## Cracked the Fermion Mass Puzzle!

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

### Cracked the Fermion Mass Puzzle!

Dear Friends,

I just posted a new file at https://jayryablon.files.wordpress.com/ ... -9-spf.pdf. Although this is a midstream draft, I want to get this into the public domain as fast as possible because it is as important to physics as can be.

I wanted you all to be the first to know that I have solved a very substantial part of the fermion mass puzzle! This proceeds from my earlier work on Dirac-Kaluza-Klein (DKK) theory. First, I connect the scalar of Kaluza-Klein theory to the Higgs field. Then I use that field to generate fermion masses. Only yesterday and today I completed and wrote up the calculations which take the six seemingly-independent quark masses, and express them in terms of the three real CKM mixing angles and the Fermi vev, within all experimental errors. Six seemingly-independent natural energy numbers whittled down to only two. This final piece of the fermion mass-to-CKM angle connection is in (13.6) of the still partially-completed section 13. Once I had this nailed, I stopped right there to make this post. I am still in that state of awe that one gets when having firmly explained empirical data that has not been explained before. Last night I had two of the three angles already connected with the up, charm and top quarks. Today I embarked on the calculation with the down, strange and bottom quarks that nailed the final third angle.

Tomorrow I will finish the first draft of section 13 and start the same exercise for the leptons. I already know how to get to the neutrino masses. As it turns out, the charged lepton masses are still resistant; they may take some more pondering.

Anyway, as I said, the minute the results hit the page for the third angle, I wanted this out in public. So here it is!

Jay
Yablon
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### Re: Cracked the Fermion Mass Puzzle!

Take a look at (13.2) which is 4.279 GeV, and the Fermi vev which is 246.2196508 GeV. These are the two minima required for the potential V used to extract the Higgs field. This means that there also has to be a maximum somewhere between these numbers.

I took an educated guess that the maximum should be right at the Higgs mass. It turns out that the Higgs mass being empirically observed is 125.18 GeV +/- 0.16 GeV is smack dab in the middle of the two minima! Average the vacua, and within the error bars, you get the Higgs mass!

Bingo! Again! I just discovered this three minutes ago, plus the time to write this note. Now I have a way to form higher order terms in the potential V, and further tighten the values for various masses.
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### Re: Cracked the Fermion Mass Puzzle!

Yablon wrote:Take a look at (13.2) which is 4.279 GeV, and the Fermi vev which is 246.2196508 GeV. These are the two minima required for the potential V used to extract the Higgs field. This means that there also has to be a maximum somewhere between these numbers...

I'm confused. If 4.279 GeV and 246.2196508 GeV are minima, how can there be a maximum between them?
FrediFizzx
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### Re: Cracked the Fermion Mass Puzzle!

FrediFizzx wrote:
Yablon wrote:Take a look at (13.2) which is 4.279 GeV, and the Fermi vev which is 246.2196508 GeV. These are the two minima required for the potential V used to extract the Higgs field. This means that there also has to be a maximum somewhere between these numbers...

I'm confused. If 4.279 GeV and 246.2196508 GeV are minima, how can there be a maximum between them?

Simple example:$y=-cos(x)$. Minimum $y=-1$ at $x=0$. Minimum $y=-1$ at $x=2 \pi$. Maximum $y=1$ between them at $x=\pi$.

Look at this: https://www.google.com/imgres?imgurl=ht ... mrc&uact=8

and imagine a second local, not global minimum (a "little dipper") close to $x=0$ on both sides of $x=0$.
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### Re: Cracked the Fermion Mass Puzzle!

Yablon wrote:
FrediFizzx wrote:
Yablon wrote:Take a look at (13.2) which is 4.279 GeV, and the Fermi vev which is 246.2196508 GeV. These are the two minima required for the potential V used to extract the Higgs field. This means that there also has to be a maximum somewhere between these numbers...

I'm confused. If 4.279 GeV and 246.2196508 GeV are minima, how can there be a maximum between them?

Simple example:$y=-cos(x)$. Minimum $y=-1$ at $x=0$. Minimum $y=-1$ at $x=2 \pi$. Maximum $y=1$ between them at $x=\pi$.

Look at this: https://www.google.com/imgres?imgurl=ht ... mrc&uact=8

and imagine a second local, not global minimum (a "little dipper") close to $x=0$ on both sides of $x=0$.

