Thursday, January 19, 2017

Dark matter’s hideout just got smaller, thanks to supercomputers.

Lattice QCD. Artist’s impression.
Physicists know they are missing something. Evidence that something’s wrong has piled up for decades: Galaxies and galaxy clusters don’t behave like Einstein’s theory of general relativity predicts. The observed discrepancies can be explained either by modifying general relativity, or by the gravitational pull of some, so-far unknown type of “dark matter.”

Theoretical physicists have proposed many particles which could make up dark matter. The most popular candidates are a class called “Weakly Interacting Massive Particles” or WIMPs. They are popular because they appear in supersymmetric extensions of the standard model, and also because they have a mass and interaction strength in just the right ballpark for dark matter. There have been many experiments, however, trying to detect the elusive WIMPs, and one after the other reported negative results.

The second popular dark matter candidate is a particle called the “axion,” and the worse the situation looks for WIMPs the more popular axions are becoming. Like WIMPs, axions weren’t originally invented as dark matter candidates.

The strong nuclear force, described by Quantum ChromoDynamics (QCD), could violate a symmetry called “CP symmetry,” but it doesn’t. An interaction term that could give rise to this symmetry-violation therefore has a pre-factor – the “theta-parameter” (θ) – that is either zero or at least very, very small. That nobody knows just why the theta-parameter should be so small is known as the “strong CP problem.” It can be solved by promoting the theta-parameter to a field which relaxes to the minimum of a potential, thereby setting the coupling to the troublesome term to zero, an idea that dates back to Peccei and Quinn in 1977.

Much like the Higgs-field, the theta-field is then accompanied by a particle – the axion – as was pointed out by Steven Weinberg and Frank Wilczek in 1978.

The original axion was ruled out within a few years after being proposed. But theoretical physicists quickly put forward more complicated models for what they called the “hidden axion.” It’s a variant of the original axion that is more weakly interacting and hence more difficult to detect. Indeed it hasn’t been detected. But it also hasn’t been ruled out as a dark matter candidate.

Normally models with axions have two free parameters: one is the mass of the axion, the other one is called the axion decay constant (usually denoted f_a). But these two parameters aren’t actually independent of each other. The axion gets its mass by the breaking of a postulated new symmetry. A potential, generated by non-perturbative QCD effects, then determines the value of the mass.

If that sounds complicated, all you need to know about it to understand the following is that it’s indeed complicated. Non-perturbative QCD is hideously difficult. Consequently, nobody can calculate what the relation is between the axion mass and the decay constant. At least so far.

The potential which determines the particle’s mass depends on the temperature of the surrounding medium. This is generally the case, not only for the axion, it’s just a complication often omitted in the discussion of mass-generation by symmetry breaking. Using the potential, it can be shown that the mass of the axion is inversely proportional to the decay constant. The whole difficulty then lies in calculating the factor of proportionality, which is a complicated, temperature-dependent function, known as the topological susceptibility of the gluon field. So, if you could calculate the topological susceptibility, you’d know the relation between the axion mass and the coupling.

This isn’t a calculation anybody presently knows how to do analytically because the strong interaction at low temperatures is, well, strong. The best chance is to do it numerically by putting the quarks on a simulated lattice and then sending the job to a supercomputer.

And even that wasn’t possible until now because the problem was too computationally intensive. But in a new paper, recently published in Nature, a group of researchers reports they have come up with a new method of simplifying the numerical calculation. This way, they succeeded in calculating the relation between the axion mass and the coupling constant.

    Calculation of the axion mass based on high-temperature lattice quantum chromodynamics
    S. Borsanyi et al
    Nature 539, 69–71 (2016)

(If you don’t have journal access, it’s not the exact same paper as this but pretty close).

This result is a great step forward in understanding the physics of the early universe. It’s a new relation which can now be included in cosmological models. As a consequence, I expect that the parameter-space in which the axion can hide will be much reduced in the coming months.

I also have to admit, however, that for a pen-on-paper physicist like me this work has a bittersweet aftertaste. It’s a remarkable achievement which wouldn’t have been possible without a clever formulation of the problem. But in the end, it’s progress fueled by technological power, by bigger and better computers. And maybe that’s where the future of our field lies, in finding better ways to feed problems to supercomputers.

33 comments:

Stuart said...

Indeed advances in technology are leaving no hiding places for particulate dark matter. As you have mentioned in your blog, theoretical physicists found a way to resuscitate the nearly dead axion hypothesis. This brings us to question whether the dark matter hypothesis is falsifiable since its advocates will work to seek ways of hiding their hypothetical particle or unicorn so that it will be forever beyond the reach of experimentalists.

Phillip Helbig said...

