what I mean is that what we define as “the W mass” and measure in different environments, and which then compare and combine into a “world average” or play tricks with (such as throwing it into a global fitter of electroweak parameters) is not necessarily a perfectly well defined quantity. Not because it is the peak of a breit wigner distribution, which is sufficiently honest to me for a foulproof definition. Rather, because it might – just might, although I do not believe it – happen that the same particle will exhibit a different behavior in the different environments, because of different physics surrounding the particle.
Of course, in the case of the W mass this is unlikely. It was just an example…
In the case of quarks, things are indeed more complex, with “mass” just not being enough for a description of what one measures. In a linear collider the mass reconstructed from the excitation curve as a function of sqrt(s) will rightly be different from that extracted from kinematic fits…
Cheers,
T.