Magnetized QCD phase diagram: critical end points for the strange quark phase transition driven by external magnetic fields
MMagnetized QCD phase diagram: critical end pointsfor the strange quark phase transition driven byexternal magnetic fields
Pedro Costa ∗ , Márcio Ferreira and Constança Providência CFisUC, Department of Physics, University of Coimbra, P-3004 - 516 Coimbra, PortugalE-mail: [email protected] , mferreira@teor.ïˇn ˛As.uc.pt , [email protected] In this work we examine possible effects of an external magnetic field in the strongly interactingmatter phase diagram. The study is performed using the Polyakov-Nambu-Jona-Lasinio model.Possible consequences of the inverse magnetic catalysis effect on the phase diagram at both finitechemical potential and temperature are analyzed. We devote special emphasis on how the locationof the multiple critical end points (CEPs) change in a magnetized medium: the presence of anexternal magnetic field induces several CEPs in the strange sector, which arise due to the multiplephase transitions that the strange quark undergoes. We also study the deconfinement transitionwhich turns out to be less sensitive to the external magnetic field when compared to the quarkphase transitions. The crossover nature of the deconfinement is preserved over the whole phasediagram.
XVII International Conference on Hadron Spectroscopy and Structure - Hadron201725-29 September, 2017University of Salamanca, Salamanca, Spain ∗ Speaker. c (cid:13) Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/ a r X i v : . [ h e p - ph ] D ec EP for the strange quark phase transition driven by external magnetic fields
Pedro Costa
The QCD phase diagram and the respective chiral critical end point (CEP), belong to a set ofquantum field theoretical phenomena that are affected by the presence of external magnetic fields(see Fig. 1) [1]. A great attention has recently been given to this subject [2, 3, 4, 5] due to itsrelevance for heavy ion collisions (HIC) measurements [6], for the physics of compact stars [7],and for the understanding of the primordial stages of the universe [8]. Having this in mind, differentscenarios involving regions of the phase diagram in the presence of external magnetic fields werestudied using the Polyakov–Nambu-Jona-Lasinio (PNJL) model with (2+1)-flavors [9, 10, 11].In some of these works, it was analyzed how the location of the CEP depends on the presenceof magnetic fields. In [9], for example, it was shown that large isospin asymmetry moves theCEP to smaller temperatures leading, eventually, to its disappearance from the phase diagram.Nevertheless, a first-order phase transition will be restored in the phase diagram if a strong enoughmagnetic field is present. M ag n e t i c F i e l d Superconductor Phases
Baryon Chemical Potential
Quark-GluonPlasma T e m p e r a t u r e Figure 1:
Schematic structure of the QCD matter in the presence of an external magnetic field.
One well known and understood mechanism induced by the presence of an external magneticfield is the catalyzing effect on the dynamical chiral symmetry breaking, the so-called MagneticCatalysis (MC) effect [12]. Lattice QCD (LQCD) studies at finite temperature have shown, how-ever, that the magnetic field has an interesting behavior in the transition temperature region: insteadof catalyzing, it weakens the dynamical chiral symmetry breaking, the so-called Inverse MagneticCatalysis (IMC) [13]. Several explanations have been proposed to clarify this unexpected effect[1]. Motivated by LQCD calculations reported in [14], the IMC effect was incorporated success-fully for the first time in [2]: with the introduction of an indirect weakening of the model scalarcoupling, G s , with B (via the Polyakov potential), it was obtained an extended (2+1)-PNJL modelthat presented an IMC effect for the quarks condensates at finite temperature. Later in [3], we con-sidered the screening effects of strong interactions through the scalar coupling ( G s ( eB ) ), achievinga qualitative agreement with LQCD results.At finite temperature and density/chemical potential, we now study how the IMC mechanism,1 EP for the strange quark phase transition driven by external magnetic fields
Pedro Costa via a magnetic field dependent coupling G s ( eB ) , affects the first order region and the position ofthe CEP. In Fig. 2 we present the phase diagram ( T − µ B plane - upper panels; T − ρ B plane -lower panels) for three different cases: eB = eB = . and G s = const . (noIMC effect) - middle panels; eB = . and G s ( eB ) (with IMC effect) - right panels. Fromthe upper panels, we conclude that the presence of a magnetic field will: a) enlarge the spinodalregion for the light sector, being more pronounced without an IMC mechanism (middle panel); b)move the light CEP to lower values of µ B , being stronger when the IMC effect is present (rightpanel); c) generate multiple first-order phase transitions for the strange sector with the respectiveappearance of multiple CEPs in this sector (for eB (cid:38) . , only one strange CEP exists).Instead of a single first-order phase transition connecting the vacuum phase to the chirally restoredphase, several intermediate first-order phase transitions take place that are generated by Landauquantization, induced by the magnetic field presence, and a succession of partial restorations of thechiral symmetry. T ( MeV ) m B ( M e V ) e B = 0 . 3 G e V G S m B ( M e V ) e B = 0 . 3 G e V G S ( e B ) m B ( M e V ) G S ( e B ) r B / r e B = 0 T ( MeV ) r B / r r B / r e B = 0 . 3 G e V G Figure 2:
The T − µ B (top panels) and T − ρ B (bottom panels) diagrams for: eB = eB = . and G s = const . , scenario with no IMC mechanism (middle); and eB = . and G s ( eB ) , scenariowith IMC mechanism (right panel). The baryonic density ρ B is represented in units of saturation density, ρ = .
