Continuing the previous post... What Alejandro Rivero actually said to me was,
"Yesterday I went to a popularisation talk of De Rujula, and I was thinking on the mismatch between vacuum energy due to higgs and vacuum energy seen in astrophysics. It sounds as the problem with the string energy scale, QCD string vs "gravity" string."
This remark helped to suggest a crackpot interpretation of the preceding Higgs-VEV numerology, as a sign that the higgsing in the Standard Model is done by the total vacuum energy, which mysteriously conforms to the new ansatz that "the zero-point energy of a quantum field is equal to the mass of one quantum of the field".
Now I want to take things a little further... One of the "movements" spun off from string theory is that of "large extra dimensions" (also sometimes called "universal extra dimensions"). In such models, the Planck scale can come all the way down to the TeV scale. Under such circumstances, the QCD string could well become a fundamental string. I don't remember the LED model-builders ever talking about this possibility, but it certainly dovetails with Alejandro's other ideas about the "sBootstrap".
So here is the new twist. As he observes, the astrophysical dark energy, which is often interpreted as vacuum energy, is orders of magnitude away from the Higgs field vacuum energy. But what if... we assume the new crackpot ansatz, that "higgsing is done by the total vacuum energy", and that the cosmologically relevant vacuum energy has been diluted by a large-extra-dimensions mechanism, perhaps similar to Randall-Sundrum? Or even by a non-geometric, noncommutative analogue of LED...
Thursday, June 13, 2013
Friday, June 7, 2013
Higgsed by the vacuum?
The Higgs mechanism for generating mass can be realized in many different ways, not just the one employed in the standard model. Theories can have multiple Higgs fields, in string theory a wide variety of scalar quantities can serve as the Higgs, and so on.
Meanwhile, what to do with the vacuum energy or zero-point energy of quantum field theory is one of the subject's outstanding problems. The leading idea still seems to be that there are numerous positive and negative contributions to the cosmological constant, and they have to cancel for anthropic reasons, but otherwise there's no particular pattern to it. But in the literature you can find numerous unlikely ideas for why the vacuum energy is cancelled or cut off or doesn't gravitate.
I mention all this as a prelude to a discussion of the curious relation mentioned in the previous post. I should mention two further things: in the standard model, it's the Higgs VEV, not the Higgs boson mass, which determines the mass scale of the other particles; and, in the standard model, the Higgs VEV and the Higgs boson mass are independent quantities, separately determined by different parameters in the Higgs potential.
Conceivably, a specific model of the Higgs field could produce a relation between Higgs VEV and Higgs boson mass. But what are we to make of a formula which relates the magnitude of the Higgs VEV to every particle with mass? And furthermore, each such particle appears exactly once, and in the same way, in the formula.
So here is today's wacky concept: (1) The zero-point energy of a quantum field is equal to the mass of one quantum of the field; (2) The sum of the squares of these energies provides the v^2 term in the Higgs potential of the standard model. Thus, it is the vacuum energy (as described by this mysterious new ansatz) which does the Higgsing.
There is a circular or bootstrap aspect to this idea, since the masses appearing in (1) are themselves supposed to be generated by yukawa couplings to this "vacuum energy" whose magnitude is a function of those masses.
I am quite aware that, even given my initial remarks about the variety of realizations of the Higgs mechanism and the various desperate ideas meant to deal with the vacuum energy problem, this is a proposal that doesn't make much sense, according to the way these concepts are normally employed. But it's the only idea I have, to explain what that formula might mean and where it could come from.
I especially regard it as significant that each massive species appears once and once only. It somehow suggests that a property of each field as a whole, rather than a property of quanta of the field, is at work here.
Meanwhile, what to do with the vacuum energy or zero-point energy of quantum field theory is one of the subject's outstanding problems. The leading idea still seems to be that there are numerous positive and negative contributions to the cosmological constant, and they have to cancel for anthropic reasons, but otherwise there's no particular pattern to it. But in the literature you can find numerous unlikely ideas for why the vacuum energy is cancelled or cut off or doesn't gravitate.
I mention all this as a prelude to a discussion of the curious relation mentioned in the previous post. I should mention two further things: in the standard model, it's the Higgs VEV, not the Higgs boson mass, which determines the mass scale of the other particles; and, in the standard model, the Higgs VEV and the Higgs boson mass are independent quantities, separately determined by different parameters in the Higgs potential.
Conceivably, a specific model of the Higgs field could produce a relation between Higgs VEV and Higgs boson mass. But what are we to make of a formula which relates the magnitude of the Higgs VEV to every particle with mass? And furthermore, each such particle appears exactly once, and in the same way, in the formula.
So here is today's wacky concept: (1) The zero-point energy of a quantum field is equal to the mass of one quantum of the field; (2) The sum of the squares of these energies provides the v^2 term in the Higgs potential of the standard model. Thus, it is the vacuum energy (as described by this mysterious new ansatz) which does the Higgsing.
