Bled Workshops in Physics Vol. 15, No. 1 p. 10 A Proceedings of the Mini-Workshop Quark Masses and Hadron Spectra Bled, Slovenia, July 6 - 13, 2014 Quark matter in strong magnetic fields Débora Peres Menezes Universidade Federal de Santa Catarina, Departamento de Física-CFM-CP 476, Campus Universitario-Trindade, CEP 88040-900, Florianopolis-SC, Brazil Abstract. In the present work we are interested in understanding various properties of quark matter described by the Nambu-Jona-Lasinio (NJL) model once it is subject to strong magnetic fields. We start by analysing the possible different phase diagram structures. Secondly, we investigate the differences arising from different vector interactions in the La-grangian densities and apply the results to stellar matter. We then look at deconfinement and chiral restauration properties at zero chemical potential with the (entagled) Polyakov NJL models. Finally, we investigate the position of the critical end point for different chemical potential and density scenarios. 1 Motivation and Results The study of the QCD phase diagram, when matter is subject to strong external magnetic fields has been a topic of intense investigation recently. The fact that magnetic fields can reach intensities of the order of B ~ 1019 G or higher in heavy-ion collisions [1] and up to 1018 G in the center of magnetars [2] made theoretical physicists consider matter subject to magnetic field both at high temperatures and low densities and low temperatures and high densities. We describe quark matter subject to strong magnetic fields within the SU(3) (E)PNJL model with vector interaction: L = ff [iy^D^ - Af] ff + £Sym + £det + Lvec + U (®,<6;T) - ^F^, (1) with 8 Lsym = G Y_ [(if fA if)2 + (f fiY5Aa!f)2] , a=0 Ldet = -K {detf [ff(1 + Y5)if] + detf [ff (1 - Y5)ff]} , where f f = (u, d, s)T represents a quark field with three flavors, Ac = diagf(mu,md,ms) is the corresponding (current) mass matrix, A0 = ^J2/31 where I is the unit matrix in the three flavor space, and 0 < Aa < 8 denote the Gell-Mann matrices. The Quark matter in strong magnetic fields 11 coupling between the magnetic field B and quarks, and between the effective gluon field and quarks is implemented via the covariant derivative D^ = 3^ — iqf Aem — iA^ where qf represents the quark electric charge, A^M = 6^2x1 B is a static and constant magnetic field in the z direction and — To describe the pure gauge sector an effective potential U (®, D; T) is chosen: U (6,6;T) _ a. (T) ® + b(T)ln [1 - 6(6® + 4(63 + 63) - 3(66)2] , >2 , _ , T4 2 where a (T) _ ao + ai (j1) + a2 (j1) , b(T) _ b^i^) • The standard choice of the parameters for the effective potential U is a0 _ 3.51, ai _ -2.47, a2 _ 15.2, and b3 _ -1.75. Besides the PNJL model, where G denotes the coupling constant of the scalar-type four-quark interaction in the NJL sector, we consider an effective vertex depending on the Polyakov loop (G 6)): the EPNJL model. This effective vertex G (6, 6)_ G [1 - a1 - a2(®3 + 63)] . (2) generates entanglement interactions between the Polyakov loop and the chiral condensate. As for the vector interaction, the Lagrangian density that denotes the U(3) V® u(3)a invariant interaction is 8 Lvec G V a=0 and a reduced NJLv Lagrangian density can be written as Lvec _-gvw>Y^)2. (4) In the SU(3) NJLv model, the above Lagrangian densities are not identical in a mean field approach and we discuss both cases next. We refer to the Lagrangian density given in Eq. (3) as model 1 (P1) and to the Lagrangian density given in Eq. (4) as model 2 (P2). Our first task was to analyse the possible different phase diagram structures at zero temperature. We have seen that the number of intermediate phases depends on the number of jumps appearing in the dressed quark masses, which in turn, depend on the number of filled Landau levels. The chiral susceptibilities, as usually defined, are different not only for the s-quark as compared with the two light quarks, but also for the u and d-quarks, yielding non identical crossover lines for the light quark sector. A typical diagram is shown in Figure 1 and details are given in Ref. [3]. Next, the effect of the vector interaction on three flavor magnetized matter was studied for cold matter within two different models usually found in the literature, a flavor dependent (P1) [4] and a flavor independent one (P2) [5]. We have seen that the flavor independent vector interaction predicts