Saturday, November 16, 2013

Fermilab Today on naturalness

Today, Fermilab Today published a nice short article about naturalness written by Jim Pivarski of CMS.

The article contains an unlikely arrangement of stones which seems to depend – much like the Higgs boson mass – on fine, unlikely cancellations. Pivarski also writes that it's unlikely for many parts of the same car to break at the same moment.

I chose another example of an unnatural arrangement of matter – one that was being offered to me by several Czech discount servers today. ;-) While the "Wine Bottle Chain Holder – Holds Bottles In the Air" seems even more extreme than the rocks above because the forces don't even seem to balance (not even in an unstable way), you may actually buy it. And just for six or ten bucks!

See the link at the bottom. You simply can't afford not to possess this miraculous wine bottle holder! ;-)

An important point to notice – a point that Pivarski sensibly points out, too – is that it may just "look" unlikely for the chain holder to keep the bottle floating in the air. In reality, there could be an underlying explanation that makes the arrangement likely – we have just been overlooking the explanation. I don't actually know "exactly" what the explanation is because I don't have the chain holder and the pictures aren't quite sufficient. It still does look like a miracle to me! ;-)

But I ultimately believe that Nature contains no miracles or contradictions.

A question is what sort of explanations of the "apparently unlikely cancellations" are kosher.

To answer this question, we must understand the reason why the arrangement (or the lightness of the Higgs boson) seems unlikely to us in the first place. It's because we may argue that the numerical parameters like the squared Higgs mass are a priori "almost uniformly distributed in an interval, like the interval\[

0\leq m_h^2 \leq m_{GUT}^2,

\] which means that the probability that \(m_h^2\) is equal to or smaller than \(10^{-30}m_{GUT}^2\) is very small, pretty much \(10^{-30}\). So we don't expect such a cancellation to occur in Nature – much like we don't expect the weird rocks or (even worse) the wine bottle chain holder to exist.

However, the LHC is showing us that the Higgs boson does exist and its being is unbearably light. That means that we either admit that \(10^{-30}\) is a high enough probability – which is pretty bad (this standard would lead us to say it's OK and not evidence of crime for someone to win $100 million in a lottery five times in a row) – or we must conclude that something in the calculation of the probability was wrong. What was really wrong was the assumption of the "uniformity" of the distribution. In the real word, it must be much more likely than \(10^{-30}\) that the Higgs mass is close to zero. In other words, the distribution must be much more non-uniform.

At the end, when we know everything about the dynamical mechanisms that determine the Higgs mass (including the choice of the right string/M-theoretical vacuum), the actual probability distribution is\[

\rho(m_h^2) = \delta (m_h^2 - 10^{-30}m_{GUT}^2),

\] a simple delta-function positioned at the correct value of the Higgs mass (which is unnaturally small). Clearly, we don't have the "full explanation" yet. But we expect to be "somewhat closer" to a partial understanding that doesn't spit out the exact value of the mass but at least some rough estimate – some probability distribution for the Higgs mass that doesn't make the observed low value of the mass insanely unlikely.

Supersymmetry makes the low figures much more likely – it guarantees some cancellations. But to do so, the SUSY breaking scale must be low enough, not too much above the Higgs mass. Well, this is a rough description people would be satisfied with years ago. As the illusion was increasingly suggesting that the superpartners are heavier or substantially heavier than the Higgs mass, people began to be much more careful about the statements that the superpartners shouldn't be "too much heavier" than the Higgs. How much heavier? Which superpartners?

Yup, the $200 lasso holder may be bought for $8.49.

It turns out that only the top squarks and perhaps higgsinos (and, due to some additional interactions, also gluinos) are really important for the naturalness argument. They shouldn't be "orders of magnitude" heavier than the Higgs. The amount of fine-tuning – how crazy arrangement of stones we find tolerable in Nature – is a matter of subjective preferences. I personally find (and I have always found) a fine-tuning at "one part in a thousand" tolerable. Several years ago, many phenomenologists would proudly reduce their tolerance and would sometimes declare even "one in ten" fine-tuning unacceptable. Well, I think that Nature has already proved them wrong. There don't seem be any particles that are important for the stabilization of the Higgs mass and whose mass is "really close" to the Higgs mass. So some fine-tuning is bound to be required.

