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Explaining the naturalness problem *April 27, 2007*

*Posted by dorigo in internet, news, physics, science.*

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I just read the insightful slides presented by Michelangelo Mangano at IFAE 2007 last month, in his plenary talk titled “*Stato e prospettive della Fisica delle Particelle*” (Status and prospects of Particle Physics). His slides are in English, and you are well advised to have a look at them.

Michelangelo points out from the outset what are the possible outcomes of the searches for the Higgs boson at the LHC. He foresees a situation when:

- the SM Higgs is found, it is light, and everything goes well. In that case, a pressing question to answer will be the one of the naturalness (see below).
- the SM Higgs is not found below 0.8-1 TeV of mass. If that happens, it may be because of either:
- cross section below SM predictions, and that is New Physics;
- Visible branching ratios below SM values, and that is also New Physics;
- H exists but has a mass above 800 GeV, and that, too, means New Physics.

Talking about the naturalness problem, Michelangelo puts things in a way even me and you can understand. He basically says: radiative corrections to the Higgs mass amount to a sum of different terms whose value gets multiplied by the square of the energy at which the Standard Model breaks down. If that energy scale is as large as the Planck mass (the scale at which quantum gravity enters the game), then one has to hypothesize that the several correction terms cancel out to a part in 10^34 (a hundred billionths of a billionth of a billionth of a billionth), if one is to make the Higgs mass smaller than a lead brick.

To see how likely that is (and here is the part where you get to touch things with your hand), he proposes you to do the following experiment: *ask 10 friends to tell you a random number of their liking between -1 and +1, but make it a irrational number. Then, add the ten numbers.* How likely is it that you come up with a number as small as 10^-32 ?

I happen to know the answer: it is the hell of a small chance.

**Michelangelo’s point is that you would rightly conclude that your friends played you a trick, and agreed in advance on the numbers they’d give you! **

And that is what theorists think too: theorists feel that the accurate cancellation of Higgs mass corrections cannot be an accident.

The naturalness problem thus becomes the basis to discuss what solutions appear to make things more credible. All these solution have a thing in common: they tie the Higgs mass to some symmetry that protects it against the quadratic divergence drawn by the Planck mass scale.

If you read this post up to here, you are strongly advised to jump to his talk… No point for me to report more of it, adding to it my own fallacies.

## Comments

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As I understand it, there can be a Higgs mechanism and a Higgs field throughout our Universe, without there being a Higgs boson and the LHC is supposed to sort this out.

I assume that this means that the LHC would produce enough Z and W pair bosons to completely eliminate background contamination, but does the production of W boson pairs guarantee that this comes directly from Higgs decay?

Do we have to directly observe the Higgs to know that there is a Higgs boson rather than a Higgs mechanism without a boson, or can we infer the correct answer the Z and/or W pairs?

Hi

In quantum theory, fields are associated with quanta; they are opposite sides of the same coin. The electromagnetic field is associated with the existence of photons, the chromodynamic colour field is associated with the existence of (confined) gluons, the gravitational field is associated with the existence of gravitons, the electron field is associated with the existence of electrons, the Higgs field is associated with the existence of Higgs Bosons. If a Higgs field is responsible for the particle masses in nature, quanta of that field (Higgs Bosons) will exist as quantized physical excitations of the field. That’s why physicists are so excited by the turn-on of the LHC. For self-consistency of the quantum mechanics of the Higgs field, there is an upper bound on the Higgs Boson mass (the so-called “triviality” bound). For any Higgs Boson mass below the bound imposed by quantum self consistency, the LHC will be able to produce, and the ATLAS and CMS detectors detect, Higgs Bosons. So either we find the Higgs Boson at the LHC (or before), or the standard model is wrong and it’s back to the drawing board. Exciting times ahead!

