We study general features of three-meson bound states using the Y(4660) as an example. Here the Y(4660) is assumed to be either a two-body bound state of the f_0(980), itself a bound state of K and Kbar, and the psi'= psi(2s), or a three-body bound state of psi', K, and Kbar. In particular, we investigate in detail the interplay of the various scales inherent in the problem, namely the f_0 binding energy, the Y binding energy, and the K-psi' scattering length. This allows us to understand under which circumstances the substructure of the f_0(980) can be neglected in the description of the Y(4660).
The equations which relate three-body and two-body symmetry violating scattering amplitudes are derived in the first order of symmetry violating interactions. They can be used to obtain three-body symmetry violating scattering amplitudes from two-body symmetry violating scattering amplitudes calculated in low energy effective field theory.
The Bethe-Salpeter equation for three bosons with zero-range interaction is solved for the first time. For comparison the light-front equation is also solved. The input is the two-body scattering length and the outputs are the three-body binding energies, Bethe-Salpeter amplitudes and light-front wave functions. Three different regimes are analyzed: ({\it i}) For weak enough two-body interaction the three-body system is unbound. ({\it ii}) For stronger two-body interaction a three-body bound state appears. It provides an interesting example of a deeply bound Borromean system. ({\it iii}) For e…
The cancellation between off-shell two body forces and three body forces implies a tremendous simplification in the study of three body resonances in two meson-one baryon systems. While this can be done by means of Faddeev equations we provide an alternative and simpler derivation using just the chiral Lagrangian and the field re-parametrization invariance.
Probing the three-body force in hadronic systems with specific charge parity
Beihang University（北京航空航天大学）；Lanzhou University（兰州大学）；École Centrale de Pékin/School of General Engineering, Beihang University（北京航空航天大学中法工程师学院/通用工程学院）；Peng Huanwu Collaborative Center for Research and Education, Beihang University（北京航空航天大学彭桓武研究中心）；Beijing Key Laboratory of Advanced Nuclear Materials and Physics, Beihang University（北京航空航天大学先进核材料物理北京市重点实验室）；Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心）
We study the scattering of a light particle on a bound pair of heavy particles (e.g., the deuteron) within the fixed center approximation in the case of light-heavy attraction, solving the integral equation for the three-body Green's function both in the coordinate and in the momentum space. The results for the three-body scattering amplitude appear to be ambiguous -- they depend on a single real parameter. This parameter may be fixed by a three-body input, e.g., the three-body scattering length. We also solve the integral equation for the three-body Green function in the momentum space, intro…
We study the three-body system with short-range interactions characterized by an unnaturally large two-body scattering length. We show that the off-shell scattering amplitude is cutoff independent up to power corrections. This allows us to derive an exact renormalization group equation for the three-body force. We also obtain a renormalized equation for the off-shell scattering amplitude. This equation is invariant under discrete scale transformations. The periodicity of the spectrum of bound states originally observed by Efimov is a consequence of this symmetry. The functional dependence of t…
We study the short distance part of the intrinsic three-nucleon interaction in a constituent quark model with color-spin interaction. For that purpose we first calculate the transformation coefficient between the tribaryon configuration and their corresponding three baryon basis. Using a formula for the intrinsic three-body interaction in terms of a tribaryon configuration, we find that after subtracting the corresponding two-baryon contributions, the intrinsic three-body interaction vanishes in flavor SU(3) symmetric limit for all quantum numbers for the three nucleon states. We further find …
Within the framework of non-relativistic scalar effective field theory it is shown that the problem of the cutoff dependence of the leading order amplitude for a particle scattering off a two-body bound state can be solved without introducing three-body forces.
The particle exchange model of hadron interactions can be used to describe three-body scattering under the isobar assumption. In this study we start from the 3->3 scattering amplitude for spinless particles, which contains an isobar-spectator scattering amplitude. Using a Bethe-Salpeter Ansatz for the latter, we derive a relativistic three-dimensional scattering equation that manifestly fulfills three-body unitarity and two-body unitarity for the sub-amplitudes. This property holds for energies above breakup and also in the presence of resonances in the sub-amplitudes.
A chiral invariant effective Lagrangian may be used to calculate the three-body interactions among low-energy pions and nucleons in terms of known parameters. This method is illustrated by the calculation of the pion-nucleus scattering length.