"I also have to admit, however, that for a pen-on-paper physicist like me this work has a bittersweet aftertaste. It’s a remarkable achievement which wouldn’t have been possible without a clever formulation of the problem. But in the end, it’s progress fueled by technological power, by bigger and better computers. And maybe that’s where the future of our field lies, in finding better ways to feed problems to supercomputers."

Rather like the proof of the four-colour theorem.


Uncle Al said...

"The strong nuclear force...could violate a symmetry called 'CP symmetry,' but it doesn’t" Big Bang matter and antimatter (baryogenesis) cancel. Matter exists! Space is trace chiral anisotropic toward hadronic matter, Noether-leaking Milgrom acceleration (no dark matter). SUSY and M-theory are empirically flawed; Chern-Simons repair of Einstein-Hilbert action.

Observe trace chiral anisotropic vacuum differential embedment energy one extremely chiral molecule at a time, left-handed versus right-handed, to 1 Hz, 4×10^(-15) electron-volt[1]. 2-Cyano-trishomocubane[2] (point group C_3): CHI = 0.884725 (CHI = 0 achiral to CHI = 1 perfect chirality[3]); dipole moment = 3.9 debyes. (Amino acid phenylalanine CHI = 0.058600.)

Look.

[1] "Molecular Fountain" doi:10.1103/PhysRevLett.117.253201, arXiv:1611.03640
[2] doi:10.1016/S0040-4020(98)00211-7 (carboxylic acid)
[3] doi:10.1063/1.532988, 10.1063/1.1484559

David Brown said...

"The second popular dark matter candidate is a particle called the “axion,” and the worse the situation looks for WIMPs the more popular axions are becoming. Like WIMPs, axions weren’t originally invented as dark matter candidates." It seems to me that the 3 most likely candidates for undiscovered fundamental particles are: the axion, the graviton, and the inflaton. Is the preceding idea correct? Besides axions, WIMPs, gravitons, & inflatons, what else might be highly plausible?

Ben said...

Hi Sabine,

I have a few somewhat pedantic comments:

(1) The relationship between axion mass and decay constant at 0 temperature (i.e., in the present-day universe) has been known for a long time and can also be calculated from chiral perturbation theory. This new paper doesn't change the position of the axion model band on the parameter space plots one usually sees. What's new is the ability to numerically calculate the evolution of this relationship with temperature (or equivalently, with time in the early universe).

The importance of this time-dependence is that it determines the relationship between axion mass and the overall cosmic density of axions today. Somewhat perversely, the cosmic energy density in axions increases with decreasing axion mass. If we assume axions constitue 100% of dark matter, the Borsanyi paper gives a prediction for the axion mass based on the present dark matter density, but there are lots of cosmological uncertainties here.

(2) The technicalities of lattice calculations go way over my head, but it's worth mentioning that another recent lattice result (https://arxiv.org/abs/1512.06746) gets a different answer, so it's probably still somewhat early to declare this question settled.

To Stuart, I will merely point out that nobody has resurrected the axion hypothesis since axions were first considered as a dark matter candidate; indeed, the very first models of axion dark matter conceived in the early 80s are still alive and well today (in marked contrast to the first WIMP models, which were ruled out long ago by experiments). The axion was first conceived as an ingredient of the Higgs mechanism (with no relation to dark matter); after this model was ruled out, theorists realized that the same mathematical mechanism with a few small changes could yield dark matter axions.

Ben

Sabine Hossenfelder said...

David,

Depends on who you ask. People find most plausible whatever it is that they are working on. Or at least they feel obliged to pretend so. Of the examples you name, the graviton is by far the most plausible one. It is very hard to avoid some variant of it.

Sabine Hossenfelder said...

Ben,

Doesn't the temperature-dependence of this relation tell you about the rate at which axions can be produced in the early universe? How could it be that this wouldn't change the constraints on axions making up dark matter?

Thanks for pointing out the reference. Best,

B.

Ben said...

Hi Sabine,

I didn't mean to imply that these results (if confirmed) do not constrain dark matter axion parameter space, but rather that we already knew where to put the red band in a plot like https://inspirehep.net/record/1263039/files/ALPplot.png because what's plotted on the x axis is the 0-temperature mass (the coupling to photons is plotted on the y-axis, but this is just inversely proportional to the decay constant with a small amount of model dependence).

The result does better constrain the allowed regions of the x-axis. But there's still a fair amount of uncertainty because there are several contributions to the cold cosmic axion population, not all of which depend on the topological susceptibility. In particular, if the PQ scale is high enough that inflation happens after PQ symmetry breaking, then the axion mass can be almost anything at all because an angle that you would otherwise average over becomes a free parameter.

Ben

Sabine Hossenfelder said...

Ben,

Thanks for the clarification. Yes, that's what I meant with improving the constraints.