Once we accept the anthropic reasoning as a factor influencing the probability distributions, many of the worries about the unnaturalness evaporate. The reason is that the anthropic reasoning allows us to assume the existence of intelligent life – a rough aspect of the observed experimental data – and the existence of intelligent life heavily favors the existence of a light Higgs boson. A light Higgs boson (and light quarks and electrons, which sort of require a light Higgs boson although the Yukawa couplings may hide the smallness, too) is needed for the stars to live for a long time (relatively to the nuclear scale) and to contain parameterically many atoms. The number of atoms in a star is pretty much a power of the Planck-to-proton mass ratio. It is only large if the Higgs boson is much lighter than the Planck mass! And a planet orbiting a 15-atom star wouldn't have too much (or enough) potential to produce moderately and occasionally intelligent animals like us.

So if you say that the probability distributions above should be modified by the knowledge that intelligent life exists, the distributions are peaked near the small values of the Higgs mass – and they similarly reproduce many hierarchies. But the existence of intelligent life, while spiritually "important", is just a vaguely defined aspect of observations. Of course that if we would be using all the observations, we could just conclude that the right distribution is the delta-function I have already mentioned:\[

\rho(m_h^2) = \delta (m_h^2 - 10^{-30}m_{GUT}^2)

\] That would give us the right results but all of them would be extracted from the experiments. The theoretical reasoning would be completely useless. We know that over the history of science, science was capable of calculating many things without measuring them. So many physicists still think about the working hypothesis that the lightness of the Higgs boson can be justified by a logic or mechanism that doesn't require the experimental data – not even their rough aspects such as the existence of intelligent beings – to be assumed. Of course that to a certain extent, it is just a hope. Even the best theories we have ever had need to assume certain things that we had to extract from the experiments. There's no guarantee that the dependence on the observable data may be eliminated entirely.

Many such potential explanations of the Higgs boson's lightness may be found in the literature. Many of them, especially if you take a strong version of them (no tolerance to even modest fine-tuning), have already been ruled out because the Higgs boson is low and the particle seems to be somewhat isolated.

It's not clear whether some physics at a near-electroweak scale has to be found. The anthropic principle may be the reason why the Higgs mass seems so unnaturally light. But even without the anthropic principle, it's plausible that there exists an overlooked explanation of the low Higgs mass that however doesn't create any new physics near the electroweak scale. Such an "intelligent targeting done from a distance" violates the lore of effective field theories but I think that string/M-theory ultimately may violate this lore. It may produce patterns and relationships that are "unexplainable" by field-theoretical reasoning itself but that may be established using stringy arguments. In fact, string theory has already produced many examples of such extra constraints. The UV-IR connections may be viewed as a place to start.

So I have always been ready to encounter the major possibility that the Higgs boson is an island of a sort. I just don't have a fantastic problem with it and I don't think it would be a revolution in physics of any kind. It's just the damn ordinary Standard Model. Just some vague arguments about naturalness, arguments that have to exclude the anthropic bias and make several other additional assumptions, would be shown illegitimate. Well, not a big deal.

I want to emphasize that this does not mean that I consider the existence of supersymmetry questionable. For theoretical reasons, SUSY is pretty much inevitable in any consistent theory of quantum gravity with fermions and at least some stability. But whether many/most superpartners must be really close to the Higgs mass is an entirely open question, as far as I can say.


  1. Hi Lubos: Nice article as usual. I wonder, is there any connection between fine tuning cancellations leading to the currently known Higgs particle and cancellations leading to small C.C. or these two are independent puzzles? Also I have heard before that intelligent life needs small C.C. otherwise there is not enough time for planet formation and evolution to take place, but I have not heard similar argument for Higgs mass. If it is in one of your previous blogs, I must have missed it. Thanks.

  2. Mustafa McGillicuddyNov 16, 2013, 12:22:00 AM

    That no processes exist in nature which would produce anything of this delicate kind of arrangement is a good metaphor for where the rubber meets the road. Hence the idea of "naturalness" and too "fine tuned," should have a real meaning in the lexicon.
    But my sense is that regarding the Higgs, there is another rather simple argument, that it may not be likely that something would exist at the fulcrum of all symmetries between forces and objects, because if there was such an kind of particle, it's existence would obey principles of an ideal equilibrium, such there would be an extreme abundance of it.

    This is a great discussion though, about where the rubber meets the road in terms of what can or cannot be a real arrangement, Hence the idea of "stuff" and "things" being different in serious ways seems to get to an idea of *proportionality and *portion (and what after all is math about but these two things?). The thing that occurs at this point is that energy throws physical law off from the balance between the mathematical ideal in a way which is governed by dimensional action, namely time. Hence the resolution of time's action on matter is the apt question, in a sense answered by Planck, but then we get into the problem that such small resolutions of time just don't mean much at larger scales, such that what is really necessary is a language which speaks to the form of how time works on objects of different scales in a way that is in proportion to their portion. At that point we can address holography and get into a picture of understanding dimension in finite "geometry" terms, such as to say at some point quanta have a relationship which is inextricably linked via entanglement ("glue"), but those links form objects which have a proportion which is attuned with temporal rules which have (this is strange) both extrinsic (spatial, environmental) influence on objects within their relevant field, and some intrinsic rules with regard to how the object itself transforms. What then does it mean when an object within a space transforms according to rules which are obedient to outside energies, within a space that imposes a local concept of temporal transformation? Hm, I dunno.