So if the x axis is energy then I guess it is all shifted over to the right side of x = 0. Then what does the y axis represent physically?
.
FrediFizzx
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### Re: Cracked the Fermion Mass Puzzle!

FrediFizzx wrote:
Yablon wrote:
FrediFizzx wrote:
Yablon wrote:Take a look at (13.2) which is 4.279 GeV, and the Fermi vev which is 246.2196508 GeV. These are the two minima required for the potential V used to extract the Higgs field. This means that there also has to be a maximum somewhere between these numbers...

I'm confused. If 4.279 GeV and 246.2196508 GeV are minima, how can there be a maximum between them?

Simple example:$y=-cos(x)$. Minimum $y=-1$ at $x=0$. Minimum $y=-1$ at $x=2 \pi$. Maximum $y=1$ between them at $x=\pi$.

Look at this: https://www.google.com/imgres?imgurl=ht ... mrc&uact=8

and imagine a second local, not global minimum (a "little dipper") close to $x=0$ on both sides of $x=0$.

So if the x axis is energy then I guess it is all shifted over to the right side of x = 0. Then what does the y axis represent physically?
.

Fred, it will be better for you to read the writeup once I am done. But here are four Figures I just prepared that will go in the paper:

https://jayryablon.files.wordpress.com/ ... gure-3.pdf
https://jayryablon.files.wordpress.com/ ... gure-4.pdf
https://jayryablon.files.wordpress.com/ ... gure-5.pdf
https://jayryablon.files.wordpress.com/ ... gure-6.pdf

Keep in mind that V has dimensions of energy to the fourth power. So Figure 3 shows the whole V curve, 4 shows a blowup of the middle, and 5 and 6 are the same but take the fourth roots so energy along both axes is scaled identically. Note how the Higgs mass establishes the second maximum in these curves.

I hope to post a revised draft with these new figures in the next 48-72 hours.

Jay

PS: I have now also fitted the mixing angles for the leptons, similarly to what I did for the quarks.
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### Re: Cracked the Fermion Mass Puzzle!

OK, all, I just finished the first draft of section 14, which along with the second part of section 13 is new since the post a few days ago. I have not even proofread this new section, because I want it in the public domain fast. Link is at:

https://jayryablon.files.wordpress.com/ ... 10-spf.pdf

The Higgs mass being smack in the middle of two vacuums which I posted about the other day five minutes after I discovered it, is now formalized at (14.3). This may well be the single most important empirical finding of the paper, because it not only gives a theoretical explanation for the Higgs mass and therefore, after more than 40 years for the$\lambda$ parameter in Higgs theory, but it then takes the Higgs mass an uses it as the driving element in the potential plots of new Figures 3 through 6. The role of the Higgs in beta decay is another very nifty new insight.

After proofing this I am on to leptons, and I can tell you that following the same approach I used for the quarks, I have already connected the electron, muon and tauon masses to the neutrino mixing angles. More generally, I have already here taken five of six quark masses and connected them to other known data thus reducing by 5, the number of independent data items needed to understand the physical world. By the end, I will do the same for the leptons, which will include obtaining ratios for the neutrino masses one to the other, and showing how the neutrinos having masses as close to zero as can be, is because for the leptons, there is a sharp Higgs potential minimum centered at zero which is the "well" that the neutrinos live in. All the other fermions draw their masses from vacuums which are centered at and possess intrinsic energies other than zero. The neutrinos draw their masses from a vacuum that is centered at zero. So the entirely of their mass content arises from quantum fluctuations, and nothing else.

Jay
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### Re: Cracked the Fermion Mass Puzzle!

"The neutrinos draw their masses from a vacuum that is centered at zero. So the entirely of their mass content arises from quantum fluctuations, and nothing else."

Jay[/quote]

This is excellent, Jay, and carries important experimental implications. E.g., radiation without annihilation.
thray

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### Re: Cracked the Fermion Mass Puzzle!

thray wrote:"The neutrinos draw their masses from a vacuum that is centered at zero. So the entirely of their mass content arises from quantum fluctuations, and nothing else."

This is excellent, Jay, and carries important experimental implications. E.g., radiation without annihilation.

I doubt that it is true however. We have that the neutrino masses are due entirely to gravitational torsion.

https://arxiv.org/abs/1705.06036

However, the trick is what sets the particular fermion masses to the values we measure? I suspect it has to be due to the geometrical-topological configuration of the quantum vacuum. I think Jay is actually exposing some of this geometry with his latest.
FrediFizzx
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### Re: Cracked the Fermion Mass Puzzle!

