my-macros.tex
%auto-ignore
 %%%%%% macros %%%%%%%%%%%%%%%%
\newcommand{\rmt}{\rm\textstyle}
\newcommand{\rms}{\rm\scriptstyle}
\newcommand{\stw}{\mbox{$\sin^2\theta_W$}}
\newcommand{\stwos}{\mbox{$\sin^2\theta_W^{\rms(on-shell)}$}}
\newcommand{\nub}{\overline{\nu}}
\newcommand{\alps}{\mbox{$\alpha_s$}}
\newcommand{\asop}{\mbox{$\frac{\alpha_s}{\pi}$}}
\newcommand{\qsq}{\mbox{$Q^2$}}
\newcommand{\qnsq}{\mbox{$Q_0^2$}}
\newcommand{\mztwo}{\mbox{$M_Z^2$}}
\newcommand{\mz}{\mbox{$M_Z$}}
\newcommand{\mw}{\mbox{$M_W$}}
\newcommand{\mtop}{\mbox{$M_{\rms top}$}}
\newcommand{\mhiggs}{\mbox{$M_{\rms Higgs}$}}
\newcommand{\lmsb}{\mbox{$\Lambda_{\overline{MS}}$}}
\newcommand{\qbar}[0]{\overline{q}}
\newcommand{\ubar}[0]{\overline{q}}
\newcommand{\pbar}[0]{\overline{p}}
\newcommand{\bbar}[0]{\overline{b}}
\newcommand{\cbar}[0]{\overline{c}}
\newcommand{\sbar}[0]{\overline{s}}
\newcommand{\dbar}[0]{\overline{d}}
\newcommand{\uubar}[0]{\mbox{$\stackrel{(-)}{u}$}}
\newcommand{\ddbar}[0]{\mbox{$\stackrel{(-)}{d}$}}
\newcommand{\nubar}[0]{\overline{\nu}}
\newcommand{\numu}[0]{\nu_{\mu}}
\newcommand{\nuebar}[0]{\overline{\nu}_{e}}
\newcommand{\nube}[0]{\overline{\nu}_{e}}
\newcommand{\nue}[0]{\nu_{e}}
\newcommand{\numubar}[0]{\overline{\nu}_{\mu}}
\newcommand{\nubmu}[0]{\overline{\nu}_{\mu}}
\newcommand{\invpb}{\mbox{${\rm pb}^{-1}$}}
\newcommand{\invfb}{\mbox{${\rm fb}^{-1}$}}
\newcommand{\E}[1]{\mbox{$\times10^{#1}{\rm cm}^{-2}{\rm sec}^{-1}$}}
\newcommand{\roots}[1]{\mbox{$\sqrt{s}=#1$~TeV}}
\newcommand{\Lv}[1]{\mbox{Level-{#1}}}
\newcommand{\met}{\mbox{$\protect \raisebox{.3ex}{$\not$}E_T$}}
\newcommand{\nunub}{\stackrel{{\footnotesize (-)}}{\nu}}
\newcommand{\txnunub}[1]{\nu_{#1}/\nub_{#1}}
\newcommand{\Kethree}{\mbox{$K^{\pm}_{e3}$}}
\newcommand{\fullKethree}{\mbox{K^{\pm}\rightarrow \pi^0e^{\pm}\nu_{e}\hspace{-0.15in}^{^{(-)}}}} 
\newcommand{\Rnu}{\mbox{$R^{\nu}$}}
\newcommand{\Rnub}{\mbox{$R^{\nub}$}}
\newcommand{\Rmeas}{\mbox{$R_{\rms exp}$}}
\newcommand{\Rmeasnu}{\mbox{$R_{\rms exp}^{\nu}$}}
\newcommand{\Rmeasnub}{\mbox{$R_{\rms exp}^{\nub}$}}
\newcommand{\ecal}{\mbox{$E_{\rms cal}$}}
\newcommand{\gLeff}{\mbox{$g_L^{\rms eff}$}}
\newcommand{\gReff}{\mbox{$g_R^{\rms eff}$}}
\newcommand{\gLReff}{\mbox{$g_{L,R}^{\rms eff}$}}
\newcommand{\uLReff}{\mbox{$u_{L,R}^{\rms eff}$}}
\newcommand{\dLReff}{\mbox{$d_{L,R}^{\rms eff}$}}

nc-reply.tex
%latex209   
\documentstyle[prl,aps,floats,epsf,times,latexsym]{revtex}
\newcommand{\makepreprint}{0}
\pagestyle{plain}

