Neutron Beta Decay and Exact Conservation of Charged Weak Hadronic Vector Current in the Standard Model
Round 1
Reviewer 1 Report
Comments and Suggestions for Authors
The current article "Neutron Beta Decay and Exact Conservation of Charged Weak Hadronic Vector Current in the Standard Model" summarizes the efforts of Andrei N. Ivanov to analyze the form factor structure of the charged weak hadronic vector current to be used in calculations of low energy reactions, where the mass differences between proton and neutron might become important.
An important role in this analysis plays the question of the ECVC effect, i.e., whether the charged weak hadronic vector current is exactly conserved, or in other words: if the form factors F_1 and F_4 of the generalization of the phenomenological ansatz of Leitner are independent.
The article references obtained expressions for the neutron decay amplitude, for the energy and angular differential decay rate, their corrections, calculated in the Standard Model, and the electron asymmetry together with the correlation coefficient that determines the asymmetry, showing also plots for the values of this correlation coefficient for different assumptions of contributions to the current.
In the discussions, the authors use results of an unpublished earlier paper to argue the need to check more angular correlations, as the measuements done until now are insensitive to their main question about the ECVC hypothesis.
The biggest plus for this paper is, that it comprises the collection and summary of the theoretical research in charged weak hadronic vector current form factors at small energies and honors it as a legacy of a deceased colleague.
The biggest shortcoming is the strong referencing of an unpublished paper (i.e [16]). Unfortunately most of the mentioned results rely on this unpublished paper!
The manuscript uses unnecessary complicated formulations, which to some extent hide the conceptually simple but interesting research question.
I recommend the authors to go through the manuscript again to simplify formulations, straighten the arguments to make them more easily understandable, and to either make their unpublished paper available or to include the needed parts of this paper into the current manuscript to make it self contained: I consider this a major revision!
Comments on the Quality of English Language
The minor editing of the English aims at making the text easier readable by avoiding complicated and artificial phrases.
One example (line 268 - 271):
"As a result, the only way to arrange a problem of invalidity of the ECVC hypothesis with scalar and tensor interactions beyond the SM and the experimental data is to take into account a complete set of contributions of scalar and tensor interactions beyond the SM, which include also the quadratic terms [7]."
- What do you want to say with "arrange a problem"? ... the whole sentence is built in a complicated way, making it hard to understand what the intention of the authors is.
Author Response
Comments 1: The biggest shortcoming is the strong referencing of an unpublished paper (i.e [16]). Unfortunately most of the mentioned results rely on this unpublished paper!
Response 1: We put some major effort to finish the unpublished paper, which was submitted to the arXiv and should appear this week and also to universe under code number 3296428. We hope this helps the publication of both articles.
Comments 2: The manuscript uses unnecessary complicated formulations, which to some extent hide the conceptually simple but interesting research question. I recommend the authors to go through the manuscript again to simplify formulations, straighten the arguments to make them more easily understandable.
Response 2: We went through the manuscript and rephrased some sections and sentences.
Comments 3: The minor editing of the English aims at making the text easier readable by avoiding complicated and artificial phrases.
Response 3: We tried to improve on the language part as well.
Finally, we want to thank the referee for his valuable comments and consideration of this article.
Reviewer 2 Report
Comments and Suggestions for AuthorsThe authors are testing the idea that the charged weak hadronic vector current stays the same in neutron β- decay with polarized neutrons and protons and electrons that are not polarized. They assess the contributions of the phenomenological term, which accounts for the exact conservation of the charged weak hadronic vector current (ECVC effect) in neutron β- decay, considering varying masses of the neutron and proton. Alongside, a comprehensive array of contributions from scalar and tensor interactions beyond the Standard Model (SM) to the correlation coefficients. The authors contend that the cumulative contributions of scalar and tensor interactions beyond the Standard Model cannot reconcile the experimental data on correlation coefficients with the contributions from the ECVC effect. One may deduce that the charged weak hadronic vector current is not conserved in the hadronic transitions of weak processes involving hadrons of varying masses.
1. The document is provided in an organized, comprehensive, and pertinent manner in the field.
2. The majority of the given references are current, pertinent articles. It doesn't contain an inordinate amount of self-citations.
