Tuesday, July 20, 2010

SUSY and dark matter

Previous and future pieces of evidence in favor of supersymmetry:
Prev: Why string theory implies supersymmetry
Prev: SUSY and gauge coupling unification
Next: SUSY and hierarchy problem
Next: SUSY exists because the number 3/2 can't be missing
In the previous text, I explained that gauge coupling unification represents a tantalizing piece of evidence that Nature respects supersymmetry.

In these two colliding clumps of matter, dark matter apparently got separated from the visible matter, as reconstructed from their gravitational effects. That's a modern observation supporting the dark matter paradigm.

Now, let us look at the dark matter candidates which offer us another reason to believe that supersymmetry is a feature of Nature. First, let's ask:

How much dark matter is there in the Universe?

Recall that 70% of the energy density in the Universe is dark energy - which is a more inclusive, politically correct term for the cosmological constant. Dark energy is not composed out of any particles. It's just a uniform source of gravity that curves the space and accelerates its expansion as soon as you insert it into Einstein's equations.

Its pressure is negative and numerically equal to the positive energy density. This fact - which is exactly true for the cosmological constant as a theoretical concept, by definition, and seems to very accurately hold for dark energy as an observed phemonenon - guarantees that its stress-energy tensor is proportional to the metric tensor - which means that the cosmological constant picks no preferred reference frame (except for this blog).

The numerical magnitude of the cosmological constant, expressed as a vacuum energy density, is by those famous 123 orders of magnitude smaller than the generic expectation from quantum gravity and/or it is by 60 orders of magnitude lower than the generic expectation of low-energy supersymmetry. This discrepancy between a rough estimate and the observed value is known as the cosmological constant problem - an arguably worst prediction in the history of fundamental physics.

The anthropic principle, postulating googols of Universes among which ours is just one that admits life (and a tiny cosmological constant is needed for that), is the only known explanation that has been accepted by a large portion of physicists which means that these folks are either right or wrong. ;-)

But in this text, we want to look at another portion of the vacuum energy density - dark matter. It constitutes about 25% of the energy density in the Universe, leaving about 4% for the gay visible matter. Unlike dark energy, dark matter is composed out of some objects or particles.

However, we don't see them in our telescopes because they don't emit light; that's where the adjective "dark" comes from. That's either because dark matter is composed out of very cold ordinary baryonic stuff that simply no longer radiates; or because it is composed out of particles that don't interact with the photons and electromagnetic fields (almost) at all.

Why is there dark matter?

You could say that it's awkward to postulate the existence of something that isn't seen. Can't it be just a physicist's method to deny that his theories have broken down? And you have a point. However, your approach can't be treated as a dogma. There surely exist many things that were postulated to fix certain theories but they can't be easily seen.

For example, the neutrino was postulated because without this new largely invisible particle, the energy conservation would be violated in the neutron decay. Fermi realized that it was unacceptable and ungentlemanly to violate a conservation law that was proved by a woman scientist, Emmy Noether, for any time-translational-invariant physical system. So he invented a new particle and gave it the funny small Italian name.

Of course, the neutrinos were later "seen" much more directly and we know quite a lot about them today.

If you look at this "visibility" issue from another perspective, there's really no reason why our eyes should "see" everything there is. After all, we only see the visible interval of the electromagnetic spectrum. With additional gadgets, we may see all frequencies of the electromagnetic spectrum. But the electromagnetic field is just one among many fields in Nature and there's no reason why every other field should have significant interactions with it. After all, electrically neutral fundamental fields don't really interact with the electromagnetic fields much.

Fine. So I was trying to convince you that it's silly to impose a "ban" on dark matter i.e. to assume that everything there is must be visible through photons. But that's a bullet against flawed negative arguments. Are there positive arguments in favor of dark matter?

You bet. It started in the 1930s when Fritz Zwicky noticed that the stars in the galaxies rotate differently than expected. Their speed should be significantly higher near the galactic center - much like in the Solar System where the planet Mercury is much faster than the planet Neptune (RIP, Pluto). Try to calculate the power law!

However, it's observed that the speed of stars (in meters per second) is pretty much constant. It is independent from their distance from the center. (Zwicky was also the guy who has noticed that all his collaborators were spherical bastards because no matter what was the direction from which he observed them, they still looked like bastards.)

This constancy of the speed means that the distribution of the gravitational sources must be different than the distribution we can see via the electromagnetic telescopes. The arguments by Zwicky were updated and quantified by Vera Rubin a few decades later which is why she remains one of the top female candidates for a physics Nobel prize.

