--- Begin Message ---
Dear Claude,
Great reading you! I am sorry for my belated reply. Your first e-mail
reached me via Rene last Friday, but in the evening already in Sydney,
and since yesterday
Monday October 2nd was a legal holiday here I found your second e-mail
only this morning (I do not have internet access where I stay). I am excited
that the first result from the data taking and analysis over so many years
is about to be reached. And yes indeed it is then important to get the
most out of such a result.
It is not in the span of a few hours, busy with other things, that I can
do a thorough analysis of all your questions, the more so since my Fortran
files do not run on the laptop I have, and I even do not have a pocket
calculator with me. But I spent some time trying to find up-dated
information
for the pion-nucleon constant, and refresh my recollection about the
calculation that was done. If necessary or useful, I could try to do better
given some time though.
***********************************************************
Coming first to your issue of the charged pion-nucleon constant. A quick
search of the more recent literature through SPIRES reveals that the
discrepancy between different approaches has not gone away since
the early 1990's. I am not a expert of the issue, and at PSI there
certainly are a few who are directly involved in the issue. From the
quick glance I took, it appears that there are mainly two groups of
values, one on the larger side as I took in 2000 for the prediction
published
in the NPA paper, and one at the lower side which Bernard et al. and
followers of that paper took in those years (beware also that either
g_{\pi-N} or
g^2_c/(4\pi) are given usually, and numerically these two values are
comparable). The most recent publications I could find are:
1. Phys. Rev. C66 (2002) 014005
T. Ericson, B. Loiseau and A. Thomas
This paper has a nice review of the problem in the Introduction,
together with a large table of values as function of history-time.
A very exhaustive analysis, up-dating the value I took in 2000
based on some preliminary results these authors achieved along the
same lines. This paper seems to have become a standard in the field,
having attracted over 50 citations already, among which quite a few
by Bernard and Meissner themselves after 2002. So I would expect this
value for g^2_c/4pi (which is on the larger side of the above interval) to
be really reliable. I am no expert, but experts now seem to
quote that value quite happily. It thus does not differ too much from
the value used in 2000 in my NPA paper with Jose Luis Lucio.
2. Eur. Phys. J. C 33 (2004) 505-509
D. V. Bugg
This paper has also a nice review of the problem and references
in the Introduction. The author seems to be an "old" player in the game.
It is the latest analysis of the issue I could find. His result is on
the lower
side of the interval. But that work does not seem to have attracted by far
as many references than the previous one. And this paper does not cite
the previous
one either, which, personaly, I find suspicious. It also seems that this
paper
was finally published, sometime after
hep-ph/0312346
was made available with M. D. Scadron as a second author. But this e-print
does not seem to ever having been published in a Journal. Nonetheless
the abstract is identical to the published paper: for which reason was
finally Scadron's name removed from it? Also there is
hep-ph/0406009
by Scadron et al., which uses the value for g^2_c/(4\pi) of Bugg, but again
does not quote the paper by Ericson et al. above.
3. Finally, prior to 2000, there were the reviews and fits leading to
the coupling as referred to in the Rev. Mod. Physics by Gorringe and
Fearing which you have yourself. No need to mention them here.
The g_{\pi-N} problem arouse in the early 1990's following the
new analysis by the Dutch group (de Swart et al.).
So much for the pion-nucleon coupling. You asked for my opinion
which is the better value to use. Being no expert I do not know, and
would have to seriously look into it making a confident statement.
If I had to made a life-or-death choice though, I'd bet for the
Ericson et al. value. In 2000, I just took the most recent up-date of
the value,
by Ericson et al. (they are not newcomers to the problem nor the field
of pion-nucleon interactions in any case!). But you may have experts at hand
at PSI and at Urbana this Friday. Please tell me whether looking into
it is of use to the final analysis of the experiment.
The only worry is that the mu-cap experiment should not become
an experiment measuring with great precision g_{\pi-N} in the
same way that Mukhopadhya/Junker used the mu-He3 capture
experiment to do the same for the pion-3He coupling. In any
event assuming chiral symmetry perturbation theory for g_P,
the mu-cap experiment may deliver an extremely precise and
useful assessment of the charged pion-nucleon coupling
conundrum, if not a final word on it. To be kept in mind as well.
**************************************************
However, even though changing a bit the value for the pion-nucleon
coupling changes a bit the chiral symmetry value for g_P to which
the final singlet capture rate is 18% sensitive in relative terms, I do not
expect this to be the dominant effect accounting for differences between
calculations
done at different times and through different methods.
Of course, as you mention, there is also the value for g_A which must be
accounted for properly since the latest up-date from the PDG has
increased it
to some extent. But another significant factor is in fact the value for
V_{ud}, or the Cabibbo mixing angle. Compared to the value I took in 2000,
V_{ud} has again decreased slightly (as given in the latest PDF'2006),
and in a way
that should be accounted for in a final exp-theory comparison. The same
applies to the
other calculations that you mention. It is a potentially important fact
to be kept in mind seriously. I did not look into it carefully, but here
may well lie one of the dominant reasons why for example the Bernard et al.
and my values for the capture rate are so close in spite of slightly
different
pion-nucleon coupling values.
