Three Decades of FCNC Studies in 3-3-1 Model with Right-Handed Neutrinos: From Z′-Dominance to the Alignment Limit

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript provides a comprehensive review of the phenomenology of FCNC processes in the 331 model with right-handed neutrinos, covering developments from the past 30 years. I believe it is useful for understanding the current status of phenomenological studies in this model, and therefore, I fully agree its publication.In the following, I list a few minor comments for the authors to consider.

1. Around Eq. (27), the Author mentions the mixing between Z and Z'. As far as I understand, such mixing affects parameters measured in electroweak precision tests, and therefore, it is an important phenomenological aspect.
   The authors state that the mixing angle is negligibly small, but I think it would be helpful to briefly explain the reason for this suppression in the manuscript. Additionally, does a similar mixing not occur between W and W'?
2.  I believe the current constraints on Higgs couplings should be discussed. Both flavor-diagonal and flavor-off-diagonal couplings are strongly constrained by the LHC Run 2 measurements of the Higgs boson mixing angle.  Figures 3, 4, and 5 show constraints on \cos(\phi+\varphi), but it would be highly informative if the authors could add a comment comparing the sensitivity of the flavor experiments discussed here relative to constraints of the Higgs coupling. 
3. In the first paragraph on p.7, shouldn’t the ratio v_{\chi'}/v_{\rm SM} be v_{\rm SM}/v_{\chi}?

Author Response

The reiewer says: This manuscript provides a comprehensive review of the phenomenology of FCNC processes in the 331 model with right-handed neutrinos, covering developments from the past 30 years. I believe it is useful for understanding the current status of phenomenological studies in this model, and therefore, I fully agree its publication.In the following, I list a few minor comments for the authors to consider.

 

Our reply: We thank for the nice comments

 

The reviewer says: 

1. Around Eq. (27), the Author mentions the mixing between Z and Z'. As far as I understand, such mixing affects parameters measured in electroweak precision tests, and therefore, it is an important phenomenological aspect.
   The authors state that the mixing angle is negligibly small, but I think it would be helpful to briefly explain the reason for this suppression in the manuscript. Additionally, does a similar mixing not occur between W and W'?

Our reply: there are many sources of constraints on this mixing angle. In Sec. 5 we discuss the paper [70] that put constraint on this mixing from meson transitions. The other sources of constraints we decided do not talk about because the paper treat of FCNC. But we refer the readers to Refs. [71], [72] and [73].  Moreover, if we look at Eq. (27) we will see that such mixing angle is proportional to m_Z^2/m^2_ Z`. For m_Z ~90 GeV and m_Z`~ 4 TeV, we see that such mixing angle  must be smaller that 10^(-4). That is pretty small. All sources of constraints on this mixing angle obtain values around 10^(-4). And, yes, it is possible to have a mixing among W and W`. But this demands that all five neutral scalars develop VEV different from zero. This involve too much complexity. 

 

The reviewer says: 

1.  I believe the current constraints on Higgs couplings should be discussed. Both flavor-diagonal and flavor-off-diagonal couplings are strongly constrained by the LHC Run 2 measurements of the Higgs boson mixing angle.  Figures 3, 4, and 5 show constraints on \cos(\phi+\varphi), but it would be highly informative if the authors could add a comment comparing the sensitivity of the flavor experiments discussed here relative to constraints of the Higgs coupling. 

Dear reviewer, your question is very compelling. However, we would like to emphasize that the purpose of this paper is to provide a concise review of FCNc investigations within the 331RHN model. Extending the discussion beyond what has been addressed in previous works would constitute an original contribution, which lies outside the scope of this review. Nevertheless, we greatly appreciate your suggestion and will consider it as a valuable direction for a future original pape

 

The reviewer says: 

1. In the first paragraph on p.7, shouldn’t the ratio v_{\chi'}/v_{\rm SM} be v_{\rm SM}/v_{\chi}?

Our reply: we corrected that. Thank you.