16 fm . Another relevant aspect for both, light and strange, transitions is that for stronger magneticfields the spinodal region is enlarged, being this region bigger for G s = G s [15]. The first-orderlines are moved to lower baryonic chemical potentials. From the bottom panels of Fig. 2, we alsoconclude that the upper baryonic densities at which the onset of both spinodal and binodal regions2 EP for the strange quark phase transition driven by external magnetic fields
Pedro Costa occur increase with B for both cases. Moreover, the spinodal region for the strange quark is muchsmaller than for the light quarks and is located at higher values of ρ B .Concerning the CEPs, we present the results in Fig. 3 (left panel). We start by comparingthe CEP’s position for the light sector ( u and d quarks) with and without the IMC mechanism.For magnetic fields lower than 0 . , we have found that the presence of an IMC mechanismhas a small effect in the CEP position, i.e., the CEPs move towards higher values of T and µ B inboth scenarios (see red and black curves). For higher magnetic fields, however, the CEP is movedto lower µ B with increasing magnetic fields for G s ( eB ) , while the temperature remains almostunchanged [10]. Indeed, the G s ( eB ) results indicate that, for high enough magnetic fields, the CEPgoes towards the µ B = G s ): above a critical magnetic field strength, the CEP location is shifted to higher values of T and µ B with increasing magnetic field [9].
300 500 700 900 1100 1300 1500050100150200250 G s = G s (eB) G s = G s eB G s = G s (eB) G s = G s eBeB T ( M e V ) � B (MeV) eB = 0.3 GeV eB = 0.6 GeV � B (MeV) T ( M e V )
0 250 500 750 1000 1250 1500
Figure 3:
Left panel: CEPs of the light (red and black) and strange (blue and magenta) quarks as a functionof B for both scenarios: a constant coupling, G s , and magnetic dependent coupling, G s ( eB ) . The magneticfield increases from 0 to 1 GeV in the arrows’ directions. Right panel: Φ ( T , µ B ) = . G s = G s (fulllines) and when G s ( eB ) (dashed lines) for eB = . (black lines) and eB = . (red lines). Let us now focus our attention on the CEP of the strange sector. As we already saw, thepresence of a magnetic field induces multiple CEPs. For both scenarios, we focus only on theCEP appearing at lower µ B ( ρ B ) in Fig. 2 that remains up to eB ∼ (the CEP at higher µ B disappears from the phase diagram at eB ∼ . ; similarly to the CEP for light sector [9]).The CEP’s position shows a different behavior depending on the presence of an IMC mechanism:while at lower values of B it moves towards lower µ B in both scenarios, at high magnetic fields the T CEP increases monotonously with the intensity of the magnetic field for a constant coupling G s ,but T CEP is a decreasing function when we have G s ( eB ) .With increasing B , the position of the CEP in the scenario with G s ( eB ) (blue line) shows somesimilarity with the CEP of the light quarks (red line) by moving to lower µ B . For the constantcoupling G s scenario (magenta line) the CEP goes to higher values of T but lower values of µ B .Finally, some considerations concerning the deconfinement transition. In the presence of amagnetic field the deconfinement transition is still a crossover, having an analytic behavior in op-position to a first-order phase transitions. The crossover transition thus allows for different def-3 EP for the strange quark phase transition driven by external magnetic fields
Pedro Costa initions of the pseudo-critical temperature. In the right panel of Fig. 3, we present the ( T , µ B ) values where Φ ( T , µ B ) = .
5, which is a possible way of defining a pseudo-critical temperaturefor deconfinement, with G s = G s (full lines) and G s ( eB ) (dashed lines) for two magnetic fieldstrengths: eB = . (black lines) and eB = . (red lines). We notice that the locationsof the deconfinement transition is quite insensitive to the presence of an external magnetic field forboth models. Furthermore, the analytic nature of the transition is preserved throughout the phasediagram. Acknowledgments
This work was supported by ’FundaÃ˘gÃˇco para a CiÃłncia e Tecnologia’, Portugal, under theproject No. UID/FIS/04564/2016 and under the Grants No. SFRH/BPD/102273/2014 (P.C.), andunder the project CENTRO-01-0145-FEDER-000014 (MF) through CENTRO2020 program. Thiswork was partly supported by ‘NewCompstar’, COST Action MP1304.
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