  3. Mustafa McGillicuddyNov 16, 2013, 12:47:00 AM

    *occurs to me...

  4. Both quantum gravitation and the standard model are pathologically incomplete. Something that obviously must be true (e.g., 180 degree triangles) empirically fails (e.g., cartography).

    The rocks' simple explanation is an embedded vertical piece of rebar. The chain's links are probably welded each to the next. The forks, cork, and needle construct is easily honestly achieved. Upon contemplation, it iterates. That is my black lab coat, three Japanese heavy duty sewing machine needles, and look carefully at the forks' masses.

    Jury-rigging a remarkable cancellation of huge excursions across a whole discipline to afford exquisitely tuned outputs is a dire warning. 1920s' QM said methane was CH2, forming a right angle with the carbon as vertex. That methane is CH4 with arccosine(-1/3) degrees internal angles was not curve fitted. Chemistry got much better wrong theory, Z. Physik 70, 204 (1931), that did not need apologies until Angew. Chemie Int. Ed. 8(11) 781 (1969).

    Physical theory has been jury rigged since 04 January 1957, having studiously ignored the same conclusion in a 1928 experiment, PNAS 14(7), 544 (1928). Shame on you.

  5. Brian G ValentineNov 16, 2013, 2:05:00 AM

    If the chain were a solid piece of metal, would the bottle holder seem so strange to you?

    The sign says "free shipping." Does that mean free shipping to the USA too? It doesn't matter to me anyway, I don't want one.

  6. John F. HultquistNov 16, 2013, 5:24:00 AM

    For strange things there is also a “belt hook” that seems to suspend a leather belt out over the
    edge of whatever it rests on. The shape is something like a Sherlock Holmes pipe. As kids we carved them from thin wood. This link . . .

    shows one from white jade, but doesn't
    show its use. Another similar thing is to place a spoon tip into the tines of a fork making a continuous curve of the two. Then place one
    end of a wood tooth pick into the fork tines and the other end over the top rim of a drinking glass. The 2 ends of the wood can be burned back (burning will stop where the wood touches the fork and the glass) and the contraption hangs in the air.

  7. If you go to the Amazon link, it allows to see the details of the photo. The chain is fused solid. It is a cantilever and balances the center of mass of the bottle over the loop on the table.

  8. Brian G ValentineNov 16, 2013, 6:25:00 AM

    Fused together, Anna? You're joking!

    And here I thought this was some sort of anti-gravity device.

    Fooled me, thanks for the clarification

    (sorry I shouldn't be so sarcastic)

  9. LOL, of course I did figure out it was solid. The issue was the shape around the bottleneck but I understand it. too.

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  11. I suppose the bottleneck would have to be stronger (thicker glass) than the rest of the bottle too, otherwise it would break, wouldn't it?

  12. LOL, a great point but I thought it works with any ordinary bottle so you must be wrong however convincing your comment sounds.

  13. Poor bottle. Must be hard on her abdominals.

  14. I don’t really understand your position Lubos. At the end of the post your statements become a little bit vague and ambiguous. You imply that naturalness is not a big issue? If yes I strongly disagree; I had a similar argumentation

    with Sabine the other day:

    As I understand it at least the SM due to Higgs mass is not natural and this is a *real* big problem for an Effective filed theory with a cut-off in the Wilsonian sense. Either you find new physics not far beyond the EW scale (and thus change the cut-off) or you find a mechanism that will explain the required fine tuning e.g. based on anthropics/multiverse (similarly to CC which is basically the same problem if you take gravity into account).

    See this for example this nice paper I like:

    You state:

    “it's plausible that there exists an overlooked explanation of the low Higgs mass that however doesn't create any new physics near the electroweak scale.”

    You imply a third road? A dynamical mechanism within the SM without anthropics/multiverse? I don't
    understand it at all to tell you the truth and I can’t imagine what this mechanism might be. It’s like praying for a miracle to my eyes.

  15. As you can see, my position wasn't that vague because you understood it very well.

    I have never thought that naturalness is something that can stand at the center of research because it's a very vague, ill-defined, low-precision idea.