\setlength{\topmargin}{0.05in}
\def\np#1#2#3   {{ Nucl. Phys.} {\bf#1}, #2 (#3) }
\def\pcps#1#2#3 {{ Proc. Cam. Phil. Soc.} {\bf#1}, #2 (#3). }
\def\pl#1#2#3   {{ Phys. Lett.} {\bf#1}, #2 (#3) }
\def\plc#1#2#3   {{ Phys. Lett.} {\bf#1}, #2 (#3); }
\def\prep#1#2#3 {{ Phys. Rep.} {\bf#1}, #2 (#3). }
\def\prev#1#2#3 {{ Phys. Rev.} {\bf#1}, #2 (#3). }
\def\prl#1#2#3  {{ Phys. Rev. Lett.} {\bf#1}, #2 (#3). }
\def\prs#1#2#3  {{ Proc. Roy. Soc.} {\bf#1}, #2 (#3). }
\def\ptp#1#2#3  {{ Prog. Th. Phys.} {\bf#1}, #2 (#3). }
\def\rmp#1#2#3  {{ Rev. Mod. Phys.} {\bf#1}, #2 (#3). }
\def\rpp#1#2#3  {{ Rep. Prog. Phys.} {\bf#1}, #2 (#3). }
\def\zp#1#2#3   {{ Zeit. Phys.} {\bf#1}, #2 (#3). }
\def\epj#1#2#3   {{ Eur. Phys. Jour.} {\bf#1}, #2 (#3). }
\def\nim#1#2#3   {{ Nucl. Instr. Meth.} {\bf#1}, #2 (#3). }

\input{my-macros.tex}
\renewcommand{\Rmeas}{\mbox{$R_{\rms exp}$}}   

\begin{document}

\twocolumn
%
%****************************************************************8*************
%%%%%%%%%%%%%%%%%%% COMMENT REPLY TEXT %%%%%%%%%%%%%%%%%%%%
%******************************************************************************

{\bf Reply to the Comment on ``A Precise Determination of Electroweak
Parameters in Neutrino-Nucleon Scattering''}

