# I Vacuum Metastability

1. Mar 23, 2018

### jtlz

What is the best theory why our vacuum may be in the edge of metastability?

Is it possible there are many false vacuum separated by energy barriers and the reason why our vacuum may be metastable is so that it is easier to cross the different false vacua (not necessarily to the true vacuum)?

2. Mar 24, 2018

Staff Emeritus
It's got to be somewhere.

3. Mar 25, 2018

### jtlz

Here may be a simpler question related to it. I read in Deep Down Things that:

"What is the physical origin of the external Higgs potential? What is the physical basis of the peer pressure–like internal organizing principle that causes the Higgs field symmetry to be hidden in a uniform manner throughout space-time? These questions, unanswerable within the Standard Model, suggest that, beyond the unearthing of the Higgs boson, there may well be some radically new facet of the natural world awaiting our discovery."

So far what are the existing proposals of the physical origin of the external Higgs potential? How related is it to the vacuum metastability?

4. Mar 25, 2018

### ohwilleke

The underlying premise of the question, it is worth noting, isn't on entirely solid ground.

It would only take the slightest of tweaks to the renormalization group of the Higgs (or including some slight usually overlooked and ignored nuance of the calculation that the metastable result relies upon) from BSM physics to nudge the universe from merely metastable to stable.

For example, the SM + quantum gravity, or a singlet dark matter particle with a Higgs portal, might cause such a slight tweak. The asymptotic gravity prediction of the Higgs boson mass that is now so famous, for example, included a quantum gravity adjustment to the renormalization of the Higgs with energy scale.

There is also a fair amount of imprecision in the top quark mass (in absolute terms even though the percentage uncertainty isn't that huge) that could give the stability-metastability question a nudge one way or the other. Probably not enough to cross the line by itself, but enough to make the necessary BSM tweak even more subtle.

5. Apr 1, 2018

### Urs Schreiber

You all should provide citations for claims you make or refer to, lest the discussion becomes arbitrary.

For the record: The plot from the original question in #1 is taken from

Giuseppe Degrassi, Stefano Di Vita, Joan Elias-Miró, José R. Espinosa, Gian Giudice, Gino Isidori,
"Higgs mass and vacuum stability in the Standard Model at NNLO",
J. High Energ. Phys. (2012) 2012: 98 (arXiv:1205.6497, doi:10.1007/JHEP08(2012)098)

This computation has meanwhile been refined in

A. V. Bednyakov, B. A. Kniehl, A. F. Pikelner, and O. L. Veretin,
"Stability of the Electroweak Vacuum: Gauge Independence and Advanced Precision",
Phys. Rev. Lett. 115, 201802 (arXiv:1507.08833, doi:10.1103/PhysRevLett.115.201802)

where the result is plotted like so:

An expository summary of this result appeared in

Alexander Kusenko,
"Are We on the Brink of the Higgs Abyss?",
Physics 8, 108 (2015)

which concludes as follows:

"[The] conclusion is that the best theoretical fit to measured parameters, including the Higgs and top-quark masses, points to a metastable Universe. However, their analysis also concludes that values of parameters are closer to a region of absolute stability than suggested by previous studies: it is possible for the Universe to be fully stable (and for the standard model to work all the way up to the Planck scale), if the true values of measured parameters are only 1.3 standard deviations away from the current best estimates."

In view of this, it seems to me that the question in #1 as phrased does make good sense: According to available data the observed Higgs vacuum is indeed very close to the edge of metastability. This necessarily brings with it that it is uncertain on which side of this edge we are, but that was not the question.

Last edited: Apr 1, 2018
6. Apr 1, 2018

### Urs Schreiber

One argument that I am aware of is the following:

A number of references argue that Higgs vacuum instability is in fact incompatible with cosmic evolution, as due to vacuum fluctuations during inflation the vacuum decay would not have been avoided (EGR 07, EEGHR 09, HKSZ 14, EGMRSST 15, EKSYZ 16) unless a further mechanism served to prevent it. That supersymmetry provides such a mechanism has been argued in (BDGGSSS 13, section 7, Kane 18 , “Clue 4”).

