Meson current in the CFL phase

A. Gerhold; T. Sch\"afer

REVIEW

Meson current in the CFL phase

A. Gerhold, T. Schäfer

High Energy Physics - Phenomenology · Submitted 30 Mar 2006 · 30 references

Pith's verdict: Solid effective-model calculation — the curCFL phase resolves the gCFL chromomagnetic instability with causal Meissner masses — but the physical claim is conditional on a hand-tuned instanton term that suppresses kaon condensation.

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arXiv IDhep-ph/0603257 (version 2)

Pith IDEE6G4Y5A, Pith's permanent record of this paper and its review

CitationA. Gerhold, T. Sch\"afer. "Meson current in the CFL phase." arXiv:hep-ph/0603257 (2006). https://pith.science/paper/EE6G4Y5A

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Claim paper

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Editor's note

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Dear Colleague,

The one thing to know: within its effective model, this paper convincingly shows that the CFL phase becomes unstable to a nonzero Goldstone-boson current near mu_s = Delta, and that the current-carrying phase has real Meissner masses. That is a genuine advance over the earlier curCFL papers [13,14]: unequal gaps, electric charge neutrality, a generalized current ansatz, and an O(b^5) expansion with explicit convergence checks.

The calculation is honest. The expansion in small parameters is controlled, and the positivity of the dangerous screening masses is the newly demonstrated result. I don't think the circularity concern applies: mu_s,crit and the Meissner masses are outputs of the free-energy minimization, not inputs. The model depends on a quadratic effective potential for the gaps and on the current ansatz, but those are stated and standard for this approach. The citation pattern is normal; the curCFL concept is properly traced to earlier work.

The soft spot is real and the paper names it. Section VI says the instanton-induced interaction needed to suppress kaon condensation is "problematic from the point of view of instanton phenomenology at zero baryon density." Inequality (31) is not derived; 1/G_i is chosen just above the threshold. If the true value is smaller, kaon condensation sets in first and the ground state near the gCFL onset is CFL+K, not curCFL. That makes the main claim conditional for real QCD, but conditional in an honest way. The authors are not hiding a flaw; they are betting on a parameter they cannot fix.

Also worth noting: the model excludes homogeneous kaon condensates by setting X=Y=1. The conclusion that curCFL resolves the chromomagnetic instability therefore carries an explicit caveat. Not a fatal one for the paper as an effective-model result, but it caps how much physical weight you can put on the final answer.

Who is this for? People working on the dense-QCD phase diagram, specifically the gCFL instability and possible LOFF/current phases. It should go to peer review. The calculation is careful, the new Meissner-mass result is concrete, and the limitations are stated rather than buried. A referee should focus on the 1/G_i dependence and on whether the current ansatz misses competing order parameters. That is a normal refereeing task, not a desk-reject situation.

Best,

Referee report

Significance

If correct, the paper offers a concrete candidate resolution of the chromomagnetic instability of the gCFL phase and gives quantitative, falsifiable predictions: the critical ratio mu_s,crit/Delta(0), the magnitude of the current, and the positivity of the dangerous Meissner components. The free-energy expansion is carried systematically to O(b^5) with explicit convergence checks at successive orders, and the authors are transparent about the main limitations of the model. The connection to the single-plane-wave LOFF state in Eq. (33) is a useful bridge to earlier work. The main concern is that the physical relevance of the curCFL phase depends on a hand-tuned instanton coupling and on the exclusion of kaon condensation, as discussed in the major comments.

Major objections (2)

[VI, Eq. (31)] Section VI: the condition for suppressing kaon condensation is the inequality 1/G_i > f_pi^2 mu_s^{3/2}/Delta_3^2 (Eq. (31)), and the value 1/G_i = 0.67 f_pi^2 Delta(0)^{-1/2} is chosen to just satisfy it. The authors themselves note that an instanton term of this magnitude is problematic from the point of view of instanton phenomenology at zero baryon density. Since the central claim that the curCFL phase resolves the gCFL instability requires this inequality to hold, a smaller true G_i would allow kaon condensation to set in before mu_s,crit, and the physical ground state would be kaon-condensed CFL rather than curCFL. A concrete test would be to compute G_i in a controlled QCD-based approximation, or to scan the allowed range of 1/G_i and demonstrate that the current instability precedes kaon condensation for a robust interval of values.
[II and VII] Section II sets X = Y = 1, which excludes homogeneous kaon condensation from the outset, and Section VII states that kaon condensation is 'likely to play an important role.' Even for a G_i satisfying Eq. (31), the paper never computes the free energy of the kaon-condensed phase or of a phase containing both a kaon condensate and a current. The calculation therefore establishes that within the restricted ansatz X = Y = 1 the current-CFL state is locally preferred, but it does not establish that curCFL is the true ground state in the relevant region. Because the resolution of the gCFL instability is a statement about the actual ground state of dense QCD, this is a load-bearing limitation. I recommend either restricting the abstract's claims to the effective model, or extending the calculation to include the kaon condensate and showing that the current instability survives or dominates.

