The prevailing assumption is that stable hadrons containing strange quarks are not possible.

But, the Bodmer-Witten hypothesis is a conjecture that under the right conditions, stable matter containing strange quarks is possible. The hypothesis is named after papers by Bodmer and Witten respectively, making this conjecture, specifically: A. R. Bodmer, Phys. Rev. D 4 (1971) 1601. doi:10.1103/PhysRevD.4.1601 and E. Witten, Phys. Rev. D 30 (1984) 272.

But, a new paper examines the conditions under which a "strange quark star" could theoretically exist even in fairly sophisticated QCD models, and what its observable properties would be. Telescopes in the relatively near future should be able to determine if any observable stars have properties that would distinguish them as strange quark stars rather than ordinary stars, exist.

The abstract of the paper is vacuous, but the introduction to the paper explains that:

The so called Bodmer-Witten hypothesis on the absolute stability of strange quark matter still represents an open issue of nuclear and particle physics and its validity would have numerous important phenomenological implications in astrophysics (strange quark stars and strangelets in cosmic rays) and, possibly, also in cosmology (strangelets as a component of baryonic dark matter).Verifying this hypothesis in terrestrial experiments is however very difficult because of the large net strangeness carried by this form of strongly interacting matter.

On the other hand, theoretical calculations of the mass and density of strange quark matter droplets and of the thermodynamic properties of bulk strange quark matter are affected by large uncertainties due to the intrinsic difficulty of solving QCD at finite (but not asymptotically large) baryon densities.

In this short contribution we will analyze two aspects related to the possibility of the existence of strange quark matter.

First, we will show that this hypothesis can be fulfilled also in a class of quark models which feature not only confinement (as the MIT bag model) but also chiral symmetry. Specifically, we will show results obtained within the so-called chiral chromodielectric model.

The second aspect concerns the astrophysical measurements of masses and radii of compact stars. Precise radii measurements (which will be feasible in the near future) could indeed unambiguously check the validity of the Bodmer-Witten hypothesis. Let us define R1.4 as the radius of a 1.4M⊙ compact star. As found in it is not possible to have a unique family of compact stars satisfying at the same time the condition R1.4 less than approximately 11km and Mmax ≤ 2M⊙. This conclusion has been confirmed also by other recent analyses. If future measurements will confirm the existence of stars for which R1.4 is less than approximately 11km, then one can conclude that strange quark stars co-exist with hadronic stars. In this two families scenario compact and light stars are hadronic stars whereas large and massive stars are strange quark stars.

The conclusion then goes on to note that:Since the ∼ 2M⊙ compact stars are, in this scenario, interpreted as strange quark stars that implies that the density of bound strange quark matter (i.e. the density corresponding to the minimum of the energy per baryon) is between 1-2 times nuclear matter saturation density. It is important to remark that although the absolute minimum of the energy per baryon of nuclear matter is located at a density similar to the density of strange quark matter they differ concerning the strangeness content. This implies that a direct transition from the metastable nucleonic state to the ground state of quark matter is suppressed because it requires multiple weak decays.

We have discussed the possibility of the existence of strange quark matter first within a purely theoretical approach, by using three different chiral models for quark matter and after within phenomenological approach through the measurements of masses and radii of compact stars.

The Bodmer-Witten hypothesis could be fulfilled only if spontaneous chiral symmetry breaking and dynamical confinement are both implemented in the adopted quark model. In particular we have shown that a pure SU(3) quark meson chiral model, even in the presence of the additional dilaton field, does not allow for the existence of strange quark matter. Instead, in a simple confining chiral model, the chiral chromo-dielectric model, it is possible to find a window of parameters for which strange quark matter is absolutely stable.

It is remarkable that the sets of parameters corresponding to these cases, are quite similar to the sets of parameters usually adopted for the study of hadronic observables.

Finally, we have discussed what are the implications for the equation of state from the existence of massive compact stars and how future measurements of radii can be used to test fundamental properties of dense matter.

In particular,Astronomy observations that could distinguish between strange quark stars and more ordinary massive small stars will soon be available to test this possibility.a strong indication of the validity of the Bodmer-Witten hypothesis will be measurements of R1.4 less than approximately 11 km.The existence of stars as massive as 2M⊙ (or more) would indicate that if the Bodmer-Witten hypothesis is correct, the (second) minimum of the energy per baryon of strongly interacting matter is located at a density slightly above the nuclear matter saturation density. Differently from the minimum corresponding to nuclear matter, this second minimum would contain a net strangeness fraction close to 1/3. The possibility to search for this kind of matter also in terrestrial experiments would be in this case very promising.

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