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Bulk matter

Bulk strange matter is a system of up, down, and strange quarks which is bound and stable at zero temperature and pressure. The quarks are not localized to individual baryons, but instead have wave functions that range over the entire size of the system. The system is large enough so that surface effects do not need to be considered. It is electrically neutral, and electrons (or positrons) are within the system as needed.

A model of bulk matter is of interest for two reasons. First, it may describe natural sources of strange matter, such as strange `neutron' stars. Second, bulk matter is the simplest strange matter system available. We can use a simple model of the bulk as a starting point for investigations into other forms of strange matter where additional effects must be considered.

The primary goal of a bulk model is to predict the stability of strange matter. Stability depends on the energy per baryon of the system. If this energy is greater than for nuclear matter, or greater than the mass of a nucleon, it will be unstable toward emission of nuclei or nucleons. Non-strange quark matter is unstable in this way (although it may be stable at high pressure). I will describe a model where the energy per baryon is lowered from the non-strange case, and stability is predicted for certain ranges of QCD parameters.

This model makes several assumptions. First, it assumes that confinement will be satisfied by a collection of 3A quarks separated from the vacuum by a phase boundary. This is necessary as quark matter is not explicitly clumped into baryons. The quarks masses are taken to be their current algebra masses. The quarks are described by a Fermi gas, and the properties of that gas are computed with renormalized perturbative QCD. As a result of these assumptions, this model is limited to fairly rough predictions. In particular, the strong coupling, tex2html_wrap_inline258 is not small at this scale.

The model contains three parameters. B is analogous to the bag constant of a bag model; it represents an external pressure which keeps the system bound. It is essentially a parameterization of the long range QCD confinement force. The other parameters are the mass of the strange quark tex2html_wrap_inline262 , and tex2html_wrap_inline264 . These are both functions of the renormalization scale. In principle, the choice of scale should have no effect on observables, but in this model only first order corrections in tex2html_wrap_inline258 are included, and tex2html_wrap_inline258 itself is not small.

The model starts with a Fermi gas of quarks and electrons. Weak processes maintain equilibrium between the various species. (The resulting dilute neutrinos gas can be ignored regardless of the neutrino mass.) The equilibrium chemical potentials are then


Since the system must be neutral,


where tex2html_wrap_inline274 is the number density for each species. This leaves a single independent chemical potential. The total energy density of the system is


where tex2html_wrap_inline278 is the thermodynamic potential. For a quark of zero mass and tex2html_wrap_inline280 , tex2html_wrap_inline282 . Corrections must be added to tex2html_wrap_inline278 for the strange mass, which will decrease the number of strange quarks in the system. Corrections must also be included in tex2html_wrap_inline278 for non-zero tex2html_wrap_inline258 . For massless quarks, this results in an additional factor of tex2html_wrap_inline290 , working to first order. The correction to tex2html_wrap_inline292 is somewhat more complex.

Higher tex2html_wrap_inline258 results in stronger effects from single gluon exchange. Single gluon exchange will be repulsive for massless, relativistic quarks, and attractive for massive non-relativistic quarks. Increased single gluon exchange will therefore shift the equilibrium to a state of more strange quarks and fewer nonstrange ones. It is possible to have a combination of large tex2html_wrap_inline258 and small tex2html_wrap_inline298 such that strange quarks are more abundant than each of the nonstrange quarks. In this case the overall charge of the quarks in the system will be negative, and positrons will be present to balance the charge. For the finite size systems discussed below, the positrons are not present within the system, and negatively charged strangelets are possible. These would be particularly unpleasant to encounter.

The overall conclusion of this model is that bulk strange matter is stable over a certain region in the three dimensional parameter space tex2html_wrap_inline300 . To see if strange matter may actually exist, it is necessary to determine if the values allowed by the model are consistent with the real world. Unfortunately this is hindered by a number of factors. The `known' values of the parameters are obtained from bag model fits to light hadron spectra. The renormalization point of the bag models is unknown, so neither tex2html_wrap_inline258 nor tex2html_wrap_inline298 can be meaningfully compared. Bag models include phenomenological parameters, and the bag values of tex2html_wrap_inline298 , tex2html_wrap_inline258 , and B will depend on those parameters. The values obtained from bag models also depend on the details of the bag-quark wave functions. While it is not possible to compare the `windows of stability' for strange matter to known values of the parameters, the windows are quite large. It is therefore quite likely that strange quark matter is bound and stable. Even if it is not, it is possible that the additional contributions from finite size effects may make smaller `nuggets' of strange matter stable.

next up previous
Next: Strangelets (A ) and Up: Forms of strange matter Previous: Forms of strange matter

Joshua Holden
Sun May 17 15:37:00 EDT 1998