FrediFizzx wrote:
thray wrote:"The neutrinos draw their masses from a vacuum that is centered at zero. So the entirely of their mass content arises from quantum fluctuations, and nothing else."

This is excellent, Jay, and carries important experimental implications. E.g., radiation without annihilation.

I doubt that it is true however. We have that the neutrino masses are due entirely to gravitational torsion.

https://arxiv.org/abs/1705.06036

However, the trick is what sets the particular fermion masses to the values we measure? I suspect it has to be due to the geometrical-topological configuration of the quantum vacuum. I think Jay is actually exposing some of this geometry with his latest.

Well, folks, I am within a day or so of an updated post. This will contain some new geometric plots, greatly-beefed up discussion of the mechanics of beta decay, and the charged lepton masses. All that is left, which I will attack after that, are the mercurial neutrinos.
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### Re: Cracked the Fermion Mass Puzzle!

OK all, here is the latest draft: https://jayryablon.files.wordpress.com/ ... 12-spf.pdf

What is new since the August 19 draft?

1) At the end of section 14, I considerably beefed up the study of beta decay for quarks.

2) In sections 12, 13 and 14 I added new Figures 2a, 2b and 2c which provide a geometric picture of how the quark masses and mixing angles all fit together. These are the pictures that are worth a thousand words and quite a few equations. I have not renumbered these figures yet; I will leave that for later because I am not in the mood right now.

3) Section 15 is brand new. It connects the charged lepton masses with the empirical data for two of the three neutrino oscillation mixing angles, within experimental errors.

4) Sound the trumpets: IN SECTION 16 I AM PREDICTING A SECOND HIGGS BOSON AFFILIATED WITH LEPTON INTERACTIONS, INCLUDING WHAT ITS MASS WILL BE. See (16.1) for the mass prediction. Odds on Stockholm, anyone?

Now I am going to finish up the neutrinos, develop the Lagrangian potential for the leptons and associated figures, and finally start to sew this whole thing up for publication. I may very well segregate all of the mass and mixing content into a separate paper from the Klauza-Klein content. But it is still somewhat miraculous that we can start with Klauza-Klein which is pure general relativistic geometry, apply Dirac theory, and end up characterizing every single one of the nine quark and charged leptons masses in terms of other known parameters, see (15.19) and the Higgs mass prediction and discussion in (16.1).

Note, the x-axis in Figures 3 to 6 actually is off by a factor of $\sqrt2$. I will simply use $\phi_1$ rather than $\phi_h$ to maintain the scale, but am not int the mood to fix that either right now.

Getting the lepton results and the new Higgs prediction into the public domain are most important right now. All of this came together the last 48 hours.

Jay
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### Re: Cracked the Fermion Mass Puzzle!

Yablon wrote:OK all, here is the latest draft: https://jayryablon.files.wordpress.com/ ... 12-spf.pdf

Everyone:

I just figured out how to pin down the scale of the neutrino masses. First, take a look at https://news.mit.edu/2018/3-questions-p ... -mass-0611. "Somewhere between 10 meV and 2eV is our playground." And multiple studies suggest 2eV as an upper limit for the sum of the neutrino masses.

Next, look at the new parameter $\delta=42.018 MeV$ in (15.17) of the draft I just posted. And also look at the definition of this in (15.11). Now, many of us have a sense that gravitation and neutrinos play footsie with one another. And of course, a key natural ratio is that of the Fermi vev over the Planck mass, $v/M_P$. And, I keep finding in this paper that square roots of masses are very important numbers. In 2013 I used these to derive a whole slow of nuclear masses and energies. And that is happening again in this new paper.

So, do the calculation that I just did 5 minutes ago:

$\delta*\sqrt {v/M_P}=0.189 eV$!!!

Bingo! This set the mass scale for neutrino. And this means that my (15.11) is actually the sum of all three charged lepton rest energies, plus the sum of all three neutrino rest energies times $\sqrt{M_P/v}$. So the numbers fit, and the context fits!

Jay
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### Re: Cracked the Fermion Mass Puzzle!

