Color plasma oscillation in strangelets

At extremely high temperature and/or baryon density, quark-gluon plasmas [1] are considered to be energetically favorable as compared with hadronic matter. Such extreme conditions prevent us from confirming the presence of quark-gluon plasmas, although it is expected in interiors of neutron stars and in ultrarelativistic heavy-ion collisions. The intriguing possibility that strange quark matter, composed of u, d, and s quarks, might be the ground state of the strong interaction was pointed out by Witten [2]. If this is correct, finite strange quark matter, which is usually referred to as strangelets, would be a more stable self-bound system than a Fe nucleus. Then, disruption of neutron stars and highly energetic heavy-ion collisions could leave behind many strangelets. This might allow us to detect quark-gluon plasmas in the form of strangelets under various experimental situations [3–5]. The ground-state properties of strangelets were described by Farhi and Jaffe [6] within the MIT bag model; finitesize effects such as surface, Coulomb, and shell effects were taken into account. In ultrarelativistic heavy-ion collisions, however, the possibly formed strangelets should be accompanied by thermally excited states. Among various excitations, we take note of spinand flavor-symmetric, longitudinal color plasmons [7,8] that represent collective counteroscillations of different color degrees of freedom. In a strangelet, these plasmons are expected not only to exhibit a dispersion relation dependent on the color dielectric property of the medium, but also to undergo a size-dependent damping as in the case of an optically excited metal cluster or nanoparticle. When the nanoparticle is small enough for the electrons to be nearly collisionless and for the electric dipole radiation to be of little significance but is too large for the shell structure to take effect, the surface plasmon excitations are damped in a time proportional to the size [9,10]. Their energy is resonantly absorbed by individual excitations of particle-hole pairs of the electrons having discrete energy levels due to the presence of the boundary. Notice that the quark-gluon plasma in a strangelet is fully relativistic in contrast to the electron gas in a nanoparticle. Consequently, new features should arise from spin-orbit interactions and from excitations involving antiquarks, both of which may affect the lifetimes of the color plasmons. Longitudinal color plasma oscillations in relativistic and degenerate bulk matter of u, d, and s quarks were investigated [7,8] by calculating the current-current correlation function within the random-phase approximation (RPA) which is valid in the weak-coupling limit. The dispersion law and damping for these oscillations are essentially the same as those examined by Jancovici [11] for electromagnetic plasma oscillations in a relativistic and degenerate electron gas. In either case, the mode properties are characterized by the corresponding plasma frequency and Landau damping as in a nonrelativistic plasma. In this paper, we estimate the long-wavelength, low-temperature properties of longitudinal color oscillation modes in a strangelet of macroscopic size, surrounded by the QCD vacuum, by incorporating the discrete energy levels of quarks into the current-current correlation function within the RPA. The vanishing color dielectric constant of the vacuum leads to the absence of the surface color charge; if present, it would modify the effective color electric field inside the strangelet according to a Mie-type formula. We thus find that the frequency of the longitudinal color plasmons in the strangelet is almost the same as that in bulk quark matter. The lifetime of the plasmons is determined by the dipole transitions from a quark state in the Fermi sea to an unoccupied one. It is shown that the quark particle-hole pairs involved damp the plasmons at a rate inversely proportional to the strangelet size. Beyond the RPA, however, the plasmons are further damped by collisions between quarks. In Sec. II, the longitudinal polarization function is calculated up to one-loop order, allowing for the discrete quark