Neutron Reflectometry and Short-Range Modifications of Gravity
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsJ.M. Rocha, F. Dahia, “Neutron reflectometry and short-range modifications of gravity”
The general idea of this article is clear, this work is correct, well written and of scientific interest. Therefore, I have no doubt that it should be published in Universe. However, first I suggest the authors to make a few corrections or additions.
- Indeed, neutron scattering methods have a number of advantages and, in particular, neutron reflectometry is one of them. However, I lack a) the analysis of one potentially false effect, on the one hand, and b) a comparison of possible mirror materials, on the other hand:
- a) The interaction of a neutron with the mirror surface is considered classically. How justified is this approach? The fact is that the energy of the quantum states of a neutron in the gravitational field of the Earth above the mirror is about 1.4x10^(-12) eV, and the critical energy of Pb-207 is 7.3x10^(-8) eV. The ratio of these values is 2x10(-5), which is comparable to the accuracy of the experiment itself. Do quantum corrections matter in this process?
- b) The authors consider one specific mirror material. Is it possible to improve the limitation if other materials are used? In particular, I propose to add a table that approximately estimates the relative uncertainty with which the boundary energies of other materials must be measured in order to obtain an equivalent constrain.
- Some articles are missing references in the text. They may have appeared when copying the list of publications from some other work. Please remove such articles. In particular, I did not find references to works [35-37].
Author Response
We would like to express our gratitude to the reviewer for the time devoted to evaluating our work, as well as for the valuable comments and suggestions, which significantly contributed to improving the manuscript in our opinion. Below are the responses to the questions raised.
a) The interaction of a neutron with the mirror surface is considered classically. How justified is this approach? The fact is that the energy of the quantum states of a neutron in the gravitational field of the Earth above the mirror is about 1.4x10^(-12) eV, and the critical energy of Pb-207 is 7.3x10^(-8) eV. The ratio of these values is 2x10(-5), which is comparable to the accuracy of the experiment itself. Do quantum corrections matter in this process?
It is important to emphasize that the process of neutron reflection by the material was examined through the formalism of quantum mechanics, by studying the behavior of a particle incident upon a potential barrier (optical potential). The outcome of this process depends on the kinetic energy of the incident neutron, which, in turn, depends on its falling height.
In reflectometry experiments, neutrons fall from a height greater than the critical height H_0. Therefore, the kinetic energy at the moment of collision with the material is greater than the potential energy, causing the reflection probability to decrease.
On the other hand, it is important to note that a neutron with energy in the pico-eV range would be completely reflected by the material and, in fact, would form a quantum bound state, as verified by the quantum bouncer experiment. Neutrons with this tiny energy are not present in the reflectometry experiment.
b) The authors consider one specific mirror material. Is it possible to improve the limitation if other materials are used? In particular, I propose to add a table that approximately estimates the relative uncertainty with which the boundary energies of other materials must be measured in order to obtain an equivalent constrain.
Yes, slightly stronger constraints can be obtained by considering the data on the scattering length of bismuth, which are also available in reference [ Snow et al]. For this reason, we decided to replace the analysis based on the element Pb-207 (previous version) with an analysis of Bi-209 (see page 6 and the new Figure on page 7).
Furthermore, in order to perform a more comprehensive comparison, we also examined the constraints that could be derived from other elements (see Table 1, on page 8), which are also listed in reference [Snow et al ].
Additionally, as suggested, we verified that the precision of the measurements related to oxygen, for example, would need to be improved by 87.5% in order to yield a constraint equivalent to that established by bismuth.
c) Some articles are missing references in the text. I did not find references to works [35-37].
We thank you for bringing the references [35-37] (numbering from the previous version) to our attention. In the updated version, they are properly cited on page 1, line 44, with new numbers [23-25].
By implementing the changes suggested by the reviewer, we believe we have achieved an improved version of our work. We hope that this new version addresses the reviewer’s concerns and meets the expected quality level.
Sincerely,
F.Dahia and J.M. Rocha.
Reviewer 2 Report
Comments and Suggestions for AuthorsThe paper Neutron Reflectometry and Short-Range Modifications of Gravity describes how existing experimental data can be reused to constrains models of large extra dimensions. Those models are motivated by the hierarchy problem: the fact that the gravitational interaction is much weaker than the others. In those models, gravity is the only interaction able to propagate into the additional dimensions and as a consequence, the strength of the gravity is modified at short distances. Observing this local modification of the gravity in existing experimental data is the main goal of the study described by this paper.
The introduction is well written and gives a clear description of the context of the study. In particular it is clear that the study is done under the assumption that the branes have a non-zero thickness which is a very specific sub-class of models.
The second part described how the extra-dimensions modify the neutron optical potential. This part is not so easy to read. But since the assumptions that are made are clearly stated, I think it is OK.
I have one question to the authors:
- Line 117: why 10^(-18)m?
The third part is focusing on experimental data and constraining the free parameters of the model. I have few comments on this part:
- In the beginning of this part, around lines 221-223, a quick introduction of a “typical setup” is given. To the best of my knowledge this is only one existing setup measuring the scattering length with the gravity reflectometry technic. I would propose to rephrase this part in this spirit.
