Ah, but who's "they"? Names of departments are determined by Congress, and Congress has not renamed the DoD. The executive branch does not normally determine the names of its own departments. If you imagine the American government to be a single coherent entity, one might say "they have full naming rights", but it isn't, and in this case, the part doing the rename isn't the part that properly has the power to do so!

OK, so the actual disagreement here seems to be whether adding same-mass right-handed neutrinos counts as a significant modification to the Standard Model. I have generally seen adding any sort of right-handed neutrinos to be considered a significant modification. I agree that certainly adding same-mass ones, like all othe fermions have, makes everything simpler and more symmetric! And in an alternate history of physics, that would have been considered the Standard Model, the baseline. But as best I've seen, in the history of physics that actually happened, "no right-handed neutrinos" got codified as the baseline, so changing over to this alternate one would to my mind be a significant change from what people mean by "the Standard Model".

But that doesn't exactly seem like something it makes a lot of sense to argue over, now that we've identified the disagreement.

> Those would be heavy neutrinos which get their mass from physics beyond the standard model. Plain vanilla standard model fermions have the same mass whether they are left- or right-handed, so quite small for neutrinos [2].

Hm, is that true? I know these experiments can only detect certain mass ranges and IIRC you're right that they were looking for heavier ones, but my understanding was that they were not getting it from physics beyond "standard model plus right-handed neutrinos" (technically beyond the standard model but only a way that is necessary to even discuss the subject!), rather they were just getting it via the ordinary Higgs mechanism? (The bit you linked regarding this doesn't appear to contradict this?) Unless by "beyond the standard model" you just mean that the right-handed mass is different from the left-handed mass, in which case, well, see above, now we're just talking about what "the standard model" normally means.

I mean you say you're a particle physicist, so I guess you'd know -- when you talk to your colleagues, what do they think "the standard model" means with regard to neutrinos? That right-handed ones don't exist? Or that they do exist and have the same mass as their left-handed counterparts? At the very least all the popularizations I've seen (generally written by particle physicists) have said it means the former... you're really sure other particle physicists mean the latter? This may sound a little silly, but have you tried taking like a quick poll or anything to make sure?

Huh. Why do other sources seem to say that's only the case for bosons? Or am I conflating two distinct problems? Sorry, once again, not a physicist.

But if that's correct then I'm confused what your objection is to what I said earlier. If a bare mass would violate electroweak gauge invariance, then instead the mass should come from the Higgs mechanism, but that has the problem of, where are all the right-handed neutrinos, then? Am I missing something here? If you can't just give the neutrinos a bare mass and call it a day (at least not w/o causing significant problems), but do in fact have to make a more significant modification like inventing sterile neutrinos or making them Majorana particles, I'd call that a "contradiction" rather than merely a "question", because no hypothesis so far is a good fit for all of what we see (searches for sterile neutrinos have come up empty, neutrinoless double beta decay remains undetected, and I assume nobody's ever observed violations of electroweak gauge invariance!). Or I guess there are more out-there hypotheses that are consistent with what we see in that they've yet to really be tested, but, y'know, nothing that's been really tested AFAIK.

So, I'm not actually a particle physicist. My understanding had been (based on something I'd read somewhere -- should try to find it again) that there is some problem caused by just declaring "neutrinos just have innate masses, they're not from the Higgs mechanism", but I could be mistaken. Obviously, if that is mistaken, then as you say it merely a question rather than a contradiction. Should try to dig that up though.

Edit: Doing some quick searching seems to indicate that giving neutrinos a bare mass term would violate electroweak gauge invariance? I don't know enough to evaluate that claim, or TBH really even to understand it. But I believe that's what I was thinking of, so maybe you can say how true and/or pertinent that is.