Re: LB17688 Decay law of magnetic turbulence with helicity balanced by chiral fermions by Axel Brandenburg, Kohei Kamada, and Jennifer Schober Dear Dr. Brandenburg, This manuscript has been reviewed by our referees. A critique from the reports appears below. Based on this we judge that the work probably warrants publication in some form, but does not meet the Physical Review Letters criteria of impact, innovation, and interest. The paper, with revision as appropriate, might be suitable for publication in one of the topical Physical Review journals or Physical Review Research. The editors of that journal will make the decision on publication, and may seek further review. However, our complete file is available. In choosing the journal, please be aware that Physical Review Research is a fully open access publication and, thus, article publication charges would apply. If you transfer this manuscript, be sure to include the usual response to all referee comments and a summary of revisions made. Yours sincerely, Kyle J. Welch, Ph.D. (he/him/his) Associate Editor Physical Review Letters Email: prl@aps.org https://journals.aps.org/prl/ Follow us on Twitter @PhysRevLett NEWS FROM THE PHYSICAL REVIEW JOURNALS View PRL’s newly updated sectioning scheme https://go.aps.org/3CPGz6f Introducing PRX Life: a first-rate venue for quantitative biological research https://go.aps.org/3Xq18Pb ---------------------------------------------------------------------- Report of Referee A -- LB17688/Brandenburg ---------------------------------------------------------------------- The authors study MHD evolution when the magnetic field has helicity and the plasma is chiral but the total helicity (defined as the sum of the magnetic helicity and chirality) vanishes. The investigations may be relevant to the early universe where magnetic helicity and plasma chirality may both be present. The analysis is based on MHD simulations that have been widely tested and the results should be reliable. There are three main points that need to be addressed by the authors: 1. Why is this particular scenario important so as to justify publication in PRL? It may be argued that the evolution discussed in this paper is another routine calculation of MHD evolution along the lines of several other analyses in the literature. What makes this analysis special? 2. In the Supplemental Material Section 2, there appears to be a puzzle related to Fig. 2 that needs clarification -- the authors find that with evolution $\mu_5$ goes to zero and they say that "This halts the decay of $H_M$.... but eventually it also decays.'' The puzzle is that once $\mu_5=0$, further evolution is just that of helical magnetic fields in a non-chiral plasma. We know $H_M$ is conserved in this situation. So why do the authors find helicity non-conservation for a non-chiral plasma? 3. Another puzzle is that the authors find (Section 1 of Supplemental Material) that the Hosking integral describes magnetic decay when $=0$, but not when $ \ne 0$. However we know from previous work [4,5,6] that for non-chiral plasmas ($\mu_5=0$) $h_tot$ is just the magnetic helicity and the Hosking integral correctly describes decay. So the statement that the Hosking integral does not give a correct description for $\ne 0$ cannot be completely correct. Perhaps the statement has some caveats that need to be spelled out. Some other minor comments that need to be addressed: 1) $k_0$ below (4) is not defined. 2) In Fig. 1 caption, is it $Sp(B)$ or $Sp(B^2)$? 3) Below Eq. (5): "grow cubically for small $R$ and is flat for larger $R$" seems inconsistent with Fig. 2(a). 4) In Fig. 3(a), $\mu_5$ label is in blue and $H_M$ label is in red, but the caption says $\mu_5$ is red and $H_M$ is blue. (Similarly in Fig. 1 of Supplemental Material.) 5) In the last sentence of Supplemental Material Section 1, $E_M$ should be $H_M$. 6) $\mu_M$ needs to be defined in Supplemental Material. I do not recommend publication of the manuscript in PRL in its present form. ---------------------------------------------------------------------- Report of Referee B -- LB17688/Brandenburg ---------------------------------------------------------------------- The authors of this manuscript study the time evolution of magnetic fields in chiral magnetohydrodynamics. They find novel scalings of the magnetic helicity and the chiral chemical potential in addition to conventional scalings of the magnetic energy and the correlation length. As a reviewer, I must say that it is hard to understand both technical aspects and physical significances of this manuscript. Regarding the technical aspects, there are numbers of quantities that are not defined in the manuscript. For example, $I_H$ in the paragraph starting with "Similarly to earlier studies of ..." is not defined. Probably, it is related to $\mathcal{I}_H$ in Eq.(1), but how? Similarly, the authors state that they set $k_0=1$ and $\rho_0=1$ for units of length and energy, but such quantities do not appear in Eqs.(2),(3),(4). Finally, $Sp(B)$ appears in the paragraph starting with "In the following, we ...", but it is not fully specified (only its normalization is specified). Because Sp(*) appears in the discussion of Fig.1, readability of this manuscript is largely spoiled. Although they may be obvious for specialists, the manuscript is not written in a way understandable to non-specialists. Regarding the physical significances, the main finding of this manuscript is scalings of various quantities out of chiral magnetohydrodynamics in Eqs.(2),(3),(4). But why such scalings are important? At the very end of this manuscript, it is only briefly stated that they have consequences for understanding the properties of the chiral magnetic effect in the early universe and young neutron stars. If so, this part should be elaborated on. Otherwise, this manuscript looks just a technical report of simulation results. Any physical significances or novel innovations cannot be found in this manuscript from the viewpoint of non-specialists. Therefore, I cannot recommend its publication in Physical Review Letters.