Minor objections (4)

[Eq. (7)] The dispersion relations are written to leading order in the small parameters b, but for epsilon_7,...,epsilon_9 the '...' notation is not specified; please state to which order the terms are retained.
[Eq. (18)] The order of limits in the Meissner mass formula is written as lim_{k->0} lim_{k0->0}; please clarify that this is the screening mass definition and whether the limits commute.
[Sec. III] The convergence of the free-energy expansion is demonstrated visually in Figs. 1 and 2; a quantitative estimate of the truncation error at the critical point would be useful.
[Eq. (8)] The quadratic potential for the gap parameters is a phenomenological input; a brief discussion of how the qualitative results depend on this choice would help readers assess the robustness of the predictions.

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The paper

The paper claims

Near the onset of gapless fermions, the CFL ground state carries a Goldstone current and all Meissner masses are real.

The reading

This paper argues that the color-flavor locked (CFL) phase of dense quark matter is unstable to the formation of a nonzero Goldstone-boson current once the strange-quark mass shift $\mu_s$ approaches the pairing gap $\Delta$, the point where gapless fermion modes appear. In the resulting current-CFL phase, the free energy has a minimum at a finite current $\ell\simeq0.15\,\Delta(0)$, and every component of the magnetic screening (Meissner) mass is real. If correct, this resolves the chromomagnetic instability that had been found in the gapless CFL regime. The calculation uses an effective Lagrangian with unequal CFL gaps and electric charge neutrality, expands the free energy in small deviations around $\mu_s=\Delta$, and checks convergence order by order. The main caveat is that homogeneous kaon condensation is excluded; the paper studies an instanton-induced interaction strong enough to suppress it.

What carries the argument

The load-bearing object is an effective Lagrangian for gapped left- and right-handed quarks coupled to color gauge fields, with CFL gap parameters $\Delta_1,\Delta_2,\Delta_3$ and pairing orientations fixed to $X=Y=1$ (no homogeneous kaon condensate). The Goldstone current is introduced as a diagonal background gauge field $\vec A_T=\frac12\vec\ell(\lambda_3+\lambda_8/\sqrt3-\lambda_0/\sqrt6)$, chosen so that electrically charged fermion modes are not shifted in energy; the current shifts the energies of neutral modes and the momenta of charged modes. The free energy is expanded in the small parameters $(\mu_s-\Delta)/\Delta$, $\widetilde A/\Delta$, $\ell/\Delta$, and $(\Delta_i-\Delta_1)/\Delta_1$, with gap equations and neutrality conditions solved order by order, and the Meissner masses are computed from current-current correlation functions. The role of the current is to remove the would-be gapless modes that make the screening masses imaginary in the gCFL phase.

Extended reading notes

Core claim

The paper's central claim is that the gapless CFL phase is not the ground state near $\mu_s=\Delta$: before the appearance of gapless fermion modes can generate an instability, the CFL ground state acquires a nonzero diagonal Goldstone-boson current. In this current phase the dangerous Meissner masses $m_{M\,\perp}^{(2)}$, $m_{M\,\parallel}^{(2)}$, $m_{M\,11\perp}$, and $m_{M\,11\parallel}$ are all real and positive, so the chromomagnetic instability found in previous studies of the gapless CFL phase disappears. The onset is at $\mu_{s,\mathrm{crit}}\simeq0.9919\,\Delta(0)$ without the instanton term, reduced to $\simeq0.964\,\Delta(0)$ when an instanton-induced interaction of the size needed to suppress kaon condensation is included; relaxing the current ansatz changes the critical point only slightly.

