Lightest scalar and tensor resonances in γγ→ππ\gamma\gamma\to\pi\pi after the Belle experiment

New high statistics Belle data on the $\gamma\gamma\to\pi^+\pi^-$ reaction cross section measured in the range of pion-pair invariant masses $\sqrt{s}$ between 0.8 GeV and 1.5 GeV are analyzed to clarify the current situation around the $\sigma(600)$, $f_0(980)$, and $f_2(1270)$ resonances in $\gamma\gamma$ collisions. The present analysis shows that the direct coupling constants of the $\sigma(600)$ and $f_0(980)$ resonances to $\gamma\gamma$ are small, and the $\sigma(600)\to\gamma\gamma$ and $f_0(980)\to\gamma\gamma$ decays are four-quark transitions caused by the $\pi^+\pi^-$ and $K^+K^-$ loop mechanisms, respectively. The chiral shielding of the $\sigma(600)$ resonance takes place in the reactions $\gamma\gamma\to\pi\pi$ as well as in $\pi\pi$ scattering. Some results of a simultaneous description of the $\gamma\gamma\to\pi^+\pi^-$ and $\gamma\gamma\to\pi^0\pi^0$ Belle data are also presented. In particular, the following tentative estimate of the $f_2(1270)\to\gamma\gamma$ decay width is obtained: $\Gamma_{f_2\to\gamma\gamma}(m^2_{f_2})\approx 3.68$ keV.Comment: 14 pages, 5 figures. Fitted for the publication in Physical Review

The analytical ππ\pi\pi scattering amplitude and the light scalars

In this work we construct the $\pi\pi$ scattering amplitude $T^0_0$ with regular analytical properties in the $s$ complex plane, which describes simultaneously the data on the $\pi\pi$ scattering, $\phi\to\pi^0\pi^0\gamma$ decay, and $\pi\pi\to K\bar K$ reaction. The chiral shielding of the $\sigma (600)$ meson and its mixing with the $f_0(980)$ meson are also taken into account. The data agrees with the four-quark nature of the $\sigma (600)$ and $f_0(980)$ mesons. The amplitude in the range $-5 m_\pi^2 < s < 0.64$ GeV$^2$ also agrees with results, obtained on the base of the chiral expansion, dispersion relations, and the Roy equations.Comment: Published version: a few clarifications are added, the Editors corrections are taken into accoun

Gapless Hartree-Fock-Bogoliubov Approximation for Bose Gases

A dilute Bose system with Bose-Einstein condensate is considered. It is shown that the Hartree-Fock-Bogolubov approximation can be made both conserving as well as gapless. This is achieved by taking into account all physical normalization conditions, that is, the normalization condition for the condensed particles and that for the total number of particles. Two Lagrange multipliers, introduced for preserving these normalization conditions, make the consideration completely self-consistent.Comment: Latex file, 22 pages, 2 figure

The Running BFKL: Resolution of Caldwell's Puzzle

The HERA data on the proton structure function, $F_2(x,Q^2)$, at very small $x$ and $Q^2$ show the dramatic departure of the logarithmic slope, $\partial F_2/\partial\log Q^2$, from theoretical predictions based on the DGLAP evolution. We show that the running BFKL approach provides the quantitative explanation for the observed $x$ and/or $Q^2$ -dependence of $\partial F_2/\partial\log Q^2$.Comment: 7 pages, Latex, 4 Figures, P

Analysis of preliminary data on e+e−→ϕ→γf0(980)→γπ0π0e^+e^-\to\phi\to\gamma f_0(980)\to\gamma\pi^0\pi^0 reaction

We perform the analysis of the preliminary data on $e^+e^-\to\phi\to\gamma f_0(980)\to\gamma\pi^0\pi^0$ reaction simultaneously with the data on $\pi\pi$ scattering and reactions $J/\psi\to\phi\pi^+\pi^-$ and $K^-p\to\pi^+\pi^-(\Lambda,\Sigma)$. It is found that the $f_0(980)$ meson mass $m_{f_0}=950$ MeV and $B(\phi\to\gamma f_0\to\gamma\pi^0\pi^0)\simeq1\cdot10^{-4}$.Comment: 8 pages, revtex, 3 ps files of figures, minor change

Light Scalar Mesons as Manifestation of Spontaneously Broken Chiral Symmetry

Attention is paid to the production mechanisms of light scalars that reveal their nature. We reveal the chiral shielding of the \sigma(600) meson. We show that the kaon loop mechanism of the \phi radiative decays, ratified by experiment, points to the four-quark nature of light scalars. We show also that the light scalars are produced in the two photon collisions via four-quark transitions in contrast to the classic P wave tensor q\bar q mesons that are produced via two-quark transitions $\gamma\gamma\to q\bar q$. The history of spontaneous breaking of symmetry in quantum physics is discussed in Appendix.Comment: Talk at The International Bogolyubov Conference "Problems of Theoretical and Mathematical Physics" devoted to the 100th anniversary of N.N.Bogolyubov's birth that was held from August 21 to August 22,2009 in Moscow at the Russian Academy of Sciences (RAS) and from August 23 to August 27, 2009 in Dubna at the Joint Institute for Nuclear Research (JINR