CKM Matrix Parameters from the Exceptional Jordan Algebra

Round 1

Reviewer 1 Report

This paper suggests a unification of forces using the Clifford algebra Cl(9), apparently including gravity (through a ``gravi-charge'', a ``gravi-colour'' and so on). I am not sure how this is supposed to overcome the Coleman-Mandula theorem, which prevents just such a possibility. 

 

Various predictions are made regarding masses of particles in the standard models and the CKM matrix. The match with observed quantities appears to be rather vague. Moreover, masses run with the energy scale; hence it is hard to see how they can possibly be explained by group theory.

 

A speculation are also offered regarding the existence of a second spacetime, which would derive along with the usual one from a six-dimensional one. I see very little evidence for this.

 

Based on all this, I am afraid I cannot recommend this paper for publication.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors have employed octonions in order to unify the electroweak and strong interactions along with gravity.  The authors propose a left-right symmetric extension of the Standard Model using complex split bioctonions, which also incorporates gravitation.  The authors also spend some time reviewing the mathematical background and structure used in the manuscript associated with group representations. The authors theoretically derive the CKM matrix parameters which are in good agreement (even without higher-order corrections) with the the experimentally measured values.

I think that the science is solid and would be very interesting to Universe readers since it is within the aim and scope of the journal due to the work being within the domain of the foundation of quantum mechanics and quantum gravity as well as the implications at the beginning of time in the GUT epoch as well as now.

The only thing that I think is an issue are some small writing issues.  Such as:

1.) the authors should consistently used, "Standard Model" where sometimes they say, "standard model", 

2.) sometimes the authors will capitalize "Algebra" and other times leave it lower case,

3.) Section 2 title is, "A few basics" which should be capitalized compared to the other headers,

4.) Section 2.2 just begins with bullet points and not with some narrative,

5.) the caption for Table 1 does not have a period like the other tables,

6.) line 116 is a sentence and then there is math for the next few lines that is not embedded in any text,

7.) I assume there should be a period or something after Eqn. 7 since there is a sentence that begins on the next line.

8.) Eqn 9 is just floating in space,

9.) as well as Eqn 11 where the sentence begins but there is no ending (without punctuation) and then a sentence begins under it.

10.) Figure 1 has a caption but no period.

11.) Table 2 has a caption with a period but the period has an odd space before it.

There are similar issues all throughout the manuscript.  I would suggest this manuscript for publication after the "ticky-tack" edits are corrected.

 

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

In this article,  a theoretical derivation of the Cabibbo-Kobayashi-Maskawa (CKM) matrix parameters and the accompanying mixing angles are described in very detail. The manuscript is described in a scientific manner and the mathematical results are given in detail. If the following points are re-investigated carefully, this article could be re-considered for publication.

1) There are many past works in the CKM matrix in the literature.
The differences of this work from the past works must be explained in more detail, so that the originality of this work can be understood more explicitly.
This is the most crucial point in this review report.

2) Cliford algebras and the standard model have been studied. The main advantage of this approach is that the spinor representations of the fundamental fermions can be constructed easily here as the left ideals of the algebra. From these results, what fundamental physics in the early universe/in the high-energy regime can be found?

3) The mixing angle values are obtained and compared with the corresponding experimentally measured values for these angles. The agreement of theory with experiment is likely to improve when running of quark masses is taken into account. What physical mechanisms can lead to these particle physics consequences?

 Moderate editing of English language required

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

The authors' detailed answers and revision are well appreciated. In the revised manuscript, the points in the report are taken, and therefore the revised manuscript could be suitable for publication.

Minor editing of English language required

Author Response

English language corrections made in manuscript:

1. In abstract, sixth line from below: comma added after Also.

2. Section 1, last para 3rd line: flavour changed to flavor, and also everywhere else in the paper.

3. Section 2, 3rd line: word `subsequent' removed.

4. Section 2.3: comma added after Also and `the' removed from 3rd-last line.

5. Section 3, line 3: commas introduced.

6. Section 3.1 line 4 full stop removed.

7. 2nd last line Section 4: Algebra changed to algebra

8. Full stop removed from sentence above Eqn. (45)

9. Section 5 5th last line: `The Left Ideal' changed to `The left ideal' 

10. Section 6 2nd line full-stop removed.

11. 2nd line below Eqn. (67): Ideal changed to ideal

12. Full stop removed from sentence above Eqn. (73)

13. Full stop removed  from sentence above Eqn. (74)

14. Idempotent changed to idempotent in line above Eqn. (82)

15. Section 7 line 4 Algebra changed to algebra

16. Caption of Table 3: Symmetry changed to symmetries

17. Above Eqn. (102): is changed to are

18. `We recall that' added at the start of Subsection 7.3

19. same subsection line 6: Idempotents changed to idempotents

20 Line above eqn. (116): Algebraic changed to algebraic

21. Two lines below Eqn. (148): It replaced by This

To the best of our understanding, the language in the rest of the manuscript, including the three appendices and the references, is fine.

Thank you,

Authors.