Hi,

Anomalous, I totally subscribe to your description, although I think Island knows all of it and then some. I can only add that the LHC will produce a embarassing rate of W and Z events, and that Higgs production will be evident only by careful analysis and accounting backgrounds with precise Monte Carlo predictions. This is certainly true if H->WW is the signature (for Mh around 160 GeV or a little below), because Standard Model production of WW pairs is much larger in cross section, although different in kinematics, and because the neutrinos emitted in WW decays prevent the reconstruction of the invariant mass of the system. For ZZ pairs, a reasonable resolution in the momentum of outgoing leptons will suffice for a substantial background rejection, because with four charged leptons you can reconstruct fully the decay and the mass, thereby cutting backgrounds at least tenfold.

Finally, I am not sure I understand Island’s last question, but in principle, if you believe the SM (why shouldn’t you) then you’d have to conclude that we already SAW the Higgs, through its effect on electroweak observable parameters measured at LEP, SLD, and at hadron colliders.

Cheers,

T.

How do you know that you are able to infer a true Higgs field, (rather than some other fundamental field of the Standard Model), from the production of characteristic particles and reactions that are predicted by the standard model to occur up to that point, anyway? I believe in the Standard Model up to the Higgs boson, and then I’m not absolutely sure how to interpret what generaly relativity says about the field with and without a Higgs boson, but I also naively see room for question if the Higgs isn’t directly observed. How do we know that pair of W bosons doesn’t come right out of a field that doesn’t produce a Higgs?

Tommaso, I also see what you’re saying about the “embarassing rate of W and Z events”, making direct observation that much more likely, though, right.?

Hi Island,

a resonance is a resonance. When you see one, you instantly believe there is a particle decay behind. If you saw the peaks of the Y or J/psi family you know what I mean: the picture of two bottom or charm quarks orbiting around each other and then decaying cannot, CANNOT, be an accident. Especially if you look at the decay pattern of charmonium and compare with positronium, for instance.

WW observation of the Higgs is slightly problematic because of the large rate of background processes and because one cannot reconstruct a mass for the resonance. But then you should still see a few ZZ decays (even if the H has a mass significantly lower than 180 GeV you get to produce a few with a virtual Z), and they do resonate. Once that is seen, I get to bet two balls, not one.

Embarassing rate means that at the LHC inclusive W or inclusive Z production are so common processes that CMS and Atlas cannot even afford to collect all of them. They are “embarassingly frequent”, but associated WW or ZZ production is still a rare phenomenon.

Cheers,

T.

How do you argue with reasoning like that?… simple, you don’t.

Beautiful.

*shipwrecked in the Jordan/Brans/Dicke sea*

Symmetry has been a wonderful crutch up to now, but it is only that. If the chemists had been restricted to symmetry in explaining the periodic table of the elements they would have had the same mess elementary physics has now. What we should be doing is looking for simple rules that generate the complicated observed structure.

carlbrannen is correct, as far as I am concerned, but I would add that the dynamics of the universe is geared toward symmetry, regardless of whether it can be obtained absolutely, or not, so that’s where your “simple (thermodynamic) rules” should appear.

Rules like, an inherent asymmetry in the energy of the universe *requires/justifies/defines* an impetus to satisfy the imbalance.

That fixes the arrow of time, while making symmetry an unattainable “goal”, and bang, beware the teleolgy that follows, but boy it sure does explain the near perfectly balanced structure and why the cc is so small, huh?… what a coincidence… NOT!

Anyway, Tommaso, as I said, your logic is perfect, so I must be missing something important. I do not believe that GR can possibly be in conflict with what is observed, but it is also pretty vague about the matter, other than to easily incorperate the Higgs field.

So I guess that my question now is, what effect on the observable electroweak parameters would you expect from a Higgs mechanism that does not rely on the Higgs boson?

What is the observable difference between the two, in other words.

“What effect on the observable electroweak parameters would you expect from a Higgs mechanism that does not rely on the Higgs boson?”

Tough question. My first answer is “Anything goes”. Until one does not specify the model, how can the model parameters be claimed to be affected a way or another ?