Reviewer 2 Report

Comments and Suggestions for Authors

The article reviews models based on SU(3) color times an elctroweak theory based on SU(3)XU(1). This brings new gauge bosons and more scalar fields. It is non-trivial to find conditions so that the theory is consistent with the standard model.

   The authors give a precise description of the "ailingment limit" in lines 556-600. Then they decribe three classifications as solutions.

The solutions for these models is not based on the principle of "naturality" as is introducedfor FCNC in the standard model. In this respect I find the absence of any mention of the works by Glasow and Weinberg PRD15 (1977) page 1958 and also the article on PRD15 (1977 )page1966. 

Author Response

  

The article reviews models based on SU(3) color times an elctroweak theory based on SU(3)XU(1). This brings new gauge bosons and more scalar fields. It is non-trivial to find conditions so that the theory is consistent with the standard model.

   The authors give a precise description of the "ailingment limit" in lines 556-600. Then they decribe three classifications as solutions.

The solutions for these models is not based on the principle of "naturality" as is introducedfor FCNC in the standard model. In this respect I find the absence of any mention of the works by Glasow and Weinberg PRD15 (1977) page 1958 and also the article on PRD15 (1977 )page1966. 

 

Our reply: we thank the referee by the comments and the suggestion of the reference, which we included it  in the text, see Ref.[16] in the introduction .

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript is a concise review of the realization of the 331 embedding right-handed neutrinos.

I found the manuscript scientifically sound a well written. I would nevertheless recommend some revision before publication according to the following remarks.

1) The authors motivate the choice of focussing on the 331 model with RH neutrinos with the absence of Landau poles. I wander if there are differences, with respect to the minimal 331 model, also from the phenomenological perspective. If yes I would recommend the authors to explicitly comment on this point.

2) The authors used, for the angles defined in eq. 41, symbols visually very similar. If possible I would suggest to use a different notation to improve the clarity.

3)  For what experimental constraints are concerned, the authors mostly focussed on meson transitions, leaving LHC to the future prospects. To my best knowledge, models, as the 331, featuring a Z' boson, are already very effectively probed. I would like to ask the authors to check the literature for potential constraint and, in case the latter are actually absent, comment expliclty on this point.

Author Response

 

The reviewer says: 

The manuscript is a concise review of the realization of the 331 embedding right-handed neutrinos.

I found the manuscript scientifically sound a well written. I would nevertheless recommend some revision before publication according to the following remarks.

 

Our reply: we thank the referee by the nice comments.

 

The reviewer: The authors motivate the choice of focussing on the 331 model with RH neutrinos with the absence of Landau poles. I wander if there are differences, with respect to the minimal 331 model, also from the phenomenological perspective. If yes I would recommend the authors to explicitly comment on this point.

 

Our reply: We agree with the reviewer. The thext lacks a mentiion that our studied concern exclusively to the 331RHN, since each 3-3-1 model has its intrinsic phenomenology. We made question to refer to this in the end of the text. Please, take a look in the end of the  last paragraph of the text. 

 

The reviewer says: The authors used, for the angles defined in eq. 41, symbols visually very similar. If possible I would suggest to use a different notation to improve the clarity.

 

Our reply: We agree with the referee that the symbols concerning those angles are very similar. However, as we are writting a review, we think interesting to keep the notation of the original papers. 

 

The reviewer says: For what experimental constraints are concerned, the authors mostly focussed on meson transitions, leaving LHC to the future prospects. To my best knowledge, models, as the 331, featuring a Z' boson, are already very effectively probed. I would like to ask the authors to check the literature for potential constraint and, in case the latter are actually absent, comment expliclty on this point.

 

Our reply: we thank the reviewer for calling our attention to such point since there are in the literature colliders constraints on Z`.  In fact there are at least two works addressing collider physics of Z`. We added these 2 references, ref.(60) and Ref. (115),  in line 906 of the text. Please, take a look