Could the OPERA tachyon be the unbroken Higgs?
September 28, 2011
In yesterday’s blog I looked at some of the numbers from the OPERA neutrino experiment, to see whether (if correct) they made any sense without invoking too many radical changes to our understanding of the Universe (other than a loss of causality, which is unavoidable once you have things travelling faster than the speed of light).
At first sight, it’s difficult to see how it can. The OPERA result would imply an “instantaneous momentum” (the tachyonic analogue of the “rest mass” of a normal bradyonic particle; see yesterday) on the order of 100 MeV. Not only doesn’t this fit at all well into the neutrino sector as we know it, it would also imply a dispersion of arrival times not seen in the experiment itself.
I speculated that the only way I could see such a “clean” (uniform) 60 ns advance in arrival times across such a spectrum of energies would be if there were some sort of “intermediate tachyon” that somehow managed to get 60 ns ahead of the speed of light, which then decayed back into the regular neutrinos that we know and love — with m^2 on the order of eV^2 or less — which would effectively travel the rest of the way to Italy at the speed of light.
Last night I was playing around with the Standard Model to see how it would react to the introduction of an exotic tachyonic intermediate particle, when it dawned on me that it already has one — in a way.
Let me roll back a little. The Higgs mechanism introduces a scalar field with a mass term that has a negative mass-squared. A tachyon? Not quite. Viewed as a pseudo-classical field theory, the wrong sign of the mass term yields a “potential energy” that is unbounded from below. So the Higgs mechanism postulates an additional fourth-order interaction term, with positive sign, so that the potential energy surface looks like the bottom of a beer bottle. The potential energy is then bounded from below, in the degenerate “ring” around the bottom of the bottle.
The vacuum is then taken to be that state in which the Higgs field is in its lowest-energy state, which has a value around 246 GeV. Since this is actually a ring of degenerate states with the same energy, the Universe arbitrarily “chooses” one such state; this is the “spontaneous symmetry breaking” of the theory.
For Feynman-diagram type calculations, we like to use perturbation theory around the vacuum state. When you crunch it through with the right gauge interactions and the right gauge chosen to remove unphysical fields, you end up with a set of particles and interactions that agrees extremely well with what we actually find in Nature, as well as a remnant “broken” Higgs boson, with a normal (bradyonic) mass (that is not, unfortunately, predicted by the theory). Moreover, the Higgs mechanism allows the Standard Model to remain renormalisable, despite having features which would otherwise make it a computational basket-case.
All that is elementary particle physics. What’s interesting is that the original, “unbroken” Higgs, with its tachyonic mass term, is still really there in the Lagrangian, albeit 246 GeV away from the vacuum state. Of course, if we were to solve the equations of motion exactly, then either viewpoint would be equivalent — it’s merely shifting to a different set of dynamical coordinates. But we’re so accustomed to using perturbative theory around the vacuum that it’s easy to forget where it all came from.
Is it possible that OPERA is creating an “unbroken Higgs” particle, i.e., a tachyonic excitation around the unbroken Higgs field at zero, rather than around its vacuum expectation value? It certainly couldn’t do that in a vacuum, with only tens of GeV available to play with. But our condensed matter colleagues never fail to admonish us for treating everything as if it were perturbations around the vacuum. What if it were possible to excite the unbroken Higgs field within the confines of condensed matter?
A possible scenario for the OPERA experiment could then be the following. As the CNGS mesons travel down the 1000 metre vacuum tunnel, they decay into muons and muon-neutrinos, which are still essentially travelling together at almost the speed of light. They enter the hadron stop. Inside that material, they convert back into an unbroken Higgs (remember that the unbroken Higgs has different quantum numbers from the normal “broken” Higgs, so this is not forbidden).
This unbroken Higgs excitation (particle) travels through the hadron stop with kinematics corresponding to its mass term — which is tachyonic. Assuming that the unbroken Higgs has a ‘w’ value (see yesterday’s post) that is much larger than the tens of GeV of the beam energy, then the unbroken Higgs will be in its “low energy regime”, regardless of whether the recombining muon and neutrino happen to be from the same original decay or not. Now, for a tachyon, a low-energy particle moves at almost infinite speed. The unbroken Higgs gets to the other side of the hadron stop in close to no time at all.
At that point, it re-emerges into the vacuum, and the condensed matter dynamical environment is gone. Unstable in this vacuum environment, it decays back into a muon and a neutrino, which continue to travel at essentially the speed of light. The muons are detected or otherwise swept away. The neutrinos continue on into the rock beyond CERN, on their way to the OPERA detector in Italy. Without their corresponding muons, the cannot convert into unbroken Higgs particles for the rest of their trip.
