Large Nc and Chiral Dynamics

We study the dependence on the number of colors of the leading pi pi scattering amplitude in chiral dynamics. We demonstrate the existence of a critical number of colors for and above which the low energy pi pi scattering amplitude computed from the simple sum of the current algebra and vector meson terms is crossing symmetric and unitary at leading order in a truncated and regularized 1/Nc expansion. The critical number of colors turns out to be Nc=6 and is insensitive to the explicit breaking of chiral symmetry. Below this critical value, an additional state is needed to enforce the unitarity bound; it is a broad one, most likely of "four quark" nature.Comment: RevTeX4, 6 fig., 5 page

Studying Kaon-pion S-wave scattering in K-matrix formalism

We generalize our previous work on \pi\pi scattering to K\pi scattering, and re-analyze the experiment data of K\pi scattering below 1.6 GeV. Without any free parameter, we explain K\pi I=3/2 S-wave phase shift very well by using t-channel rho and u-channel K^* meson exchange. With the t-channel and u-channel meson exchange fixed as the background term, we fit the K\pi I=1/2 S-wave data of the LASS experiment quite well by introducing one or two s-channel resonances. It is found that there is only one s-channel resonance between K\pi threshold and 1.6 GeV, i.e., K_0^*(1430) with a mass around 1438~1486 MeV and a width about 346 MeV, while the t-channel rho exchange gives a pole at (450-480i) MeV for the amplitude.Comment: REVTeX4 file, 11 pages and 3 figure

Scalar meson dynamics in Chiral Perturbation Theory

A comparison of the linear sigma model (L$\sigma$M) and Chiral Perturbation Theory (ChPT) predictions for pion and kaon dynamics is presented. Lowest and next-to-leading order terms in the ChPT amplitudes are reproduced if one restricts to scalar resonance exchange. Some low energy constants of the order $p^4$ ChPT Lagrangian are fixed in terms of scalar meson masses. Present values of these low energy constants are compatible with the L$\sigma$M dynamics. We conclude that more accurate values would be most useful either to falsify the L$\sigma$M or to show its capability to shed some light on the controversial scalar physics.Comment: 9 pages, REVTeX 4.0. Final version accepted for publicatio

Meson resonances, large N_c and chiral symmetry

We investigate the implications of large N_c and chiral symmetry for the mass spectra of meson resonances. Unlike for most other mesons, the mass matrix of the light scalars deviates strongly from its large-N_c limit. We discuss the possible assignments for the lightest scalar nonet that survives in the large-N_c limit.Comment: 14 page

BB Intermeson Potentials in the Quark Model

In this paper we derive quark model results for scattering amplitudes and equivalent low energy potentials for heavy meson pairs, in which each meson contains a heavy quark. This "BB" system is an attractive theoretical laboratory for the study of the nuclear force between color singlets; the hadronic system is relatively simple, and there are lattice gauge theory (LGT) results for V_BB(r) which may be compared to phenomenological models. We find that the quark model potential (after lattice smearing) has qualitative similarities to the LGT potential in the two B*B* channels in which direct comparison is possible, although there is evidence of a difference in length scales. The quark model prediction of equal magnitude but opposite sign for I=0 and I=1 potentials also appears similar to LGT results at intermediate r. There may however be a discrepancy between the LGT and quark model I=1 BB potentials. A numerical study of the two-meson Schrodinger equations in the (bqbar)(bqbar) and (cqbar)(cqbar) sectors with the quark model potentials finds a single "molecule", in the I=0 BB* sector. Binding in other channels might occur if the quark model forces are augmented by pion exchange.Comment: 30 pages, 5 figures, revtex and epsfig. Submitted to Phys. Rev.

Optically induced coherent intra-band dynamics in disordered semiconductors

On the basis of a tight-binding model for a strongly disordered semiconductor with correlated conduction- and valence band disorder a new coherent dynamical intra-band effect is analyzed. For systems that are excited by two, specially designed ultrashort light-pulse sequences delayed by tau relatively to each other echo-like phenomena are predicted to occur. In addition to the inter-band photon echo which shows up at exactly t=2*tau relative to the first pulse, the system responds with two spontaneous intra-band current pulses preceding and following the appearance of the photon echo. The temporal splitting depends on the electron-hole mass ratio. Calculating the population relaxation rate due to Coulomb scattering, it is concluded that the predicted new dynamical effect should be experimentally observable in an interacting and strongly disordered system, such as the Quantum-Coulomb-Glass.Comment: to be published in Physical Review B15 February 200

DCC dynamics with the SU(3) linear sigma model

The SU(3) extension of the linear sigma model is employed to elucidate the effect of including strangeness on the formation of disoriented chiral condensates. By means of a Hartree factorization, approximate dispersion relations for the 18 scalar and pseudoscalar meson species are derived and their self-consistent solution makes it possible to trace out the thermal path of the two order parameters as well as delineate the region of instability within which spontaneous pair creation becomes possible. The results depend significantly on the employed sigma mass, with the highest values yielding the largest regions of instability. An approximate solution of the equations of motion for the order parameter in scenarios emulating uniform scaling expansions show that even with a rapid quench only the pionic modes grow unstable. Nevertheless, the rapid and oscillatory relaxation of the order parameters leads to enhanced production of both pions and (to a lesser degree) kaons.Comment: 29 pages, RevTeX, 11 postscript figures, discussion about anomaly term adde

Analysis of the nature of the ϕ→γπη\phi\to\gamma\pi\eta and ϕ→γπ0π0\phi\to\gamma\pi^0\pi^0 decays

We study interference patterns in the $\phi\to(\gamma a_0+\pi^0\rho)\to\gamma\pi\eta$ and $\phi\to(\gamma f_0+\pi^0\rho)\to\gamma \pi^0\pi^0$ reactions. Taking into account the interference, we fit the experimental data and show that the background reaction does not distort the $\pi^0\eta$ spectrum in the decay $\phi\to\gamma\pi\eta$ everywhere over the energy region and does not distort the $\pi^0\pi^0$ spectrum in the decay $\phi\to\gamma\pi^0\pi^0$ in the wide region of the $\pi^0\pi^0$ system invariant mass, $m_{\pi\pi}>670$ MeV, or when the photon energy is less than 300 MeV. We discuss the details of the scalar meson production in the radiative decays and note that there are reasonable arguments in favor of the one-loop mechanism $\phi\to K^+K^-\to\gamma a_0$ and $\phi\to K^+K^-\to\gamma f_0$. We discuss also distinctions between the four-quark, molecular, and two-quark models and argue that the Novosibirsk data give evidence in favor of the four-quark nature of the scalar $a_0(980)$ and $f_0(980)$ mesons.Comment: 15 pages, 7 figures, title is changed, a few clarifying remarks are added, accepted for publication in Physical Review

Instantons and Scalar Multiquark States: From Small to Large N_c

We study scalar quark-anti-quark and two-quark-two-anti-quark correlation functions in the instanton liquid model. We show that the instanton liquid supports a light scalar-isoscalar (sigma) meson, and that this state is strongly coupled to both $(\bar{q}q)$ and $(\bar{q}q)^2$. The scalar-isovector $a_0$ meson, on the other hand, is heavy. We also show that these properties are specific to QCD with three colors. In the large $N_c$ limit the scalar-isoscalar meson is not light, and it is mainly coupled to $(\bar{q}q)$.Comment: 24 page