    The point is that there is no sharp enough point at which it starts to matter. A 1-in-300 fine-tuning is clearly acceptable so the superpartners may surely be several TeV in mass. Arguments claiming that superpartners - or other physical phenomena meant to "solve the hierarchy problem" - should be much closer to the Higgs mass scale have never stood on firm ground, they have always been a sort of wishful thinking, an ideology, I have always been saying the same thing, and experiments seem to support this position so far.

  16. One more related comment.

    This hype that "it's very important for the LHC to decide in between these roads" seems preposterous to me especially if I imagine it in practice.

    Just assume that the LHC sees no new physics in the 13-14 TeV run - which, as far as I can say, may very well happen. It's not guaranteed that it will happen but it may happen just like it has happened so far.

    Fine. So what will you do with your "important crossroad with two roads"? Will you declare Nature unnatural? WTF? Nature is, by definition, natural. It's just the stupid humans who sometimes misunderstand the rules that distinguish "natural" from "unnatural'.

    Those who made the prediction that "there has to be something new in the LHC range" will be proven wrong, and if someone is proven wrong, it is a *bad* idea to become more dogmatic about his philosophy. On the contrary, one should go away from his theories or his ideology, at least a bit.

    The more he is proven wrong, the more he should admit that he doesn't understand what's going on, so the more open to completely different solutions he should be. The "two road" approach to the hierarchy problem is prejudices and irrational and it seems to become even more prejudiced as it is gradually proven a wrong way to think. Too bad.

  17. But Naturalness was such a good guiding principle so far. Why QED respect it? Why QCD respect it? Why scalars wouldn’t?

    Sorry I’m not willing to sweep this under the rag and pretend nothing happened. This what PW advocates for crying out loud; he praises the SM and advocates that you don’t need any new physics/ideas to explain the SM Higgs mass and the whole discussion is based on unfounded dogmas.

    I need an explanation on the
    other hand. I’m not saying LHC energies impose a threshold and a decision milestone.This is debatable.

    You say

    “The full theory is clearly
    string/M-theory and whoever is "shocked" by any incompleteness of an effective field theory - or all effective field theories - in the understanding of a particular thing is utterly failing to understand this elementary point (that EFT can't be a TOE).”

    You are turning this upside down, I am the one advocating the above statement and I respect every lesson late Wilson taught to the world
    regarding EFT. Naturalness is implied by the Wilson’s EFT approach. That’s why you must lower the cut-off of SM.

  18. Dear Giotis, could you please be more specific about the correct yet nontrivial insights we could have done using naturalness?

    It's great you have been convinced that there has to be new physics, and so have I. But my view is that there is no hard-scientific argument that would imply that the new physics has to be nearby. So I have clearly very different reasons to believe new physics itself. It's almost quantum gravity (and also dark matter and a few phenomenological things, but not so much naturalness).

    I don't think that Wilson's EFT implies that we have to trust arguments based on the concept of naturalness. Naturalness would hold as a usable argument only if field theory were the full story - but it's the very point of "effective" field theory that it doesn't have to be the full story, so it may completely fail to understand the reasons for the values of parameters, even their order-of-magnitude estimates, and other patterns.

    Even if I believed these arguments effectively assuming that an EFT is the full story, I would still find it OK for quantities to be fine-tuned by 1 part in 1,000 or so simply because it seems clear to me that similar "tolerance" has been required from physicists in the past many times, too.

  19. Does antimatter bomb qualify? ;-)

  20. The payload would be larger (less parasitic weight) and process simplified (no launch platform) by loading the seeds inside the balloon, to be released upon bursting. A chip accelerometer turns on each seed upon release. Launch when the jet stream is overhead. Use balsa wood for the wings.

    One contemplates biocaching with opium poppy (2000 - 3000 seeds/gram) or cannabis (40 seeds/gram) intra-balloon payloads. Weaponize with poison ivy seeds.

  21. Well if somebody asks you where I should put the cut-off in the SM langranian what would be your answer? I would answer based on
    naturalness and I wouldn’t even hesitate.

    I agree with your point that ‘no new physics at LHC’ does
    not automatically imply multiverse/ anthropics. We need much more for such a
    paradigm shift as you say; no doubt about that…

    Nevertheless this would still be a problem waiting for a
    solution and anthropics could be a plausible answer.

    As it stands with a cut-off at GUT or Planck scale the SM is unnatural and problematic and we know it’s an EFT without a doubt.

    Anyway now I’m more confused because in the post above you make a reference to another post of yours about naturalness (
    ) with which I completely agree. These are exactly the points I wanted to stress
    here (see also my debate about that with Sabine).

