# Strangeness neutrality and QCD thermodynamics

### Submission summary

 As Contributors: Fabian Rennecke Arxiv Link: https://arxiv.org/abs/1808.00410v1 (pdf) Date submitted: 2018-08-12 02:00 Submitted by: Rennecke, Fabian Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Phenomenology Nuclear Physics - Theory Approach: Theoretical

### Abstract

Since the incident nuclei in heavy-ion collisions do not carry strangeness, the global net strangeness of the detected hadrons has to vanish. We investigate the impact of strangeness neutrality on the phase structure and thermodynamics of QCD at finite baryon and strangeness chemical potential. To this end, we study the low-energy sector of QCD within a Polyakov loop enhanced quark-meson effective theory with 2+1 dynamical quark flavors. Non-perturbative quantum, thermal, and density fluctuations are taken into account with the functional renormalization group. We show that the impact of strangeness neutrality on thermodynamic quantities such as the equation of state is sizable.

### Ontology / Topics

See full Ontology or Topics database.

###### Current status:
Has been resubmitted

### Submission & Refereeing History

Resubmission 1808.00410v2 on 29 November 2019

Submission 1808.00410v1 on 12 August 2018

## Reports on this Submission

### Anonymous Report 2 on 2018-11-12 Post-Editorial Recommendation Report (Invited Report)

• Cite as: Anonymous, Report on arXiv:1808.00410v1, delivered 2018-11-12, doi: 10.21468/SciPost.Report.653

### Strengths

First investigation of enforcing strangeness conservation in the context of functional renormalization group applied to PQM.

### Weaknesses

No error bars are presented on the final results which indicate the level of theoretical uncertainty.

### Report

Overall I find the paper to be well-written, however, I have some questions that need to be addressed by the authors.

### Requested changes

(1) Since the authors work in a FRG-improved PQM there are only mesonic and quark degrees of freedom present. This leads me to two points of confusion: (a) What happens at very large temperatures to the pressure and trace anomaly? Does the result for the pressure go to the Stefan-Boltzmann limit for QCD as T -> infty? It would seem to me that the answer is no because there are no dynamical gluons (extra Nc^2 -1 massless degrees of freedom). If I can't go to T-> infty, what is the highest temperature at which I would expect such a model to be trustworthy? (b) What is the impact of throwing out baryons/resonances as one approaches Tc? Traditionally one expects to be sensitive to higher mass states as one approaches Tc.

(2) There are no uncertainties lies in Tables I or II. These were determined by some fitting procedure. It would be nice to know the uncertainties and the impact these uncertainties have on the final results.

(3) In the intro the authors state that they will "go beyond mean field level". This seems to be true for mesonic fluctuations but not for the Polyakov loop itself. This should be stated clearly in the intro elsewhere where it's stated that you are going beyond mean field level.

• validity: good
• significance: good
• originality: good
• clarity: good
• formatting: excellent
• grammar: excellent

### Anonymous Report 1 on 2018-11-6 (Invited Report)

• Cite as: Anonymous, Report on arXiv:1808.00410v1, delivered 2018-11-06, doi: 10.21468/SciPost.Report.639

### Strengths

1 - A three flavour Polyakov-quark-meson model analysis within a FRG framework in local potential approximation including baryon and strangeness chemical potential

2 - Illustrative examples Figs 3 - 5 for the strangeness density as well as strange chemical potential as functions of temperature and chemical potentials.

3 - Discussion of the influence of strangeness neutrality on the isentropes in the phase diagram (Fig 8).

### Weaknesses

1 - lengthy explanation of three flavour QCD at low energy, in particular parts of Sections II and III which are ultimately not used in the work.

### Report

The manuscript discusses the impact of strangeness neutrality on the QCD thermodynamics and its phase structure. The dynamics of the quarks and mesons and to some extent also the baryons at finite baryon and strangeness chemical potentials are tackled by a renormalization group approach with a 2+1 quark flavour quark-meson model truncation augmented with a Polyakov loop. The authors conclude that the impact of strangeness neutrality on the thermodynamics and on the equation of state is sizeable.

The topic of this work is contemporary and very interesting. The reference list is exhaustive and gives a fair account of the existing literature on these issues. However, before I can recommend the manuscript for publication in SciPost the following points need to be addressed by the authors:

1) In Eq(16) it is stated that this expression at some finite RG scale k is the total thermodynamic potential which seems to be a little misleading. For the physical quantities the solution of a gap equation is needed which is not mentioned.

2) The setup described in Sec II und III, in particular the one in Sec III, are quite lengthy, to some extent irrelevant for the present work and off-putting to the reader. Let me give a concrete example: on page 7 in Sec B wave function renormalizations are introduced but later these quantities are not even used since a local potential approximation (LPA) is employed. This is distracting from what is actually done and should be adjusted accordingly. Furthermore, it is not clear whether the chosen flat Litim regulator is a valid regulator beyond a local potential approximation. This is not addressed, and in the absence of a solution it suggests that general discussions beyond LPA should be refrained from.

3) In Fig 7 the chiral transition defined by the inflection point of the subtracted chiral condensate at strangeness neutrality and at vanishing strangeness chemical potential is shown.
From this result it is stated that strangeness neutrality leads to a larger critical temperature as compared to $\mu_s =0$. This statement is not clear since both curves are almost identical.

4) In Fig 8 it would be helpful to include the crossover line.

5) In App B it is stated that the deconfinement transition in SU(3) Yang-Mills theory is of second-order in contradiction to other findings.

6) Fig 4 the colour coding is hard to read and several word duplications like the the etc appear in the main body.

### Requested changes

1) In Eq(16) it is stated that this expression at some finite RG scale k is the total thermodynamic potential which seems to be a little misleading. For the physical quantities the solution of a gap equation is needed which is not mentioned.

2) The setup described in Sec II und III, in particular the one in Sec III, are quite lengthy, to some extent irrelevant for the present work and off-putting to the reader. Let me give a concrete example: on page 7 in Sec B wave function renormalizations are introduced but later these quantities are not even used since a local potential approximation (LPA) is employed. This is distracting from what is actually done and should be adjusted accordingly. Furthermore, it is not clear whether the chosen flat Litim regulator is a valid regulator beyond a local potential approximation. This is not addressed, and in the absence of a solution it suggests that general discussions beyond LPA should be refrained from.

3) In Fig 7 the chiral transition defined by the inflection point of the subtracted chiral condensate at strangeness neutrality and at vanishing strangeness chemical potential is shown.
From this result it is stated that strangeness neutrality leads to a larger critical temperature as compared to $\mu_s =0$. This statement is not clear since both curves are almost identical.

4) In Fig 8 it would be helpful to include the crossover line.

5) In App B it is stated that the deconfinement transition in SU(3) Yang-Mills theory is of second-order in contradiction to other findings.

6) Fig 4 the colour coding is hard to read and several word duplications like the the etc appear in the main body.

• validity: ok
• significance: good
• originality: good
• clarity: high
• formatting: excellent
• grammar: excellent