Bethe-Salpeter and light-front bound state equations for three scalar particles interacting by scalar exchange-bosons are solved in ladder truncation. In contrast to two-body systems, the three-body binding energies obtained in these two approaches differ significantly from each other: the ladder kernel in light-front dynamics underbinds by approximately a factor of two compared to the ladder Bethe-Salpeter equation. By taking into account three-body forces in the light-front approach, generated by two exchange-bosons in flight, we find that most of this difference disappears; for small exchan…
This contribution is an advertisement for applying effective field theory (EFT) to many-body problems, including nuclei and cold atomic gases. Examples involving three-body interactions are used to illustrate how EFT's quantify and systematically eliminate model dependence, and how they make many-body calculations simpler and more powerful.
Resonant hadronic systems often exhibit a complicated decay pattern in which three-body dynamics play a relevant or even dominant role. In this work we focus on the $a_1(1260)$ resonance. For the first time, the pole position and branching ratios of a three-body resonance are calculated from lattice QCD using one-, two-, and three-meson interpolators and a three-body finite-volume formalism extended to spin and coupled channels. This marks a new milestone for ab-initio studies of ordinary resonances along with hybrid and exotic hadrons involving three-body dynamics.
We present the renormalization scheme used in and the characteristic features of GRACE/SUSY-loop, the package of the program for the automatic calculation of the MSSM processes including one-loop order corrections. The two-body and three-body decay widths of charginos in one-loop order evaluated by GRACE/SUSY-loop are shown.
Motivated by the existence of candidates for exotic hadrons whose masses are close to both of two-body and three-body hadronic thresholds lying close to each other, we study degenerate two-body and three-body coupled-channel systems. We first formulate the scattering problem of non-degenerate two-body and three-body coupled-channels as an effective three-body problem, i.e.\ effective Alt-Grassberger-Sandhas (AGS) equations. We next investigate the behavior of $S$-matrix poles near the threshold when two-body and three-body thresholds are degenerate. We solve the eigenvalue equations of the ker…
We start from a field-theoretical model of zero range approximation to derive three-dimensional relativistic two- and three-body equations on a null plane. We generalize those equations to finite range interactions. We propose a three-body null-plane equation whose form is different from the one presented earlier in the framework of light-cone dynamics. We discuss the choices of the kernels in two- and three-body cases and apply our model to the description of meson and baryon Regge trajectories. Our approach overcomes some theoretical and phenomenological difficulties met in preceding relativ…
From dispersion relation approach, a formalism that describes final state interaction among three particles in a coupled-channel system is presented in this work. Different representations of coupled-channel three-body formalism with only spinless particles in both initial and final states are derived.
It is often assumed that few- and many-body systems can be accurately described by considering only pairwise two-body interactions of the constituents. We illustrate that three- and higher-body forces enter naturally in effective field theories and are especially prominent in strongly interacting quantum systems. We focus on three-body forces and discuss examples from atomic and nuclear physics. In particular, we highlight the importance and the challenges of three-nucleon forces for nuclear structure and reactions, including applications to astrophysics and fundamental symmetries.
In this work, based on consideration of periodicity and asymptotic forms of wave function, we propose a novel approach to the solution of finite volume three-body problem by mapping a three-body problem into a higher dimensional two-body problem. The idea is demonstrated by an example of two light spinless particles and one heavy particle scattering in one spatial dimension. This 1D three-body problem resembles a two-body problem in two spatial dimensions mathematically, and quantization condition of 1D three-body problem is thus derived accordingly.
In this talk I discuss three-body decays of the SUSY Higgs bosons which proceed via intermediate two-body states in which one of the particles is off-mass-shell. Some of these decays will be shown to have substantial branching ratios in some range of the SUSY parameter space.
Three body heavy meson decays allows one to extract important quantities for flavour physic, however the phenomenological analysis has some open problems to be solved in order to make possible to extract physical parameters with precision. After many years and some experience accumulated, we have learned new features and we expect to learn much more from data coming mainly from B three body decays. In this paper we address these aspects and we present a proposal to modify the Dalitz fit amplitude method in order to allow further studies.
Three-body final states are included in the calculation of cross section and neutrino production in neutralino annihilations. In some regions of the parameter space, three-body channels maybe important and can enhance the neutrino flux by a few times.
We calculate the cross section for s-wave neutralino annihilation to three-body final states below the W^+ W^- and t-bar t thresholds. Such three-body channels may dominate the annihilation cross section if the neutralino mass is not too much less than m_t and m_W respectively. Furthermore, because neutrinos produced in these channels are much more energetic than those from the $b\bar{b}$ or tau^+ tau^- channels, they can dominate the energetic-neutrino fluxes from neutralino annihilation in the Sun or Earth far below these thresholds and significantly enhance the neutrino signal in certain re…
The group theoretical description of the three-particle problem provides successful techniques for the solution of different questions. We present here a review of this approach.