Load-bearing premise

The analysis assumes the CFL pairing orientations stay perfectly locked (no homogeneous kaon condensate) and relies on an instanton-induced interaction whose strength is chosen by hand to be just large enough to suppress kaon condensation; if kaon condensation really occurs first, the predicted current phase need not be the physical ground state.

Editorial extensions

If this is right

At $\mu_s$ above a critical value just below $\Delta$, the CFL phase is unstable and a Goldstone-boson current with magnitude of order $0.15\,\Delta(0)$ develops.
The chromomagnetic instability of the gapless CFL phase is cured: all Meissner masses in the current phase are real, not just the ones that were previously reported imaginary.
The curCFL phase is equivalent to a single plane-wave LOFF state with gap matrix $\mathrm{diag}(\Delta_1 e^{-i\vec x\cdot\vec\ell},\Delta_2,\Delta_2)$, distinguishing it from other LOFF ansatze studied near the pairing boundary.
An instanton-induced interaction large enough to suppress kaon condensation lowers the critical $\mu_s$ to about $0.964\,\Delta(0)$ and splits $\Delta_3$ from $\Delta_{1,2}$ but does not change the qualitative conclusion.
The results are stable through fifth order in the small expansion parameters and under a more general current ansatz, so the existence of the current phase is not an artifact of the simplest truncation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the real instanton-induced interaction is weaker than the value assumed here, kaon condensation would preempt the curCFL window; a two-order-parameter calculation including both the kaon condensate and the current is the direct way to decide which phase wins.
Because the current phase is a plane-wave LOFF state, the small-current expansion of this paper should connect continuously to the large-current LOFF calculations near the point where pairing between different flavors is exhausted; mapping that interpolation would extend the phase diagram beyond the present window.
Applying the same expansion to two-flavor quark matter, where the current couples differently to charged modes, would test whether real Meissner masses are a generic consequence of a spontaneous meson current or a special feature of the three-flavor CFL pattern.

Original abstract

We study the stability of the color-flavor locked (CFL) phase of dense quark matter with regard to the formation of a non-zero Goldstone boson current. We show that an instability appears in the vicinity of the point $\mu_s=\Delta$ which marks the appearance of gapless fermion modes in the CFL phase. Here, $\mu_s=m_s^2/(2\mu)$ is the shift in chemical potential due to the strange quark mass and $\Delta$ is the gap in the chiral limit. We show that in the Goldstone boson current phase all components of the magnetic screening mass are real. In this work we do not take into account homogeneous kaon condensation. We study the effects of an instanton induced interaction of the magnitude required to suppress kaon condensation.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,873 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.97 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.08 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We study the stability of the color-flavor locked (CFL) phase of dense quark matter with regard to the formation of a non-zero Goldstone boson current. We show that an instability appears in the vicinity of the point $\mu_s=\Delta$ which marks the appearance of gapless fermion modes in the CFL phase. Here, $\mu_s=m_s^2/(2\mu)$ is the shift in chemical potential due to the strange quark mass and $\Delta$ is the gap in the chiral limit. We show that in the Goldstone boson current phase all components of the magnetic screening mass are real. In this work we do not take into account homogeneous kaon condensation. We study the effects of an instanton induced interaction of the magnitude required to suppress kaon condensation.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study the stability of the color-flavor locked (CFL) phase of dense quark matter with regard to the formation of a non-zero Goldstone boson current.	contribution 0.99	0.91	0.10	unclear 0.57
s1	We show that an instability appears in the vicinity of the point $\mu_s=\Delta$ which marks the appearance of gapless fermion modes in the CFL phase.	result 1.00	0.94	0.64	asserted 1.00
s2	Here, $\mu_s=m_s^2/(2\mu)$ is the shift in chemical potential due to the strange quark mass and $\Delta$ is the gap in the chiral limit.	background 0.92	0.23	0.04	asserted 0.98
s3	We show that in the Goldstone boson current phase all components of the magnetic screening mass are real.	result 1.00	0.91	0.23	asserted 1.00
s4	In this work we do not take into account homogeneous kaon condensation.	limitation 1.00	0.84	0.03	asserted 0.99
s5	We study the effects of an instanton induced interaction of the magnitude required to suppress kaon condensation.	contribution 0.76	0.85	0.04	asserted 0.81

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.97.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 4.** FIG. 4: Meissner masses squared

Showing 4 of the paper's 5 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-ph/0603257 by the authors.

