Development of Bethe-Salpeter theory for dealing with unstable system

Abstract

In the framework of relativistic quantum field theory, the solution of homogeneous Bethe-Salpeter equation for two-body bound state can not describe unstable system, so we develop Bethe-Salpeter theory to investigate resonance which is regarded as an unstable two-body system. Based on Bethe-Salpeter wave function, we consider the time evolution of two-body bound state determined by the total Hamiltonian. The total matrix element for arbitrary decay channel is expressed in terms of the Heisenberg picture, and Mandelstam's approach is generalized to calculate the matrix element between bound states with respect to arbitrary value of the final state energy. Some innovations to Feynman diagram are made so that the key features of dispersion relation can be more clearly exhibited. This new resonance theory in quantum field theory is applied to investigate exotic particle which is considered as an unstable meson-meson molecular state.

arXiv commentarXiv admin note: text overlap with arXiv:2210.01563

References in corpus (20)

• Feshbach Resonances in Ultracold Gases
• Diquark-Antidiquarks with Hidden or Open Charm and the Nature of X(3872)
• Isospin breaking of the narrow charmonium state of Belle at 3872 MeV as a deuson
• Pion mass and decay constant
• Short Range Structure in the X(3872)
• Observation of a near-threshold omega-J/psi mass enhancement in exclusive B-->K omega J/psi decays
• Amplitude analysis of the $B^{+}\to D^{+}{D}^{-}{K}^{+}$ decay
• Masses of heavy tetraquarks in the relativistic quark model
• Are Y(4260) and {\rm Z${}_2^{+}$(4250)} ${\mathrm{D}}_1\mathrm{D}$ or ${\mathrm{D}}_0{\mathrm{D}}^{\ast }$ Hadronic Molecules?
• Hadronic molecule structure of the Y(3940) and Y(4140)
• Survey of heavy-meson observables
• Y(4143) is probably a molecular partner of Y(3930)
• Decay channels and charmonium mass-shifts
• Indications of a Four-Quark Structure for the X(3872) and X(3876) Particles from Recent Belle and BABAR Data
• Interquark potential with finite quark mass from lattice QCD
• B- to light-meson transition form factors
• Investigation of the possible $D{\bar{D}}^{\ast }$/$B{\bar{B}}^{\ast }$ and $D{D}^{\ast }$/$\bar{B}{\bar{B}}^{\ast }$ molecule states
• Search for B decays to final states with the eta_c meson
• Mass of Y(3940) in Bethe-Salpeter equation for quarks
• Radiative decay of hadronic molecule state for quarks

Cited by in corpus (1)

• Calculation of mass and width of unstable molecular state using the developed Bethe-Salpeter theory