More specifically, I think LEP alone demonstrated, and the other experiments together furthered, that there is something circulating in virtual loops within electroweak particles propagators, and that you need to break EW symmetry somehow. Now, a simple Higgs scalar field seems to do both things well, and the best fits indicate it would have to be light. Would other things do? A set of SUSY higgses would too, but you’d have to add more machinery to break SUSY masses. Other models for electroweak symmetry breaking have their own explanation for the observed value of radiative corrections, but I am not the person to ask about them. As for models without a SM Higgs that imply a different value for electroweak parameters from what is observed, well, they are either still-born or dead, so I’d leave them RIP.

All the above is kind of vague because I am not an expert in the theory of electroweak symmetry breaking. I am just a soldier, not a general… Well, ok, let’s say a sarge.

Cheers,

T.

Okay Sarge, thanks, I’m just trying to determine if Einstein could still be right about what causes inertia, (in a specific past discussed model).

It’s important that we get this out in advance or the assumptions will run rampant among theorists about all the crazy possibilities that would explain how the standard model can be correct, yet we still can’t understand gravity. … and may heaven help us when that starts again!

From what you’ve said, I still think it’s going to require direct observation of the Higgs to rule out a field mechanism that doesn’t require the boson… and Dr. E. would be happy about that… ;)

I’m gonna salute ya anyway…

Hi

The question of the correctness of the Higgs mechanism as the origin of mechanical mass in the standard model is competely unrelated to the question of whether GR is the correct low energy effective description of gravity.

If you want a Newtonian analogy, the mass provided by the Higgs field is the “inertial mass” that appears in Newton’s second law. This would be a well defined concept even in the absence of the force of gravity in our universe.

To have it appear in a theory of gravity you need to assume that the charge of an object under gravity (its “gravitational mass”) is proportional to its inertial mass; this is the

equivalence of inertial and gravitational mass assumed by Newton based on the previous observations of Galileo (cf. the experiments with objects dropped from the tower in Pisa). Note that if the value of Newton’s Gravitational Constant G_N is taken to zero then gravity disappears, and there is no way to measure (hence to define) a “gravitational mass”; in the absence of a gravitational force it makes no sense to define a “gravitational charge”.

In relativistic theory, essentially the same division is true: if we take the Lagange density for the particle physics standard model coupled to GR we have (ignoring the cosmological constant term, which is certainly irrelevant for laboratory experiments) a single term specifying the dynamics of gravity, the Einstein-Hilbert term multiplied by G_N the Newtonian Gravitational Constant. Again we can turn off gravity by taking G_N->0 to get the standard model without gravity. But the standard model without gravity still has the problem of generating the “inertial masses” of the leptons, quarks, and electroweak vector bosons. This is what the Higgs mechanism does in the standard model, and what must be done in any correct theory of nature even if the standard model is not the correct description.

P.S. I don’t understand your reference to a “field mechanism that doesn’t require the boson…” As noted in my previous post, if you have a field you have the associated quantum excitations. They may be composite (if the field is) confined, Higgsed, Fermionic or Bosonic, or whatever. But in quantum theory fields have quanta, and the coherent superpostion of virtual quanta produces the field.

The discussing of “what if there is no gravity” is a very interesting one. If G approaches zero, then there is no spacetime curvature, the universe will be perfectly flat and extend to infinity both in time and in space. The end result is this result in a universe of infinite, described by an infinite quantum entropy. In an infinite world, nothing could be unique any more because out of infinity you can always find an exact duplication. I personally think an infinite universe is impossible. So a finite universe mandates the existance of a none-zero gravity to bound the spacetime.

Similarly we can ask what if quantum mechanics doesn’t exist. In another word, what if hbar approaches zero? We are going to end up with infinite many quantum micro-states, and atoms will become infinitely small because the Bohr Radius will be infinitesimal. This again leads to an infinite universe with infinite quantum entropy. If you believe the universe should be finite, then it mandates that we must have a cutoff at microscopic scale, and hbar can not be zero.

You see, by simply demanding that the universe MUST be finite and be describable in finite amount of quantum entropy, you have lead to both gravity AND quantum mechanics. You have unified the two theories by such a simple argument. And it directly explains the Dirac’s Large Number Hypothesis. This is the correct approach where physics should be moving. And I am working on that theory. My name Quantoken reflects that reality. People looking for extra dimentions are wasting their time.

tommaso can go home now. qantcoken is going to solve all of physics!

