Thermal fluctuations of gauge fields and first order phase transitions in color superconductivity

Matsuura, Tetsuya; Iida, Kei; Hatsuda, Tetsuo; Baym, Gordon

doi:10.1103/physrevd.69.074012

Cited by 37 publications

(50 citation statements)

References 30 publications

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“…This value of T c is larger than the BCS value of ≃ 0.57∆ due to the two-gap structure of the quark excitations (−∆ and 2∆ for octet and singlet quarks, respectively) [28]. We note, however, that in a situation in which CFL quark matter behaves as a type-I color superconductor, thermal fluctuations in the gauge fields could play a role in changing the phase transition from second to first order and in lowering the transition temperature [14]. The analysis of this situation is beyond the scope of the present paper.…”

Section: A Self-consistency Equationsmentioning

confidence: 78%

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Collective excitations in a superfluid of color-flavor locked quark matter

Fukushima

Iida

2005

Phys. Rev. D

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We investigate collective excitations coupled with baryon density in a system of massless threeflavor quarks in the collisionless regime. By using the Nambu-Jona-Lasinio (NJL) model in the mean-field approximation, we field-theoretically derive the spectra both for the normal and colorflavor locked (CFL) superfluid phases at zero temperature. In the normal phase, we obtain usual zero sound as a low-lying collective mode in the particle-hole (vector) channel. In the CFL phase, the nature of collective excitations varies in a way dependent on whether the excitation energy, ω, is larger or smaller than the threshold given by twice the pairing gap ∆, at which pair excitations with nonzero total momentum become allowed to break up into two quasiparticles. For ω ≪ 2∆, a phonon corresponding to fluctuations in the U (1) phase of ∆ appears as a sharp peak in the particle-particle ("H") channel. We reproduce the property known from low energy effective theories that this mode propagates at a velocity of vH = 1/ √ 3 in the low momentum regime; the decay constant fH obtained in the NJL model is identical with the QCD result obtained in the mean-field approximation. We also find that as the momentum of the phonon increases, the excitation energy goes up and asymptotically approaches ω = 2∆. Above the threshold for pair excitations (ω > 2∆), zero sound manifests itself in the vector channel. By locating the zero sound pole of the vector propagator in the complex energy plane we investigate the attenuation and energy dispersion relation of zero sound. In the long wavelength limit, the phonon mode, the only low-lying excitation, has its spectral weight in the H channel alone, while the spectral function vanishes in the vector channel. This is due to nontrivial mixing between the H and vector channels in the superfluid medium. We finally extend our study to the case of nonzero temperature. We demonstrate how Landau damping smears the phonon peak in the finite temperature spectral function. We find a pure imaginary pole of the H propagator in the complex energy plane, which can be identified as a diffusive mode responsible for the Landau damping. From the pole position we derive the thermal diffusion constant.

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Section: A Self-consistency Equationsmentioning

confidence: 78%

“…Transverse excitations will be ignored in the present study, but play a role in breaking up phase coherence in the superfluid state and hence are relevant for responses to magnetic field and rotation [9,13] and for reduction in the transition temperature [14].…”

Section: Introductionmentioning

confidence: 99%

Collective excitations in a superfluid of color-flavor locked quark matter

Fukushima

Iida

2005

Phys. Rev. D

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“…[8], and so this work leaves the same open questions enumerated in Ref. [8]; how gauge field fluctuations affect the critical point and the order of respective phase transitions [35], what the nature of K 0 -condensation in the gCFL phase is and how it affects instability [36,37], what difference the 't Hooft (instanton) interaction makes that induces an interaction like ∼ |∆ 3 | 2 M s , where the chiral phase transition is located and how our (M 2 s /µ-T ) phase diagram is mapped onto the (µ-T ) plane with M s solved dynamically.…”

Section: Summary and Open Questionsmentioning

confidence: 94%

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

Fukushima

2005

Phys. Rev. D

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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 .

