure of the low energy $\pi\pi$ scattering amplitudes is studied using a proper chiral unitarization method combined with crossing symmetry and the low energy phase shift data. It is found that the $\sigma$ pole position is at $M_\sigma=470\pm 50MeV$, $\Gamma_\sigma=570\pm 50MeV$. The existence of the virtual state pole in the IJ=20 channel is reconfirmed. Various threshold parameters are estimated and are found in general in good agreement with the results obtained from the Roy equation analyses.Comment: Minor corrections made and references added. Final version accepted for publication as JHEP02(2005)04