Dark matter searches and energy accumulation and release in materials

First, I need to thank the referee for his/her thoughtful and helpful comments and suggestions.

Required changes:
My main goal is to make this paper clear and easy to understand- and this is a difficult task for a limited paper volume and method I need to use to come to conclusions. There is a common problem I can see in all low-energy threshold detectors looking for dark matter particles: they all have low-energy background events with the number of events rising to lower energy (a form of the spectrum), and they are not nuclear recoils caused by atmospheric or solar neutrinos or by dark matter particles, because there are too many of these events, and a number of these events is rising with energy which is pumped into detector’s material. My hypothesis is that in different detectors we see a process of energy pumping in materials/detectors and delayed release events, while release events can be avalanche-like and mimic interactions with particles [4].
In different detectors, we see different features of this type of process, and we have no solid experimental proof of this dynamics for a single detector; only a large picture points out that we have a process of this type.
So, I need to refer to a large number of papers – about Noble Liquid detectors, NaI(Tl) detectors, and Solid State low-temperature detectors. I am referring separately to different noble liquid detector projects and DAMA -LIBRA projects. For solid-state detectors several recent Excess workshops collect data in a single place- so I refer to workshop publications and one “review” paper describing results from many projects -references [2,3]. I am afraid, that currently there are no separate publications from each of these projects which describe properties of excess low-energy background; so, I need to refer readers to these two papers.
Physical mechanisms of energy/charge storage and interactions between excitations/energy/charge bearing states are very specific for Noble Liquid detectors, so I refer readers to my paper [4] and to publication in the proceeding of much more special Noble Elements conference [5]. (I have not submitted this paper to arXiv yet but will do.)
I tried to rewrite the paper following the referee’s suggestion. I also tried to point out clearly where I am hypothesizing, and I suggested experiments to check these hypotheses. It would be good to add/reproduce several pictures from other publications to make some points easier for readers to understand, but the size of my paper is already large. Would the editor allow it, I will be glad to add a couple of pictures.
I added line numbers.

Detailed comments:
• Liquid noble detectors are mentioned in the introduction but then never again.
I explained above- it need separate paper(s)

• Reference [5]: As I understand “Scientific American” is a popular science journal. Please reference scientific information from scientific journals
Sorry,” Scientific American” often publishes high-quality review papers.

• Headline of section 2: please use shorter headlines
I changed headlines

• In several places in the manuscript are spaces missing, this should be easy to fix with a spellchecking program.
• Beginning of section 2: I think 10-1 eV should mean 10-1000 eV.
Solid state detectors indeed detect 1-10eV energy depositions

• Right after this sentence: The claim, that many experiments observe an increase of background with thermomechanical stress dearly needs references. To the best of my knowledge, this is at the moment a hypothesis and only confirmed in one measurement (Ref. [7] in the manuscript). In this paragraph, the author needs to be very specific about which observations were made in which measurements, instead of generalizing from one measurement to an unspecified number of excesses.
Ref. [3]( in rewrite paper) is bringing examples, new experiments

• “Thus, the low-energy background we see is a natural relaxation process of mechanical stress release in single crystals and solids in general.” This is a hypothesis but presented in the manuscript as if it was a result.
I fixed this. The actual hypothesis is that at room temperature and at low temperature relaxation of mechanical stress leads to photon, phonon and quasiparticle emission and can lead to bursst of photon. phonon, and quasiparticles emission
• Beginning of section 3: are the used target materials all amorphous? To the best of my knowledge the target crystals are monocristalline. Please specify for which detectors the theory of glasses is applicable. Also, please add some references for the statements in this paragraph.
In new version, I separated discussions of glasses (disordered solids) and solid-state low-temperature detectors which use single-crystal targets.
I added more glass properties and effects, though not everywhere I can find good references.

• Ref. [14, 15, 16]: They are listed together with phenomena that seem unrelated to the content of the text above and below. Please specify how they are relevant for the arguments.
The general statement is that at low temperatures we generally see more glass-like relaxation/behavior in all materials, including single crystals. This is due to “subsystems” like defects, charges, magnetic moments,etc. I illustrated this statement by examples; these examples are, in fact, are important for understanding different noise mechanisms

• Section 3, start of third paragraph: I don’t see on which arguments the conclusion that is drawn here is based. Please explain in detail and avoid basing scientific statements on “parallels and analogies”.
When you apply force or an electric field to a material with glass-like relaxation properties, it starts to relax toward a minimal energy state for the case of applied force or field. When you remove the force or field, the material is further away from the minimal energy state for zero force or field, i.e., you deposit some extra energy into the material. It can take a long time for this energy to “go out”.