References

Works cited (30)

[1]

M. Alford, K. Rajagopal and F. Wilczek, Nucl. Phys. B537, 443 (1999) [hep-ph/9804403]

View on Pith Pith review arXiv 1999
[2]

T. Sch¨ afer, Nucl. Phys. B 575, 269 (2000) [hep-ph/9909574]

View on Pith Pith review arXiv 2000
[3]

is the quark charge matrix and Ae is an electro-static potential. The ﬁelds X, Y determine the ﬂavor orientation of the left and right handed gap terms and trans form as X → LXC T , Y → RY C T under ( L, R) ∈ SU (3)L × SU (3)R and C ∈ SU (3)C, and ∆ k (k = 1 , 2, 3) are the CFL gap parameters. The gauge ﬁeld Aµ appears transposed because of the transforma...

View on Pith
[4]

− 1 Gi √µs∆ 2 3 + 3µ22 8π2 − µ2 4π2 ∫ dp ∫ dt 9∑ i=1 (|ǫi| − |p|), (8) with t = cos θ. Here, G ﬁxes the magnitude of the gap in the chiral limit and Gi takes into account instanton eﬀects. The structure of the instanton term is determined by vacuum ex- pectation value of the ’t Hooft interaction. The value of Gi can be computed in perturbative QCD [26] b...

View on Pith
[5]

P. F. Bedaque and T. Sch¨ afer, Nucl. Phys. A 697, 802 (2002) [hep-ph/0105150]

View on Pith Pith review arXiv 2002
[6]

N. Evans, J. Hormuzdiar, S. D. Hsu and M. Schwetz, Nucl. Ph ys. B 581, 391 (2000) [hep-ph/9910313]

View on Pith Pith review arXiv 2000
[7]

T. Sch¨ afer and F. Wilczek, Phys. Rev. Lett. 82, 3956 (1999) [hep-ph/9811473]

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[8]

S.-T. Wu, S. Yip, Phys. Rev. A 67, 053603 (2003) [cond-mat/0303185]

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[9]

M. Alford, C. Kouvaris and K. Rajagopal, Phys. Rev. Lett. 92, 222001 (2004) [hep-ph/0311286]

View on Pith Pith review arXiv 2004
[10]

M. Alford, C. Kouvaris and K. Rajagopal, Phys. Rev. D 71, 054009 (2005) [hep-ph/0406137]

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[11]

M. Alford and Q. H. Wang, J. Phys. G 31, 719 (2005) [hep-ph/0501078]. 14

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[12]

M. Huang and I. A. Shovkovy, Phys. Rev. D 70, 051501 (2004) [hep-ph/0407049]

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[13]

R. Casalbuoni, R. Gatto, M. Mannarelli, G. Nardulli and M. Ruggieri, Phys. Lett. B 605, 362 (2005) [Erratum-ibid. B 615, 297 (2005)] [hep-ph/0410401]

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[14]

T. Sch¨ afer, Phys. Rev. Lett. 96, 012305 (2006) [hep-ph/0508190]

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[15]

K. Fukushima, Phys. Rev. D 72, 074002 (2005) [hep-ph/0506080]

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[16]

A. Kryjevski, preprint, hep-ph/0508180

View on Pith Pith review arXiv
[17]

R. Casalbuoni, R. Gatto, N. Ippolito, G. Nardulli and M. Ruggieri, Phys. Lett. B 627, 89 (2005) [hep-ph/0507247]

View on Pith Pith review arXiv 2005
[18]

M. G. Alford, J. A. Bowers and K. Rajagopal, Phys. Rev. D 63, 074016 (2001) [hep-ph/0008208]

View on Pith Pith review arXiv 2001
[19]

R. Casalbuoni and G. Nardulli, Rev. Mod. Phys. 76, 263 (2004) [hep-ph/0305069]

View on Pith Pith review arXiv 2004
[20]

I. Giannakis and H. C. Ren, Phys. Lett. B 611, 137 (2005) [hep-ph/0412015]

View on Pith Pith review arXiv 2005
[21]