\vspace{0.05in}
In a recent comment~\cite{thomas-comment}, Miller and Thomas correctly
indicate that if nuclear shadowing effects differed significantly between
neutrino neutral current (NC) and charged current (CC) interactions, this
difference would impact NuTeV's measurement of $\stw$.  
%
%  Kevin rewrite
%
%Miller and Thomas, 
%however, consider a vector meson dominance (VMD) shadowing model~\cite{VMD} 
%that cannot account for the NuTeV discrepancy. Most notably, they argue that 
%nuclear shadowing within the VMD model is weaker for $Z^0$ exchange than for 
%$W^{\pm}$ exchange~\cite{VMDsize}, thereby increasing the predictions for 
%$\Rnu$ and $\Rnub$ for a portion of the NuTeV data in the low $Q^2$ shadowing 
%region. 
As motivation, they offer a specific vector meson dominance (VMD)
shadowing model~\cite{VMD} and argue that nuclear shadowing within the
VMD model is weaker for $Z^0$ exchange than for $W^{\pm}$
exchange~\cite{VMDsize}, thereby increasing the predictions for $\Rnu$
and $\Rnub$ for a portion of the NuTeV data in the low $Q^2$ shadowing
region. This effect of VMD models, though, has the {\em wrong sign}, since 
NuTeV measures ratios for neutrino and antineutrino scattering processes,
$\Rmeasnu$ and $\Rmeasnub$, that are both smaller than expected.
%
% Nuclear shadowing, which
% suppresses deep inelastic scattering (DIS) at low $x$ can be modeled 
% by Pomeron exchange models~\cite{pomeron} in the region $10^{-3}<x<10^{-1}$.
% Such models predict a logarithmic dependence in $Q^2$ and identical 
% shadowing for interactions involving exchanges of $\gamma$, $W^\pm$, or 
% $Z^0$ bosons. In this interpretation of shadowing, it therefore follows 
% that the measured neutral to charged current cross-section ratios, $\Rnu$ 
% and $\Rnub$, and the Paschos-Wolfenstein $R^-$ would be unaffected by 
% shadowing in a cross-section model which absorbs shadowing into parton 
% distribution functions (PDFs).
%
%short%However, 
% In their comment, Miller and Thomas consider another shadowing
% model, a specific vector meson dominance (VMD) model~\cite{VMD}.  
% In VMD models, the effect on $Z^0$ exchange, as a fraction of the
% cross-section, is about $1/3$ of that in $W^\pm$ exchange,
% which is in turn about $1/2$ of that in $\gamma$ exchange.
% Therefore, a significant VMD contribution to shadowing 
%short%which is not
%short%accounted for in the analysis of the NuTeV data 
% would further increase the predictions for $\Rmeasnu$ and $\Rmeasnub$.
% The effect is in the {\em wrong direction} as the NuTeV data separately 
% measures $\Rmeasnu$ and $\Rmeasnub$ which are both smaller than their
% predictions.
Furthermore, this class of 
models in general and the specific model offered, both fall well short of 
providing an explanation for the NuTeV observations for a number of reasons.

%rev2 ======================================================
%rev2 First, the specific model is not supported by charged-lepton 
%rev2 deep inelastic scattering (DIS) data in the relevant kinematic regime. 
First, shadowing by VMD is not supported by charged-lepton 
deep inelastic scattering (DIS) data in the relevant kinematic regime. 
%rev2 ======================================================
%The VMD model cited by Miller and Thomas predicts larger 
%shadowing in charged-lepton than in neutrino scattering.  
%%
%% From Boros: ``the relative contribution of the VMD contribution in neutrino
%% scattering should be roughly half of that in the corresponding charged
%% lepton case ... although the coupling is twice as large in the neutrino
%% induced reaction as in the muon induced one, the SF is larger by about
%% a factor 18/5.''
%%
The VMD model can be tested by looking for deviations from logarithmic 
$Q^2$ dependence of shadowing, particularly at low $Q^2$, where VMD models 
would predict a $Q^2$ dependence of the form $1/(Q^2+m_V^2)$, $m_V$ 
being the mass of the vector meson.  The most precise data which overlaps 
NuTeV's kinematic region
%
% I made this up by looking at the log Q^2 and x plots on p.85 of
% Sam's thesis (log x would be more useful)
% NEED TO CHECK THIS <--- Sam checks this with blitztup, fraction is 92%  
% for 1<Q^2<100, 0.02<x<0.6; change to NMC kinematics from F2Sn/S2C paper 
% --> 97% for 0.01<x<0.75, 1<Q^2<140
%
($97\%$ of the NuTeV data is contained within $1<Q^2<140$~GeV$^2$, 
$0.01<x<0.75$) comes from the NMC experiment, which observes only the
logarithmic $Q^2$ dependence predicted by perturbative QCD
%short%and sees no hint of VMD 
%short%low $Q^2$ shadowing
~\cite{nmc}. 
%
%
%
%  here's my (Kevin's) attempt to reinsert the argument about why what we did
%  isn't crazy...
%
%rev2 ======================================================
%rev2 The lack of evidence for strong $Q^2$ dependence of shadowing in the
%rev2 NuTeV kinematic region suggests that the conventional modeling of shadowing 
%rev2 as a change in parton distribution functions is appropriate~\cite{pomeron}. 
The lack of evidence for strong $Q^2$ dependence of shadowing suggests
that the conventional modeling of shadowing as a change in parton
distribution functions is appropriate in the NuTeV kinematic
region~\cite{pomeron}.
%rev2 ======================================================
%rev2 ======================================================
%rev2 Significant $Q^2$ dependence is observed in charged-lepton scattering  
%rev2 in the photoproduction region, but this region 
%rev2 is irrelevant for NuTeV.
Significant $Q^2$ dependence is observed in charged-lepton scattering  
at low $Q^2$, but in a region irrelevant for NuTeV.
%rev2 ======================================================