By the way, note also that as far as I could make out, none of the
other calculations that you mention took care of properly renormalising
the muon-proton wave function at the origin to account for the finite
charge distribution of the proton, as Jim Congleton had done for 3He
and I took over for hydrogen. It brings in a 0.4% correction to the
final result,
which is at the level of the experimental precision you announce,
and thus again this is a significant factor. Of course, in my mind,
it is a "plus" of our calculation with Jose Luis Lucio, which the other
authors did not seem to want to bother about, and I do not understand
really why (except for their insistence that EVERYTHING needs to be
expanded in 1/M_nucleon, and this seems to be their reason also
to totally dismiss off-hand my work with J.L. Lucio). This correction
should also go some way in explaining the small final difference between
Bernard et al.'s and our predictions, because the overlap factor is less
than unity.
I have always said that the day the final experimental result would become
available, a new theoretical value should be computed using the detailed and
explicit analytical expression available from papers (in particular ours),
and the latest up-dated values for V_{ud}, G_F, g_A, g_{pi-N}. For the
former
three there appears to be consensus, but the latter still suffers a few %
disagreement between authors. It is time for such a analysis. My codes
are ready for that, but are in Fortran and I cannot run them
on the laptop I have with me on my sabbatical leave (I should also
find out again how to use them). But in any case a numerical re-evaluation
of the prediction will not modify its relative precision standing at
a little less than 1% ((688.4 +- 3.8)/s with the 2000 values for the
inputs).
I understand you are to be all together to finalise the first result of
the experiment this Friday. By then, it is not possible for me to do
such a numerical re-calculation. But given some time I should manage
somehow. Please let me know what would be best. But all necessary
expressions are also given in the NPA paper with J. L. Lucio, and
it is straightforward to particularise them to the Standard Model case.
Also, the evaluations of the sensitivity of the capture rate to different
form factors and couplings (see Table 3 of the NPA paper)
should also suffice to extrapolate the prediction of the 2000 NPA paper
to account for the slightly modified values of inputs for g_{\pi-N}, g_A
and g_P.
If I could get my hands on a pocket calculator here, I should manage at
least that.
But working "backwards" from the experimental result to extract g_P, and
finally g_{pi-N},
with the error bars, requires the Fortran (or other) codes that I have.
********************************************************
I do not know when nor where you'll be reading all this, but I wish you
a most pleasant trip to the US (Mr. W. Bush's country ... which for my part
presently does not attract me too much!), and certainly a very rewarding
mu-cap meeting in Urbana Champaign. Please give my best regards
to the whole team, but especially to Peter and Alexei, and also Tom Banks
who I met last November in Belgium where he purposely made the trip
just to discuss the theoretical work. I hope he defended now his PhD
on the experiment.
I was very glad having news, and reading you again (I would curious
to know what Tim Gorringe has to say about the pion-nucleon coupling).
All the very best,
Jan
Claude Petitjean wrote:
> Dear Jan,
>
> as you see from my mail to Tim Gorringe below, we will
> finally have the "unblinding" of our first mu-capture data
> set, which we measured 2 years ago. This will yield a first
> experimental result on the singlet mu-p capture rate.
>
> I am presently trying to understand what is the most accurate
> theoretical prediction of the rate.
>
> If I compare your prediction g_P=8.475(76) using g_piNN=13.37(9)
> with Bernard et al.: she gets g_P=8.26(16) using g_piNN=13.10(35).
> But both calculations end up at almost the same singlet rate of
> 688.4/s and 687.4/s.
>
> Bernard comments, that with g_piNN=13.4, she would get 681.9/s.
>
> On the other hand, Ando,Myhrer et al. gets, using g_piNN=13.4,
> a larger capture rate of 695/s.
>
> Have you a comment about the discrepancies and what g_piNN is
> preferable to assume today?
>
> All authors have taken g_A(0)=1.267. Today the PDG lists
> g_A=1.2695(29) which is slightly larger than previously.
>
> We would appreciate getting your comments, because eventually
> our experimental error will just be about the same as above
> deviations of theoretical expectation, namely about 1%.
>
> I understand from Rene, that you are in Australia. So I wish
> you a good time there!
>
> With best regards, yours
>
> Claude
>
> ********* mail to Tim Gorringe **************
>
>
> Dear Tim,
>
> For the upcoming unblinding meeting, I am presently preparing
> a short report about the relation g_P vs Lambda_s and what is
> predicted by various theorists - such that we can agree how
> to formulate our first result in terms of g_P.
>
> Now I have noticed that you published just this relationship
> in Figure 2 of your recent review with Fearing (Rev. Mod. Phys.
> 76 (2004) 31). Alas, the figure is not precise enough to read
> off the relevant numbers.
>
> Could you please provide us this figure, either in more precise
> form or by explicit formula or numerically. That would be nice
> indeed.
>
> I noticed further, that there are some discrepancies between
> Bernard et al. (Nucl. Phys. A 686 (2001) 290, being consistent
> with your quotations) and Ando et al. (Phys.Rev. C 63 (2001)
> 15203) and Govaerts et al. (Nucl.Phys. A 678 (2000) 110).
>
> Ando and Govaerts quote some 1-2% larger theory expectations
> of the singlet mu-p capture rate. Have you a comment on these
> papers and about the origin of the discrepancies?
>
> Another comment would be interesting if one can believe the
> small error of g_piNN (13.05 +- 0.08). Bernard quotes 0.35
> as error, and Ando, govaerts take a significantly higher
> value g_piNN = 13.4.
>
> I hope that you can do this before the meeting and look
> foreward to see you next week in Champaign.
>
> With best regards
>
> Claude
>
>
--- End Message ---