In the present work we use the large-Nc approximation to investigate quark matter described by the SU(2) Nambu-Jona-Lasinio model subject to a strong magnetic field. The Landau levels are filled in such a way that usual kinks appear in the effective mass and other related quantities. β-equilibrium is also considered and the macroscopic properties of a magnetar described by this quark matter is obtained. Our study shows that the magnetar masses and radii are larger if the magnetic field increases but only very large fields (≥ 10 18 G) affect the EoS in a non negligible way.

Although asymptotic freedom is an essential feature of QCD, it is absent in effective chiral quark models like the Nambu-Jona-Lasinio and linear sigma models. In this work we advocate that asymptotic freedom plays a key role in the recently observed discrepancies between results of lattice QCD simulations and quark models regarding the behavior of the pseudocritical temperature T pc for chiral-symmetry restoration in the presence of a magnetic field B. We show that the lattice predictions that T pc decreases with B can be reproduced within the Nambu-Jona-Lasinio model if the coupling constant G of the model decreases with B and the temperature. Without aiming at numerical precision, we support our claim by considering a simple ansatz for G that mimics the asymptotic-freedom behavior of the QCD coupling constant 1/α s ∼ ln(eB/ 2 QCD ) for large values of B.

We use the nonperturbative linear δ expansion method to evaluate analytically the coefficients c1 and c ′′ 2 which appear in the expansion for the transition temperature for a dilute, homogeneous, three dimensional Bose gas given by Tc = T0{1+c1an 1/3 +[c ′ 2 ln(an 1/3 )+c ′′ 2 ]a 2 n 2/3 +O(a 3 n)}, where T0 is the result for an ideal gas, a is the s-wave scattering length and n is the number density. In a previous work the same method has been used to evaluate c1 to order-δ 2 with the result c1 = 3.06. Here, we push the calculation to the next two orders obtaining c1 = 2.45 at order-δ 3 and c1 = 1.48 at order-δ 4 . Analysing the topology of the graphs involved we discuss how our results relate to other nonperturbative analytical methods such as the self-consistent resummation and the 1/N approximations. At the same orders we obtain c ′′ 2 = 101.4, c ′′ 2 = 98.2 and c ′′ 2 = 82.9. Our analytical results seem to support the recent Monte Carlo estimates c1 = 1.32 ± 0.02 and c ′′ 2 = 75.7 ± 0.4.