\section{W mass measurement}
\subsection{Motivation}
At the loop level, W boson is connected with top quark the Higgs boson
(radiative corrections to the W mass). Hence precise measurements of
the masses of the top quark and W boson allow us to constrain the
most probable value of the Higgs boson mass. Current world average
for M(W) is 80.399$\pm$0.025 GeV. Current world average
for M(top) is 172.4$\pm$1.2 GeV. This current precision leads
to a constraint on the Higgs mass: $<$ 154 GeV $@$ 95\%CL.
What happens if we get better precision for M(top) and M(W) ?
\begin{enumerate}
\item if $\Delta_M(top)$ 1.2 GeV decreases to 1.0 GeV then Higgs Mass constraint 154 GeV 
$\to$ 153 GeV
\item if $\Delta_M(W)$ 25 MeV $\to$ 15 Mev then Higgs Mass constraint 154 GeV $\to$ 119 GeV
\item if both 1. and 2.,  then Higgs Mass constraint 154 GeV $\to$ 117 GeV
(These numbers and projections are taken from the talk ``GLOBAL ELECTROWEAK FITS AND 
 THE HIGGS BOSON MASS" by Pete Renton at ICHEP-2008 conference.)
\end{enumerate}
So our current ability to constrain the Higgs mass depends stronger on 
the W mass measurement.

\subsection{Brief description of the measurement}
D0 measures W boson mass using the W$\to e \nu$ decay channel.
Since the 4-momentum of the neutrino cannot be determined,
the invariant mass of the W boson cannot be reconstructed directly.
The W mass is extracted from the template fitting to the variables,
which are sensitive to the W mass. These variables are 
W transverse mass, electron transverse momentum, and
missing transverse energy. 
The central part of the analysis
is building the fast MC model, with which the templates for the mass fit
are made. Before measuring W mass in data, the measurement
is performed on full detector simulation W$\to e \nu$ sample.
Hence we have two fast MC models -- for the full simulation and for the
data. Fig.~\ref{fig:mt} shows the transverse mass of the W boson.

The data that is used
for the W mass measurement analysis was collected during
2003-2006 and corresponds to the integrated luminosity of approximately 1 fb$^{-1}$.
This data sample is referred to as Run2A sample.
The remaining D0 data that is currently available for analysis
was taken during 2006-2008 and corresponds to  the integrated luminosity 
of approximately 2.6 fb$^{-1}$. This sample is referred to as Run2B sample.
Run2A analysis has been ongoing for about three years,
whereas Run2B analysis just started recently.
\begin{figure}[htp]
\begin{center}
%photographs files were made by linux>convert photo.JPG photo.eps
\includegraphics[scale=0.5, angle=0]{mtfrombmp.eps}\newline
\end{center}
\caption{Distribution of the transverse mass of the W boson.
Red points represent data. Blue points correspond to fast Monte Carlo model.
Modeling of backgrounds is indicated as well by the shaded regions.
\label{fig:mt}}
\end{figure}

\subsection{D0-Olemiss group involvement in the W mass measurement}
\subsubsection{Run2A}
Alex Melnitchouk has been working mainly on electron energy scale.
His responsibilities involve
deriving electron energy scale for data and full MC,
verifying that procedure is unbiased (pull plots for the
ensemble of data-like toy samples),
verifying the results by template fitting the Z mass peak,
produced with fast MC with the known true value of the Z mass.
Fig.~\ref{fig:zmasstempfit} illustrates the results of the latter.
\begin{figure}[htp]
\begin{center}
%photographs files were made by linux>convert photo.JPG photo.eps
\includegraphics[scale=0.7, angle=0]{z.100108.eps}\newline
\end{center}
\caption{Fitting $Z \to ee$ data with Z mass templates.
To verify that the scale and offset were derived correctly,
we generate fast MC Z mass templates using the set of Z mass hypotheses
and the found values of scale and offset. Found value (91192 $\pm$ 31 MeV) is consistent with the input Z mass value of 91188 MeV
that was used for scale,offset templates generation.
\label{fig:zmasstempfit}}
\end{figure}

Alex Melnitchouk also studied the stability of the energy scale under the variations
in the fast MC model and has been responsible for retuning energy scale 
as the fast MC model has been evolving.
Finally, Alex Melnitchouk propagated scale uncertainty into W mass and W width measurements.

