Magnetic Color-Flavor Locking Phase in High-Density QCD

Abstract

We investigate the effects of an external magnetic field in the gap structure of a color superconductor with three massless quark flavors. Using an effective theory with four-fermion interactions, inspired by one-gluon exchange, we show that the long-range component B of the external magnetic field that penetrates the color-flavor locked (CFL) phase modifies its gap structure, producing a new phase of lower symmetry. A main outcome of our study is that the B field tends to strengthen the gaps formed by Q-charged and Q-neutral quarks that coupled among themselves through tree-level vertices. These gaps are enhanced by the field-dependent density of states of the Q-charged quarks on the Fermi surface. Our considerations are relevant for the study of highly magnetized compact stars.PACS numbers: 12.38. Aw, 24.85.+p After the suggestion that three-flavor quark matter may actually be the ground state of strong interactions [1], quark stars were postulated as possible astrophysical objects. It is also very likely that quark matter occupies the inner regions of neutron stars. Our present knowledge of QCD at high baryonic density indicates that this new state of matter might be in a color superconducting phase (for reviews, see [2]). On the other hand, it is well-known [3] that strong magnetic fields, as large as B ∼ 10 12 − 10 14 G, exist in the surface of neutron stars, while in magnetars they are in the range B ∼ 10 14 − 10 15 G, and perhaps as high as 10 16 G [4]. The physical upper limit to the total neutron star magnetic field, as arising from comparing the magnetic and gravitational energies, is of order B ∼ 10 18 G [3]. If quark stars are self-bound rather than gravitational-bound objects this upper limit could go higher. In this Letter we investigate the effect of a strong magnetic field in color superconductivity, with the aim of further studying its possible astrophysical implications.We will start by considering three massless quarks. In this case, it is well established that the ground state of high-dense QCD corresponds to the CFL (color-flavor locked) phase [5]. In this phase, quarks form spin-zero Cooper pairs in the color-antitriplet, flavor-antitriplet representation, thereby breaking the original SU (3) color × SU (3) L ×SU (3) R ×U (1) B symmetry to the diagonal subgroup SU (3) color+L+R . One can now ask how this scenario will change when a magnetic field is switched on. Would the external field affect the pairing phenomena? In a conventional electromagnetic superconductor, since Cooper pairs are electrically charged, the electromagnetic gauge invariance is spontaneously broken and the photon acquires a mass that can screen a weak magnetic field: this is the Meissner effect. In spin-zero color superconductivity, although the color condensate has nonzero electric charge, there is a linear combination of the photon and a gluon that remains massless [5]. The unbroken U (1) group is generated, in flavor-color space, by Q = Q × 1 − 1 × Q, where Q is the electromagnetic charge generator [6]. Thus a spi...

Quark Matter in a Strong Magnetic Background

“…To write the one-loop quark propagator in the background of the magnetic field we make use of the Leung-Ritus-Wang method [55], which allows to expand the propagator on the complete and orthonormal set made of the eigenfunctions of a charged fermion in a homogeneous and static magnetic field. This is a well known procedure, discussed many times in the literature, see for example [56,57,59,58]; therefore it is enough to quote the final result:…”

Directional dependence of a color superconducting gap in two-flavor QCD in a magnetic field

“…This contrasts with the studies based on models with point-like interactions in Refs. [21][22][23], where the gaps are always isotropic.…”

“…This is in qualitative agreement with the findings in Refs. [21][22][23], where the models with short-range interactions were used. We also find that, because of the partial localization of quasiparticles in a strong magnetic field, the corresponding dynamics is essentially local and there is no directional dependence of the gap.…”

“…The recent studies revealed many interesting qualitative features of the magnetic 2SC and CFL phases [21][22][23]. However, all such studies share a common shortcoming: they are performed in the framework of Nambu-Jona-Lasinio (NJL) models with contact interactions.…”

“…Recently, the study of color superconductivity in the presence of magnetic fields attracted a lot of attention [21][22][23][24][25]. This interest is primarily driven by potential astrophysical applications, where magnetic fields play an important role.…”