There is a circular or bootstrap aspect to this idea, since the masses appearing in (1) are themselves supposed to be generated by yukawa couplings to this "vacuum energy" whose magnitude is a function of those masses.
I am quite aware that, even given my initial remarks about the variety of realizations of the Higgs mechanism and the various desperate ideas meant to deal with the vacuum energy problem, this is a proposal that doesn't make much sense, according to the way these concepts are normally employed. But it's the only idea I have, to explain what that formula might mean and where it could come from.
I especially regard it as significant that each massive species appears once and once only. It somehow suggests that a property of each field as a whole, rather than a property of quanta of the field, is at work here.
Wednesday, May 22, 2013
t, H, W, Z again
(A continuation of "t, H, W, Z".)
A recent paper informs us that
(mH)2 + (mW)2 + (mZ)2 + Σquarks(mq)2 + Σleptons(ml)2 = (HiggsVEV)2
... almost identical to the formula
(mH)2 + (mW)2 + (mZ)2 + (Σquarksmq)2 + (Σleptonsml)2 = (HiggsVEV)2
which appeared as part of the very first exercise of physics numerology examined by this blog (in July 2011), due to A. Garcés Doz. (I cannot find the formula in any of his papers at vixra.org - search for "author=doz" for a full listing - but perhaps it's there too.)
The similarity may be attributed to the fact that the top mass, mt, is so much greater than all the other fermions, that it hardly matters whether you add the masses and square them, or square the masses and then add them. Just the following formula still works quite well:
(mH)2 + (mW)2 + (mZ)2 + (mt)2 = (HiggsVEV)2
Curiously, when Garcés Doz posted his formula two years ago, he was using mH = 119 GeV, a value which must have come from someone's supersymmetric model; but the value of the Higgs VEV is then off by a few GeV. It actually works much better using mH = 125 GeV, the measured value; so he could have actually predicted the Higgs mass using this formula.
(Caution: I have been a little careless in checking these facts and calculations; will check them more closely, later.)
A recent paper informs us that
(mH)2 + (mW)2 + (mZ)2 + Σquarks(mq)2 + Σleptons(ml)2 = (HiggsVEV)2
... almost identical to the formula
(mH)2 + (mW)2 + (mZ)2 + (Σquarksmq)2 + (Σleptonsml)2 = (HiggsVEV)2
which appeared as part of the very first exercise of physics numerology examined by this blog (in July 2011), due to A. Garcés Doz. (I cannot find the formula in any of his papers at vixra.org - search for "author=doz" for a full listing - but perhaps it's there too.)
The similarity may be attributed to the fact that the top mass, mt, is so much greater than all the other fermions, that it hardly matters whether you add the masses and square them, or square the masses and then add them. Just the following formula still works quite well:
(mH)2 + (mW)2 + (mZ)2 + (mt)2 = (HiggsVEV)2
Curiously, when Garcés Doz posted his formula two years ago, he was using mH = 119 GeV, a value which must have come from someone's supersymmetric model; but the value of the Higgs VEV is then off by a few GeV. It actually works much better using mH = 125 GeV, the measured value; so he could have actually predicted the Higgs mass using this formula.
(Caution: I have been a little careless in checking these facts and calculations; will check them more closely, later.)
Thursday, May 9, 2013
Cosmic numerology from Texas
Sunday, April 28, 2013
A model-building resource for cosmic numerologists
"Stationary dark energy" presents a model of energy transfer between dark energy, dark matter, and baryonic matter, in which the density fractions can asymptote to desired values: "Choosing the parameters we can ensure that the final state is, for instance, Ωϕ = 0.7 and Ωm = 0.3. Once reached, these values will remain fixed forever." (ϕ is a dark-energy scalar.) So if your theory of everything requires that ΩDE should be 2/3, or 1-1/π, or 9/4π, here's a phenomenological model, complete with equations, that you can build on.
Thursday, April 25, 2013
2/3^n
The quantities 2/3, 2/9, 2/27 show up in the world of Koide numerology as angles (in radian units) appearing in mass formulas.
Last year, Marni Sheppeard had a paper in which she tried to derive Louise Riofrio's cosmological dark-sector numerology from the "2/9".
This year, the Planck satellite has given us some new estimates for the dark-sector density fractions. As already noted here, one quantity is close to 1 - 1/π, which could be the starting point for a new cosmic numerology.
However, it amused me to notice that, with much less precision, the density fractions for dark energy, dark matter, and baryonic matter, are not too far from that sequence, 2/3, 2/9, 2/27.
In conventional cosmology, all these density fractions evolve throughout the history of the universe, such that it shouldn't make much sense to focus on their values at a specific moment in cosmic history (like now) as a clue to anything deep.
However, it's also true that conventional cosmology has a notorious multiple coincidence problem in explaining why those density fractions are even of the same order of magnitude. (Some conventional papers trying to explain these coincidences: 1 2. A less conventional paper: 3.)