Do the numbers add up? The OPERA paper states that the hadron stop is 18 metres long. Anything travelling at essentially the speed of light would take 60 nanoseconds to traverse it. The unbroken Higgs, on the other hand, gets across it almost instantaneously. The neutrinos would therefore be 60 nanoseconds ahead of where they were supposed to be. For the rest of the trip to Italy, they travel at their expected speed of essentially the speed of light. The arrival time distribution is advanced by 60 nanoseconds, for all energies.
This is a seductive calculation, but it has one fatal flaw: If it were true, then the muons detected after the hadron stop would also be 60 nanoseconds ahead of where they were supposed to be. OPERA reported no such effect, and since the nice juicy charged muons right there at CERN are much easier to detect than the poltergeist neutrinos 730 kilometres away, one would have to hazard the guess that such an effect was not present.
September 29, 2011 at 5:21 am
In the context of supersymmetry, there have been attempts to obtain the Higgs from the neutrino’s scalar superpartner, starting with
http://www.sciencedirect.com/science/article/pii/0550321375906367
In particular, the tau sneutrino may mix with the Higgs boson
http://arxiv.org/abs/hep-ph/0005295
or even provide some particle masses
http://arxiv.org/abs/1107.4634
So there may be some serious model-building ahead, along these lines.
September 29, 2011 at 5:57 am
Quite possible, Mitchell, although I tend not to go for anything exotic until it has some definite evidence for it. (I’ve still got the superstring volumes sitting on my shelf as perhaps the only books in my library that I haven’t read cover to cover.)
I find it quite remarkable that the hadron stop is exactly the same length (18 metres or 60 light-nanoseconds) as the energy-independent time advance seen by OPERA.
I like the fact that, with a bit of condensed matter magic, the unbroken Higgs potential may be brought within the range of this relatively low-energy beam — i.e. that it may not require the Standard Model to be extended exotically at all. But the details of that would still have to be worked out (and, like Cooper pairs, etc., might not be a trivial calculation).
Reading through some PhD theses of OPERA students, it seems possibly that the arrival times of the muons were not checked, although I’m not sure about that yet. It’s also clear that the Near Detector / Far Detector symmetry of MINOS may not have allowed the same opportunity for this “hadron stop” effect.
Which raises the question of what the conditions are for it to happen at all. Above I made a vague comment about the muons being detected or swept away. For the former I was thinking of the quantum mechanical maxim that “detection is selection”, i.e. that the coherence of the muon/mu-neutrino pair may be destroyed by the measurement process. But it’s probably more likely that it something simple, related to the material of the hadron stop, that makes this tachyonic mode of transport across it (and not normal rock) possible. Or maybe it’s beam divergence, or the muons simply being stopped in the rock … or maybe it doesn’t rely on the muon being present at all. (Although why it would then happen in the hadron stop and not in rock would be more difficult to understand — as well as the problem with ascribing quantum numbers to this mode.)
Just guesses for now, but it seems to be more plausible than extra dimensions twisted weirdly to avoid any energy-dependence.
September 30, 2011 at 9:46 pm
When I saw the OPERA talk I was also struck by the fact that their hadron stop is 18.2 meters according to their slices, which is exactly in the middle of the error bars of their measurement (60.7 ns / c = 18.2 m) . It’s probably a coincidence, but it might be worthwhile to look at the MINOS setup and see if a pattern appears (MINOS also measured superluminal neutrino speeds a few years ago).
However I’m a bit reluctant to throw causality out the window at this point and was thinking along the same lines as John Costella. The pion/kaons decay in flight at a very relativistic speed into a muon/neutrino pair. The decay energy is small and the muon is much heavier than the muon neutrino, so the angle of divergence is tiny. I haven’t crunched the numbers, but this might fall in the realm where the uncertainty principle becomes very significant (i.e. the Dirac equations in this relativistic case).
The hadron stopper might observe the position and momentum of the muon/neutrino pair in such a way that you could triangulate to the pion/kaon and break the uncertainty principle. Perhaps the muon gets a disproportionate share of the required randomness to avoid this and the effect disappears once the neutrinos reach the the end of the hadron stopper – all very speculative and again I haven’t crunched the numbers. Both MINOS and T2K have a near detector, so it’ll be very interesting to see what their results are.
September 30, 2011 at 11:50 pm
I haven’t thought about it in terms of the Uncertainty Principle, but I suppose my vague comment about “coherence” are along the same line of country. Interesting.
I don’t have as much information about the MINOS layout as I do on OPERA, but at first glance it seems to me that the use of a Near Detector and Far Detector would “factorise out” anything that was “upstream” of the Near Detector. Of course, if there is some strange effect in play allowing neutrinos (or mu/nu pairs) to jump across metres of space in essentially no time, then until the effect is nailed down and understood, one can’t really exclude anything. Perhaps there is something “downstream” of the Near Detector in MINOS that plays the same role as the hadron stop at OPERA; the biasing of their central value to be advanced by 126 nanoseconds or 38 light-metres (with much larger errors) would tend to suggest that (if this is a real effect) there must be.
