Search

We extend the formalism pioneered by Callan, Coote and Gross to investigate the meson-meson scattering within the framework of 't Hooft model, i.e., the two-dimensional QCD in the $N_c\to \infty$ limit. We derive the analytic expressions for various two-body meson-meson scattering amplitudes, concentrating on those quark diagrams which may be identified as the meson-meson contact interaction vertex in the context of the mesonic effective lagrangian in $1/N_c$ expansion. We also carry out a detailed numerical study for the meson-meson scattering for various quark flavors, and observe the near-threshold enhancement in some channels. This may be viewed as the hint of the existence of the tetra-quark state below two-meson threshold., Comment: 15 pages, 14 figures, 1 table

We study the $N_c$ scalings of pion-nucleon and nucleon-nucleon scatterings and find that a consistent large $N_c$ counting can be established if we assume Witten's counting rules are applied to matrix elements or scattering amplitudes which use the relativistic normalization for the nucleons. With the pionless effective field theory, we also find that the $S$-wave nucleon-nucleon interaction is so strong that it should be treated nonperturbatively at the leading order in the $1/N_c$ expansion. By summing all the leading order diagrams, we find that the deuteron binding energy is of order $1/N_c$. In contrast, meson-meson interaction is so weak that loosely-bound meson-meson molecular states may not exist in the large $N_c$ limit., Comment: 9 pages, 4 figures, journal version

We study the production line shape of $B^\ast\bar B$ near threshold, where the $B^\ast \bar B$ pair comes from the resonance $X_b$. Our study shows that the line shape depends sensitively on the binding energy and the probability of finding an elementary state in the physical bound state. Both of the two parameters are crucial to identify the structure of $X_b$. Therefore, the line shape measurement can shed light on the structure of $X_b$., Comment: 7 pages, 7 figures, submit to Modern Physics Letters A

With a combined analysis of data on $\Upsilon(5S)\rightarrow h_b(1P,2P)\pi^+\pi^-$ and $\Upsilon(5S)\rightarrow B^{(\ast)}\bar B^{(\ast)}\pi$ in an effective field theory approach, we determine resonance parameters of $Z_b$ states in two scenarios. In one scenario we assume that $Z_b$ states are pure molecular states, while in the other one we assume that $Z_b$ states contain compact components. We find that the present data favor that there should be some compact components inside $Z_b^{(\prime)}$ associated with the molecular components. By fitting the invariant mass spectra of $\Upsilon(5S)\rightarrow h_b(1P,2P)\pi^+\pi^-$ and $\Upsilon(5S)\rightarrow B^{(\ast)}\bar B^{\ast}\pi$, we determine that the probability of finding the compact components in $Z_b$ states may be as large as about $40\%$., Comment: Discussions added, version published in EPJC

We revisit the compositeness theorem proposed by Weinberg in an effective field theory (EFT) and explore criteria which are sensitive to the structure of $S$-wave threshold states. On a general basis, we show that the wave function renormalization constant $Z$, which is the probability of finding an elementary component in the wave function of a threshold state, can be explicitly introduced in the description of the threshold state. As an application of this EFT method, we describe the near-threshold line shape of the $D^{\ast 0}\bar D^0$ invariant mass spectrum in $B\rightarrow D^{\ast 0}\bar D^0 K$ and determine a nonvanishing value of $Z$. It suggests that the $X(3872)$ as a candidate of the $D^{\ast 0}\bar D^0$ molecule may still contain a small $c\bar{c}$ core. This elementary component, on the one hand, explains its production in the $B$ meson decay via a short-distance mechanism, and on the other hand, is correlated with the $D^{\ast 0}\bar D^0$ threshold enhancement observed in the $D^{\ast 0}\bar D^0$ invariant mass distributions. Meanwhile, we also show that if $Z$ is non-zero, the near-threshold enhancement of the $D^{\ast 0}\bar D^0$ mass spectrum in the $B$ decay will be driven by the short-distance production mechanism. This conclusion is still true even if the long-distance production is enhanced by some unexpected mechanism., Comment: version to be published in Chinese Physics C

We study the anomalous cross-section lineshape of $e^+e^-\rightarrow D\bar D$ with an effective field theory. Near the threshold, most of the $D\bar D$ pairs are from the decay of $\psi(3770)$. Taking into account the fact that the nonresonance background is dominated by the $\psi(2S)$ transition, the produced $D\bar D$ pair can undergo final-state interactions before the pair is detected. We propose an effective field theory for the low-energy $D\bar D$ interactions to describe these final-state interactions and find that the anomalous lineshape of the $D\bar D$ cross section observed by the BESII collaboration can be well described., Comment: 10 pages,6 figures, redo the calculation with PDS scheme and more discussions added, accepted by Phys.Lett.B