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A quasi-anthropic stringy reason why dark matter is no WIMP?

Why my followers, moderate anthropic believers, may only believe some anthropically sounding arguments

Brilliant physicist Bobby Acharya has tweeted about the media coverage, e.g. in Phys.ORG, of their April 2016 paper

The lightest visible-sector supersymmetric particle is likely to be unstable
that appeared in PRL two weeks ago.

The dark matter particle hasn't been directly detected on Earth although it could have been. So the probability that it is a WIMP – a weakly interacting massive particle – has decreased. It hasn't decreased "spectacularly" but it has arguably decreased "visibly", by a factor of two or something like that. Dark matter may be composed of LIGO-style black holes or axion-like ultralight scalars. Or it could refuse to exist – and some sort of MOND, perhaps with ideas analogous to Verlinde's recent speculations explaining it microscopically, could explain the phenomena mostly attributed to dark matter.

But in the paper we discuss now, Acharya, S. Ellis, G. Kane, B. Nelson, and M. Perry propose something else. The dark matter could be a superpartner but it's very likely that if string theory is right, it should be a superpartner of a particle that doesn't belong to the Standard Model. Not only the dark matter particle hasn't been observed yet; its "original" superpartner isn't known yet, either.

So even though an LSP WIMP has been the preferred dark matter candidate of most supersymmetry phenomenologists and even though the spacetime supersymmetry is a feature of all realistic stringy descriptions of reality (claims to the contrary exist but let me not distract you), the authors claim that string theorists should actually believe that Nature does not use the pro-WIMP "cosmic coincidence".

To defend this proposition, they make some observations about the spectrum of light particle species in the string-theoretical vacua:
  1. Almost all vacua in string theory – F-theory, M-theory, free-fermionic heterotic strings, and others – contain hidden sectors, usually many of them.
  2. These sectors may contain particles and superpartners that may be lighter than the Standard Model particles and given the larger number of the sectors and the absence of a reason why they shouldn't be lighter, the hidden sector particles that are lighter probably exist.
  3. String theory seemingly unavoidably predicts nonzero interactions between the Standard Model fields and those in the hidden sectors, especially various \(F^{\rm SM}_{\mu\nu}F^{\mu\nu}_{\rm hidden}\) kinetic mixing of \(U(1)\) gauge fields. So the lightest Standard Model superpartner is likely to be allowed to decay to hidden sector particles and the decay proceeds much more quickly than at cosmological timescales.
It's a fun argumentation and I feel uncertain whether I should take it seriously. Needless to say, the most problematic phrase is "most string vacua" which refers to typicality and some sort of the anthropic principle. Is it acceptable?

One may accept this sort of argumentation or refuse it.

Moderate anthropicism

In the past, I have repeatedly suggested that I can imagine that Nature prefers some "middle of the road" attitude to the anthropic reasoning. The full egalitarianism may be wrong but "some arguments" of this flavor may be right.

Acharya's and pals' specific proposal helped me to articulate the "middle of the road" reasoning a bit more explicitly than ever before. Why and how?

There's a reason why I don't buy most arguments in the literature that claim that "we are generic" or "our cells have to be typical" or "our architecture of life is the most represented one" or "all vacua in string theory are equally likely" – but why I tend to take the Acharya et al. argument more seriously. Do I have double standards?

I think that there is a difference between the "most outrageous" examples of the reasoning based on typicality on one side; and this typicality of vacua that is used to deduce that the lightest Standard Model superpartner is unstable. What's the difference? Well, the difference is that the vacua in the paper by Acharya et al. are sufficiently similar to each other for us to treat them as a "nation" where everyone has the same right or a similar probability to be the foundation of the world around us.

In more outrageous examples of the anthropic reasoning, this "democracy" has no good reason and there may exist very good reasons why the people, stars, Boltzmann Brains, or whatever the anthropic radicals love to talk about are not equally likely.