7. Apr 2, 2018

### Urs Schreiber

As Philip Gibbs kindly points out to me, he was maybe the first to highlight the core of these points and arguments way back in 2011, right before the official announcement of the Higgs detection:

Philip Gibbs,
"What would a Higgs at 125 GeV tell us?",
in "Seminar Watch (Higgs Special), Rumoured Higgs at 125 GeV and What Would a Higgs at 125 GeV Tell Us?",
Prespacetime Journal, December 2011, Vol. 2 Issue 12 pp. 1899-1905 (web)

Last edited: Apr 3, 2018
8. Apr 3, 2018

### Urs Schreiber

It is also interesting to note how the precision analysis of Bednyakov et al 15. seems to invalidate the now famous suggestion by Shaposhnikov-Wetterich 09 (which was motivated from the principle of "asymptotic safety") that the beta function $\beta_\lambda$ for the quartic Higgs self-coupling $\lambda$ should vanish asymptotically. According to their precision plot (p. 17-18) it does not asymptotically vanish at all:

9. Apr 3, 2018

### jtlz

Thanks for the paper. It explained a lot.
However, is there no mathematical or theoretical possibility for there to be new physics that doesn't affect the Higgs coupling or Higgs potential? Or are they all categorically related. Perhaps some new forces of nature didn't have any virtual particle contribution at all? With regards to this paragraph:

"If the LHC ﬁnds Higgs couplings deviating from the SM prediction and new degrees of freedom at the TeV scale, then the most important question will be to see if a consistent and natural (in the technical sense) explanation of EW breaking emerges from experimental data. But if the LHC discovers that the Higgs boson is not accompanied by any new physics, then it will be much harder for theorists to unveil the underlying organizing principles of nature. The multiverse, although being a stimulating physical concept, is discouragingly diﬃcult to test from an empirical point of view. The measurement of the Higgs mass may provide a precious handle to gather some indirect information"

Up to what TeV before we can say that there is no physics at the TEV? Is it 1 TeV? 10 TeV? 100?

And does it always have to involve energy.. for example.. general relativity was a new physics last century that didn't involve TeV.

10. Apr 3, 2018

### Urs Schreiber

Just out of interest: I take that to mean that you did not get the plot in your message #1 from that paper? Where did you get it from?

11. Apr 3, 2018

### jtlz

I used yahoo.com.. type "vacuum metastability" and several dozens of images came up. I chose the clearest picture.

12. Apr 3, 2018

### Urs Schreiber

I find it hard to tell what you are asking here, as it sounds a little garbled. You should be asking whether the renormalization group flow of the Higgs self-coupling to the Planck scale as shown here is computed with the assumption that there is no new physics in between the weak scale and the Planck scale (called the "great desert" assumption). And the answer to that is: Yes.

And then the logic turns around: Since under the "great desert"-assumption the RG flow is seen to run at least extremely close to the point where the Higgs vacuum would become unstable, one may argue that this assumption must be wrong, and that there should be some new physics kicking in, which prevents that. Such as, possibly, supersymmetry or something else. This is not a solid proof, of course, but that's the kind of plausibility argument usual in phenomenology.

13. Apr 3, 2018

### jtlz

In the same paper.. if there were this "new scalar field, non-minimally coupled to gravity the slows down the inflationary phase".. is it possible it is new physics but doesn't belong between the weak scale and planck scale.. it other words, can new scalar field exist that doesn't have a corresponding particle? remember we are not even sure gravity has gravitons. So generally could any new physics occur that doesn't belong between weak and planck scale? Nature may use very exotic organizing principles that is not naturalness, multiverse, sabine cosmic lotto, etc.

"If the Higgs field is trapped in the false vacuum during the early universe, it can cause inﬂation. The normalization of the spectrum of primordial perturbations, which is determined by Vmin, can be appropriately selected by tuning the ratio λ∗/b. The main diﬃculty of this scenario is to achieve a graceful exit from the inflationary phase. Two mechanisms have been proposed. The ﬁrst one [24] employs a new scalar ﬁeld, non-minimally coupled to gravity, that slows down the expansion rate, thus allowing for quantum tunneling of the Higgs out of the false vacuum. The second mechanism [25] uses a scalar field weakly coupled to the Higgs which, during the cosmological evolution, removes the barrier in the Higgs potential in a process analogous to hybrid inflation. So, in practice, the minimality of the SM is lost and one may wonder if there is any conceptual gain with respect to adding a new scalar playing the role of the inflaton. Nevertheless, it is interesting to investigate whether the Higgs and top masses are compatible with the intriguing possibility of a false vacuum at large field value."