Miller and Thomas do not supply a theoretical framework 
for evaluating the impact of the model on the NuTeV results, nor are their 
estimates
relevant for the NuTeV  kinematics (the mean NuTeV $Q^2$ is 
$25.6$~GeV$^2$ for $\nu$ events and $15.4$~GeV$^2$ for $\nubar$ events).
%
% the effect of the specific model is significantly overstated 
% given the kinematic region spanned by the NuTeV data.
%
%Without a functional form for the $x$ and $Q^2$ dependence of 
%the shadowing correction for both NC and CC interactions, it is difficult
%to evaluate the exact size of the effect on the NuTeV result. With guidance 
%from the authors of the comment, we estimate the effect using the predicted 
%shadowing correction provided in Reference~\cite{Boros} scaled by a 
%$Q^2$ dependence of the form, $1/(Q^2+m^2_\rho)$. In addition, we include 
%a NC shadowing contribution that is 1/8 the size of the CC
%contribution.
%
% Nevertheless, this model can be blindly applied to the NuTeV data
%sohrt%.  To do
%short%so, we use 
%
We attempt to apply their model by including the small effect of 
VMD neutral current shadowing and 
using the $x$ dependence 
%% of shadowing in $\nu$ charged current scattering 
as given at $5$~GeV$^2$ in Ref.~\cite{Boros}, %short%scale
scaled with the above $Q^2$ dependence assuming $m_V=m_\rho$ 
(the %short%assumption 
%short%of the 
lowest possible vector meson mass gives the maximum effect). We 
find that the predictions for $\Rmeasnu$ and $\Rmeasnub$ increase 
by $0.6\%$ and $1.2\%$, respectively. 
%
% redundant (Kevin)
%
%Note that the larger effect is in $\Rmeasnub$. NuTeV, on the
%otherhand, observes a discrepancy in $\Rmeasnu$. 
While these numbers are
somewhat consistent with the $\epsilon$ and 
$\overline{\epsilon}$ values~\cite{epsilon} which Miller and Thomas claim 
account for the entire NuTeV discrepancy, they neglect to include the high 
degree of correlation between the neutrino and antineutrino ratios in 
evaluating the effect on $R^-$. This brings us to the final point.

%short%respectively, 
% significantly below the estimates given in the comment.
% This is 
%short%simply 
% because the NuTeV mean $Q^2$ of $25.6$~GeV$^2$ for $\nu$
% events and $15.4$~GeV$^2$ for $\nubar$ events is 
%short%much 
% higher than 
%short%the
% $5$~GeV$^2$ at which Ref.~\cite{Boros} evaluates shadowing and because
% we 
%short%additionally 
% include the (small) effect of VMD neutral current shadowing.

%
% Kevin rewrite (July 8, 2002) to remove some redundancy
%
Differences in neutral and charged current shadowing will affect
$\Rnu$ and $\Rnub$ significantly.  However, the NuTeV result derives
$\sin^2\theta_W$ from the Paschos-Wolfenstein
$R^-=(\Rnu-r\Rnub)/(1-r)$, where $r$ is the ratio of $\nubar$ to $\nu$
charged current cross-sections ($r\approx1/2$). %short%, thus explicitly
%short%removing sensitivity to cross-section contributions which are
%short%identical for neutrino and anti-neutrino scattering, namely scattering
%short%from the sea.  
This approach was chosen by NuTeV to limit sensitivity
to suppression of charged current production of charm quarks from
scattering on the strange sea, yet it is also equally effective at
reducing sensitivity to other parts of the cross-section common
to $\nu$ and $\nubar$, such
as $R_L$ or differences in neutral and charged current nuclear
shadowing.  A low $x$ phenomenon like nuclear shadowing affects
primarily sea quark cross-sections which contribute equally to
$\nu$ and $\nub$ cross-sections.  For this reason, the $\epsilon$ and
$\overline{\epsilon}$ parameters introduced in the
comment~\cite{thomas-comment} will be highly correlated, regardless of
the specifics of the shadowing model, and will affect $R^-$ only slightly. 
The NuTeV
data themselves therefore rule out {\em any} such explanation because of the
enormous shifts in $\Rnu$ and $\Rnub$ individually required to induce
a significant shift in $R^-$.