You are right of course that there are many other factors that enter the calculations, so maybe it won't play all that much of a role in practice. We will see. Still, I find it a neat result. Best,

B.







Ben said...

I agree that it's a cool result, and if nothing else, it heralds the beginning of an era where the QCD uncertainty in axion physics can be eliminated or greatly reduced, leaving us only with the uncertainty from cosmology (which is emphatically still progress!). I'm also gratified that axions are receiving more recent attention in general.

This is just one of those cases where working in a field close to a widely publicized result makes you aware of all the caveats and extra parameter space dimensions which are suppressed for simplicity in most work targeting a broader audience.

Best wishes,
Ben

Maurice said...

>As a consequence, I expect that the parameter-space in which the axion can hide will be much >reduced in the coming months.

Huh? "In the coming months"?? As Ben told you they already did reduce the parameter space drastically in their paper! But also he didn't summarize their punchline. It is this:
If dark matter is made of axions, their mass must be in the range 50 \mueV - 1500 \mueV (legend of fig.3). The large uncertainty is mainly due to a lack of knowledge about the contribution axions due to the decay of topological strings. If we trust their result, just ruling out this
mass range experimentally, will rule out the axion as a dark matter candidate for good.

andrew said...

The paper in Nature has, at least temporarily, been made available on an open access basis.

Uncle Al said...

The French Connection

The THREE MEN turn again to stare at the Lincoln. The MECHANIC lowers the hoist, thoughtfully.

MECHANIC, “I ripped everything out except the Rocker panels.”
DEVEREAUX. “What's that?”

They look at each other for a long moment.

MECHANIC starts to undo the side Rocker pans. JIMMY pulls the pan off and sticks his arm into the enclosure. Feeling around inside he pulls out the first kilo-sized plastic container as several others start tumbling out after. BUDDY and DOYLE are smiling at each other as they continue to pull the bags out."

Look for gravitation under the rocker panels. Physical theory has looked everywhere else.

Stuart said...

I concur with you Bee on the idea that the graviton is the most plausible dark matter candidate.It may be that the graviton being a low energy,long wavelength particle begins to reign at galactic scales and accelerations below Milgrom's or the Hubble's acceleration,Hc.Hence the galaxy rotation curve problem could be a manifestation of quantum gravity below certain critical values just as quantum effects such as superconductivity occur below certain critical conditions.

Sabine Hossenfelder said...

Maurice,

I meant it will take some while to include this result into the models.

Maurice said...

OK after explaining their main conclusion one should take a _critical_ look at it. They assume that their mechanism produces a mass fraction from 0.5 to 0.01 of the total dark mass density without giving ANY reason or reference for these numbers. Even in cosmology one cannot just
plug numbers "out of thin air". Also it is very strange to "hide" their main conclusion in a caption of a figure and not even mention it in the abstract (this is probably why u completely missed it). The referees (Maria Lombardo being presumably one of them) did a really bad job: they should have never accepted the manuscript in this form.

Sabine Hossenfelder said...

Maurice,

What is 'their mechanism' that you are even talking about? And what makes you think that you are to tell the authors what's the main conclusion of their paper?

I've found the Nature article poorly written to the point of being entirely incomprehensible for someone not from the field like me. The article that I linked to is in a somewhat better shape.

Maurice said...

> What is 'their mechanism' that you are even talking about?

The misalignemnt axion production mechanism they discuss in their paper.

> And what makes you think that you are to tell the authors what's the main conclusion of their paper?

It does not need anybody to "tell the authors", for somebody who understood the paper their main conclusion is obvious. See also here for quotes of one author and other experts that makes clear that the mass determination is generall considered to be their main conclusion:
http://www.independent.co.uk/news/science/dark-matter-made-of-axions-universe-galaxies-astronomy-a7393536.html

Sabine Hossenfelder said...

Maurice,

The misalignment axion production is not 'their mechanism'. It's an old story. I think you've misunderstood that quote. What they calculate is the dependence of the mass on the temperature. As I explained in my post. Also read Ben's comments above. Best,

B.

Maurice said...

> The misalignment axion production is not 'their mechanism'. It's an old story.

Of course it is. They explicitely say so in the paper. Where did I claim otherwise? "Their mechanism" was meant as "the mechanism they assumed in the quantitative calculation of axion mass".

>I think you've misunderstood that quote.
>What they calculate is the dependence of the mass on the temperature.

Do you put into doubt that their final, decisive result is the mass of the axion as a function of
the assumed contribution of axions produced by the misalignment process to the total cosmic mass density (with the final result given for an assumed fraction between 0.01 and 0.5)?

Ben also told you that but in a bit cryptic manner:
>The result does better constrain the allowed regions of the x-axis.
and the x-axis in the figure he refers to, shows the mass of the axion...

Sabine Hossenfelder said...