M. Ciminale, G. Nardulli, M. Ruggieri and R. Gatto, prep rint, hep-ph/0602180

View on Pith Pith review arXiv
[22]

M. Mannarelli, K. Rajagopal and R. Sharma, preprint, he p-ph/0603076

View on Pith arXiv
[23]

E. V. Gorbar, M. Hashimoto, V. A. Miransky and I. A. Shovk ovy, preprint, hep-ph/0602251

View on Pith Pith review arXiv
[24]

M. Huang, Phys. Rev. D 73, 045007 (2006) [hep-ph/0504235]

View on Pith Pith review arXiv 2006
[25]

D. K. Hong, preprint, hep-ph/0506097

View on Pith Pith review arXiv
[26]

T. Sch¨ afer, Phys. Rev. D 65, 094033 (2002) [hep-ph/0201189]

View on Pith Pith review arXiv 2002
[27]

A. Kryjevski and T. Sch¨ afer, Phys. Lett. B 606, 52 (2005) [hep-ph/0407329]

View on Pith Pith review arXiv 2005
[28]

A. Kryjevski and D. Yamada, Phys. Rev. D 71, 014011 (2005) [hep-ph/0407350]

View on Pith Pith review arXiv 2005
[30]

D. T. Son and M. A. Stephanov, Phys. Rev. D 61, 074012 (2000) [hep-ph/9910491]. 15

View on Pith Pith review arXiv 2000
[31]

In this basis ∆ AB = − 1 2 ∆ abεijaεrsbλA irλB js, ∆ ab = diag(∆ 1, ∆ 2, ∆ 3)ab. (3) 3 We will assume that X = Y = 1 which excludes the possibility of kaon condensation. This assumption signiﬁcantly simpliﬁes the calculation of the fermion disper sion relations and the current correlation functions. It is possible to suppress kaon condensation by includin...

View on Pith

How the literature uses it

2 arXiv papers cite this in 3 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

We show that the color-flavor locked (CFL) phase of dense quark matter is unstable with respect to the formation of a Goldstone boson current in the vicinity of the point $m_s^2=2\mu\Delta$.

Chromomagnetic stability of the CFL phase with a meson current · 0.99

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

M. Alford, K. Rajagopal and F. Wilczek, Nucl. Phys. B537, 443 (1999) [hep-ph/9804403]

View on Pith Pith review arXiv 1999

[2] [2]

T. Sch¨ afer, Nucl. Phys. B 575, 269 (2000) [hep-ph/9909574]

View on Pith Pith review arXiv 2000

[3] [3]

is the quark charge matrix and Ae is an electro-static potential. The ﬁelds X, Y determine the ﬂavor orientation of the left and right handed gap terms and trans form as X → LXC T , Y → RY C T under ( L, R) ∈ SU (3)L × SU (3)R and C ∈ SU (3)C, and ∆ k (k = 1 , 2, 3) are the CFL gap parameters. The gauge ﬁeld Aµ appears transposed because of the transforma...

View on Pith

[4] [4]

− 1 Gi √µs∆ 2 3 + 3µ22 8π2 − µ2 4π2 ∫ dp ∫ dt 9∑ i=1 (|ǫi| − |p|), (8) with t = cos θ. Here, G ﬁxes the magnitude of the gap in the chiral limit and Gi takes into account instanton eﬀects. The structure of the instanton term is determined by vacuum ex- pectation value of the ’t Hooft interaction. The value of Gi can be computed in perturbative QCD [26] b...

View on Pith

[5] [5]

P. F. Bedaque and T. Sch¨ afer, Nucl. Phys. A 697, 802 (2002) [hep-ph/0105150]

View on Pith Pith review arXiv 2002

[6] [6]

N. Evans, J. Hormuzdiar, S. D. Hsu and M. Schwetz, Nucl. Ph ys. B 581, 391 (2000) [hep-ph/9910313]

View on Pith Pith review arXiv 2000

[7] [7]

T. Sch¨ afer and F. Wilczek, Phys. Rev. Lett. 82, 3956 (1999) [hep-ph/9811473]

View on Pith Pith review arXiv 1999

[8] [8]

S.-T. Wu, S. Yip, Phys. Rev. A 67, 053603 (2003) [cond-mat/0303185]

View on Pith Pith review arXiv 2003

[9] [9]