%% update with rewording suggested by Un-Ki (09/04/02 gpz)
%%Specifically, even if this VMD model somehow {\em
%%underestimates} the effect and is able to explain the NuTeV $R^-$, NuTeV's 

Even if we arbitrarily {\em increase} the effect of the VMD model in order
to explain the NuTeV $R^-$, NuTeV's
separate measurements 
of $\Rmeasnu$ and $\Rmeasnub$ still cannot be accommodated.  
Defining $\Delta R=\Rmeas-\Rmeas^{\rms (SM)}$, NuTeV has measured:
%  .00319/.39158=.00814, .00131/.39158=.00334
%  .00162/.40503=.00400, .00278/.40503=.00686
\begin{eqnarray*}
\Delta R^{\nu}=-0.0032\pm0.0013=\Rmeasnu\times(0.9919\pm0.0033),\\
\Delta R^{\nubar}=-0.0016\pm0.0028=\Rmeasnub\times(0.9960\pm0.0069),
\end{eqnarray*}
with a correlation coefficient between the uncertainties of $0.638$.
This VMD model would therefore increase the discrepancy in $\Rmeasnu$
from $2.5$ to $4.5$ standard deviations and in $\Rmeasnub$ from $0.6$
to $2.3$ standard deviations, and clearly a larger effect would be
more disfavored.  Also, note that the VMD model predicts
the largest change in $\Rmeasnub$ whereas NuTeV
observes a discrepancy primarily in $\Rmeasnu$. 
%short%Therefore, NuTeV's individual
%short%measurements of $\Rmeasnu$ and $\Rmeasnub$ already conclusively rule out
%short%this VMD model. 
%
% redundant (Kevin)
%
%A model with an even larger effect capable of explaining the NuTeV $\stw$ 
%result would be even more disfavored by NuTeV's individual measurements 
%of $\Rmeasnu$ and $\Rmeasnub$.

% In conclusion, the VMD shadowing model used in this
% comment~\cite{thomas-comment} to motivate the possibility of a large
% difference in neutral and charged current shadowing is not motivated
% by charged lepton DIS in the NuTeV kinematic region, has a smaller
% effect on the NuTeV measurement than is stated, and is conclusively
% excluded by the NuTeV data. 
%rev2 ======================================================
In conclusion, the VMD mechanism used in this
comment~\cite{thomas-comment} to motivate the possibility of a large
difference in neutral and charged current shadowing is not motivated
by charged lepton DIS data in the NuTeV kinematic region, and would have a
smaller effect on the NuTeV measurement than is stated.  Furthermore,
VMD shadowing of sufficient size to explain the NuTeV $\stw$ is 
conclusively excluded due to inconsistency with the NuTeV data itself.
%rev2 In conclusion, the VMD shadowing model used in this 
%rev2 comment~\cite{thomas-comment} to motivate the
%rev2 possibility of a large difference in neutral and charged current
%rev2 shadowing is highly disfavored from charged lepton DIS data, has a
%rev2 smaller effect on the NuTeV measurement than is stated,
%rev2 and is conclusively excluded by the NuTeV data.  
%rev2 ======================================================
More
generally, because any model of different neutral and charged current
nuclear shadowing will change $\Rmeasnu$ and $\Rmeasnub$
more than $R^-$, it is unlikely that any such model could explain the
discrepancy in NuTeV's measurement of $\stw$. 

