Kahana and Kahana predicted Higgs mass, top mass in 1993

At dinner, I spoke to Peter Higgs and said that I hope he wasn't offended by my statement - he wasn't. Then he said, "You're from Brookhaven, right. Make sure to tell Sid Kahana that he was right about the top quark 175 GeV and the Higgs boson 125 GeV".
--M.J.Tannenbaum, "Waiting for the W and the Higgs", arXiv:1608.06934

In 2009, Shaposhnikov and Wetterich successfully predicted the Higgs boson mass, by assuming that quantum gravity is asymptotically safe. Asymptotic safety remains a minority research program, but the paper itself is now well-known among people studying the metastability of the electroweak vacuum, with over 100 citations.

However, there was a paper which in 1993, predicted the Higgs mass and the top quark mass, and which remains almost unknown - though it was known to Peter Higgs himself, as the quote above reveals.

I'd say there are three relevant papers.

D.E. Kahana, S.H. Kahana. "Standard Model Bosons As Composite Particles". Phys.Rev. D43 (1991) 2361-2368. inSPIRE record

D.E. Kahana, S.H. Kahana. "Top and Higgs Masses in Dynamical Symmetry Breaking". Phys.Rev. D52 (1995) 3065-3071. arXiv:hep-ph/9312316

D.E. Kahana, S.H. Kahana. "Higgs and Top Masses from Dynamical Symmetry Breaking - Revisited". arXiv:1112.2794

The 1991 paper (available as a KEK scanned document) introduces the model. The 1993 paper (published in 1995) makes the predictions. The 2011 paper revisits the predictions on the eve of the official Higgs discovery.

The model itself is based on the well-known NJL model of Nambu and Jona-Lasinio. The NJL model is an ancestor of the standard model's electroweak+Higgs sectors, and it's also an approximation to the low-energy scalar sector of QCD (i.e. pions and sigma meson), and it is still studied in many forms.

Kahana and Kahana modify it in an unusual way. The NJL model has emergent scalars and pseudoscalars. Kahana and Kahana add vector interactions in order to produce the electroweak gauge bosons as bound states.

They do a few other things that seem a little strange, too. But in the end they get the Higgs boson mass, the top quark mass, and even the weak mixing angle. And it's a renormalization group argument, as is that used by Shaposhnikov and Wetterich. There may even be some relationship.

This forum contains a number of fans of the prediction from asymptotic safety (I am one of them); I think we should also want to understand how this other, earlier, broader prediction works too.

The approximate top and Higgs mass were known from precision electroweak experiments, everything else is cherry-picking. Thomas Schucker maintained a list of Higgs mass predictions until 2011: 0708.3344. In the relevant range, there was about 1 prediction per GeV, with a typical uncertainty of several GeV this means many predictions had to be "right" just by chance.

Two more entries from the prediction list as example:

Feldstein, Hall & Watari 2006, "superstring inspired landscape of vacua and some probability density for the parameters of the Higgs potential"
Higgs mass 121 +- 6 GeV, and a postdiction of the top mass as 176 +- 2 GeV.

Djouadi, Heinemeyer, Mondragon & Zoupanos 2004, "a supersymmetric version of SU (5)"
Higgs mass 122 +- 10 GeV, and a postdiction of the top mass as 174-183 GeV.Shaposhnikov and Wetterich also made a prediction of 150 +- 24 GeV with a slightly different approach.

what are the implications of theories that predict the wrong Higgs mass i.e SUSy theories that predict too low or too high, connes noncommutative geometry etc?

Well, that particular model with this exact set of assumptions is ruled out then.

mfb said:

Well, that particular model with this exact set of assumptions is ruled out then.

the models that predicted a 126 gev higgs would seem to support those models with those assumptions

It is a weak piece of Bayesian evidence, but given the large number of predictions that doesn't say anything.

mfb said:

It is a weak piece of Bayesian evidence, but given the large number of predictions that doesn't say anything.

what about the naturalness problem in the higgs sector? the whole point of SUSY and MSSM is to explain why the higgs is so light when GUT or QG scale physics would result in a Planck scale sized higgs mass.

do those models that predicted the correct higgs mass without SUSY, explain the naturalness problem? i.e does 2009, Shaposhnikov and Wetterich - quantum gravity is asymptotically safe show there's no naturalness problem

mfb said:

The approximate top and Higgs mass were known from precision electroweak experiments

I might agree about the top, not about the Higgs. More importantly, we now know that they are "near-critical", and the Kahana model apparently offers an explanation of this. It would be folly for theorists to refuse to understand it.