M. Alford, C. Kouvaris and K. Rajagopal, Phys. Rev. Lett. 92, 222001 (2004) [hep-ph/0311286]

View on Pith Pith review arXiv 2004

[10] [10]

M. Alford, C. Kouvaris and K. Rajagopal, Phys. Rev. D 71, 054009 (2005) [hep-ph/0406137]

View on Pith Pith review arXiv 2005

[11] [11]

M. Alford and Q. H. Wang, J. Phys. G 31, 719 (2005) [hep-ph/0501078]. 14

View on Pith Pith review arXiv 2005

[12] [12]

M. Huang and I. A. Shovkovy, Phys. Rev. D 70, 051501 (2004) [hep-ph/0407049]

View on Pith Pith review arXiv 2004

[13] [13]

R. Casalbuoni, R. Gatto, M. Mannarelli, G. Nardulli and M. Ruggieri, Phys. Lett. B 605, 362 (2005) [Erratum-ibid. B 615, 297 (2005)] [hep-ph/0410401]

View on Pith Pith review arXiv 2005

[14] [14]

T. Sch¨ afer, Phys. Rev. Lett. 96, 012305 (2006) [hep-ph/0508190]

View on Pith Pith review arXiv 2006

[15] [15]

K. Fukushima, Phys. Rev. D 72, 074002 (2005) [hep-ph/0506080]

View on Pith Pith review arXiv 2005

[16] [16]

A. Kryjevski, preprint, hep-ph/0508180

View on Pith Pith review arXiv

[17] [17]

R. Casalbuoni, R. Gatto, N. Ippolito, G. Nardulli and M. Ruggieri, Phys. Lett. B 627, 89 (2005) [hep-ph/0507247]

View on Pith Pith review arXiv 2005

[18] [18]

M. G. Alford, J. A. Bowers and K. Rajagopal, Phys. Rev. D 63, 074016 (2001) [hep-ph/0008208]

View on Pith Pith review arXiv 2001

[19] [19]

R. Casalbuoni and G. Nardulli, Rev. Mod. Phys. 76, 263 (2004) [hep-ph/0305069]

View on Pith Pith review arXiv 2004

[20] [20]

I. Giannakis and H. C. Ren, Phys. Lett. B 611, 137 (2005) [hep-ph/0412015]

View on Pith Pith review arXiv 2005

[21] [21]

M. Ciminale, G. Nardulli, M. Ruggieri and R. Gatto, prep rint, hep-ph/0602180

View on Pith Pith review arXiv

[22] [22]

M. Mannarelli, K. Rajagopal and R. Sharma, preprint, he p-ph/0603076

View on Pith arXiv

[23] [23]

E. V. Gorbar, M. Hashimoto, V. A. Miransky and I. A. Shovk ovy, preprint, hep-ph/0602251

View on Pith Pith review arXiv

[24] [24]

M. Huang, Phys. Rev. D 73, 045007 (2006) [hep-ph/0504235]

View on Pith Pith review arXiv 2006

[25] [25]

D. K. Hong, preprint, hep-ph/0506097

View on Pith Pith review arXiv

[26] [26]

T. Sch¨ afer, Phys. Rev. D 65, 094033 (2002) [hep-ph/0201189]

View on Pith Pith review arXiv 2002

[27] [27]

A. Kryjevski and T. Sch¨ afer, Phys. Lett. B 606, 52 (2005) [hep-ph/0407329]

View on Pith Pith review arXiv 2005

[28] [28]

A. Kryjevski and D. Yamada, Phys. Rev. D 71, 014011 (2005) [hep-ph/0407350]

View on Pith Pith review arXiv 2005

[29] [30]

D. T. Son and M. A. Stephanov, Phys. Rev. D 61, 074012 (2000) [hep-ph/9910491]. 15

View on Pith Pith review arXiv 2000

[30] [31]

In this basis ∆ AB = − 1 2 ∆ abεijaεrsbλA irλB js, ∆ ab = diag(∆ 1, ∆ 2, ∆ 3)ab. (3) 3 We will assume that X = Y = 1 which excludes the possibility of kaon condensation. This assumption signiﬁcantly simpliﬁes the calculation of the fermion disper sion relations and the current correlation functions. It is possible to suppress kaon condensation by includin...

View on Pith