14. Apr 3, 2018

### Urs Schreiber

jtlz, you are rambling now in a non-educated way. What is it that you actually want to know?

15. Apr 3, 2018

### jtlz

In more technical term. New physics can affect the computation of the renormalization group flow of the Higgs self-coupling to the Planck scale but what if that new physics was more fundamental than QFT or something where QFT and gravity were emergent. So my inquiry was whether it is possible to have new physics that is not in between the weak scale and planck scale but outside of them.

In other words. There may be a simpler alternative to multiverse from Occam razor and it is that the organizing principles of nature is simply because they were made that way. So the new physics may be related to the causal mechanism behind the scene or behind our Standard Model.. meaning any new physics can be independent of Higgs coupling or Higgs potential and the virtual particles. For example Microsoft programmer can rewrite the program in different ways (using C or Fortran or newer version) without our commercial Windows software being affected. May I know what is the official language for this description of other ways to have new physics in our current theoretical physics?

16. Apr 3, 2018

### jtlz

What I meant is. Our constants of nature is so incredibly fined tuned. The following are the possibilities:

1. Naturalness (like Calabi-Yau where the constants could be in the form of moduli, etc.)
2. Multiverse
3. One universe but constants chosen like Lotto Win

Right now we have utter division in the field with Sabine and company into the third and many into second and the others into the first possibility. Isn't it legit to have other possibilities like our constants of nature were designed and only one universe. So it's either the designed used specific calabi-yau shapes chosen at Big Bang or other new physics that guide them. I was asking if there is official name for this new physics that guide them. Something along the line of perhaps actual implementation of AdS/CFT? Right now it's just toy model because it is not our spacetime. Could there be new implementation where it can use our spacetime. Or similar to the concept. This is the context of my question. Our constants of nature are incredibly fined tuned we need to think of all possibilities. Hence my question are not rambling in non-educated way but reflect the great division now going on in theoretical physics and the confusion (This is the theme of Sabine new book coming soon).

17. Apr 3, 2018

### jtlz

I just read http://backreaction.blogspot.com/ where Sabine reviews the book "Farewell to Reality: How Fairytale Physics Betrays the Truth for Scientific Truth".

Sabine doesn't believe in naturalness or supersymmetry or even Multiverse. She reasoned seemingly fined tuned stuff like the vacuum metastability just happens (like winning lotto) without formula because there is no Bayesian background. But I found her belief even weirder. So what if all of them are wrong and there should be other options. That's all. Hierarchy problem, vacuum metastability if confirmed were just too strange especially if there was no naturalness, no supersymmetry, no multiverse.. and Sabine model of cosmic lotto doesn't work (someone correct me if I got Sabine position wrong but I think's that's the contents of her book "Lost in Math".)

18. Apr 3, 2018

### Urs Schreiber

One option is missing:
• Having a theory that explains the numbers.
"The arguments based on ‘naturalness’ are basically like saying the weather tomorrow should be the same as today. The opposite of naturalness is having a theory. […] It would have been nice if the naturalness arguments had worked, but they did not. Since they were not predictions from a theory it is not clear how to interpret that. [...] The failure of naïve naturalness to describe the world tells us we should look harder for a theory that does [work at high energies], an ‘ultraviolet completion’. [...] The alternative to naturalness, often neglected as an alternative, is having a theory." (Kane 17)

If you just think about it, you will realize that the universe is full of extreme ratios and hierarchical scales. Say the radius of the hydrogen atom over that of its nucleus, or the power emitted in a supernova over that of an ordinary burning star, to name just two. Without a theory of nature, these large ratios may seem mystifying. With a theory of nature they follow from basic laws and the mystery disappears.

Last edited: Apr 3, 2018
19. Apr 3, 2018

### ohwilleke

It is worth noting that the beta function used by Shaposhnikov-Wetterich 09 is not the Standard Model beta function of the Higgs boson. It is modified to reflect the beta function that would exist in the Standard Model plus quantum gravity in the form of an asymptotic gravity massless spin-2 graviton that modifies the beta function of the Higgs boson from the Standard Model version. The asymptotic behavior of the tweaked Higgs boson beta function probably reflects this modification. So, the Shaposhnikov-Wetterich 09 beta function should not behave the same way that the different Higgs boson beta function modeled in Bednyakov et al 15 does.

