Referee:

The authors address two issues for chiral quark matter models of the (P)NJL type: 

1) the too large pseudo-critical temperature of the chiral transition when compared with lattice QCD, 
2) the response of the chiral condensate to a strong external magnetic field. 

Both topics are of high actual interest, in particular when also the strangeness degree of freedom is included, and original results deserve publication. 
The authors suggest that a better agreement between the PNJL model and lattice QCD results can be achieved by scaling the coupling constants G and K 
in dependence on temperature and magnetic field. This has been demonstrated already in earlier publications of partially these authors [5-7] for the two-flavor NJL model. 

Authors:

Thanks for the comments and for the careful reading of our manuscript.

Referee:

In the present paper these results are extended to three flavors in the Polyakov-loop improved NJL model. 
Before the present paper can be recommended for publication a few questions have to be answered. 

- what happens with the couplings in Fig. 2 for T>180 MeV ? Do they continue to drop linearly? 

Authors:

This is an interesting point. At high temperatures, condensates changes very little and couplings of Fig. 2 
are supposed not to change as well. So, they drop linearly up to 180 MeV and keep constant at their smallest 
value for higher temperatures. 

Referee:

- can the non-monotonous behaviour of the couplings in Fig. 3 be justified ? 

Authors:

What is important about this behavior is that the change in slope is occurs around the phase transition.
So it may be justified by a good description of the phase transition observed in lattice calculations.
Nevertheless, we still need to investigate the thermodynamic consequences of such couplings. Then we
may be in position to understand the underlying reason for the non-monotonous behavior.   

Referee:

- while the magnetic catalysis of the (P)NJL model gets stopped by the scaling of couplings, 
  an inverse magnetic catalysis as seen in lattice QCD simulations does not become apparent. 
  Can the authors provide an explicit comparison with lattice data in their Fig. 4 ? 

Authors:

Also an interesting point. Lattice QCD results are available only for few temperatures and thus calculation of thermal susceptibilities 
cannot be performed without an interpolation. But our fit describes the lattice condensates almost perfectly so that susceptibilities 
shown in Fig. 4 can be viewed as what lattice susceptibilities would look like if there were more points to compute de derivative. 

Referee:

- it has been demonstrated that the behaviour of the chiral condensate can well be understood within a hadron resonance gas model 
  [J. Jankowski et al., PRD 87 (2013) 105018] or in a Polyakov linear- sigma model [A. Tawfik et al., PRC 90 (2014) 015204; PRC 91 (2015) 015206]. 
  In the present work there are no hadronic states included at all. How could this possibly be justified? 

Authors:

The idea of using thermo-magnetic couplings is to mimic all few-body and many-body effects at once in a simple way.
That is the main reason we don’t consider specific hadronic states in our mean field approach.

Referee:

Technical remarks: 

Abstract, line 1: “... strange quark and the Polyakov loop.” 

Section 2, first line: “In a recent letter [5], we presented an SU(2) NJL ...” 4th and 5th line: SU(2) and SU(3) in roman or italics? Please unify notation! 

Section 3, line 3: “... decrease in both couplings is ...” 

Figure 3, Caption and Final remarks: change “B=...” to “eB=...” 

Ref. [9]: Szbo → Szabo; JHEP 02 → JHEP 1202 

Ref. [10]: JHEP 08 → JHEP 1408 

Authors:

Fixed. Thanks.