- Equation 16: please check the denominator. In both ref 23 and 24 the denominator reads: 1+sqrt(1-H0/H) not 1+sqrt(1+H0/H). If this is not a typo, please comment in the text why.
- At the end you have to constrain 2 parameters with one measurement. Still you could give a lower bound on Lambda (from the plot I would guess 11-12 GeV). Why don’t you give such a bound? I would find such a bound more interesting than your discussion lines 275-281.
- Why did you decide to work with lead 207? In ref 24 there is also a measurement of Bi209 which is more accurate and heavier at the same time. Bi209 would give a better result?
In the last part, the perspectives of the work are given. The key idea is to use all existing data to have a global constrain. This is in line with the assumption made for the gamma parameter line 185. To me this is indeed a very promising path and I would advice to include this study in this paper. Since the corrected data is available in ref 24, it does not seem to be a large effort and will significantly improve the quality of the paper.
In conclusion, as it is this paper is not really giving a constrain on the effective energy scale of the gravitational interaction in the higher-dimensional space. But the attempt to do so is an original work.
I advise its publication after major corrections.
Author Response
We would like to express our gratitude to the reviewer for the time devoted to evaluating our work, as well as for the valuable comments and suggestions, which significantly contributed to improving the manuscript in our opinion. Below are the responses to the questions raised.
a) I have one question to the authors: Line 117: why 10^(-18)m?
This length scale corresponds to an energy scale of the order of TeV, which is reached in high-energy colliders. We have added reference [33, Giudice et al.], which confirms this information, at the end of line 117.
b) In the beginning of this part, around lines 221-223, a quick introduction of a "typical setup" is given. To the best of my knowledge this is only one existing setup measuring the scattering length with the gravity reflectometry technic. I would propose to rephrase this part in this spirit.
We have replaced the expression "typical setup" with "the experimental configuration".
c) Equation 16: please check the denominator. In both ref 23 and 24 the denominator reads: 1+sqrt(1-H0/H) not 1+sqrt(1+H0/H).
Thank you for bringing this to our attention. We have corrected this typo in Equation (16).
d) At the end you have to constrain 2 parameters with one measurement. Still you could give a lower bound on Lambda (from the plot I would guess 11-12 GeV). Why don't you give such a bound? I would find such a bound more interesting than your discussion lines 275-281.
In this paragraph, our intention was to compare the new bounds obtained in this work with those derived from muonic atom spectroscopy. However, in this work, the constraint on Lambda is given in terms of the nuclear scattering length b_N, whereas the spectroscopic bound expresses Lambda in terms of the charge radius of the alpha particle r_\alpha. To enable a meaningful comparison, we needed a common criterion that does not rely on either b_N or r_\alpha. The approach adopted was to estimate the bound by assuming that the anomalous term could not exceed the experimental uncertainty of the measurements.
e) Why did you decide to work with lead 207? In ref 24 there is also a measurement of Bi209 which is more accurate and heavier at the same time. Bi209 would give a better result?
Yes, slightly stronger constraints can be obtained by considering the data on the scattering length of bismuth, which are also available in reference [ Snow et al]. For this reason, we decided to replace the analysis based on the element Pb-207 (previous version) with an analysis of Bi-209 (see page 6 and the new Figure on page 7).
f) In the last part, the perspectives of the work are given. The key idea is to use all existing data to have a global constrain. This is in line with the assumption made for the gamma parameter line 185. To me this is indeed a very promising path and I would advice to include this study in this paper. Since the corrected data is available in ref 24, it does not seem to be a large effort and will significantly improve the quality of the paper.
One of the most important results of our work was the derivation of Equation (13). It is an original equation which allows us to identify the relevant parameter of the extra-dimensional model (the effective energy( \lambda \)) which can be constrained by reflectometry experiments. Furthermore, it enables us to determine quantitatively the influence of hidden dimensions on the scattering length of the neutron--nucleus interaction. By using this equation and studying the case of bismuth (in the updated version), we were able to assess the potential of extracting empirical bounds from reflectometry data on brane models.
In the future work we proposed in the final section, we intend to carry out a more comprehensive survey of scattering data, such as that presented in Ref. [ V. V. Nesvizhevsky et al], which includes more than one hundred elements. The data collection, as well as its statistical analysis, will require significant effort and a considerable amount of time. For this reason, we believe this investigation should be adressed in a separate paper.
Nevertheless, in order to provide a broader analysis of our problem, in response to the reviewer, we have included in our study (see Table 1, on page 8) data from several elements listed in reference [ Snow et al].
By implementing the changes suggested by the reviewer, we believe we have achieved an improved version of our work. We hope that this new version addresses the reviewer's concerns and meets the expected quality level.
Sincerely,
F.Dahia and J.M. Rocha.
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsI propose to accept the paper in present form.
Reviewer 2 Report
Comments and Suggestions for AuthorsI would like to thank the authors for their changes to the paper.
I have no more concern or question regarding this paper.