OPERA seems somewhat unique in that they (a) measure the time of flight at all (this is shared with MINOS, of course) and (b) measure it all the way back to the proton bunch itself. That latter aspect gives rise to additional laborious calibrations in their timing chain, but could it also have rendered them sensitive to an effect between the proton bunch and what you would normally think of as the “neutrino launch place” (after the hadron stop and muon detectors) on their journey to Gran Sasso?
The other interesting aspect to all this is that, if there really is some sort of tachyonic jump going on at these energies when things pass through condensed matter, it would really throw the cat among the pigeons for any of these high-energy experiments (particularly Higgs searches). The kinematics, timing cuts, etc. have all been calculated assuming the good old Einsteinian kinematics that has served us well for over century. If particles here and there have been jumping across materials nanoseconds ahead of where they were supposed to be, then the experiments may well have been missing out on the very events they were designed to detect.
The first thing for MINOS, OPERA and T2K to determine is whether this is really an O(10^{-5}) effect across 730 km of neutrino propagation, or an O(1) effect across tens of metres of solid matter. The latter should actually be easier to test.
October 1, 2011 at 4:08 am
Well, we should know pretty soon whether or not the SM
Higgsfairy exists.October 1, 2011 at 5:09 am
As long as there’s not some bizarre effect like this throwing out the kinematics. Go back through all the “fairy” searches and ask yourself what would happen if particle tracks were able to get ahead of where they were supposed to be. Not good.
(For the record, 19 years ago while chowing down on clam chowder in Seattle during my visit to the INT I staked my bet on the top quark existing and the Higgs not, so I’m not unsympathetic …)
October 8, 2011 at 6:31 pm
I like the way you think John,
but one thing –
how we are supposed to ‘fit in’, more so understand the ‘instantaneous’ jumps across space-time? (math aside)
I mean trying to explain the FTL by bringing in the infinite speed tachyons, not sure if it helps any –
not that I don’t like it : )
instantaneous jumps – do sound a bit like ‘macroscopic’ QT effects – pretty much anything goes if we start to plug the holes with it.
neutrinos following different geometry (and speed limitations) does sound more ‘down to earth’ to me : ) ?
great blog btw.
October 9, 2011 at 1:04 am
Hi Dragan,
If correct and confirmed, the OPERA result will change our view of physics fundamentally — causality will be a casualty. There’s no way to avoid that.
The conjecture that it is the neutrinos travelling at slightly faster than the speed of light might seem to be the simplest explanation consistent with the facts (again, assuming the OPERA result is correct), but deeper analysis shows that it really doesn’t fit. There have been good papers already by Ellis and colleagues, and Glashow and colleague, showing that a slightly tachyonic neutrino, together with the rest of physics as we know it, just wouldn’t give the OPERA results and everything else we have seen neutrinos do.
My conjecture is possibly the next-simplest one: if there are tachyons at play here, then why not use the one tachyon that is already in the Standard Model of particle physics? We still don’t know the mass of the Higgs (if it exists), and hence don’t know the “instantaneous momentum” of the unbroken Higgs originally put into the Standard Model (they’re related fairly trivially), but it’s fair to guess that the energy scale would be on the hundreds of GeV, which would make the OPERA muon/neutrino pairs low-energy excitations.
A low-energy tachyon travels at almost infinite speed. This is unfamiliar to us (a low-energy bradyon travels at almost zero speed, compared to the speed of light), but that’s just because of our lack of experience with these beasts.
When I say that this is possibly the next-simplest conjecture, I’m saying that along the lines of Occam’s Razor. I’m not adding any new laws of Nature at all. I’m introducing no new free parameters. Of course, I haven’t performed an explicit calculation to show that the Standard Model in condensed matter could cause this unbroken Higgs (or some other tachyonic excitation of the underlying dynamics of quantum field theory, if the Higgs mechanism isn’t the way the Universe really works) to be excited in this way. But given what we know from other fields (e.g. superconductivity), it’s plausible. Moreover, because the unbroken Higgs in the Standard Model is a genuine tachyonic field — in a sense more fundamental than the spontaneously broken excitations we see around the vacuum — it doesn’t seem out of the question for real signals to be propagated faster than the speed of light across the 18 metres of iron (i.e. this isn’t just one of those curious cases where the phase velocity or group velocity in a medium exceeds c but the signal velocity doesn’t; in this case signals really would violate the speed of light and hence causality).
