Hyperfine Splitting of Excited States of New Heavy Hadrons and Low-Energy Interaction of Hadronic Dark Matter with Photons, Nucleons, and Leptons

Round 1

Reviewer 1 Report

The paper is interesting and the arguments are well discussed and presented.

I recommend the manuscript for publication in its present state.

Author Response

We are grateful for attention to our work.

With the best regards,

authors.

Reviewer 2 Report

The manuscript aims at describing interactions of hadronic dark matter (DM), characterized by the presence of new heavy quarks in its structure, with leptons, photons, and nuclei, and excited states of these new hadrons.

The most general aspect making me puzzled is the fact that DM-DM annihilation in leptons, photons and nucleons is neither described nor discussed at all. The authors should appropriately address this point, as well as all other elements listed in the following, with reference to more specific parts of the manuscript:

1) line 1 of the abstract "low-energy" interactions. Are really "low-energy" or are they "non-relativistic" ?

2) line 50 "pseudoscalar heavy mesons": why "pseudoscalar" ? Other configurations are also possible ?

3) line 73 and formula (2): the authors seem to use heavy-quark masses renormalized in the MSbar scheme. The issue that I see in formula (2) is the fact that while masses of hadrons appear on the left hand side, masses of quarks appear on the right hand side of the formula: we observe hadrons, but we never observe quarks, due to QCD confinement. What is the exact nature of the masses on the right hand side: renormalized masses or what ? If I work in a renormalization scheme or in another, I got different numbers. This affects also all the consequent discussion and the possibility of really quantifying with precise numbers the values of the mass splittings.

4) line 83: assuming for LambdaQCD a value of 0.1 GeV is not it a bit too small ?

5) line 96: if the interaction gamma-M0 become large, can I still classify M0 as "dark matter" ?

6) line 104: why the interaction Q-Qprime-W, where both Q and Qprime represent new quarks (e.g. quarks from a fourth generation) is not discussed (similar u-dbar-W) ?

7) eq(10): how small can be the masses of the DM hadrons M0, M- ?

8) Section 4: besides the general comment at the beginning of this report, I see several typos, the authors should reread carefully and correct them.

What I think is also weak is the connection with real measurements. How could one distinguish if this model, instead of many others on the markets, would be realized in nature ? Could we have any smoking gun of it ? What kind of observables one should look at ?

Best regards.

Author Response

Dear Reviewer, we are very grateful for your useful remarks and comments, which are taken into account in revised version of the manuscript.

General aspect: the DM annihilation was considered in our previous papers [4-6]. We have not a strict theory of this high-energy process and approximately described it at the sub-process
level. The aim of this work is the description of only low-energy processes of the DM interaction with ordinary matter (nucleons and leptons). However, we take into account your remark and
include some comments into the Section 1 and 4 (lines 26 and 283).

1)Line 1(1) (in Abstract) The term "low-energy" designates the energy limits of validity of effective lagrangians which describe interaction of non-relativistic DM particles with
nucleons and leptons. From the analysis of kinematics it follows that nucleons should be non-relativistic (or "weakly" relativistic) and light leptons (electron and muon) can not be
ultra-relativistic.

2)Line 57(50) Of course, other configurations are also possible. We begin from pseudoscalar states as the lowest (ground) states. We modify the sentence on line 57 and add some
comments.

3)Line 83,86(73) As a rule, in Heavy Quark Effective Theory (HQET) the masses of constituent quarks are used in calculation, although this way is model-dependent, so the masses are defined approximately. We modify the part of the text and formulas (1) and (2) with account of these properties. We should note that the mass-splitting is estimated approximately (an order of magnitude).

4)Line 93(83) We modify the formula (4), which only illustrates the previous result and give more exact values of \Lambda.

5)Line 106(96) In the scenario under consideration, the hadronic DM becomes not absolutely dark at high energy of photons. To describe this effect in more detail we should build potential
model of these superheavy-light states.

6)Line 116(104) In this work, we consider vector-like models of the SM extension where new heavy quark do not interacts with W-boson.

7)Line 160(144) In the previous works, we estimate the mass of new hadron, M\approx 10 TeV (and it can be larger).

8)In the revised version, we noted a new possibility of scenario with the hadronic DM for the cosmology investigation  and the most interesting low-energy effect which can be registered (see
the  Section 4, lines 249 and 277 and Section 5, line 316).

With the best regards, authors.

Reviewer 3 Report

See peer-review.

Comments for author File: Comments.pdf

Author Response

Dear Reviewer, we are very grateful for your attention to our work.

Below we give two responses on your couple of comments.

-A response against the usual belief that the DM is composed of non-hadronic matter is formulated and presented in our previous papers [7,4-6]. In the scenario with hadronic DM new heavy
particles are two-quark states, that is they are mesons, not baryons. The main reason of usual belief that the DM is composed of non-baryonic (or non-hadronic) matter follows from the
observational evidences of weak interaction of DM with usual matter. Moreover, there are rigid cosmochemical restrictions on abundance of anomalous hydrogen and helium which exclude
baryonic DM with standard properties. As was shown in Refs.[4-7], hadronic DM is not excluded if DM particles are new meson states with quark content (qQ), where q is standard light
quark and Q is new heavy quark with vector-like interactions. It was shown that new mesons have repulsive interaction potential with nucleons and do not form the coupled states with
them at the modern stage of evolution. This effect makes it possible to escape the problem of anomalous hydrogen and helium. We also should note that the scenarios with strongly
interacting DM (SIMP) become actual after the excluding of wide class of weakly interacting DM (WIMP) by strong experimental restriction reported in [1].

-In the Section 4 (line 249 and 277) and 5 (Discussion, line 316), we add some comments which illustrate the role of new option for the DM in observational Cosmology. In particular,
the hadron scenario of DM provides a new aspect of connection between galaxies and their DM haloes which can introduce some specific details and features into the galaxy formation process [16]. We note also, the important signal of the interaction of DM particles with atmosphere - the appearance of the metastable heavy charge particles M^- which can be registered by the ground
devices. We are going to study these effects in more details in further work.

With the best regards, authors.