We thank the referee for a detailed reading and complete summary.
We have made some clarifications and think the paper can now be published.
Re: the referee's concern over the value of A_betaGT for 1/2+ to 3/2+,
we are happy to check our expressions.
We checked again Jackson, Treiman, and Wyld and Holstein,
and the expression for beta- decay for increasing I for pure G-T decay is
Abeta = + Ii/(Ii+1), which we now include in the text.
Then Ii=1/2 gives Abeta=+1/3 as in our paper.
(We of course also checked the same-I expression for 1/2+ to 1/2+,
and now include that in text as well.)
We note in addition that this slightly reduced expression can be found in a number of experimental references, including e.g. Hirayama et al PRC 91 024328
https://doi.org/10.1103/PhysRevC.91.024328
where it is used to deduce spins and parities of progeny states.
This is, of course, formally unnecessary for our paper, but it simply builds confidence we have not made a trivial error in the
interpretation of the expressions.
Hopefully the referee has made some kind of typo or trivial error themselves. If not, we would appreciate a derivation or reference to which we can compare. Agreed if the value were different, it would change the extraction of the isospin mixing physics from the lower-statistics observable "pseudoAbeta." This would not change any of our paper's qualitative conclusions, but our centroid results would quantitatively change a small amount. So we agree it is critical to get this right, and appreciate the referee's care in making this sanity check.
Since this is not a typo, it should be clear the referee's other concern is
alleviated.
For completeness, we note here that our average
AbetaGT=-0.467 = 0.80 * -2/3 + 0.20 *1/3, then we simply vary 0.80 +- 0.02
(and of course the completely correlated 0.20 -+ 0.02) to get -0.467+-0.020.
Otherwise we would have to take into account all the subtleties of correlations between the main branch uncertainty determination and the others, detailed in Smith.
The referee is correct that we can ignore the energetics of the extra 3/2+
states at the level of accuracy needed. We devote in the paper a short paragraph to the potential effect of the uncertainty of the forbidden transitions.
We make four small changes:
We now include in text the reduced expressions for AbetaGT
(-1/(Ii+1) and Ii/(Ii+1)) for the two main transitions. We agree this will
help the reader's confidence and better convey what we are doing.
We also change J -> I in the inline equation for f(M_F), consistent with I in the rest of the paper.
To the references for Eqs. 3 and 4, we now include Holstein Rev Mod Phys. It is simpler there to see a sign convention for the F-GT term "f(M_F)" we know to be consistent with Holstein's recoil-order corrections.
We have fixed more capitalization errors in references, continuing to patch curiousities from downloaded bibtex citations.