% \item The authors neglect to include the high degree of correlation
%        between the neutrino and antineutrino data (i.e., $\epsilon$ and 
%        $\overline{\epsilon}$) in evaluating the effect on $R^-$.
%  \item Again, their observation has the {\em wrong sign}. The NuTeV data 
%        separately measures $\Rnu$ and $\Rnub$ which are both {\em smaller} 
%        than expected.
% However, as previously
% indicated, the NuTeV data disfavors this model through separate measurements 
% of $\Rnu$ and $\Rnub$ which are both observed to be lower than their 
% predictions.
%
% Finally, one expects minimal shadowing effects in $\stw$ extracted from 
% separate measurements of $\Rnu$ and $\Rnub$. This is because shadowing, 
% being a low $x$ phenomenon, affects sea quark distributions which are 
% common between $\nu$ and $\nub$ cross-sections, and therefore cancel in $R^-$.
% Hence, to be able to induce a significant change in $\stw$, one must 
% effect large shifts in $\Rnu$ and $\Rnub$ (2--3 times larger than the above
% estimates, and in the opposite direction) with the correct correlation. 
\vspace{-0.2in}

\begin{references}
\vspace*{-0.65in}
\bibitem{thomas-comment} G.~A.~Miller and A.~W.~Thomas, hep-ex/0204007, 
                        April 2002.

\bibitem{VMD} W. Melnitchouk and A.~W.~Thomas,\prev{C52}{3373}{1995}

\bibitem{VMDsize} In VMD models, the effect on $Z^0$ exchange, as a fraction 
                  of the cross-section, is about $1/3$ of that in $W^\pm$ 
                  exchange, which is in turn about $1/2$ of that in $\gamma$ 
                  exchange. 

\bibitem{nmc} M.~Arneodo {\em et al.}, [NMC Collaboration], 
              \np{B487}{3}{1997} , \np{B481}{23}{1996} .

\bibitem{pomeron} J.~Kwiecinski and B.~Badelek, Phys. Lett. {\bf B208}, 508
                  (1988),
                  B.~Balelek and J.~Kwiecinski, Nucl. Phys. {\bf B370}, 278 
                  (1992),
                  N.~N.~Nikolaev and B.~G.~Zakharov, \zp{C49}{607}{1991} 

\bibitem{Boros} C.~Boros {\em et al.}, \prev{D59}{074021}{1999}

\bibitem{epsilon} As defined in the comment~\cite{thomas-comment}, 
                  $\epsilon = \delta\Rnu/\Rnu$ and 
                  $\overline{\epsilon} = \delta\Rnub/\Rnub$.
%****************************************************************************

\end{references}
\end{document}


hep-ex0207052.extracted_bib
\bibitem{thomas-comment} G.~A.~Miller and A.~W.~Thomas, hep-ex/0204007, 
                        April 2002.


\bibitem{VMD} W. Melnitchouk and A.~W.~Thomas,\prev{C52}{3373}{1995}


\bibitem{VMDsize} In VMD models, the effect on $Z^0$ exchange, as a fraction 
                  of the cross-section, is about $1/3$ of that in $W^\pm$ 
                  exchange, which is in turn about $1/2$ of that in $\gamma$ 
                  exchange. 


\bibitem{nmc} M.~Arneodo {\em et al.}, [NMC Collaboration], 
              \np{B487}{3}{1997} , \np{B481}{23}{1996} .


\bibitem{pomeron} J.~Kwiecinski and B.~Badelek, Phys. Lett. {\bf B208}, 508
                  (1988),
                  B.~Balelek and J.~Kwiecinski, Nucl. Phys. {\bf B370}, 278 
                  (1992),
                  N.~N.~Nikolaev and B.~G.~Zakharov, \zp{C49}{607}{1991} 


\bibitem{Boros} C.~Boros {\em et al.}, \prev{D59}{074021}{1999}


\bibitem{epsilon} As defined in the comment~\cite{thomas-comment}, 
                  $\epsilon = \delta\Rnu/\Rnu$ and 
                  $\overline{\epsilon} = \delta\Rnub/\Rnub$.
%****************************************************************************