Today, we have many more piece of evidence: see the second section of dark matter at Wikipedia. Gravitational lensing statistical surveys and WMAP analyses of the cosmic microwave background are among them.

The alternative approach to solve all these discrepancies is to postulate that there's no dark matter but the laws of gravity markedly differ from Newton's and Einstein's laws when you get to the galactic scale - or longer. We usually talk about MOND theories - modified Newtonian dynamics.

It's pretty difficult to design a theory of gravity that is as successful as Einstein's if not more so. People have tried, anyway. Most of these theories have been killed by various recent observations, including the clusters on the picture at the top. The clusters show that the location of dark matter may literally get segregated from the location of the visible matter. So unless your theory admits some kind of "negative interference", a modification of the force exerted by the visible matter won't be enough to explain the observations.


So what is the dark matter made of?

Dark matter must be invisible to the telescopes. But it may still be composed out of large, robust, heavy objects - MACHOs or RAMBOs - or small sissies that are technically known as WIMPs. We will see that all these three terms are technical acronyms and all of them are male. There exists no female dark matter candidate. For the sake of equality, I encourage all women scientists to look for female types of dark matter. ;-)

RAMBO, a dark matter candidate. Who will win the battle for 25% of the Universe: RAMBO or Superman? Note that unlike the Superman, RAMBO is still too ordinary a man.

RAMBOs are robust associations of massive baryonic objects - such as clusters of white and brown dwarfs. MACHOs are massive astrophysical compact halo objects. The names are funny but it's pretty clear that most of the dark matter can't be baryonic, anyway. This statement boils down to nucleosynthesis: when the nuclei were born during the first three minutes, their number simply couldn't be too high. It's vaguely compatible with the observed density of visible matter - there's not enough room for the five-fold bigger amoount of dark matter.

So there has to be a non-baryonic component of dark matter, a WIMP: a weakly interacting massive particle. Neutrinos and axions are candidates but for additional reasons, they can't be the only thing that there is - I think that not even the axions are progressive enough (even though they haven't been seen yet). There has to exist a new kind of particle (or several new kinds of particles).

What we demand from the candidates

The particle must be electrically neutral, so that it doesn't emit photons, and it must have very weak interactions with all known particles of the Standard Model, too.

To keep the particles' velocity low enough, so that they have the observed tiny pressure (i.e. for the dark matter to be cold dark matter), they can't be too light - because light particles would behave as radiation at the temperatures of the Universe. They can't be too heavy, either. It just turns out that the allowed interval for the new particle's mass is 100 GeV - the electroweak scale - plus minute two orders of magnitude or so.

Moreover, the new particle has to be stable - for billions of years. However, it must be possible to annihilate it a little bit (most likely, by pairwise collisions) to reduce the initial expected huge concentrations to some plausible concentrations at the present.

When you look at the previous paragraph quantitatively, it becomes immensely natural for the dark matter particle to carry some "Z_2" charge that can only be equal to 0 or 1, and 1+1 is defined as 0 (that's the mod-two addition of the "Z_2" group) which means that they can annihilate in pairs.

If you think about the paragraph before that, it is pretty bizarre why the new unknown particle should be as heavy as the electroweak particles - such as the W and Z bosons. That's not a natural scale e.g. for sterile neutrinos. Just to be sure, the new particle can't be the Higgs boson or anything of the sort because the Higgs is unstable and interacts too strongly. Because the Higgs has a nonzero vev, it must carry no new charges except for the electroweak ones (discrete "Z_2" charges that we want to be preserved - to make the dark matter particle stable).

What new, stable, weakly interacting particle may be naturally linked to the electroweak scale? Well, the electroweak scale may be protected by supersymmetry - remember the hierarchy problem - and supersymmetry offers a natural dark matter candidate!

The virtues of the neutralino

The neutralino is a fermionic, spin-1/2 superpartner of several bosonic particles such as the photon, Z-boson, and the Higgs boson. All these spin-1/2 superpartner particles have the same spin and conserved charges (no electric charge and no color). That's why you must consider all these types simultaneously. Their mass is given by a matrix that generally includes off-diagonal, "mixing" entries. You must re-diagonalize all of them and you obtain a couple of the so-called neutralinos with different masses.

That's why we can't "exactly" say that the new particle is a photino, zino, or higgsino. However, it's true that the dark matter neutralino is typically "mostly bino", i.e. a superpartner of the hypercharge U(1) gauge boson, or "mostly photino", if you want to use a slightly rotated basis relevant for the very low-energy observations. Recall that the photon is mostly B0, with a small mixture of the third (neutral) component of the W-boson; the mixture is given by the Weinberg angle. There is a small mixture of the other types in the linear combination, too.