I didn't find a blueband plot from earlier than 1995, but here is the Higgs mass estimate from 2008. "Between 115 and 150" is a reasonable estimate based on it.

mitchell porter said:

I might agree about the top, not about the Higgs. More importantly, we now know that they are "near-critical", and the Kahana model apparently offers an explanation of this. It would be folly for theorists to refuse to understand it.

Very interesting paper! I actualy chuckled out loud reading the name of the last author :')

Their idea that near-criticality of physical constants (such as the Higgs mass and the cosmological constant) might be a way to explain specific numerics statistically without resorting to any talk about anthropic arguments or naturalness is as far as I can tell an actually legitimate argument in favor of some kind of multiverse; I myself would just call it a state space and avoid the need for invoking a multiverse altogether. In any case, I like that they both look at dimensional as well as dimensionless couplings and take the possible qualitative differences between these two forms of near-criticality seriously.

After reading the paper, I'm tempted to even take things one step further: assuming the validity of (near)criticality as a selection mechanism, is it possible to select the correct compactification of extra dimensions from the ##10^{500}## landscape using similar arguments? Has this already been tried? I kind of dislike string theory let alone reviewing its literature, but I'd honestly be surprised if this idea hasn't been tried already.

mitchell porter said:

In 2009, Shaposhnikov and Wetterich successfully predicted the Higgs boson mass, by assuming that quantum gravity is asymptotically safe. Asymptotic safety remains a minority research program, but the paper itself is now well-known among people studying the metastability of the electroweak vacuum, with over 100 citations.

However, there was a paper which in 1993, predicted the Higgs mass and the top quark mass, and which remains almost unknown - though it was known to Peter Higgs himself, as the quote above reveals.

I'd say there are three relevant papers.

D.E. Kahana, S.H. Kahana. "Standard Model Bosons As Composite Particles". Phys.Rev. D43 (1991) 2361-2368. inSPIRE record

D.E. Kahana, S.H. Kahana. "Top and Higgs Masses in Dynamical Symmetry Breaking". Phys.Rev. D52 (1995) 3065-3071. arXiv:hep-ph/9312316

D.E. Kahana, S.H. Kahana. "Higgs and Top Masses from Dynamical Symmetry Breaking - Revisited". arXiv:1112.2794

The 1991 paper (available as a KEK scanned document) introduces the model. The 1993 paper (published in 1995) makes the predictions. The 2011 paper revisits the predictions on the eve of the official Higgs discovery.

The model itself is based on the well-known NJL model of Nambu and Jona-Lasinio. The NJL model is an ancestor of the standard model's electroweak+Higgs sectors, and it's also an approximation to the low-energy scalar sector of QCD (i.e. pions and sigma meson), and it is still studied in many forms.

Kahana and Kahana modify it in an unusual way. The NJL model has emergent scalars and pseudoscalars. Kahana and Kahana add vector interactions in order to produce the electroweak gauge bosons as bound states.

They do a few other things that seem a little strange, too. But in the end they get the Higgs boson mass, the top quark mass, and even the weak mixing angle. And it's a renormalization group argument, as is that used by Shaposhnikov and Wetterich. There may even be some relationship.

This forum contains a number of fans of the prediction from asymptotic safety (I am one of them); I think we should also want to understand how this other, earlier, broader prediction works too.

You are correct that my father and brother first correctly predicted the mass. This is Sid's daughter.
He was friends, and worked with Peter Higgs, when he was a graduate student at Edinburgh. He still sent my father holiday cards and one of them said congratulations on the prediction of the mass. I’m not sure why this and the papers are not well known, I was unaware of that. It’s sad if that’s true.

My father was working on a new particle discovery to do with neutrinos as well. Unfortunately, he was murdered by Covid, and was not able to complete the work. Rip to my father, a brilliant man.

Here is a pic of that card…

sue said:

This is Sid's daughter. [...] I’m not sure why this and the papers are not well known, I was unaware of that.

Thank you for stopping by! You've encouraged me to look at the papers again, along with the background concepts ("NJL model", "NJL model with vector interactions"), and I'm actually inclined to think that they are telling us something about reality.

That might seem obvious, given that they got the numbers right, so far in advance of experiment. But there's always so many tantalizing ideas, and they can't all be right. What now encourages me to be optimistic about this one, is that it doesn't make big theoretical commitments. It takes a way of thinking which in one form ("generalized NJL model") is simply equivalent to the standard model, and adds some extra boundary conditions to it.

