We propose a modified Polyakov-loop Nambu–Jona-Lasinio (mPNJL) model in which the Polyakov potential is given by an explicit dependence on the quark chemical potential, allowing it to remain finite at zero temperature and thus to describe the confinement-deconfinement transition in cold dense matter. Combining this modified quark sector with hadronic equations of state via a Maxwell construction, we find that, depending on the model parameters, the equation of state can exhibit either two phase transitions, from hadronic matter to confined (quarkyonic) quark matter and subsequently to deconfined quark matter, or a single transition directly from hadronic to deconfined quark matter or from hadronic to quarkyonic quark matter. Stable massive cold hybrid stars with only quarkyonic and/or deconfined quark phases are obtained. We systematically examine how the parameters of the modified Polyakov potential and the quark vector interactions control the location of these transitions, and find that repulsive vector interactions are essential to obtain a stable quark core. Hybrid stars with quarkyonic and/or a deconfined core can reach maximum masses above 2M⊙, provided a sufficiently stiff hadronic equation of state is used at low density. In the core of the maximum-mass configurations, the speed of sound exceeds the conformal limit,

 square of speed of sound = 1/3, for the quarkyonic core stars. This work establishes the qualitative role of each model parameter in shaping hybrid-star structure.

One figure is attached : This figure shows the baryonic density profile from center (r=0) towards surface (r=R ~14 km) for a maximum mass stable star containing three phases : (i) Deconfined quark (ii) Confined quark ( Quarkyonic) (iii) Hadronic.

Hadronic tau decays provide a unique low-energy laboratory for the charged-current interaction between quarks and leptons. Their use as an electroweak precision sector is, however, limited by nonperturbative QCD dynamics in the resonance region, encoded in hadronic form factors. In this work we show that angular information in two-hadron tau decays can be used to construct observables in which these form factors cancel, leading to first-principles Standard Model predictions up to light-quark-mass and radiative corrections. We derive the fully differential distributions for arbitrary two-pseudoscalar final states, including tau polarization, and extend them to the Weak Effective Field Theory at linear order in new-physics couplings. We then illustrate our strategy with several benchmark observables, for both unpolarized and polarized taus, whose Standard Model predictions can be obtained without modelling the dominant hadronic form factors and which receive characteristic beyond-the-Standard-Model corrections, in particular from tensor currents. These results provide concrete targets for Belle II, polarized-tau proposals such as Chiral Belle, and future high-statistics facilities, including super-tau-charm factories and FCC-ee, to test the electroweak structure of hadronic tau decays.

Contrary to naive expectations, poles used to define hadron resonances rigorously in the physical world may not evolve continuously to become degenerate in the SU(3) flavor and chiral limits of QCD. Instead, other shadow poles, usually ignored, may be the ones that degenerate and characterize the resonances in these limits. This feature is general, and we illustrate it first with the simple and familiar light-vector mesons, followed by the much-discussed light-scalar case. Their shadow poles and their degeneracy are found using the QCD low-energy effective theory unitarized to one loop.

Based on: 2606.14634