σ-Mesons with Dibaryons

The effect of narrow dibaryon resonances to nuclear matter and structure of neutron stars is investigated in the mean-field theory (MFT) and in the relativistic Hartree approximation (RHA). The existence of massive neutron stars imposes constraints to the coupling constants of the ωand σ-mesons with dibaryons. We conclude that the experimental candidates to dibaryons d1(1920) and d’(2060) if exist form in nuclear matter a Bose condensate stable against compression. This proves stability of the ground state for nuclear matter with a Bose condensate of the light dibaryons. The prospect to observe the long-lived H-particle predicted in 1977 by R. Jaffe [1] stimulated considerable activity in the experimental searches of dibaryons. It was proposed to examine the H-particle production in different reactions [2]. The experiments [3] did not give a positive sign for the H-particle, however, the existence of the H-particle remains an open question which must eventually be settled by experiment. The nonstrange dibaryons with exotic quantum numbers, which have a small width due to zero coupling to the NN -channel, are promising candidates for experimental searches [4]. The data on pion double charge exchange (DCE) reactions on nuclei [5] exhibit a peculiar energy dependence, which can be interpreted [6] as evidence for the existence of a narrow d’ dibaryon with quantum numbers T = 0, J = 0 and the total resonance energy of 2063 MeV. Recent experiments at TRIUMPF (Vancouver) and CELSIUS (Uppsala) seem to support the existence of the d’ dibaryon [7]. A method for searching narrow, exotic dibaryon resonances in the double proton-proton bremsstrahlung reaction is discussed in Ref. [8]. Recently, some indications for a d1(1920) dibaryon in this reaction have been found [9]. When density of nuclear matter is increased beyond a critical value, production of dibaryons becomes energetically favorable. Dibaryons are Bose particles, so they condense in the ground state and form a Bose condensate [10, 11]. An exactly solvable model for a one-dimensional Fermi-system of fermions interacting through a potential leading to a resonance in the two-fermion channel is analyzed in Ref. [12]. The behavior of the system with increasing the density can be interpreted in terms of a Bose condensation of two-fermion resonances. The effect of narrow dibaryon resonances on nuclear matter in the mean field theory (MFT) is analyzed in Refs. [13, 14]. In the limit of vanishing decay width, a dibaryon can be approximately described as an elementary field. Despite the dibaryon Bose condensate does not exist in ordinary nuclei, dibaryons affect properties of nuclear matter and the ordinary nuclei through a Casimir effect. Presence of the background σ-meson mean field inside of nuclei modifies the nucleon and dibaryon masses and in turn modifies the zero-point vacuum fluctuations of the nucleon and dibaryon fields. This effect contributes to the energy density and pressure. It can be evaluated within the relativistic Hartree approximation (RHA). For nucleons, this effect is well known [15]. In the loop expansion of quantum hadrodynamics (QHD), MFT corresponds to the lowest approximation (no loops), while RHA corresponds to the oneloop approximation in a calculation of the equation of state for nuclear matter. At zero temperature, a uniformly distributed system of bosons with attractive potential is energetically unstable against compression and collapses [16]. In such a case, the long wave excitations (sound in the medium) have imaginary dispersion law: The square of the sound velocity is negative a2s < 0. The amplitude of these excitations increases with the time, providing instability of the system. It is necessary to analyze dispersion laws of other elementary excitations also. We shall see, however, that in MFT and RHA only sound waves can generate an instability. The ground state of nuclear matter with a Bose condensate of dibaryons is stable or unstable against small perturbations according as the repulsive ω-meson exchange or the attractive σ-meson exchange is dominant between dibaryons. In this paper, we investigate the hypothesis that the dibaryon matter is unstable against compression. In such a case, formation of dibaryons in nuclear matter can be treated as a possible mechanism for a phase transition into the quark matter. If central density of a massive neutron stars exceeds a critical value for formation of dibaryons, the neutron star should convert into a quark star, a strange star, or a black hole. Some of the observed pulsars are identified quite reliably with ordinary neutron stars [17]. From the requirement that the dibaryon formation is not energetically favorable at densities lower than the central density of neutron stars with a mass 1.3M⊙, we derive constraints to the coupling constants of the mesons and dibaryons d1(1920) and d (2060) and conclude that narrow dibaryons in this mass range can form a Bose condensate stable against perturbations only. The effect of the dibaryons to stability and structure of neutron stars in different phenomenological models is analyzed in Refs. [11, 18]. Constraints to the binding energy of strange matter [19] from the existence of massive neutron stars are discussed in Ref. [20]. The dibaryonic extension of the Walecka model [15] is obtained by including dibaryons to the Lagrangian density [13, 14] L = Ψ̄(i∂μγμ −mN − gσσ − gωωμγμ)Ψ + 1 2 (∂μσ) 2 − 1 2 m2σσ 2 − 4 F 2 μν + 1 2 m2ωω 2 μ + (∂μ − ihωωμ)φ ∗(∂μ + ihωωμ)φ− (mD + hσσ) φφ. (1) Here, Ψ is the nucleon field, ωμ and σ are fields of the ωand σ-mesons, Fμν = ∂νωμ−∂μων , φ is the dibaryon isoscalar-scalar (or isoscalar-pseudoscalar) field. The values mω and mσ are the ωand σ-meson masses and the values gω, gσ, hω, hσ are coupling constants of the ωand σ-mesons with nucleons (g) and dibaryons (h). The σ-meson mean field σc determines the effective nucleon and dibaryon masses in the medium m∗N = mN + gσσc, (2) m∗D = mD + hσσc. (3) The nucleon scalar density in the RHA is defined by expression [15] ρNS =< Ψ̄(0)Ψ(0) >= γ ∫ dp (2π) m∗N E(p) θ(pF − |p|)− 4m 3 Nζ(m ∗ N/mN ) (4)