    So what is happening? Behind the lines I have the feeling that you start having second thoughts about Naturalness due to LHC not seeing SUSY yet. I.e. if SUSY (or other physics) is not there
    to explain Higgs mass then Naturalness is not really an issue (sorry if I misunderstand
    you). If this is the case I disagree with this reasoning and of course it ain’t over till the fat lady sings. Like you I’m still expecting new physics and SUSY in particular but even if nothing appears I’m not willing to abandon naturalness without a physical explanation.

    Finally I don’t understand the connection you want to make
    with String theory. How it could be relevant at such low energy scales without introducing a new cut-off? How it could affect the RG flow? Or you suggest something completely novel that I don’t understand?

  22. Dear Giotis, what is the exact meaning of the question "where should I put the cutoff"? The location of a cutoff is a property of the effective theory, not a property of Nature per se, so this is not a question about science.

    At any rate, I would answer "at infinity" - or an exponentially high scale where the Landau pole appears. I find it natural - and a good scientific habit - to extrapolate a theory as far as I can.

    I suppose you would choose the cutoff near the electroweak scale itself? I find it utterly silly and I always have.

    Also, I don't have any second thoughts. I haven't changed my opinions about these matters because there was no reason.

    Whether the LHC would see new physics was always 50-50 uncertain. For example, see the 50% line for SUSY at the LHC in this April 2007 blog post:

  23. Thanks Lubos. The last
    two paragraphs about String theory and what it can teach us about the low energy EFTs is something I’ve never seriously thought before to tell you the
    truth. I used to think in QFT terms for these issues.

    Before the LHC I would put the cut-off around 1TeV, no doubt
    about it. Now the issue has become more complicated…

  24. Nice articly thanks for this Lumo :-)

    And I also enjoyed your discussion with Giotis.

    Could you give some more examples examples of how string theory can do things that can not be explained by EFTs ? This somehow picks me and I am not 100 % sure if people on MathOverflow would be amused if I have to ask there...;-P. Some of them seem to be quite interested in theoretical physics though ...

  25. The blog post put me in a philosophical spin. Off balance I'm not, though. To prove it I'll electronically print the following comment (a statement supporting a for me sufficiently stable stance on this subject of TRFic scrutiny):
    What can't be doesn't exist - except, of course, as fundamentally false figments of (sometimes feverishly figuring and believing) brains. %-}

  26. I always thought that by naturalness argument all scalar masses need to be around the cutoff scale of the theory but now you are saying naturalness implies a uniform probability density for the scalar masses.
    Although Higgs is unnatural in both of these cases, do we have an example of a natural toy model (without SUSY) which has scalars at all scales? I mean what cancels the quadratic divergences of scalar masses which are far from cutoff?

  27. Dear August, the scalar masses are just "likely" to be "near" the cutoff scale because "most numbers in the interval (0,1) are of order one", so to say. But there's always a nonzero probability that you get a more accurate cancellation than the "worst case scenario".

    Natural non-SUSY models with a light Higgs we have predict strongly coupled physics or very light or very heavy Higgs or similar things excluded by the experiment. I wouldn't bet on them.

    But my point is that SUSY with first new particles at a few TeV is just natural enough, and with some extra discrete structure, it may be "completely natural", too.

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  29. It could have been a different gimmick , as for example in this one legged chair . A transparent support somewhere, that is why I looked at the details.

    You must be theoretically inclined , no?

  30. Dear Lubos,
    Thanks for your response. I guess my point is that let's say you have an effective QFT with 1000 scalars and a cutoff of 1000TeV.
    A "typical" spectrum of this theory is when the masses are scattered between 0-1000TeV? Do you call it natural if one of the scalars is 100Gev? My point is that in this case, how can you cancel quadratic divergencies, so to speak, for the light scalars?

  31. Dear August, there's no "canonical" measure on the parameter space of this theory but roughly speaking, yes, I do think that the masses will be scattered. But one should really do it with the masses as understood at short distances, the UV, flow the RG equations to lower energies to see what the high-energy parameters imply for low energies.

    I think that if the scalars are really independent and there's no "universal" way to cancel the divergences, like SUSY, then the degree of fine-tuning from having many light scalars will be "even more extreme", like a power.

    SUSY cancels the quadratic divergences for all the scalars. So yes, I think you outlined another loophole. If there were many Higgs scalars, for example, with randomly scattered masses of order the superpartner scales at 10 TeV, for example, it would be more natural for at least one of the Higgses to remain light, and that could be the observed one.

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