A 2019 proposal by Davoudiasl suggested that the population of O(10 M⊙)O(10\ M_\odot) black holes observed by LIGO/Virgo could be primordial black holes (PBHs) formed at a first-order QCD confinement phase transition in a deformed early-universe theory, "QCD'", in which a light scalar keeps all six Standard Model quarks light until the transition, pushing the confinement temperature down to an estimated TQCD′∼50T_{QCD'}\sim 50--100100 MeV and thereby raising the QCD-epoch horizon mass to O(10 M⊙)O(10\ M_\odot). Both pillars of the proposal rest on rough one-loop matching and uncomputed cosmology: the nonperturbative confinement temperature and the order of the six-light-flavor transition have never been determined on the lattice, and the PBH mass function, required primordial density-contrast distribution, relic abundance fraction, and stochastic gravitational-wave spectrum of the scenario have not been computed. The open problem is to establish, from the underlying gauge dynamics rather than one-loop estimates, whether a six-light-flavor confinement transition at tens of MeV can quantitatively account for the LIGO/Virgo black-hole population.

Background

The LIGO/Virgo collaborations have observed a population of black holes of roughly ten solar masses in binary mergers. Beyond astrophysical formation channels, it has long been discussed whether such objects could be primordial black holes (PBHs) — black holes formed in the early Universe from the collapse of rare large-amplitude primordial density fluctuations. Production of PBHs is expected to be enhanced at the QCD confinement transition: when the cosmic plasma cools through the transition, the effective number of relativistic degrees of freedom g∗g_* drops, the equation of state softens (the pressure response to compression, governed by the speed of sound, becomes weak), and the horizon-mass scale at that epoch concentrates the resulting PBH masses. The horizon mass — the mass of energy content within one cosmic horizon — scales as MPBH(T)≈2.4γM⊙61.75/g∗(160 MeV/T)2M_{PBH}(T)\approx 2.4\gamma M_\odot\sqrt{61.75/g_*}(160\ \mathrm{MeV}/T)^2, where γ\gamma is an order-one collapse efficiency factor depending on the amplitude of the overdensity. In the Standard Model (SM), however, lattice QCD calculations with physical quark masses (Bhattacharya et al., Phys. Rev. Lett. 113, 082001 (2014)) show that the finite-temperature QCD transition at T≈155T\approx 155 MeV is a smooth crossover, not a phase transition, and the corresponding QCD-epoch horizon mass is only O(1 M⊙)O(1\ M_\odot). Effective-field-theory arguments by Pisarski and Wilczek (Phys. Rev. D 29, 338 (1984)) indicate that with three or more massless quark flavors the chiral confinement transition should be first order (a transition proceeding by bubble nucleation between two coexisting phases, with latent heat); in the SM the strange-quark mass spoils this condition, consistent with lattice results, and a lattice confirmation of the chiral-limit expectation is a continuing subject of lattice research (D'Elia, Nucl. Phys. A 982, 99 (2019)). Davoudiasl (Phys. Rev. Lett. 123, 101102 (2019)) therefore proposed a deformation of early-universe QCD, dubbed QCD′', in which a very light scalar ϕ\phi (mass ∼10−12\sim 10^{-12} eV, itself a dark-matter candidate) couples through vectorlike color-triplet fermions F1,2F_{1,2} (heavy quarklike fermions whose left- and right-handed components transform identically under the Standard Model gauge group, so that their large masses do not require electroweak symmetry breaking) so that all six SM quark Yukawa couplings (the couplings to the Higgs field that generate the quark masses) are suppressed and the quarks stay light, mq≪ΛQCDm_q\ll\Lambda_{QCD}, until the confinement transition at T∗≲100T_*\lesssim 100 MeV. With Nf=6N_f=6 light flavors the one-loop running of the strong coupling αs\alpha_s (its leading-order logarithmic dependence on the energy scale), matched so that αs\alpha_s reaches its confinement value αs∼5\alpha_s\sim 5 at the same coupling strength as in the standard Nf=3N_f=3 case, places the confinement scale at μ6∼50\mu_6\sim 50 MeV (with g∗=93.25g_* = 93.25 counting the light quarks and the still-relativistic SM particles), giving a typical PBH mass MPBH∼20γ M⊙M_{PBH}\sim 20\gamma\ M_\odot — the LIGO/Virgo scale. A first-order transition would further enhance PBH production because the pressure response of the fluid nearly vanishes, so horizon-scale overdensities collapse more readily. The proposal was deliberately order-of-magnitude: the author states that the one-loop estimate "is not meant to be a precision treatment", that the relic PBH abundance is not addressed, and that the required distribution of the density contrast δ\delta was simply assumed. Quantitative PBH formation studies at the QCD epoch exist only for the SM crossover transition with an accurate lattice equation of state (Byrnes, Hindmarsh, Young and Hawkins, JCAP 2018, 041), not for a first-order six-flavor transition; PBH formation in soft generic transitions has been modeled in other frameworks (e.g. Escrivà and Subils, Phys. Rev. D 107, L041301 (2023), using holographic crossover dynamics) but not for this scenario. The open problem is the quantitative establishment — or exclusion — of the scenario from the underlying gauge dynamics and cosmology.

Problem Statement

Establish, from the underlying strong-interaction dynamics rather than one-loop matching, whether the QCD′' scenario can quantitatively account for the LIGO/Virgo black-hole population, by determining: (i) the equilibrium finite-temperature confinement transition of QCD deformed so that all six Standard Model quarks are light (mqm_q well below the confinement scale) at the transition — its critical temperature in MeV, testing the one-loop estimate Tc∼50T_c\sim 50 MeV, and whether the transition is first order (with its latent heat and nucleation parameters) or a crossover; (ii) from those transition inputs, the primordial black hole production at this transition: the resulting PBH mass function — expected, on the horizon-mass scaling MPBH∝g∗−1/2Tc−2M_{PBH}\propto g_*^{-1/2}T_c^{-2} with g∗=93.25g_*=93.25, to peak near O(10 M⊙)O(10\ M_\odot) — together with the primordial density-contrast distribution δ\delta required to yield the observed population, and the relic abundance fraction ff of dark matter in such PBHs, confronted with LIGO/Virgo binary-merger rates and with existing PBH constraints (microlensing, cosmic-microwave-background accretion, dynamical); and (iii) the stochastic gravitational-wave spectrum implied by the same transition parameters, with its detectability at pulsar timing arrays (networks of millisecond pulsars whose timing residuals probe nanohertz gravitational waves) and future detectors. Deliverables (i)-(iii) serve one common objective — the quantitative viability of a first-order six-light-flavor confinement transition at T≲100T\lesssim 100 MeV as the origin of the LIGO/Virgo black holes — and are linked: (ii) and (iii) both take their physical input (equation of state, order of transition, latent heat, nucleation dynamics) from (i), so an acceptable answer must either supply that input nonperturbatively or state and justify the effective framework in which it is modeled. A defensible exclusion of the scenario using (i) and (ii) alone resolves the task, with (iii) then optional; otherwise all of (i)-(iii) are required.

References

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