One more breakthrough this last minute, plus time to write this:

If you follow along with my newest draft at https://jayryablon.files.wordpress.com/ ... 12-spf.pdf, you will know that I have reparameterized all of the quark masses and charged lepton masses. So I am down to three neutrino masses needing three separate parameters. The easy one is that I still have one PMNS angle left to use up, so that gets down to two. What I just posted in the last hour sets the scale for neutrino mass at .189 MeV, using the Newton gravitational constant G, since that is where the Planck mass comes from and the Fermi vev is already used up. So now we are down to one parameter before all twelve fermion masses will have been parameterized. And if you follow my paper to date and particularly what happened with the "leftover" angle for the isospin-down quarks at (13.6), you will know that that one leftover parameter will be the leftover mass mixing angle for the neutrinos. So we need one more independent parameter which is an angle.

So I am asking myself what relevant parameters are still out there to use. And, I am thinking that at (15.16) we used up the electromagnetic running coupling $\alpha(M_W^2)$, which is an electroweak hybrid. And I am thinking that perhaps what we need to use is the weak coupling $g_w$, because that is just about all that is left on the table. But we need an angle related to $g_w$, not merely a coupling. And there it is: The Weinberg weak mixing angle! That is the last parameter, totally appropriate for the context, and now all twelve fermion masses are re-parameterized.

Out of what I said here tonight, I will be able to make exact predictions for the three neutrino masses. Writing this up will be my project for the coming week. Then I am off to visit my elder grandson, now almost 18 months!

Jay
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### Re: Cracked the Fermion Mass Puzzle!

Yablon wrote:4) Sound the trumpets: IN SECTION 16 I AM PREDICTING A SECOND HIGGS BOSON AFFILIATED WITH LEPTON INTERACTIONS, INCLUDING WHAT ITS MASS WILL BE. See (16.1) for the mass prediction.

I have just worked this through in detail. Out of the four possible masses for the new Higgs that I showed in (16.1), it turns out that the correct mass, and the one I will definitively predict next time through, is 964.524 MeV, on the lower-right of (16.1). This is not the mass I thought most likely in the paragraph following (16.1). This updated view is based on now having a much deeper understanding of the neutrino masses, and is arrived at by very carefully comparing Figures 2c and 8 of the draft that I posted the other day.
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### Re: Cracked the Fermion Mass Puzzle!

Yablon wrote:
Yablon wrote:4) Sound the trumpets: IN SECTION 16 I AM PREDICTING A SECOND HIGGS BOSON AFFILIATED WITH LEPTON INTERACTIONS, INCLUDING WHAT ITS MASS WILL BE. See (16.1) for the mass prediction.

I have just worked this through in detail. Out of the four possible masses for the new Higgs that I showed in (16.1), it turns out that the correct mass, and the one I will definitively predict next time through, is 964.524 MeV, on the lower-right of (16.1). This is not the mass I thought most likely in the paragraph following (16.1). This updated view is based on now having a much deeper understanding of the neutrino masses, and is arrived at by very carefully comparing Figures 2c and 8 of the draft that I posted the other day.

Congratulations, Jay, for all these new results. I hope you succeed also in publishing them. I haven't been paying much attention as I am still engaged in old battles of my own, but hopefully Fred is keeping an eye on your results. Although I have been silent, I am sure you know that you have my full support in your endeavors.

***
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### Re: Cracked the Fermion Mass Puzzle!

Joy Christian wrote:
Yablon wrote:
Yablon wrote:4) Sound the trumpets: IN SECTION 16 I AM PREDICTING A SECOND HIGGS BOSON AFFILIATED WITH LEPTON INTERACTIONS, INCLUDING WHAT ITS MASS WILL BE. See (16.1) for the mass prediction.

I have just worked this through in detail. Out of the four possible masses for the new Higgs that I showed in (16.1), it turns out that the correct mass, and the one I will definitively predict next time through, is 964.524 MeV, on the lower-right of (16.1). This is not the mass I thought most likely in the paragraph following (16.1). This updated view is based on now having a much deeper understanding of the neutrino masses, and is arrived at by very carefully comparing Figures 2c and 8 of the draft that I posted the other day.

Congratulations, Jay, for all these new results. I hope you succeed also in publishing them. I haven't been paying much attention as I am still engaged in old battles of my own, but hopefully Fred is keeping an eye on your results. Although I have been silent, I am sure you know that you have my full support in your endeavors.

***

Thanks Joy, I greatly appreciate your support, as do I support you.

I can now report out another prediction:

The sum of the three neutrino masses is 0.133 eV.

I expect that in the next 48 hours I will have predictions for each individual neutrino as well. It is always good to be able to tell the labs here to look for masses, rather than them having to do so scattershot.

I may post an interim update later today, just to keep you all on the cutting edge with me.

Jay
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