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“…As we shall see in weak coupling (m s , Λ QCD ≪ µ), the effects of nonzero m s and electric neutrality are important in that they induce multiple phase transitions that change the pattern of diquark pairing as T increases. In particular, we find a new phase, which we call "dSC," as an interface between a modified type of color-flavor locked (mCFL) phase and an isoscalar two-flavor (2SC) phase.Throughout this Letter, we adopt the GinzburgLandau (GL) approach near the transition temperatures, which was previously used to study the massless threeflavor case [4,5,6] and is a more advantageous framework to weak coupling calculations than other mean-field approaches [7,8]. In a realistic situation, the GL potential acquires the following corrections.…”

mentioning

confidence: 99%

“…Throughout this Letter, we adopt the GinzburgLandau (GL) approach near the transition temperatures, which was previously used to study the massless threeflavor case [4,5,6] and is a more advantageous framework to weak coupling calculations than other mean-field approaches [7,8]. In a realistic situation, the GL potential acquires the following corrections.…”

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confidence: 99%

Melting Pattern of Diquark Condensates in Quark Matter

et al. 2004

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Thermal color superconducting phase transitions in high density three-flavor quark matter are investigated in the Ginzburg-Landau approach. Effects of nonzero strange quark mass, electric and color charge neutrality, and direct instantons are considered. Weak coupling calculations show that an interplay between the mass and electric neutrality effects near the critical temperature gives rise to three successive second-order phase transitions as the temperature increases: a modified colorflavor locked (mCFL) phase (ud, ds, and us pairings) → a "dSC" phase (ud and ds pairings) → an isoscalar pairing phase (ud pairing) → a normal phase (no pairing). The dSC phase is novel in the sense that while all eight gluons are Meissner screened as in the mCFL phase, three out of nine quark quasiparticles are gapless. 12.38.Mh,26.60.+c Unraveling the phase structure at high baryon density is one of the most challenging problems in quantum chromodynamics (QCD). Among others, color superconductivity in cold dense quark matter has been discussed from various viewpoints [1,2]. In relation to real systems such as newly born compact stars in stellar collapse, it is important to study the color superconductivity not only as a function of the quark chemical potential µ but also as a function of the temperature T . This is because the possible presence of color superconducting quark matter in a star affects the star's thermal evolution [3].The purpose of this Letter is to investigate phase transitions in color superconducting quark matter with three flavors (uds) and three colors (RGB) near the transition temperatures. We consider a realistic situation in which nonzero strange quark mass m s , electric and color charge neutrality, and direct instantons take effect. As we shall see in weak coupling (m s , Λ QCD ≪ µ), the effects of nonzero m s and electric neutrality are important in that they induce multiple phase transitions that change the pattern of diquark pairing as T increases. In particular, we find a new phase, which we call "dSC," as an interface between a modified type of color-flavor locked (mCFL) phase and an isoscalar two-flavor (2SC) phase.Throughout this Letter, we adopt the GinzburgLandau (GL) approach near the transition temperatures, which was previously used to study the massless threeflavor case [4,5,6] and is a more advantageous framework to weak coupling calculations than other mean-field approaches [7,8]. In a realistic situation, the GL potential acquires the following corrections. First of all, nonzero m s affects the potential through the s quark propagator [8] in such a way as to lower the temperature at which a diquark condensate with s quarks dissolves. This is because the pairing interaction due to one-gluon exchange is effectively diminished by m s if the pair contains the s quark. Secondly, when quark matter with nonzero m s is beta equilibrated and neutralized by electrons near the transition temperatures, the chemical potentials between d, s quarks and u quarks differ. Through this chemical potentia...

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Thermal fluctuations of gauge fields and first order phase transitions in color superconductivity

Cited by 37 publications

References 30 publications

Collective excitations in a superfluid of color-flavor locked quark matter

Collective excitations in a superfluid of color-flavor locked quark matter

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

Melting Pattern of Diquark Condensates in Quark Matter

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