Maurice,

I don't think the exact numbers they have in that particular figure are remotely as decisive as you seem to think they are because, as they also state, there are various means to produce axions, not to mention that there are various axion models to begin with. Consequently, as I wrote (and as the abstract of the paper says), the interesting result is the temperature-dependence of the mass. How to obtain constraints from that on particular models depends on many other assumptions. Hope that explains it.

I have absolutely no interest to continue a discussion with you about why you think I should find interesting what you think is interesting, hence I won't approve further comments from you. Bye,

B.

Phillip Helbig said...

"I concur with you Bee on the idea that the graviton is the most plausible dark matter candidate."

I don't think that she ever claimed that. Source?

She did agree with another poster that the graviton is a plausible candidate for an as yet undetected particle. Pedantically, gravitons are dark matter, but not the dark matter. Not even a significant fraction.

Sabine Hossenfelder said...

Stuart,

As Phillip points out, I never said that gravitons are the most plausible dark matter candidates. They are certainly not.

Thanks, Phillip, I had missed that.

Best,

B.

naivetheorist said...

"And maybe that’s where the future of our field lies, in finding better ways to feed problems to supercomputers." as a paper-and-pencil theoretician (i make too many mistakes to use 'pen-on-paper') i deeply regret the trend towards replacing model building wth computer simulation but it's already happening in the so-called 'non-fundamental' subfields of theoretical physics, e.g. in the study of molecular systems such as soft matter physics. I don't expect that this trend can be reversed but it will turn certain individuals, those prefer to set up and solve equations over writing computer programs, away from theoretical physics which will be a huge loss to to the community of knowledge seekers.

Uncle Al said...

"I deeply regret the trend towards replacing model building with computer simulation"

Ab initio calculate a modest molecule with a cluster-week and a fat wallet. Semi-empirical calculate (HyperChem Lite, ($(USD)100 purchase) 32,000 iterations in five minutes, personal computer, within 3% of crystal structure. Deep knowledge versus curve-fit utility. Silly results can obtain both ways.

Building in silico is not making in Pyrex. Nature does not calculate. Everybody is missing gravitation's better handle. Look where it is not. All the fun is in the footnotes.

Bill said...

"This result is a great step forward in understanding the physics of the early universe."

Requiring next-generation-and-beyond supercomputers to process a minor theory is a bit like needing linear accelerators the diameter of the observable universe to see if there's anything new on the particle front.

If that's what's needed to advance particle physics, then it's time for a different approach. I'm not having any of it.

Greg Metcalfe said...

Bill,

I'm a layman, as you apparently are too: linear accelerators more properly characterized, even in pop-sci circles, by length. They have no diameter, other than something like the diameter of the beamline, which would perhaps be more related to accelerator physics & design. Both sorts of accelerator are important to industry as well as fundamental physics e.g. the ion implanters used in semiconductor manufacturing (one my old fields, at Intel and others), and in light sources, as in the Stanford Synchrotron Radiation Lightsource http://www-ssrl.slac.stanford.edu/content/about-ssrl/about-stanford-synchrotron-radiation-lightsource.

Accelerators of any sort are not cheap, but how one places a value on that is a bit of a personal matter. How do you weight acquiring new knowledge for it's own sake?

However you decide that, exascale computers will certainly be built. In fact, the US timeline has recently been pulled in by a couple of years. Partly a 'prestige' thing (though others are likely to arrive first), but also because these are national lab machines, with heavy DoE funding. Especially given that they will be built in any event, I consider running fundamental physics codes a wise (and cost-effective) means of getting some science done.

This are, of course, just my thoughts as some random US taxpayer. Fundamental research *always* pays off.

kashyap vasavada said...

Hi Bee!
Detecting such micro EV particles must be much more difficult and uncertain technology than in the case of high mass particles.Are people confident of their methods?Is there some comprehensive review reference of the experimental methods?

Stuart said...

The mantra for Dark Matter hunters is " Absence of evidence is not evidence of absence " and yet the scientific method dictates that " Absence of evidence is evidence of absence "

TheBigHenry said...

Absence of evidence is not evidence of absence, but it is not entirely devoid of implication.

akidbelle said...

Stuart, TheBigHenry,

dark matter hunters are particles hunters. There is evidence that they do their job.

Now the evidence of absence is growing, but these guys have no limit to apply and it seems they won't ever have any. So the only way to stop the hunt - except for lack of money - is a modified gravity theory that makes unexpected but verifiable predictions (and of course fits the facts).

As far as I understand from this blog we are a million miles away from this theory.

J.

8c7793aa-15b2-11e5-898a-67ca934bd1df said...

akibelle, you realize that searching for axions in the QCD derived energy range has not yet occurred right? Axion haloscopes in that energy range have yet to be built.

akidbelle said...

Yes, I understand.

J.