W−Z-top-quark bags

Abstract

We discuss a new family of multiquanta-bound states in the standard model which exist due to the mutual Higgs-based attraction of the heaviest members of the standard model, namely, gauge quanta $W$, $Z$, and (anti)top quarks, $\overline{t}$, $t$. We use a self-consistent mean-field approximation, up to a rather large particle number $N$. In this paper we do not focus on weakly bound, nonrelativistic bound states, but rather on ``bags'' in which the Higgs vacuum expectation value is significantly modified or depleted. The minimal number $N$ above which such states appear strongly depends on the ratio of the Higgs mass to the masses of $W$, $Z$, $\overline{t}$, $t$: For a light Higgs mass, ${m}_{H}\ensuremath{\sim}50\text{ }\text{ }\mathrm{GeV}$, bound states start from $N\ensuremath{\sim}O(10)$, but for a ``realistic'' Higgs mass, ${m}_{H}\ensuremath{\sim}100\text{ }\text{ }\mathrm{GeV}$, one finds metastable/bound $W$, $Z$ bags only for $N\ensuremath{\sim}O(1000)$. We also found that in the latter case pure top bags disappear for all $N$, although top quarks can still be well bound to the $W$ bags. Anticipating the cosmological applications (discussed in the following Article [Phys. Rev. D 82, 073019]) of these bags as ``doorway states'' for baryosynthesis, we also consider here the existence of such metastable bags at finite temperatures, when standard-model parameters such as Higgs, gauge, and top masses are significantly modified.