These are important tasks because electron energy scale uncertainty is
the largest uncertainty ($\approx$35 MeV) that contributes to the total
W mass uncertainty of $\approx$45 MeV. Besides, the response of the
hadronic system (the non-electron part of the W$\to e \nu$ event) is tuned
based on the electron system response.
Alex Melnitchouk also worked on describing different aspects of the W
mass analysis in the D0 internal notes for editorial board review.

\subsubsection{Run2B}
Alex Melnitchouk has been involved in the electron energy calibration, 
preparation of full Monte Carlo $Z \to ee $ and $W \to e\nu$ samples, 
as well as preparing the unsuppressed zero bias data for overlay
with the full Monte Carlo samples. Alex Melnitchouk also works
on skimming the data for the W mass measurement.

Sudeep Bhatia is going to get actively involved in the Run2B
measurement in February 2009. Alex Melnitchouk is going to supervise
Sudeep Bhatia's work. Both Alex Melnitchouk and Sudeep Bhatia
during 2009 are going to work on various aspects of building the Run2B
fast MC model. The latter would involve parameterizations of electron ID
efficiencies, electron energy scale, electron energy resolution, as well
as, possibly, hadronic response model components.

\subsection{Current Status}
\subsubsection{Run2A}
Full Monte Carlo measurement reproduces true values of both W mass and W width,
within statistical uncertainties.
The fit results are found to be stable under the variation of fitting ranges.
The documentation describing the full MC measurement
for editorial board review is being finalized. 
Recent improvements in the full Monte Carlo measurement
are being propagated into the data measurement. 
In particular, Alex Melnitchouk is working on the re-deriving the constant term
that describes electron energy resolution. With the newly
fitted constant term available, 
he is going to re-derive electron energy scale and offset.

\subsubsection{Run2B}
First stage electron energy calibration was performed.

Currently skimming setup is in preparation. Three skims are intended:
two EM objects ($Z \to ee$ data), one EM object and large
missing transverse energy ($W \to e\nu$ data), and 
one EM object plus one jet (for determining electron misidentification rates).

$Z \to ee$ and $W \to e\nu$ full Monte Carlo production requests have been submitted.
Normally at D0 full Monte Carlo samples are produced with the overlay
of zero bias data in order to model the effects of detector noise,
event pileup, and additional proton-antiproton interactions in the detector.
However, it is zero-suppressed data that is being overlaid.
This does not satisfy the level of precision aimed at by the W mass group.
For W mass samples, the unsuppressed data needs to be overlaied with
the simulated hard scatter event and then zero suppression applied
only after the overlay. Currently unsupressed zero bias samples
are in preparation. 

 \subsection{Plans and Prospects}
D0 Run2A plan is to have preliminary results for the spring conferences 
in 2009 and then a publication. The goal is $\approx$45 MeV uncertainty
on the W mass,
which would be comparable with the current CDF measurement.

D0 Run2B plan is to have preliminary results for the spring conferences in 2010.
We can expect $\approx$45 MeV from Run2B measurement too. In principle,
this is a conservative estimate, because our largest error scales with 
the integrated luminosity.
On the other hand ,Run2B data was taken with higher instantenous 
luminosity, hence more hadronic activity. 
This would increase some errors relative to their Run2A estimates.
Then the combined Run2A and Run2B D0 result would be $\approx$32 MeV.
Combination with a similar result from CDF would result in $\approx$22 MeV.
CDF can be expected to do better, since their $\approx$45 MeV result
was obtain just with a few hundered pb$^{-1}$ of Run2A data. 
Then, in the most optimistic scenario, combined Tevatron Run2A and Run2B
result could be as precise as $\approx$15 MeV.

\end{document}