Ultra-Cold Neutrons in qBounce Experiments as Laboratory for Test of Chameleon Field Theories and Cosmic Acceleration
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsReview of "Ultra-cold neutrons in qBounce experiments as laboratory for test of chameleon field theories and cosmic acceleration" by D. Altarawneh and R. Höllwieser
This paper presents a theoretical work on the influence of a hypothetical chameleon-type force on the gravitational quantum states of ultracold neutrons bouncing above a mirror. The topic is timely and relevant, since the qBounce experimental program is ongoing, and the search for new fundamental interactions is one of its motivations. The specific problem concerns quantum state transitions when neutrons fall down a micrometer-scale step. The modification of the transition probability amplitudes Ck due to the chameleon field is calculated. This problem has not been previously studied and is of experimental relevance. The paper includes original contributions and could merit publication, provided the following concerns are addressed:
1) Missing and inconsistent description of the physical setup.
No schematic of the configuration under study is provided, which makes it difficult to understand the problem considered. Although a figure is implicitely mentioned (lines 74–75), it is absent. In addition, the definitions of the geometry are slightly inconsistent. In particular, the inequality on line 75 appears incorrect and may need to be z^2 < d^2/4 rather than z^2 < d^2/2. In passing, D is defined as the height of the step and should not appear as a prefactor in the chameleon potential (Eq. 7). A clear and coherent description in needed.
2) Inconsistent treatment of the chameleon perturbation.
The initial neutron state before the step is assumed to be the unperturbed wavefunction psi1 (Eq. A1), while the final states after the step are derived using the chameleon-modified potential (Eq. 10). This is inconsistent. If the chameleon field is present, it should modify the wavefunction both before and after the step. This issue requires correction or proper justification.
3) Figures are unclear and not sufficiently informative.
Both Figures 1 and 2 lack clarity. Figure 1 shows Ck as a function of k and D, but the meaning of this plot is not clear. It is cited after Eq. (15), which concerns the modified transition amplitudes, yet the figure show the unmodified ones. Its relevance is therefore unclear. Figure 2 contains five unlabeled curves that do not match the caption, and their meaning cannot be inferred. The figures do not support the discussion as intended. Improved figures are needed, ideally including one that illustrates the central physical effect, namely the modification of quantum state populations due to the chameleon field after the step.
4) Ambiguity regarding constraints on chameleon parameters.
Although the authors state that setting bounds is not the main focus, Eq. (21) presents such a bound without clear experimental justification. The origin and interpretation of this constraint must be clarified. If it reflects the limit of validity of the perturbative treatment, is is not a bound on the parameter, this should be stated explicitly. In addition, the discussion beginning at line 174 refers to experimental data, but no specific experiment or reference is provided. It is not acceptable to cite experimental results without precise reference.
Author Response
1– Comment: Missing and inconsistent description of the physical setup. No schematic of the configuration under study is provided, which makes it difficult to understand the problem considered. Although a figure is implicitely mentioned (lines 74–75), it is absent.
Answer: We added a sketch of the setup from the corresponding literature.
– Comment: In addition, the definitions of the geometry are slightly inconsistent. In particular, the inequality on line 75 appears incorrect and may need to be z2 < d2/4 rather than z2 < d2/2.
Answer: We thank the reviewer for pointing out this inconsistency in the definition of the spa tial region between the mirrors. The correct condition should indeed be z2 < d2/4
– Comment: In passing, D is defined as the height of the step and should not appear as a prefactor in the chameleon potential (Eq. 7). A clear and coherent description in needed.
Answer: (−D) is the position of the mirror and not the actual height of the step, there is a typo in equation 7, thanks for pointing this out, otherwise the chameleon potential agrees with the literature, the wrong factor ΛD was not taken into account in the further calculation.
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- Comment: Inconsistent treatment of the chameleon perturbation. The initial neutron state before the step is assumed to be the unperturbed wavefunction psi1 (Eq. A1), while the f inal states after the step are derived using the chameleon-modified potential (Eq. 10). This is inconsistent. If the chameleon field is present, it should modify the wavefunction both before and after the step. This issue requires correction or proper justification.