So I think, like the better known paper by Shaposhnikov and Wetterich, it's telling us something important about high-energy physics. But why is it so little known? It descends from the work of one Nobelist (Nambu, the N in NJL), and was appreciated by another Nobelist (Higgs)...

Part of the reason must simply be, that it doesn't fit the dominant paradigms. The NJL model just isn't a standard part of thinking about new physics. Instead, it appears most often in low-energy theories of hadrons, as a way to sidestep the intractable complexities of quark-gluon strong interactions. Also, the Kahanas don't predict new particles, and there is a big theoretical bias in favor of ideas that predict new particles, because that gives experiment something to look for.

Unlike some other neglected ideas, there's nothing in these papers that is actually at odds with the basic paradigms of quantum field theory, or even string theory. NJL-style models absolutely can arise within gauge theories and string theories. It's just not the kind of answer that the mainstream was looking for!

Yes that could be one reason. You would have to talk to my brother about the more technical things. I am not a physicist and it has been a very traumatic time and also a while since my father talked about it. I think the new particle he was working on was something all together different.

He first became known in his early career for doing another calculation ( not the one he did on Salam’s suggestion).His thesis advisor was also a nobel winner from Pakistan, Salam I think, and suggested he do a calculation on something. Which he did, in a miraculously quick fashion. But then he was called back to Canada because his brother was ill and he never wrote the calculation down. He had to spend a lot of time caring for his brother who was in a crisis then. Later he said he couldn’t remember it anymore well enough to recreate it. I hope you and others continue to explore the possibilities of their ideas/ work.

* I thought someone else posted here some other articles related to this read, after I first replied but I can’t see them now, if anyone knows let me know. I would like to read them. Maybe it was somewhere else.

sue said:

Unfortunately, he was murdered by Covid, and was not able to complete the work. Rip to my father, a brilliant man.

My condolences. A tragedy for humanity and science as well as for your family.

mitchell porter said:

Part of the reason must simply be, that it doesn't fit the dominant paradigms. The NJL model just isn't a standard part of thinking about new physics. Instead, it appears most often in low-energy theories of hadrons, as a way to sidestep the intractable complexities of quark-gluon strong interactions. Also, the Kahanas don't predict new particles, and there is a big theoretical bias in favor of ideas that predict new particles, because that gives experiment something to look for.

Unlike some other neglected ideas, there's nothing in these papers that is actually at odds with the basic paradigms of quantum field theory, or even string theory. NJL-style models absolutely can arise within gauge theories and string theories. It's just not the kind of answer that the mainstream was looking for!

I think that part of the issue is the focus on the composite boson model, which reads to a casual observer a lot like the Technicolor composite Higgs boson model which fell apart to a great extent when a seemingly fundamental Higgs boson with properties and decays consistent with a Standard Model Higgs boson was discovered starting in 2012 and with each new data release constrained to be more similar to the SM Higgs. Whether this criticism is fair or not as applied to this series of papers is another question.

Likewise predictions that were close based upon supersymmetry models and SU(5) unifications gathered less attention because the LHC, direct dark matter detection experiments, and non-detection of proton decay at longer and longer mean lifetimes for a proton, have weakened the most plausible parameters spaces for supersymmetry and SU(5) unifications.

In contrast, asymptotic safety gravity didn't have to contend with unfavorable results from collider physics. There isn't much affirmative evidence to single it out relative to other theoretical models in quantum gravity, but there really isn't anything to rule it out either.

The focus on the renormalization group evolution in both the work of Shaposhnikov and Wetterich, and in the work of Kahana and Kahana, certainly makes a lot of sense.

We can calculate beta function formulas for the top quark and Higgs boson exactly, without knowing exact measured values of the physical constants that need to be plugged in, from the Standard Model. By 1993, we knew lots of the physical constants at satisfactory levels of precision and we had a reasonable ballpark range for the physical constants we knew with less precision, allowing for a much more focused inquiry. We also knew already back in 1993 the theoretical relationship in electroweak theory of the W boson, Z boson, top quark, and Higgs boson masses.

Both pairs of scientists were building on this foundation of what was already known to make the final leap into the unknown and conjectural points.

Asymptotic gravity and the NJL model also both have solid foundations outside electroweak theory, affording a patina of respectability and plausibility to the leap to use these methods in the basically electroweak sector matters of estimating the Higgs and top masses.

ohwilleke said:

My condolences. A tragedy for humanity and science as well as for your family.

Thank you Losing him in this way was the most painful thing and always will be, but it would have always been the worst loss for me whatever the circumstances. I understand it is a loss for those as well.