3. The work satisfies scientific standards, and more experimental validation is necessary to validate the idea.
4. Based on the information provided in the Discussions and Proposals section, the results of the publication can be replicated in a future experiment scenario.
5. The figures are appropriate, accurate, depict the data, and simple to read and comprehend. Throughout the article, the figures data are interpreted correctly and consistently.
6. The following conclusions align with the arguments and supporting data in the manuscript:
Using polarized neutrons and unpolarized protons and electrons, the authors are testing the viability of the theory concerning the exact conservation of the charged weak hadronic vector current in neutron beta-decay. Contributions from the phenomenological factor, which accounts for the Exact Conservation of the charged weak hadronic Vector Current (ECVC effect) in neutron beta-decay even in the presence of different neutron and proton masses, are computed as part of their study. By including all the contributions from scalar and tensor interactions outside the Standard Model (SM), they compute correlation coefficients. They suggest that in the hadronic transitions of weak processes involving different masses of incoming and outgoing hadrons, the conservation of the charged weak hadronic vector current is not preserved if the combined effects of scalar and tensor interactions beyond the SM do not agree with the experimental data on correlation coefficients along with the contributions of the ECVC effect.
I recommend publishing the manuscript in the present form.
Author Response
We want to thank the referee for his valuable time and consideration of this article. We are very pleased that he fully supports the research and recommends publication of the manuscript!
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsIn the current iteration the paper has the same structure, so I can copy the part of the review of version 1, that described the content of the paper:
The current article "Neutron Beta Decay and Exact Conservation of Charged Weak Hadronic Vector Current in the Standard Model" summarizes the efforts of Andrei N. Ivanov to analyze the form factor structure of the charged weak hadronic vector current to be used in calculations of low energy reactions, where the mass differences between proton and neutron might become important.
An important role in this analysis plays the question of the ECVC effect, i.e., whether the charged weak hadronic vector current is exactly conserved, or in other words: if the form factors F_1 and F_4 of the generalization of the phenomenological ansatz of Leitner are independent.
The article references obtained expressions for the neutron decay amplitude, for the energy and angular differential decay rate, their corrections, calculated in the Standard Model, and the electron asymmetry together with the correlation coefficient that determines the asymmetry, showing also plots for the values of this correlation coefficient for different assumptions of contributions to the current.
In the discussions, the authors use results of a still (?) unpublished earlier paper to argue the need to check more angular correlations, as the measuements done until now are insensitive to their main question about the ECVC hypothesis.
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Comment on the logic of the main argument:
When reading the text, especially after reading the supplied reference [16], I get the suspicion, that there is a flawed logic:
1) The experimental papers cited for the measured values measure the SM values using the assumption of a conserved hadronic current - as far as I can see from the theory.
- the paper[10] of Leitner uses the additional term that makes the off shell current conserved, too, but it is not used for setting the SM values used in the paper.
2) The authors use for their differential rates (eq.(7), (10), (13), (14), etc.) the derivation of ref[7], which does not use the ECVC term the authors claim to discuss. They add the dependence in the formulas (7), (10), (13), (14), etc, by adding terms containing \Delta, that parametrizes the mass difference between neutron and proton, claiming it to be a standard intermediate calculation, which is not documented.
3) The authors now compare the new functions using the SM determined variables with the correlation coefficients calculated in the SM without their additional terms and find that the terms give different values.
4) But this is no surprise, since the SM values were obtained without the ECVC term. But to test the ECVC hypothesis, the experimental SM parameter values should be obtained with the ECVC term in the direct analysis of data.
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Comment on conclusions of the paper:
1) the analysis done in appendix A, showing that the ECVC term has little influence on the quasi elastic cross section and the inverse beta decay, is important to giude the further experimental effort.
2) I am not convince about the argument using the neutron lifetime measurement, but also cannot point to a statement, that I would consider wrong.
3) The argument about the cancellation between the ECVC term and the Fierz term coming from second order scalar and tensor corrections is still confusing me. That might indicate, that the formulation of the argument is not simple and clear enough.