Answer: We thank the reviewer for this careful and constructive observation. In the revised manuscript, we have clarified the reasoning behind our treatment of the chameleon perturbation. Specifically, in the region between the two mirrors — where ultra-cold neutrons are initially confined — the spatial extent is extremely limited and bounded by dense material surfaces. In such environments, the chameleon field is effectively screened or varies only minimally. As shown in prior studies (e.g., Ivanov et al., Phys. Rev. D 87, 105013 (2013)), under these conditions, the chameleon potential becomes effectively constant across the confined region. We have added a paragraph in Section 2 of the manuscript to explain this assumption and cite relevant references. This clarification ensures consistency and improves the phys- ical interpretation of our model.
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- Comment: Figures are unclear and not sufficiently informative. Both Figures 1 and 2 lack clarity. Figure 1 shows Ck as a function of k and D, but the meaning of this plot is not clear. It is cited after Eq. (15), which concerns the modified transition amplitudes, yet the figure show the unmodified ones. Its relevance is therefore unclear. Figure 2 contains five unlabeled curves that do not match the caption, and their meaning cannot be inferred. The figures do not support the discussion as intended. Improved figures are needed, ideally including one that illustrates the central physical effect, namely the modification of quantum state populations due to the chameleon field after the step.
Answer: We updated and improved figures and captions, Fig. 2 may be removed if the referee insists, selected values of Ck are also shown in Table 1. In order to illustrate the chameleon effects we include binding energy corrections.
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- Comment: Ambiguity regarding constraints on chameleon parameters. Although the authors state that setting bounds is not the main focus, Eq. (21) presents such a bound without clear experimental justification. The origin and interpretation of this constraint must be clarified. If it reflects the limit of validity of the perturbative treatment, is is not a bound on the parameter, this should be stated explicitly. In addition, the discussion beginning at line 174 refers to experimental data, but no specific experiment or reference is provided. It is not acceptable to cite experimental results without precise reference.
Answer: Equation 21 does not represent an experimentally derived constraint on the chameleon–matter coupling constant β. Rather, it defines a theoretical upper limit that ensures the validity of the first order perturbative treatment employed in this analysis. We added this comment and a reference to the experimental data.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThe research of the presented manuscript is related to a most fascinated field of fundamental physics which trying to find answers about origin of the so-called “dark energy” and expansion of our universe. The research team has a unique experimental approach by using a relatively simple table-top setup with an incredibly precise energy resolution, which is possible because the experiment is using ultracold neutrons. The manuscript is well written and can be published without any revision.
Author Response
We sincerely thank the reviewer for his encouraging comments and for recognizing the clarity.
relevance and scientific quality of our work. We appreciate the recommendation for publication
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsI have reviewed the manuscript "Ultra-cold neutrons in qBounce experiments as laboratory for test of chameleon field theories and cosmic acceleration" by Altarawneh and Höllwieser. This paper describes and elucidates solutions of the Schrödinger equation for a free uiltracold neutron traveling between two closely spaced mirrors in the combined Earth's gravitational potential and the potential due to a hypothetical chameleon field. While the plausible parameter space for the "standard" chameleon field has been mostly ruled out by a variety of experiments, more generally scalar field theories remain relevant to possible explanations of cosmic acceleration. The audience of interest for this work is probably narrowly confined to scientists working on gravitational states of ultracold neutrons and atoms such as the qBounce experiment at the ILL. Nevertheless I believe the merit of this paper to be sufficiently high that I recommend it be published in the Journal of Nuclear Engineering. I find the manuscript to be clearly written and highly stimulating. I found no substantive errors or omissions, just some editorial issues that should be corrected prior to publication.
Comments:
1. In many places throughout the manuscript μm (micrometers) is misrendered as "-m".
2. The English is overall good, but requires improvement in some places, for example:
line 10: delete "with"
line 45: "concerns strongly of" -> "depends strongly on"
Author Response
We have carefully addressed the comments. In addition, we have performed a general review of
the manuscript to further improve clarity and grammar. Thank you again for your helpful comments and
recommendation for publication. Your input has significantly improved the final version of our manuscript
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe authors have adressed the remarks formulated at the previous iteration of the review, I recommend to publish the article in the present form.