20. Apr 3, 2018

### Urs Schreiber

True, I was wondering about this. But Bednyakov et al. cite Shaposhnikov-Wetterich on their p, 17, right before they point out failure of asymptotically vanishing beta, as if in reply to that claim. But it's true, it's not clear (to me) whether they really operate on the same assumptions. Would be good to sort this out...

21. Apr 4, 2018

### jtlz

There seems to be many meanings of Naturalness so it's good to sort the subtleness of each meaning. In the paper depicting the vacuum metastability illustration in the initial message.. the conclusion in the paper started with the sentence "One of the most important questions addressed by the LHC is naturalness.". I found three good reference about naturalness after you emphasized opposite of naturalness is having a theory.. (I thought naturalness means exclusively having equations that gives the values or relationship.. and I mentioned these references so in the future I can refer to these if I forgot them):

http://backreaction.blogspot.com/2018/02/what-does-it-mean-for-string-theory.html

"That the mass be natural means, roughly speaking, that getting masses from a calculation should not require the input of finely tuned numbers".

and https://arxiv.org/pdf/1501.01035.pdf

"In implementing ’t Hooft’s notion of naturalness, we have so far considered symmetries of a sort familiar from quantum mechanics, generated by a charge operator which is a scalar under rotations. But there is another type of symmetry, allowed by general principles of quantum mechanics and relativity, where the symmetry generators are spinors. This symmetry is known as supersymmetry. We will consider it, ﬁrst, as a global symmetry, but the symmetry can be elevated to a local, gauge symmetry."
[...]
"it is still possible that nature is “natural”, in the sense of ’t Hooft. Future runs of the LHC might provide evidence for supersymmetry, warped extra dimensions, or some variant of technicolor. But the current experimental situation raises the unsettling possibility that naturalness may not be a good guiding principle. Indeed, naturalness is in tension with another principle: simplicity. Simplicity has a technical meaning: the simplest theory is the one with the smallest number of degrees of freedom consistent with known facts. Contrast, for example, the minimal Standard Model, with its single Higgs doublet, with supersymmetric theories, with their many additional ﬁelds and couplings. So far, the experimental evidence suggests that simplicity is winning. The observed Higgs mass is in tension with expectations from supersymmetric theories, but also technicolor and other proposals."

----

If the masses of the superpartners are very high.. what mechanism in superstring theory besides Kane's (his 0.5 TeV bino was already excluded) that can solve the Hiearchy Problem without 't Hooft notion of naturalness or natural supersymmetry (In the sense of the above paragraph at low masses)?
I'm interested for now in theory that can solve for them (instead of Multiverse or real fine tuning between quadratic radiative corrections and the bare mass being put there on purpose by design (if these were the mechanism chosen by nature. Then we should have new fields that can maintain the constants values without possibly any formulas).

And is the solution to the Hiearchy Problem independent of the Vacuum metastability issue (to what extend can solution of each be solution of the other)? Thank you.

22. Apr 4, 2018

### Urs Schreiber

No, naturalness is a principle imposed in the absence of any known equation for the actual numbers. In the absence of an explanation, cancellations of large numbers against each other seems a weird coincidence, and naturalness means that weird coincidences should not happen. It's a qualitative principle akin to the principles of the times of "natural philosophy" before physics became a maths-based science.

What you call "Kane's theory" is called the $G_2$-MSSM, which became a serious contender for realistic model building with the result of Acharya-Witten 01.
This model does not predict explicit numbers without feeding in some concrete assumptions on the precise nature of the compactification (if it did we would be living in a Douglas Adams novel), but -- and that's really the point that Kane et al. have been driving home over the years -- it does make generic predictions that hold irrespective of the detailed numbers that describe the choice of compactfication.