a smaller strangeness content and, therefore, harder equations of state. On the other hand, the flavor dependent vector interaction favors larger strangeness content the larger the vector coupling, as can be seen in Figure 2. At low densities 12 Debora Peres Menezes I r M ' / A' / / " / / 350 - /// iMlu l / 7/ Iii A° i > 01 340 - 'Ci 1 ¡' i 0 \! k TL 330- -- XU ; j! / ; 320 -310- --- XH V ¡I d B \ • 0.1 GeV2 only one CEP exists. This is an important result because it shows that a strong magnetic field is able to drive a system with no CEP into a first order phase transition. More details are given in Ref. [8]. Acknowledgements. The co-authors of different parts of this work are Constanca Providencia, Marcus Benghi Pinto, Norberto Scoccola, Luis R. B de Castro, Pedro Costa, Marcio Ferreira and Ana G. Grunfeld and this work was partially 14 Débora Peres Menezes 200 150 > o 100 50 ---* tsrfd'i*» . P JL * \ « Vd&ñr° - * Pu=Pd=P. A ß-equili rium ' JL (•» * 800 850 900 950 1000 1050 110 MMeV) Vd-hs Mu- Mj* 0 ■ tid-1.45^4 -0 600 700 800 900 1000 1100 1200 Hg (MeV) Fig. 4. Left - Location of the CEP on a diagram T vs the baryonic chemical potential under different scenarios and models (NJL, PNJL). No external magnetic field is considered. Right - Effect of an external magnetic field on the CEP location within PNJL model for three different scenarios. supported by CNPq (Brazil), CAPES (Brazil) and FAPESC (Brazil) under project 2716/2012,TR 2012000344. References 1. K. Fukushima, D. E. Kharzeev and H. J. Warringa, Phys. Rev. D 78 (2008) 074033; D. E. Kharzeev and H. J. Warringa, Phys. Rev. D 80 (2009) 034028. 2. R. Duncan and C. Thompson, Astrophysical Journal, Part 2 - Letters 392 (1992) L9-L13; C. Kouveliotou et al, Nature 393 (1998) 235. 3. Ana G. Grunfeld, Debora P. Menezes, Marcus B. Pinto and Norberto Scoccola, Phys. Rev. D (2014) in press, arXiv:1402.4731v1 [hep-ph]. 4. S. Klimt, M. Lutz, and W. Weise, Phys. Lett. B 249 (1990) 386; M. Hanauske, L. M. Satarov, I. N. Mishustin, H. Stocker and W. Greiner, Phys. Rev. D 64 (2001) 043005. 5. K. Fukushima, Phys. Rev. D 78 (2008) 114019. 6. Debora P. Menezes, Marcus B. Pinto, Luis R. B de Castro, Constanca Providencia and Pedro Costa, Phys. Rev. C 89 (2014) 055207. 7. M. Ferreira, P. Costa, D.P. Menezes, C. Providencia and N. Scoccola, Phys. Rev. D 89 (2014) 016002. 8. Pedro Costa, Marcio Ferreira, Hubert Hansen, Debora P. Menezes, Constanca Providencia, Phys. Rev. D 89 (2014) 056013. Povzetki v slovenščini 61 Kvarkovski propagator v coulombski umeritvi kvantne kromodinamike Y. Delgadoa, M. Paka, M. Schröckb a Institut für Physik, Karl-Franzenz Universität Graz, 8010 Graz, Austria b Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Roma Tre, Rome, Italy Proučujemo kvarkovski propagator na konfiguracijah gasenega umeritvenega polja v coulombski umeritvi. Pri tem uporabimo kiralno simetrične "prekrivalne fermione". V tejumeritvi lahko povezemo "funkcijo oblacenja" kvarkovskega propagatorja s priporom in kiralno simetrijo kromodinamike. Pripor lahko pripi-semo infrardece divergentni vektorski "funkciji oblacenja". Izvrednotimo "funkcije oblacenja" kvarkovskega propagatorja, razberemo dinamicno maso kvarka in ekstrapoliramo vse te kolicine proti kiralni limiti. Koncno razpravljamo, kako se odstranijo nizke Diracove ekscitacije. Mase oblečenih kvarkov in barionska spektroskopija W. Plessas Theoretical Physics, Institute of Physics, University of Graz, A-8010 Graz, Austria Prikazemo hierarhijo mas oblecenih kvarkov, ki prevladujejo v efektivnih modelih kvantne kromodinamike, zlasti v relativisticnem modelu z oblecenimi kvarki. Opazimo, da je presežek dinamicno generirane mase nad golo maso boljali manj neodvisen od okusa kvarkov in znasa Am « (370 ± 30) MeV. Podobne vrednosti dajo tudi alternativni efektivni opisi barionske spektroskopije, na primer Dyson-Schwingerjev pristop. Primerjava jedrskih potencialov za hiperon Lambda in za nukleon Bogdan Povha in Mitja Rosinab'c a Max-Planck-Institut für Kernphysik, Postfach 103980, D-69029 Heidelberg, Germany b Fakulteta za matematiko in fiziko, Univerza v Ljubljani, Jadranska 19, p.p.2964, 1001 Ljubljana, Slovenija c Institut J. Stefan, 1000 Ljubljana, Slovenija Raziskujeva verjetni mehanizem, zakajcuti hiperon A dvakrat sibkejse jedrsko polje (okrog -27 MeV) kot nukleon (okrog -50 MeV). Digitalna knjižnica Slovenije - dLib.si
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