On causality, unitarity and perturbative expansions

We present a pedagogical case study how to combine micro-causality and unitarity based on a perturbative approach. The method we advocate constructs an analytic extrapolation of partial-wave scattering amplitudes that is constrained by the unitarity condition. Suitably constructed conformal mappings help to arrive at a systematic approximation of the scattering amplitude. The technique is illustrated at hand of a Yukawa interaction. The typical case of a superposition of strong short-range and weak long-range forces is investigated.Comment: 12 pages, 12 figure

Does the enhancement observed in γγ→DDˉ\gamma\gamma\to D\bar{D} contain two PP-wave higher charmonia?

Solved is a new puzzle raised by the observation of an enhancement structure Z(3930) in $\gamma\gamma\to D\bar{D}$. If categorizing Z(3930) as $\chi_{c2}(2P)$ suggested by Belle and BaBar, we must explain why $\chi_{c0}(2P)$ dominantly decaying into $D\bar{D}$ is missing in the $D\bar{D}$ invariant mass spectrum. In this work, we propose that the Z(3930) enhancement structure may contain two $P$-wave higher charmonia {$\chi_{c0}(2P)$} and $\chi_{c2}(2P)$. We show that this assumption is supported by our analysis of the $D\bar{D}$ invariant mass spectrum and $\cos\theta^\ast$ distribution of $\gamma\gamma\to D\bar{D}$. This observation would not only provide valuable information of two P-wave higher charmonia $\chi_{c0}(2P)$ and $\chi_{c2}(2P)$, but also serve as the crucial test of our novel proposal to the observed enhancement structure Z(3930), especially at the forthcoming BelleII and the approved SuperB.Comment: 5 pages, 2 tables, 3 figures. More contents and discussions adde

On kinematical constraints in boson-boson systems

We consider the scattering of two-bosons with negative parity and spin 0 or 1. Starting from helicity partial-wave scattering amplitudes we derive transformations that eliminate all kinematical constraints. Such amplitudes are expected to satisfy partial-wave dispersion relations and therefore provide a suitable basis for data analysis and the construction of effective field theories. Our derivation relies on a decomposition of the various scattering amplitudes into suitable sets of invariant functions. A novel algebra was developed that permits the efficient computation of such functions in terms of computer algebra codes.Comment: 14 pages, 8 table

Electromagnetic transitions in an effective chiral Lagrangian with the eta-prime and light vector mesons

We consider the chiral Lagrangian with a nonet of Goldstone bosons and a nonet of light vector mesons. The mixing between the pseudoscalar mesons eta and eta-prime is taken into account. A novel counting scheme is suggested that is based on hadrogenesis, which conjectures a mass gap in the meson spectrum of QCD in the limit of a large number of colors. Such a mass gap would justify to consider the vector mesons and the eta-prime meson as light degrees of freedom. The complete leading order Lagrangian is constructed and discussed. As a first application it is tested against electromagnetic transitions of light vector mesons to pseudoscalar mesons. Our parameters are determined by the experimental data on photon decays of the omega, phi and eta-prime meson. In terms of such parameters we predict the corresponding decays into virtual photons with either dielectrons or dimuons in the final state.Comment: 17 pages, extended discussion on mixin

Mass spectrum of the axial-vector hidden charmed and hidden bottom tetraquark states

In this article, we perform a systematic study of the mass spectrum of the axial-vector hidden charmed and hidden bottom tetraquark states using the QCD sum rules, and identify the $Z^+(4430)$ as an axial-vector tetraquark state tentatively.Comment: 24 pages, 38 figures, slight revisio

Phenomenology of Pc(4380)+, Pc(4450)+ and related states

The $P_c(4380)^+$ and $P_c(4450)^+$ states recently discovered at LHCb have masses close to several relevant thresholds, which suggests they can be described in terms of meson-baryon degrees of freedom. This article explores the phenomenology of these states, and their possible partners, from this point of view. Competing models can be distinguished by the masses of the neutral partners which have yet to be observed, and the existence or otherwise of further partners with different isospin, spin, and parity. Future experimental studies in different decay channels can also discriminate among models, using selection rules and algebraic relations among decays. Among the several possible meson-baryon pairs which could be important, one implies that the states are mixtures of isospins 1/2 and 3/2, with characteristic signatures in production and decay. A previous experimental study of a Cabibbo-suppressed decay showed no evidence for the states, and further analysis is required to establish the significance of this non-observation. Several intriguing similarities suggest that $P_c(4450)^+$ is related to the $X(3872)$ meson.Comment: 16 pages, 1 figure. Journal version (some very minor changes from arXiv v1

Possibility to observe higher n(3)D(1) bottomonium states in the e(+)e(-) processes

The possibility to observe new bottomonium states with JPC=1 - in the region 10.7-11.1 GeV is discussed. The analysis of the dielectron widths shows that the (n+1)S13 and nD13 states (n 3) may be mixed with a rather large mixing angle, θ 30°, and this effect provides the correct values of Γee(Υ(10580)) and Γee(Υ(11020)). On the other hand, the S-D mixing gives rise to an increase by 2 orders of magnitude of the dielectron widths of the mixed Υ (nD13) resonances (n=3, 4, 5), which originate from pure D-wave states. The value Γee(Υ (3D))=0.095-0.025+0.028keV is obtained, being only ∼3 times smaller than the dielectron width of Υ(10580), while Γee(Υ (5D))∼135eV appears to be close to Γee(Υ(11020)) and therefore this resonance may become manifest in the e+e- experiments. The mass differences between M(nD) and M((n+1)S) (n=4, 5) are shown to be rather small, 50±10MeV. © 2009 The American Physical Society