The neutralino is stable because it is the lightest supersymmetric particle, or LSP for short. Supersymmetry doubles the number of known particles by adding the superpartners. It turns out that all the known particles may be defined to carry a vanishing "Z_2" charge (0) while all their superpartners may carry a non-trivial "Z_2" charge (1). This new discrete charge, added modulo two, is called the R-parity.

R-parity should be preserved - exactly or almost exactly - in any supersymmetric model to keep the proton stable and to do many other things. And indeed, there are models where it works. The R-parity neatly plays the role of the "Z_2" charge mentioned above. It allows the lightest particle with the "Z_2" charge to be stable - because the R-parity conservation prevents it from decaying to R-parity uncharged objects, while the energy conservation prevents it from decaying to all other R-parity charged (and, by assumption, heavier) objects.

R-parity is a nearly unique natural solution

This is a cute picture. There is a natural "Z_2" (binary) quantum number that supersymmetry predicts and it's exactly the right ingredient to ensure one stable particle species that can annihilate in pairs.

If you think about other types of "Z_2" symmetries, you will find out that the "generic" possibilities are usually contrived. You will have to invent a new "Z_2" symmetry but all the Standard Model particles have to be neutral under this "Z_2". However, you will have to add your dark matter candidate that is charged.

Why are there so many neutral particles but just the new dark-matter one(s) is or are charged under the "Z_2"? It surely looks like that you only added a "Z_2" because you wanted a new stable particle but this "Z_2" doesn't have any independent explanation. It's actually pretty unlikely that such exact, random "Z_2" symmetries that don't transform the known particles exist.

It's much more natural if the numbers of "Z_2"-neutral and "Z_2"-charged objects are equal to each other (or at least nearly equal), which is the case of the R-parity emerging from supersymmetry. But for you to find such a charge, you need to be able to produce a "charged partner" for every neutral particle of the Standard Model.

So in some sense, you are led to the doubling of the Standard Model. The dark matter considerations make the doubling of the Standard Model spectrum very natural. Supersymmetry is the most natural realization of this concept.

The WIMP on the left, Clark Kent, one routinely observed via its gravitational impact, could actually be a Superman on the right.

To be sure, supersymmetry is not quite the unique realization.

In fact, you can also associate that Standard Model particles with their partners that move in extra dimensions. Because of quantum mechanics, the momentum is quantized and the particles with each allowed value of the extra-dimensional momentum will look like new particle species in 3+1 dimensions, the so-called Kaluza-Klein modes of the known (and unmoving, in extra dimensions) particles. The minimum unit of "momentum" in the extra dimensions, let's call it "p=1" (and let's imagine a circular new dimension for a while), may sometimes be defined to be the charged states under the R-parity.

The discovery of the extra dimensions would surely be at least as exciting as the discovery of supersymmetry. I want to make you sure that in principle, it's possible to find a similar "Z_2" group that emerges from some types of extra dimensions and that plays the role of the R-parity in supersymmetric models.

The corresponding lightest particles moving in the extra dimensions are known as LKPs - the lightest Kaluza-Klein particles - and they're stable for the same (or isomorphic) reason as LSPs in supersymmetric theories. However, the spectrum doubles (or gets multiplied by infinity) and the new, extra-dimensional particles actually have the same statistics as the original particles in the Standard Model; in supersymmetry, the R-parity-charged particles have the opposite statistics.

Without supersymmetry and extra dimensions, it will be very hard for you to associate new "partners" to each Standard Model particle. It's especially hard with the gauge bosons: you can't just add new gauge bosons because that would extend the gauge group and add new symmetries and charges. But you kind of want the new fermions etc. to carry the same "old" charges as our well-known fermions under our well-known gauge groups instead.

While new dimensions would be more shocking "geometrically", supersymmetry is actually more revolutionary from the "algebraic" viewpoint. It's stunning that one can construct an interacting theory in which all the properties of bosons and fermions are exactly linked.

The fact that such a theory - when spontaneously broken - may still reproduce all the facts about the Standard Model - and to exceed the Standard Model in the explanations of dark matter (because it naturally predicts a particle that has all the required properties to behave as dark matter) - is another non-trivial reason to take supersymmetry very seriously.

And that's the memo.

1 comment:

  1. Dear Sir,

    Can Dark Matter coagulate to form Blackholes. And if so, in what respect would it differ from the known Blackholes?

    Best Regards,