One of these generic predictions is that there is an exponential hierarchy between the Planck scale and the gravitino mass scale, hence the susy breaking scale, hence the electroweak scale. This argument is due to Acharya-Kane-Kumar 12, section V.A.2 (pages 10-11) , and it is not hard to follow:

First, the higher gauge symmetry of the supergravity C-field implies "shift symmetry" of its KK-modes $\Phi_j$. But the perturbative superpotential must be a holomophic function of the $\Phi_j$ and under shift symmetry this is only possible if perturbatively it vanishes identically. As a result, one deduces that in these models the superpotential consist entirely of non-perturbative contributions, such as membrane instantons, which are known to break the shift symmetry. But these non-perturbative contributions are negative exponentials in the instanton contributions, and hence imply that the gravitino mass (hence the susy breaking scale) is exponentially smaller than the Planck mass. This is the required exponential hierarchy.

This is not a mathematical proof, but it is a decent scientific argument based on an actual theory, and it makes clear that exponential hierarchies between the susy breaking scale and the Planck scale have a good scientific explanation from first principles, just as the exponential scale between the power of a supernova and that of an ordinary star does, both of which may look suprprisingly "unnatural" to the mathematically un-aided observer.

Last edited: Apr 4, 2018
23. Apr 4, 2018

### jtlz

What I was asking in your reply was the following especially the unknown contribution (glad to find this today as this vocalizes my concern):

https://profmattstrassler.com/artic...ics-basics/the-hierarchy-problem/naturalness/
"Fig. 5: Summing up the energy from the quantum fluctuations of known fields (schematically shown, upper row) up to the maximum energy scale vmax(down to the minimum distance scale) where the Standard Model still applies, and adding to this contributions from unknown effects from still higher energies and shorter distances (schematically shown, middle row), we must somehow find what experiment tells us is true: that the Higgs field’s average value is 246 GeV and the Higgs particle’s mass is 125 GeV/c2. If vmax is much larger than 500 GeV, this requires a very precise cancellation between the known and unknown sources of energy, one that is highly atypical of quantum theories."

Do you have a more mathematical version of it in your site in terms of renormalization group flow and Higgs self-coupling, etc that described the same stuff? If Vmax is just 500 GeV instead of planck scale.. does it mean the Higgs self-coupling cover up to 500 GeV only instead of up to planck scale? What stuff must the LHC produce so Vmax is up to 500 GeV only? Matt wrote in the commentary after the article:

"The obvious solution is indeed that vmax is near 500 GeV. And if that is true, the LHC will discover as-yet unknown particles, and other predictions of the Standard Model will fail as well. The strongest evidence against it — inconclusive at this time — is that the LHC has not yet discovered any such non-Standard-Model particles, and there are no known deviations from the Standard Model at the current time. Arguably we should have seen subtle deviations already by now. But I will get to this issue soon."

24. Apr 4, 2018

### Urs Schreiber

The problem with this folklore story is that it is trying to nail jelly to the wall by arguing about the size of quantum corrections in the presence of renormalization freedom.

The fact of the matter is that the space of renormalization choices is an affine space (i.e. like a vector space, but with no origin singled out) which means first of all that there is no absolute concept of "size" of a quantum correction. This only appears once one fixes a renormalization scheme, which is like a choice of coordinate chart. It has no physical meaning. Even if we fix a renormalization scheme (which is implicitly assumed in discussions such as you quote) then it still remains a fact that there is an arbitrary freedom in choosing renormalization constants, large or not.

In conclusion, to make progress on these kinds of matters, one needs more theoretical input than just low energy effective perturbative quantum field theory with its arbitrary renormalization freedom, or otherwise one is going in circles forever. As Kane 17 points out, "we should look harder for a theory that does provide a UV-completion".

Notice how the solution of the hierarchy problem observed by Acharya-Kane-Kumar 12, section V.A.2 (p. 10-11) deals with this issue: They invoke a UV-completion that goes beyond perturbation theory. In that theory one knows 1) that the superpotential is protected against perturbative renormalization freedom and 2) the form of the non-perturbative corrections is known. Namely these are exponentials in the inverse coupling. This yields the exponential hierarchy that is to be explained.

You see, this works not by long story-telling and analogies and showing colorful pictures, but by a logical deduction from a theoretical framework.
(Not fully mathematically rigorous, but fairly solid by the standards of phenomenology.)

25. Apr 5, 2018

### protonsarecool

To come back to the original question, here is another very recent calculation regarding meta-stability of our universe:

Scale-invariant instantons and the complete lifetime of the standard model
Anders Andreassen, William Frost, and Matthew D. Schwartz
Phys. Rev. D 97, 056006 – Published 12 March 2018
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.97.056006