A recent experimental paper measures a difference between the top quark and anti-top quark masses:

Fermilab-Pub-11-062-E, CDF Collaboration, Measurement of the mass difference between $t$ and $\bar{t}$ quarks

We present a direct measurement of the mass difference between $t$ and $\bar{t}$ quarks using $t\bar{t}$ candidate events in the lepton+jets channel, collected with the CDF II detector at Fermilab's 1.96 TeV Tevatron $p\bar{p}$ Collider. We make an event by event estimate of the mass difference to construct templates for top quark pair signal events and background events. The resulting mass difference distribution of data is compared to templates of signals and background using a maximum likelihood fit. From a sample corresponding to an integrated luminosity of 1/5.6 fb, we measure a mass difference, $\mathrm{M}_{t} - > \mathrm{M}_{\bar{t}}$ $= -3.3 \pm > 1.4(\textrm{stat}) \pm 1.0(\textrm{syst})$, approximately two standard deviations away from the CPT hypothesis of zero mass difference. This is the most precise measurement of a mass difference between $t$ and its $\bar{t}$ partner to date.


This seems to pile on to the recent evidence showing differences between the masses of the neutrinos and anti-neutrinos. But unlike neutrinos, quarks can't be Majorana spinors. So what theoretical explanations for this are possible?

  • $\begingroup$ The CDF paper mentions bit.ly/eVxxqj and bit.ly/gVb8tR as "well-motivated extensions of the Standard Model allowing CPT violation". Thanks for pointing this paper out. This result is very interesting since a violation of CPT would mean a violation of Lorentz invariance too. (bit.ly/eatLrX) The CDF measurement appears to be consistent with an earlier D0 measurement (arxiv.org/abs/0906.1172) which however wasn't precise enough to indicate CPT violation. I'm really looking forward to answers from experts that will shed light on this intriguing measurement. $\endgroup$
    – dbrane
    Mar 17, 2011 at 3:05
  • $\begingroup$ @dbrane; Yeah, I threw this out here to start a conversation. The strange thing about this paper is that no one seems to have blogged it yet. Admittedly the statistics are not that good, but the trend with the neutrinos is fairly convincing. Moral: Don't release your big papers while the world is in disaster movie mode. $\endgroup$ Mar 17, 2011 at 3:22
  • $\begingroup$ I have blogged one sentence about it, in an article dedicated to another HEP topic (a more exciting rumor), and the essence of my blogging about it was equivalent to Matt Reece's answer. One shouldn't pay attention to 2-sigma bumps especially if the interpretation is meant to make extraordinary claims such as CPT-violation, and the right way "not to pay attention" is not to blog about it at all. It's sad that the top, antitop masses are measured so inaccurately but that's the only thing to say here. $\endgroup$ Mar 17, 2011 at 7:37

2 Answers 2


There is one simple, obvious, and almost certainly correct theoretical explanation: two-sigma effects show up all the time and, like most of them, this one is not real.


I suppose it will be a painful wait for the 5 sigma. Well, quarks are confined, so maybe it's OK for them to exhibit genuine CPT violation, whereas the neutral particles need renaming according to the mirror picture. But on the other hand, the quark braids have neutral strands, and if we mix (say for the proton) the uud, udu and duu sets, then there are enough neutral strands for component Majorana states.


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