The decay of the muon has been studied at PSI with several precision measurements: The longitudinal polarization PL(E) with the muon decay parameters ξ′, ξ′′, the Time- Reversal Invariance (TRI) conserving transverse polarization PT1(E) with the muon de- cay parameters η, η′′, the TRI violating transverse polarization PT2(E), with α′/A, β′/A and the muon decay asymmetry with Pμξ. The detailed theoretical analysis of all mea- surements of normal and inverse muon decay has led for the first time to a lower limit |g V | > 0.960 ("V − A") and upper limits for nine other possible complex couplings, espe- cially the scalar coupling |g S | < 0.550 which had not been excluded before.

Current status:

Has been resubmitted

Reports on this Submission

Report 2 by Adrian Signer
on 2021-7-5
(Invited Report)

Cite as: Adrian Signer, Report on arXiv:scipost_202106_00032v1, delivered 2021-07-05, doi: 10.21468/SciPost.Report.3190

Report

We (the editors Cy Hoffman, Klaus Kirch, Adrian Signer) had the opportunity to review an earlier draft of the article and were in communication with the authors before the submission. All our comments and suggestions have been taken into account. Hence, we think the paper can now be published in the current form.

validity: -

significance: -

originality: -

clarity: -

formatting: -

grammar: -

Anonymous Report 1
on 2021-6-22
(Invited Report)

Cite as: Anonymous, Report on arXiv:scipost_202106_00032v1, delivered 2021-06-22, doi: 10.21468/SciPost.Report.3103

I appreciate the thorough report of the referee. Let me begin with comments to the content:

26) In this approximation the interaction is local,
27) and following: replaced "point interaction" by "contact interaction",
28) Yes, it refers to Fierz identities,
31) I agree, the physics does not depend on the basis. On the other hand, it seemed reasonable to include lepton number conservation which implied the change from charge retention to charge changing form.
37-38) This statement is correct; there really are four coupling constants, and all leptons are left-handed.
40) Replaced "handedness" by "chirality";
40) who in turn use -> which in turn uses,
41) I believe it suffices to continue with the matrix element where the relevant coupling constants are defined.
42) G_F; since F stands for Fermi, it is not unobservable and it should be roman and not italic.
43-49) The chiralities are indeed fixed by \gamma: For \gamma=V the chirality of the outgoing particle is equal to the chirality of the incoming particle; for scalar and tensor interaction, the chirality changes.
50) I use „definitely“ because of widespread use of the term right-and left-handed both for the spinors and for the helicities.
53) A left-handed spinor transforms under a Lorentz boost always to a left-handed spinor part of (complex ) C2.
57) I prefer to introduce reduced energy already here and define air shortly after because I need to define W_e\mu first.
59) In order not to define not too many observables, I prefer to start with a general formula which displays the angular and energy distribution. Thus the detailed definition of P_T1, P_T2 and P_L strongly relies on Figure 1.
65) At this point it suffices to mention that the decay distribution depends on these four decay parameters. They will be discussed in detail with the relevant measurements.
68) The SM is only one of the ten interactions treated, so masses could be different from zero.
71) x is the reduced energy, while x_1, x_2 and x_3 are vectors in space.
72) For the Standard-Model coupling -> Within the Standard Model.
79) CP-violation would follow for CPT invariance.
84) Here, only effects of the normalized decay distributions are discussed.
111) about the decay interaction - > about the interaction
113) yielding the V-A value of 3/4-> yielding the value 3/4 as predicted by V-A.
116) True
118) decay interaction -> interaction
125) and the others -> while the others
126) Yes, they are!
129) muon and electron observables
133) Yes, the muon lifetime is also needed.
179) The transverse…

Comments to the style:
I have added commas and periods to equations, as suggested by the referee. On the other hand I will keep my way of citing equations without the Eq. in front of the equation number, since this is a style question and is used by the authors of the other PSI papers.

## Author: Wulf Fetscher on 2021-07-04 [id 1543]

(in reply to Report 1 on 2021-06-22)I appreciate the thorough report of the referee. Let me begin with comments to the content:

26) In this approximation the interaction is local, 27) and following: replaced "point interaction" by "contact interaction", 28) Yes, it refers to Fierz identities, 31) I agree, the physics does not depend on the basis. On the other hand, it seemed reasonable to include lepton number conservation which implied the change from charge retention to charge changing form. 37-38) This statement is correct; there really are four coupling constants, and all leptons are left-handed. 40) Replaced "handedness" by "chirality"; 40) who in turn use -> which in turn uses, 41) I believe it suffices to continue with the matrix element where the relevant coupling constants are defined. 42) G_F; since F stands for Fermi, it is not unobservable and it should be roman and not italic. 43-49) The chiralities are indeed fixed by \gamma: For \gamma=V the chirality of the outgoing particle is equal to the chirality of the incoming particle; for scalar and tensor interaction, the chirality changes. 50) I use „definitely“ because of widespread use of the term right-and left-handed both for the spinors and for the helicities. 53) A left-handed spinor transforms under a Lorentz boost always to a left-handed spinor part of (complex ) C2. 57) I prefer to introduce reduced energy already here and define air shortly after because I need to define W_e\mu first. 59) In order not to define not too many observables, I prefer to start with a general formula which displays the angular and energy distribution. Thus the detailed definition of P_T1, P_T2 and P_L strongly relies on Figure 1. 65) At this point it suffices to mention that the decay distribution depends on these four decay parameters. They will be discussed in detail with the relevant measurements. 68) The SM is only one of the ten interactions treated, so masses could be different from zero. 71) x is the reduced energy, while x_1, x_2 and x_3 are vectors in space. 72) For the Standard-Model coupling -> Within the Standard Model. 79) CP-violation would follow for CPT invariance. 84) Here, only effects of the normalized decay distributions are discussed. 111) about the decay interaction - > about the interaction 113) yielding the V-A value of 3/4-> yielding the value 3/4 as predicted by V-A. 116) True 118) decay interaction -> interaction 125) and the others -> while the others 126) Yes, they are! 129) muon and electron observables 133) Yes, the muon lifetime is also needed. 179) The transverse…

Comments to the style: I have added commas and periods to equations, as suggested by the referee. On the other hand I will keep my way of citing equations without the Eq. in front of the equation number, since this is a style question and is used by the authors of the other PSI papers.