Phase Diagram, Scalar-Pseudoscalar Meson Behavior and Restoration of Symmetries in (2+1) Polyakov-Nambu-Jona-Lasinio Model

We explore the phase diagram and the modification of mesonic observables in a hot and dense medium using the (2+1) Polyakov-Nambu-Jona-Lasinio model. We present the phase diagram in the ($T,\,\mu_B$)-plane, with its isentropic trajectories, paying special attention to the chiral critical end point (CEP). Chiral and deconfinement transitions are examined. The modifications of mesonic observables in the medium are explored as a tool to analyze the effective restoration of chiral symmetry for different regions of the phase diagram. It is shown that the meson masses, namely that of the kaons, change abruptly near the CEP, which can be relevant for its experimental search.Comment: 25 pages, 11 figures, 2 table

CMB statistical isotropy confirmation at all scales using multipole vectors

We present an efficient numerical code and conduct, for the first time, a null and model-independent CMB test of statistical isotropy using Multipole Vectors (MVs) at all scales. Because MVs are insensitive to the angular power spectrum $C_\ell$, our results are independent from the assumed cosmological model. We avoid a posteriori choices and use pre-defined ranges of scales $\ell\in[2,30]$, $\ell\in[2,600]$ and $\ell\in[2,1500]$ in our analyses. We find that all four masked Planck maps, from both 2015 and 2018 releases, are in agreement with statistical isotropy for $\ell\in[2,30]$, $\ell\in[2,600]$. For $\ell\in[2,1500]$ we detect anisotropies but this is indicative of simply the anisotropy in the noise: there is no anisotropy for $\ell < 1300$ and an increasing level of anisotropy at higher multipoles. Our findings of no large-scale anisotropies seem to be a consequence of avoiding \emph{a posteriori} statistics. We also find that the degree of anisotropy in the full sky (i.e. unmasked) maps vary enormously (between less than 5 and over 1000 standard deviations) among the different mapmaking procedures and data releases.Comment: v4: additional analysis which increased statistical sensitivity, including new plots and tables; extended discussion; 15 pages, 14 figures, 7 tables. Matches published versio

Building models of quarks and gluons with an arbitrary number of colors using Cartan-Polyakov loops

In this work we introduce the concept of Cartan-Polyakov loops, a special subset of Polyakov loops in the fundamental representation of the $\mathrm{SU}(N_c)$ group, with charges $k=1,\ldots,(N_c-1)/2$. They constitute a sufficient set of independent degrees of freedom to parametrize the thermal Wilson line. Using properties of the characteristic polynomial of the thermal Wilson line, we write a non-Cartan-Polyakov loop charge decomposing formula. This formalism allows one to readily build effective models of quarks and gluons with an arbitrary number of colors. We apply it to the Polyakov$-$Nambu$-$Jona-Lasinio model and to an effective glue model, in the mean field approximation, showing how to directly extend these models to higher values of $N_c$.Comment: 26 page

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This paper proposes a gain-scheduling control design strategy for a class of linear systems with the presence of both input saturation constraints and norm-bounded parametric uncertainty. LMI conditions are derived in order to obtain a gain-scheduled controller that ensures the robust stability and performance of the closed loop system. The main steps to obtain such a controller are given. Differently from other gain-scheduled approaches in the literature, this one focuses on the problem of H∞ loop shaping control design with input saturation nonlinearity and norm-bounded uncertainty to reduce the effect of the disturbance input on the controlled outputs. Here, the design problem has been formulated in the four-block H∞ synthesis framework, in which it is possible to describe the parametric uncertainty and the input saturation nonlinearity as perturbations to normalized coprime factors of the shaped plant. As a result, the shaped plant is represented as a linear parameter-varying (LPV) system while the norm-bounded uncertainty and input saturation are incorporated. This procedure yields a linear parameter-varying structure for the controller that ensures the stability of the polytopic LPV shaped plant from the vertex property. Finally, the effectiveness of the method is illustrated through application to a physical system: a VTOL “vertical taking-off landing” helicopter

The strange critical endpoint and isentropic trajectories in an Extended PNJL Model with Eight Quark Interactions

In this work, we explore the possible existence of several critical endpoints in the phase diagram of strongly interacting matter using an extended PNJL model with 't Hooft determinant and eight quark interactions in the up, down and strange sectors. Besides, we also study the isentropic trajectories crossing both (light and strange) chiral phase transitions and around the critical endpoint in both the crossover and first-order transition regions.Comment: 12 pages, 3 figure