I should also point out that I’m not saying that the speed would be infinite, but simply that it would be much greater than c. Maybe it takes the excitation one nanosecond to traverse the hadron stop (for example).
Lorentz-violating geometry might be fun (although it doesn’t appeal to my sense of aesthetics), but it is very much a huge extension to the Einsteinian model of spacetime that we have had for the last century. If it is true, then experiments will show that to be the case, and Einstein will be wrong. But for my money, right now, I’m betting on the simplest possible explanation that doesn’t involve any extensions of the standard laws of physics at all, just simply a possibly horrendously difficult theoretical condensed matter calculation — which is our shortcoming, not the Standard Model’s.
(And thanks for the kind words.)
John
October 10, 2011 at 7:49 am
“a possibly horrendously difficult theoretical condensed matter calculation”
There are qualitative problems with your idea which are the immediate challenge to its viability. For example, what does the Higgs have to do with muon neutrinos? Why does the tachyonic Higgs remember to decay back into a neutrino?
There are models in which the Higgs is a neutrino-antineutrino condensate (bound by beyond-standard-model interactions), so that would make a neutrino/Higgs switcheroo marginally more comprehensible.
In fact, there’s an extremely interesting paper from New Zealand that came out on Friday – http://arxiv.org/abs/1110.1162 – which proposes that the apparently spacelike motion of the neutrino is actually due to a Feynman zigzag – pair creation of neutrino-antineutrino midway between CERN and OPERA, with the initial neutrino annihilating with the antineutrino, and the created neutrino being the one which reaches Italy. But the created neutrino-antineutrino pair has to have a source. If the Higgs really is just a neutrino condensate, that would fit very nicely with the New Zealand idea.
November 6, 2011 at 11:13 am
Hi John,
I have trouble with your idea because a muon-muon neutrino pair do not have the quantum numbers of the vacuum -they are a charged system.
Cheers,
T.
November 6, 2011 at 10:21 pm
Hi Tommaso,
Why would they need to have the quantum numbers of the vacuum?
Cheers,
John
November 6, 2011 at 1:47 pm
It is indeed important to recall that quantum mechanics allows for tiny excursions outside the light cone that are perfectly consistent with Relativity. This may provide the most natural interpretation of OPERA anomaly, see below:
http://arxiv.org/abs/1110.1162
It also may lend support to the idea that photons and long-range neutrinos having ultra-relativistic rest-frame masses (consistent with zero) can be described as components of the same gauge doublet:
http://www.vixra.org/abs/1111.0010
Ervin
November 6, 2011 at 10:28 pm
Hi Ervin,
I like the direction of the first reference better — it ties in with the general argument I gave in the previous post, and is elegant. We always throw around spacelike intermediate particles in quantum field theory, but rarely stop to consider the “mechanical” (kinematical) by-product of such beasts. Perhaps this shows us where it may become measureable?
I’m not a fan of supersymmetry, but I know that many are.
Thanks,
John
November 7, 2011 at 2:30 am
John,
I am not a fan of supersymmetry either. I think it is pointing in the wrong direction.
Having said that, it looks like photons and nearly massless neutrinos (Weyl fermions) propagating in Earth at distances much larger than the EW scale meet all requirements for qualifying as partners of a SUSY-like gauge doublet.
The net benefit of this interpretation is that Lorentz symmetry survives regardless of the relative speed of neutrinos and their average energy.
Ervin
November 16, 2011 at 11:29 pm
All those still following this post: Rumour on the wires is that OPERA has confirmed the time of flight with pulses only 2 or 3 nanoseconds long:
http://motls.blogspot.com/2011/11/opera-neutrinos-ftl-even-at-3-ns.html
Press conference expected within two days.
November 17, 2011 at 6:00 am
Perhaps they could double the size of their hadron stop and see if that increases the time anomaly to 120ns?
That would be a ‘smoking gun’.
November 17, 2011 at 6:08 am
Absolutely. Or, better, still, halve it and check for 30 ns. (A priori it’s not guaranteed that any such coherent behaviour — if that’s the right guess — would last the full 36 metres; but if it lasts 18 metres, then it should definitely last 9.)
I originally thought that detecting the muon arrival times (at the end of the hadron stop) would be even easier, but with these 2 or 3 ns pulses they’ve shown the ability to obtain results within weeks anyway — every neutrino is a measurement.
If this yields the same 60 ns result, then the other possibility (along the lines of my previous post) is that the “instantaneous 18 metre jump” is an inherent property of the decay process (say, representing the kinematics of a spacelike intermediate particle), and the length of the hadron stop was just an incredible coincidence. Detecting muons close-by (at CERN) would then be the way to distinguish this from tachyonic neutrinos going through the rock to Gran Sasso.