While it's very unlikely that the cosmic densities are actually such a direct echo of whatever it is that produces the Koide patterns... it might still be worth trying to make a model in which that is the case, because it would take us in new directions and make us think of new things.
So I'm recording here an idea about where to start in such an effort. It's simply the nuMSM of Asaka and Shaposhnikov, coupled to the cosmon field of Wetterich, which for him serves as both inflaton and dynamical dark energy. And in the quest for a deeper theory, one might start with Q6 symmetry.
What is the logic of this proposal? The angle 2/9, like Koide's original formula, applies to leptons. But here we want to see it show up as the cosmic density fraction for dark matter; and in the nuMSM, the dark matter is leptonic, a keV-mass sterile neutrino.
Meanwhile, Wetterich's cosmology is wacky enough that the universe might even be shrinking, rather than expanding; and yet (he says; I haven't verified) it can be transformed through a change of frame into a far more standard cosmology. It's the best opportunity I can see, to start with something that's at least semi-orthodox, but in which it might actually make sense to model the time evolution of the density fractions as "2/3^n + ϵ_n(t)", the second term being a time-dependent correction with - one hopes - a deeper explanation.
Finally, the finite group Q6 shows up in an attempt to explain the nuMSM's odd neutrino mass spectrum. The hope would be that this could be joined up with an explanation of Koide relations, perhaps via the group S3.
Last year, Marni Sheppeard had a paper in which she tried to derive Louise Riofrio's cosmological dark-sector numerology from the "2/9".
This year, the Planck satellite has given us some new estimates for the dark-sector density fractions. As already noted here, one quantity is close to 1 - 1/π, which could be the starting point for a new cosmic numerology.
However, it amused me to notice that, with much less precision, the density fractions for dark energy, dark matter, and baryonic matter, are not too far from that sequence, 2/3, 2/9, 2/27.
In conventional cosmology, all these density fractions evolve throughout the history of the universe, such that it shouldn't make much sense to focus on their values at a specific moment in cosmic history (like now) as a clue to anything deep.
However, it's also true that conventional cosmology has a notorious multiple coincidence problem in explaining why those density fractions are even of the same order of magnitude. (Some conventional papers trying to explain these coincidences: 1 2. A less conventional paper: 3.)
While it's very unlikely that the cosmic densities are actually such a direct echo of whatever it is that produces the Koide patterns... it might still be worth trying to make a model in which that is the case, because it would take us in new directions and make us think of new things.
So I'm recording here an idea about where to start in such an effort. It's simply the nuMSM of Asaka and Shaposhnikov, coupled to the cosmon field of Wetterich, which for him serves as both inflaton and dynamical dark energy. And in the quest for a deeper theory, one might start with Q6 symmetry.
What is the logic of this proposal? The angle 2/9, like Koide's original formula, applies to leptons. But here we want to see it show up as the cosmic density fraction for dark matter; and in the nuMSM, the dark matter is leptonic, a keV-mass sterile neutrino.
Meanwhile, Wetterich's cosmology is wacky enough that the universe might even be shrinking, rather than expanding; and yet (he says; I haven't verified) it can be transformed through a change of frame into a far more standard cosmology. It's the best opportunity I can see, to start with something that's at least semi-orthodox, but in which it might actually make sense to model the time evolution of the density fractions as "2/3^n + ϵ_n(t)", the second term being a time-dependent correction with - one hopes - a deeper explanation.
Finally, the finite group Q6 shows up in an attempt to explain the nuMSM's odd neutrino mass spectrum. The hope would be that this could be joined up with an explanation of Koide relations, perhaps via the group S3.
Tuesday, April 9, 2013
Return of the dark lepton jets
A year ago I made a silly post, "Dark matter and powers of two", proposing a connection between Weniger's gamma-ray line, and the alleged "lepton jets" that had caused a brief blog-scandal (when Tommaso Dorigo opined that a theory paper by Arkani-Hamed and Weiner must have been written with advance knowledge of the lepton-jet claim; Tommaso later retracted his allegation).
Today I see two papers talking about multi-tau states in connection with the AMS-02 confirmation of an excess positron fraction at high energies, that might be due to dark matter annihilation: Cholis and Hooper, and Jin, Wu and Zhou... I suppose the serious physics issue is this: it would be interesting if the lepton jets were real, and if they had a role in producing the positron excess; and conversely, it would be interesting if the intermediate states producing the lepton jets (assuming them to be real!) were dark-matter states.
Today I see two papers talking about multi-tau states in connection with the AMS-02 confirmation of an excess positron fraction at high energies, that might be due to dark matter annihilation: Cholis and Hooper, and Jin, Wu and Zhou... I suppose the serious physics issue is this: it would be interesting if the lepton jets were real, and if they had a role in producing the positron excess; and conversely, it would be interesting if the intermediate states producing the lepton jets (assuming them to be real!) were dark-matter states.
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