Over the last year, we spent quite some time in the Electroweak Working 
group of the TEV2000 workshop to look at the potential of a high precision
measurement of the W mass and width, as well as the forward backward
asymmetry, A_FB, at a superluminous Tevatron. In the course of our
investigations we were left with a number of questions, which I believe
are important to follow up, and Snowmass looks as the right format.

1) Multiple interactions will be the limiting factor in a traditional 
   measurement of the W mass using the transverse mass distribution.
   There are ideas how to get around this by splitting the data sample
   up into subsamples accoring to the number of interactions (Bill
   Carithers). Is this going to work? 

2) The W mass can also be measured from the lepton p_T or energy
   distribution, having the advantage of not depending on the missing
   energy resolution (which gets screwed up by multiple interaction
   effects). In the past those quantities did not yield a competitive
   measurement of M_W, but this might change now. This MUST be
   investigated.

3) On the theoretical side: if one attempts to measure the W mass to 20
   or 30 MeV, we must understand not only the QCD corrections
   sufficiently well, but also the electroweak corrections. It is time
   to look at what calculations exist, and what needs to be done. Since
   these calculations take (a lot of) time, we need to do this now. We
   also need to get an idea of how important multiple photon brem
   effects are. In other words: attempting to measure the W mass to a
   few 10's of MeV, we essentially need the same theoretical precision
   as for the Z mass measurement at LEP1. With the additional
   complication of QCD corrections. 

4) So far, nobody looked at the potential of the LHC to measure M_W.
   There are known drawbacks, but this should be looked at. Same for the
   NLC? In other words: it would really nice to have a comparative study
   of the potential of a high precision W mass measurement at the
   Tevatron (with various integrated luminsoities), LEP2 (exists from
   LEP2 workshop), LHC and NLC.

5) On the experimental frontier, we would need experts from CDF and D0
   to look in more detail at all those systematic uncertainties which go
   into a W mass analysis. I would like to recruite those people (Larry
   Nodulman, Young-Kee Kim, Marcel Demarteau, Steve Errede etc....) for
   the subgroup.

6) Interesting constraints might well also come from A_FB. One can try
   to extract the Higgs mass from both the W mass and the A_FB
   measurement. Our TEV2000 studies indicate that the precision is
   comparable. Can one combine the two? What does one gain? As Frank
   Merritt and Hugh Montgomery pointed out in the DPF report, comparing
   the Higgs mass extracted from high precision measurements with the
   results of a direct measurement at the LHC and other machines. So,
   this is important.