• Section 4: This section seems very important in the line of arguments that interpret the experimental results that are presented later on. However, there is not a single reference listed in this section, and the statements that are made are not trivial.
In a new version, I provide a reference on a book [10] that describes temperature-stimulated luminescence and electron emission in materials exposed to ionizing radiation. These effects demonstrate that energy is accumulating in materials under irradiation.

• “The author posits that exposure of the solid-state detector to ionizing radiation or UV light should lead to delayed low-energy background events with events spectrum and decay time resembling those caused by mechanical stress.” This hypothesis was rejected for at least one experiment (arXiv:2207.09375), that does not see an increase in the low energy background after intervals of strong exposure to calibration sources. Please specify which excesses should be explained by this.
Paper (arXiv:2207.09375) describes a rather strong/high-energy events background. “Mechanical energy” (defects) can be pumped into the crystal during cool-down due to “suspension” and due to thermal gradients inside a large crystal. Was heat exchange gas used during cool-down? Another suspect is the different contraction of the crystal and TES sensor; in this case, excess energy is delivered directly into the sensor. When the background is already large, it could be difficult to see a small change.

• Section 5: This section contains very interesting information about current open questions about glasses. However, the relevance of this information to the rest of the manuscript is not clear to me and should be explained in more detail.
TLS model is not expecting energy-up conversion events, which could be present. So, I am suggesting to look for these events.

• Section 6: Please describe your experimental setup, your analysis chain, and your results in more detail, quantitatively and in this order. Were the experiment and analysis performed by yourself alone? Otherwise, I recommend referencing/acknowledging collaborators.
Reference [28] is provided.

• Section 6: A reference to the criticized Saint-Gobain analysis would be helpful.-added

• Section 6: “The photon flux detected by DAMA-LIBRA and similar experiments consists of delayed luminescence photons (mostly random) and bursts of photon emission produced as a fast/immediate response to external particles.” Is this a result or a hypothesis? If the former, then please reference, if the latter, please formulate as such.
When we see a flux of uncorrelated photons coming out of NaI(Tl), there should be some energy source for this. This could be residual stress, but this energy should disappear over time. Energy influx due to muons and residual radioactivity is always present. TSL is known for NaI(Tl), so we know that radioactivity is pumping energy into the material. When we add more pumping, we see an increase in random photon flux. As for pulses- they could be real, i.e., produced by particles, and fake- produced by correlations in energy releases due to interactions of states storing energy. So, the hypothesis here is that “fake pulses” can be present.

• Section 6: “This suggests that other environmental factors also can affect delayed luminescence response and cause modulation of the DAMA-LIBRA signal; the time of the maximum intensity of random/uncorrelated delayed luminescence can be different from the maximum of muon flux which pumps energy into the system (this was not yet checked).” This argument seems to be one of the most central ones of the manuscript and deserves some more discussion. Which environmental impacts? Could the delay really shift the peak of the event rate? How would this work? In your experimental results the delayed luminescence is released on an exponential scale after the UV irradiation, how would that shift a peak?
Particles produce an immediate response and delayed luminescence. Both components can depend on temperature, pressure, electric and magnetic fields, presence of IR or microwave radiation. Photon bunching in delayed luminescence also can depend on these factors. Muon flux is pumping energy into material and is modulated. Solar neutrinos can produce hot phonons and trigger stoa red energy release; solar neutrino flux is modulated. The main point is that we do not know the material response in sufficient detail.

• Section 7: The conclusion does mostly state that further work needs to be done, but does not summarize the results, statements, and significance of the work at hand. I strongly recommend adding this. In the last sentence, the decoherence in quantum sensors is mentioned for the first time in the manuscript, I would either explain this claim earlier or remove it.
Energetic particles can cause correlated errors in quantum processors, but spontaneous energy release even of 1 eV scale is also sufficient to cause a qubit transition to the excited state. We use microwave signals to control qubits. Microwave photon energy is below the gap in a superconductor. But microwave photons can pump energy into materials, so energy up-conversion events would be a problem.

• Page 6: I recommend putting the figures in the position in the document where they are discussed, not at the end of the document. Also, a smaller figure size would still transport all the information but free up space for text.
-done

• Fig 1: Was the figure made specifically for this paper or published elsewhere? In the latter case, please reference
-provided.

• Fig 1: I don’t understand the second plot (b). What decay time is expected of the scintillation light pulses from this target? Are these pulses from particle hits not always several tens of milliseconds long? How can a statistic be made for the number of pulses per mus? Are these pulses really so fast?
-explained

• References: I recommend using BibTex or a similar references manager. Otherwise, please implement common formatting, indentations, border width, etc.
I improve the formatting (sorry, still working to learn using the reference manager…)

I tried to rewrite the paper following the referee’s recommendations.
Please, provide me feedback if it is easier to read now.
Thanks,
Sergey Pereverzev