To the Editors of Physical Review Letters,

We have reviewed the comments of the two referees on our paper, "A New
Determination of alpha_s From Neutrino-Nucleon Scattering." We believe
that the paper presents new important results including the best
determination of the strong coupling constant using the very clean
deep-inelastic scattering process. Therefore, we strongly feel that
the manuscript is suitable for publication in PRL.  We believe that
all the comments by the referees can be adequately addressed by
modifications of the manuscript. 


In the following paragraphs, we address the main concerns of the
referees. Referee A did not favor acceptance of the paper. Here are
the reasons given and our responses:

-- "The title 'A New Determination...' is misleading. There is no new
data presented." The paper does discuss a new determination of alpha_s
as indicated by the title. The previous paper only compared the data
to a non-singlet QCD evolution; the current paper presents the results
of comparing both F2 and xF3 to a a simultaneous singlet and
non-singlet QCD evolution. This reduces the statististical error by a
factor of two and allows for a determination of the gluon density. To
make this clear, we have added the following sentence to the beginning
of our discussion of PQCD in the paper: "The previous CCFR result only
compared the SF to the non-singlet evolution."

   This determination of alpha_s is also new because of the inclusion
of the systematic errors in the fitting procedure. The combination of
the reduced statistical error and a better treatment of the systematic
uncertainties for this measurement have reduced the final error in
alpha_s by a factor of four from the earlier publication. We feel the
inclusion of additional data in the determination of alpha_s warrants
the designation "New" rather than "Revised".

-- "The publication should contain tables of measured structure
functions..." Even in the context of a longer paper, the publication
of our complete data in tables would not be very useful. There are 117
x,Q2 bins, each with 2 data points, three statistical errors, and
eighteen systematic errors. The structure-function tables in
Seligman's thesis are 70 pages long. The printed tables would need to
be first translated to computer files before it for any
analysis. Instead, the tables have been made available on-line, and
already the groups that perform phenomenological global fits (CTEQ,
MRS, GRV) are making use of that data. We have included an additional
footnote in the paper which reads: "\bibitem{URL} Complete tables of
the CCFR SF results can be obtained from the World Wide Web via the
URL http://www.nevis.columbia.edu/~seligman/ccfr/seligman."

-- There is a large shift between the results presented in this paper
and the values presented in the earlier paper by our collaboration
[Quintas et al., PRL 71: 1307 (1993)]. Although we state in the
current paper that the shift is mostly due to our new energy
calibration, the shift is outside the error quoted in the earlier
paper. In response we heavily amended a paragraph in the current
paper:

"SFs extracted from the CCFR data have been previously presented
\cite{PZQprl}.  In the earlier analysis, the muon and hadron energy
calibrations were determined using a Monte Carlo technique in an
attempt to reduce the dominant source of systematic error in the
analysis, the relative calibration between the muon and hadron
energies.  Our subsequent analysis determined that the control of
systematic errors for this technique was insufficient to justify its
continued use.  This paper presents a re-extraction of the SFs that
uses the calibrations directly determined from the test beam data
collected during the course of the experiment \cite{hadcal,mucal},
which results in a net change of +2.1\% in the relative calibration
and an increase in the corresponding systematic error to 1.4\%.  Other
changes in the SF extraction include more complete radiative
corrections \cite{radcorr}, and the value of $R$ now used in the
extraction comes from a global fit to the world's measurements \cite
{Rworld}. In addition, the estimates of the experimental and
theoretical systematic errors in the analysis are improved \cite
{WGSthesis}. The structure functions are corrected for radiative
effects \cite{radcorr}, the non-isoscalarity of the Fe target, the
charm-production threshold \cite{Bar76,TMC}, and the mass of the
$W$-boson propagator.  The SFs with statistical errors, along with the
QCD fits described below, are shown in Fig.~\ref{fig:SF} \cite{URL}."

-- "For the important aspect of the analysis of the relative
determination of the neutrino and anti-neutrino fluxes, reference is
made to an published thesis and not to any paper, or indeed preprint,
readily available to the reader." We have extended the reference to
include Auchincloss et al., Z. Phys. C48: 411 (1991) and Belusevic and
Rein, PRD 38: 2753 (1988).

-- "The errors on correcting for 'nuclear' effects are not discussed."
This error is small (about 5% of the size of the error bars shown in
Fig. 2 of the paper). 

-- "The errors for correcting for the differences of the strange and
charm sea are not discussed." The strange and charm seas used in the
5/18ths rule come from the CTEQ4D parton distributions.  The global
fit results do not include any error estimates. Even if we
conservatively assume a 20% error in the difference between the
strange and charm seas (s - c) in our lowest x-bin, it only results in
a 3% error in the 5/18ths rule.

    To address the issues of the previous two paragraphs, we have
added this sentence to the paragraph in the paper that follows the
definition of the 5/18ths rule: "The errors on the nuclear and charge
corrections are small compared to the statistical and systematic
errors on both the CCFR and NMC data."


Referee B, who favored the acceptance of the paper, made the following
comments:

-- "One issue that would be useful to clarify would be how the value
of alpha_s would vary taking into account the muon data." We have
added the following to the next-to-last paragraph of the paper: "The
low-x discrepancy in F2 between CCFR and NMC has a negligible effect
on the alpha_s measurement which is derived mainly from the high-x
data."

-- "Second, little mention in made of other neutrino structure
function measurements such as the CDHSW analysis." It is true that the
only other neutrino scattering experiment in the same kinematic regime
as the CCFR experiment is CDHSW. The CDHSW data has been viewed by the
scientific community as having underestimated systematic errors. For
this reason the CDHSW data is not currently being used by global
analysis groups for the determination of parton distributions in the
nucleus. We feel that it serves no purpose to belabor this point in
our article.

-- "Finally, how much is the value of alpha_s affected by using models
other than the Duke and Owens NLO programs?" The Duke and Owens
program is not a model unto itself, but an implementation of the
predictions of NLO QCD in FORTRAN. It is just an implementation and
does not introduce systematic uncertainty.


The measurement of alpha_s from our analysis is the most precise of
all the deep-elastic scattering experiments. We feel that the
measurement is of general interest and particularly important to
researchers in high-energy physics. The concerns of both referees have
been addressed as indicated above. We therefore request a
re-evaluation of the decision to publish the article in Physical
Review Letters.


William Seligman
Michael Shaevitz
Wesley Smith