Analytical and numerical evaluation of the Debye and Meissner masses in dense neutral three-flavor quark matter

Abstract

We calculate the Debye and Meissner masses and investigate chromomagnetic instability associated with the gapless color superconducting phase changing the strange quark mass Ms and the temperature T . Based on the analytical study, we develop a computational procedure to derive the screening masses numerically from curvatures of the thermodynamic potential. When the temperature is zero, from our numerical results for the Meissner masses, we find that instability occurs for A1 and A2 gluons entirely in the gapless color-flavor locked (gCFL) phase, while the Meissner masses are real for A4, A5, A6, and A7 until Ms exceeds a certain value that is larger than the gCFL onset. We then handle mixing between color-diagonal gluons A3, A8, and photon Aγ, and clarify that, among three eigenvalues of the mass squared matrix, one remains positive, one is always zero because of an unbroken U(1)Q symmetry, and one exhibits chromomagnetic instability in the gCFL region. We also examine the temperature effects that bring modifications into the Meissner masses. The instability found at large Ms for A4, A5, A6, and A7 persists at finite T into the u-quark color superconducting (uSC) phase which has u-d and s-u but no d-s quark pairing and also into the two-flavor color superconducting (2SC) phase characterized by u-d quark pairing only. The A1 and A2 instability also goes into the uSC phase, but the 2SC phase has no instability for A1, A2, and A3. We map the unstable region for each gluon onto the phase diagram as a function of Ms and T .

Extensive study of phase diagram for charge-neutral homogeneous quark matter affected by dynamical chiral condensation: unified picture for thermal unpairing transitions from weak to strong coupling

“…The gCFL phase has been extensively studied and claimed to be the most promising candidate of next phase down in density at vanishing temperature [11] and is also known to lead an interesting astrophysical consequence on the cooling history of an aged compact star [12]. It should be, however, noted here that the gapless phases are usually accompanied by some transverse gluonic modes with imaginary Meissner mass at low temperature [13,14], indicating the existence of more stable exotic states [15][16][17][18][19][20][21]. Although the resolution of the instability or finding the possible new stable state is now one of the central issues in this field, we won't deal with this problem; nevertheless we will give some suggestions to possible resolution on the basis of the results obtained in this work.…”

“…As for the (T = 0) case, we need a numerical evaluation of the Meissner Masses to verify the stability since there is no such analytic formula as above for the instability condition. The numerical calculations show, however, that the singularity associated with the gapless modes is smoothed out by thermal quasi-particles at T = 0, which implies that the system at T = 0 is free from the instability as long as that at T = 0 is stable [13,14]. Thus one can conclude that there is no instability in the entire phase diagram for the (extremely) strong coupling case.…”

“…A number of papers have been devoted to the resolution of the imaginary Meissner masses in the gapless phases [13,14]. These include; (i) exploring a possibility of the mixed phase [15] along the line suggested earlier [54][55][56], (ii) the baryon current generation [16], (iii) examining the crystalline pairing phases [57] taking the neutrality constraints into account [17,18], (iv) investigating a possible secondary gap formation [19], (v) the gluon condensation in the g2SC [20], and (vi) an inhomogeneous (p-wave) Kaon condensate [21].…”

The phase diagram of dense QCD

“…In [222,223,224,225,226] the Meissner (magnetic screening) masses in the g2SC and gCFL phases have been calculated and turned out to be imaginary. That is, there appear negative eigenvalues from the mass-squared matrix in colour space,…”

Anomalous Specific-Heat Jump in a Two-Component Ultracold Fermi Gas

“…The entropy of ASC is defined in terms of the temperature derivative of the free energy S S ÿ@F =@T. The specific heat follows as C V T @S S =@T ÿT @ 2 F =@T 2 . The local stability requires that the free energy is a convex function of the appropriate variables and it has been established that homogeneous ASC could become unstable in this sense [16,24,25,32,33,35,39,41,42]. Specifically, (A) the system is unstable against phase separation unless the curvature matrix ij @ 2 F S =@ i @ j is positive definite.…”