4) Arguing that further experimental determination of corelation functions is needed for a deeper understanding of the neutron is definitely correct.
Comments on the Quality of English Language
Comment on the rephrasing:
The authors did a very minor rephrasing of the text, but left the complicated sentences and formulations without simplifying them.
Examples:
The sentence in lines 164 - 171 (more than 1/2 a paragraph !) is very hard to understand. Can it not be formulated simpler and clearer?
eq(14) and eq.(18):
all equations in the same reference (either 14 or 18) have the same denominator. Would it not be easier to read, if one defines an abbreviation for this denominator and uses it in all equations of (18), making them a single line each and easier to read?
lines 302-303: "However, it is obvious that without contributions of interactions beyond the SM such a hypothesis cannot be fulfilled in the SM." ... is logically not very sensible. :-(
lines 304-307: again a single quite complicated sentence. Is it really not possible to formulate the content in a more clear and understandable way? I do not think the text has to be formulated as short as possible, but rather as clear as possible.
lines 308-314: again a single sentence for a whole paragraph. Why?
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there is a typo in line 230: (lefr) -> (left)
Author Response
Comment: In the discussions, the authors use results of a still (?) unpublished earlier paper to argue the need to check more angular correlations, as the measuements done until now are insensitive to their main question about the ECVC hypothesis.
Response: The unpublished paper is under review as Universe article no. 3296428 and openly accessible via https://doi.org/10.20944/preprints202410.2486.v1
Comments on the logic of the main argument:
When reading the text, especially after reading the supplied reference [16], I get the suspicion, that there is a flawed logic:
Response: We are not sure we understand the confusion of the referee as detailed below:
1) The experimental papers cited for the measured values measure the SM values using the assumption of a conserved hadronic current - as far as I can see from the theory. The paper[11] of Leitner uses the additional term that makes the off shell current conserved, too, but it is not used for setting the SM values used in the paper.
Response 1) The conservation of the charged hadronic vector current in Leitner [11] holds only in the sense of the vanishing matrix element of the n -> p transition, see also [13], that's why we use a new parametrization introducing \Delta...
2) The authors use for their differential rates (eq.(7), (10), (13), (14), etc.) the derivation of ref[7], which does not use the ECVC term the authors claim to discuss. They add the dependence in the formulas (7), (10), (13), (14), etc, by adding terms containing \Delta, that parametrizes the mass difference between neutron and proton, claiming it to be a standard intermediate calculation, which is not documented.
Response 2) \Delta = m_n - m_p is given below Eq. (7)
3) The authors now compare the new functions using the SM determined variables with the correlation coefficients calculated in the SM without their additional terms and find that the terms give different values.
Response 3) We only compare our theoretical results with and without the ECVC and Fierz effects, the analysis of experimental data has to decide which ones are more accurate.
4) But this is no surprise, since the SM values were obtained without the ECVC term. But to test the ECVC hypothesis, the experimental SM parameter values should be obtained with the ECVC term in the direct analysis of data.
Response 4) We use standard SM parameters and add beyond SM conntributions.
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Comments on conclusions of the paper:
1) the analysis done in appendix A, showing that the ECVC term has little influence on the quasi elastic cross section and the inverse beta decay, is important to giude the further experimental effort.
Response 1) We fully agree.
2) I am not convince about the argument using the neutron lifetime measurement, but also cannot point to a statement, that I would consider wrong.
Response 2) That's something experimentalists have to settle, neutron lifetime measurements are known to be very sensitive to beyond SM effects.
3) The argument about the cancellation between the ECVC term and the Fierz term coming from second order scalar and tensor corrections is still confusing me. That might indicate, that the formulation of the argument is not simple and clear enough.
Response 3) This is a matter of reference [16], to account for a non-negligible increase of the neutron lifetime due to the CVC effect we can only rely on interactions beyond the SM, [16] considers the contribution of the Fierz interference term.
4) Arguing that further experimental determination of corelation functions is needed for a deeper understanding of the neutron is definitely correct.
Response 4) We fully agree.
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Comments on the Quality of English Language:
Response: We rephrased parts of the text and the criticized sections and simplified some formulas.