Hi Carl,

I understand your point, but I would not call symmetry a crutch. It is the source of structure after all, almost everywhere we look. Then, we need to understand the underlying mechanism. And in fact symmetry breaking is something extra…

But you well know all of that. Only, my point is that the interplay between symmetries and conservation laws, and from there to stability of matter through Pauli’s principle or other wonderful incidents, is simply one of the most beautiful things there is to contemplate in our world. Hail to symmetry!

Cheers,

T.

Anomalous cowherd, thank you for your clear explanation.

Quantoken, your ideas might be interesting, but they remain sketchy until you put on the table something exact. One thing I think we all agree on is that there ARE laws of physics which describe the universe, and determine its organization and its evolution. So one cannot argue until one puts his stack of chips on the table behind a set of formulas. Unfortunately, the current status of quantum gravity, string theory, particle physics and cosmology is embarassing in that respect too… So after all I am not against the free discussion of ideas without a clear theoretical framework at their basis.

One point, though: “My name Quantoken reflects that reality.” –> until you exit anonymity, your name is only a kind concession from me. It identifies you only until somebody decides to use the same name, as happened a month ago here to Guess Who.

Cheers,

T.

I see people are talking about me. ;)

Busy, busy, but can’t resist making two quicks comments regarding the “anomalous coward/cowherd” posts (love both names).

#1: It is NOT obvious that the Higgs mechanism requires a Higgs boson. Even when you start out with fundamental scalars in a Goldstone-style potential and couple them to gauge fields, the question of whether one or more of those scalars survive as independent degrees of freedom (which you can identify with particles) after symmetry breaking depends on the group-theoretic details of the model. Remember, in the Standard Model you start out with four real scalar components; three become the longitudinal components of the W+- and Z0, only one lives on as an independent Higgs boson. If you move on to technicolor-style models, where the scalars really are fermion bound states, it is even less obvious that there must be a Higgs boson.

#2: The Einstein-Hilbert term describes the dynamics of the metric. You can set it to zero and still have gravity in your Lagrangian: just keep the non-Minkowski metric in all Lorentz index contractions. What you get then is standard QFT on curved spacetime, i.e. you consider the metric as a given fixed background and ignore the backreaction from your fields. It’s obviously an approximation, but given the weakness of gravity compared to the other interactions it’s an excellent one below energy densities way beyond anything we are close to reaching.

Dorigo:

I agree with you one should be able to stack chips behind a set of formulas. My theory has some sounding ideas to start with. But it is indeed still in a very sketching state. If have a set of formulas that I can stack my chips on, I should have been publishing books and going around giving lectures instead of anonymous discussion of my ideas on blogs. It is still in early development. But it is the only thing so far that really put GR and QM in one simple framework, and only thing that gives a rational explanation of Dirac Large Number Hypothesis. That alone should make it interesting. My ideas are easily to describe logically, but to form some exact mathematics formulation that is harder. I know string theorists could easily throw out tons of mathematics formalism that can scare a lot of people to death, but none of them describes any physical reality so none of they are any where close to useful.

If you are interested have a look at some of my old blog entries. I calculated netron mass to 9 decimal place accuracy, CMB temperature to exactly within the experimental error bar, solar constant, helium abundance, baron density and “age” of universe, even the whole framework remains sketchy. All calculations are without a single freely adjustable parameter. The only thing I can not get an accurate result is my predicted G is larger than the official value by 2%, although we know the G is not very accurately determined.

If I were younger I would study more human nature. Philosophers!Before casting a stone, know thyself and the best way to do that is look at others as if looking into a mirror.

Geuss Who saved me…

I dunno, who…?… heheh

Won’t the perturbative computation of radiative corrections to the Higgs mass break down far before the Planck scale when the cut off approaches the scale of symmetry breaking (i.e., the height of the Mexican hat in the Mexican hat potential)? After that the appropriate perturbative expansion will be around Φ = 0 and everything starts off massless.

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