Group differences in ancient Rome

We may explain these comments by a political metaphor. Imagine that you find yourself living in a forest in ancient Rome. You've forgotten about your previous life – who you are. And someone asks you whether you are a patrician or a plebeian. He tells you that the numbers of members of these two groups are very different. Let's ignore the history and assume that the number of plebeians was 100 times higher than the number of patricians.

If you were a mindless anthropic believer who lives in the forest, you could immediately say that you are probably a plebeian – because the number of plebeians is so much higher. But is it a valid reasoning? The reason why I don't find it too good is that the plebeians and the patricians are very different groups. There was no democracy making them "equally valued". And in fact, only the patricians formed the ruling class and participated in the democracy. This "restricted democracy" is what I needed in the metaphor and why I picked ancient Rome as my example. (I didn't want unproductive off-topic exchanges with fanatical defenders of women's suffrage, either LOL.)

This political difference wasn't quite a silly coincidence. It has largely boiled to some innate or historical differences between these two groups. (I don't want to argue about the question whether those statements were really right in ancient Rome. You may surely imagine a civilization where they are right.) In particular, a patrician may be much more likely to think about the validity of statistical arguments such as the quasi-anthropic argument designed to "prove" that he is a plebeian. One reason is that you may have needed a training in statistics (in the past) to statistically think at all and only the patricians have received this training.

So I don't really think that it's right for you, a guy in the forest in ancient Rome, to conclude that you are probably a plebeian. The large number of plebeians may be a positive reason to favor the idea that you are a plebeian. But there are arguments going in the opposite direction, too. One of them is that it's more likely for a patrician to carefully think about such matters. And because you're thinking about them, it increases the probability that you are a patrician. It's not quite clear which of these two arguments – pushing the answer to opposite directions – is stronger if any. The correct answers depend on a comparison of some numbers and those numbers aren't known, at least not accurately enough.

Analogously, when you're picking string vacua, the extreme anthropic believers want to say that "all string vacua are equally likely" and things like that. So if they find the largest group of string vacua – which is e.g. larger by hundreds of thousands of orders of magnitude than others – their way of thinking makes them conclude that our world must be one of those very numerous vacua.

I don't believe the conclusion and I think that this whole way of thinking is fallacious. The reason is that each of the elements of the set of vacua that has 10272,000 elements may very well be about 10500,000 times less likely than the elements of classes of vacua which have far fewer elements. The universe may have heavily punished these "plebeians" during the vacuum selection process because their being plebeians is so visible. There's just no reason for this "group difference" not to exist. If the suppression by 10-500,000 exists, it's virtually impossible for your world to be one of the 10272,000 vacua, despite their high number.

You may see why I think that the defenders of the radical anthropic principle tend to be far left politically.

My point is the following. Whenever someone uses a typicality argument, you should think whether it is a
  • "Lumo-indefensible typicality argument" or
  • "Lumo-defensible typicality argument".
It's the former (invalid application of the anthropic reasoning) if the elements in the subset and its complement are "intrinsically or historically different", the differences is "immediately obvious" (you don't need to wait or run complicated tests to find the difference), and there are good reasons to think that there might be big "group differences" similar to the differences between the plebeians and the patricians. It's the latter (tolerable application of the anthropic reasoning) if there are no mechanisms (or at least no known mechanisms) how the "group differences" could have evolved.

Acharya et al. are comparing vacua in a set that does look like the set of patricians, a "politically uniform nation". If most of them have hidden sectors and sufficient interactions to destabilize the lightest Standard Model superpartners, you may interpret this fact as a vote by the patricians and you may want to take the result seriously.

Isn't the stability of the lightest Standard Model superpartner a characteristic that divides the set in the same way as the Romans may have been divided to patricians and plebeians? The answer is probably "No" because the decay of the Standard Model superpartners is a consequence of the choice of the vacua, something that decides about the distant future. But it is probably not a cause that has affected the very process of vacuum selection.

In other words, I want to say that a more careful, weaker, Lumo-approved version of the anthropic principle doesn't say that the probability that we live in the \(n\)-th vacuum is \(P_n={\rm const}\), a constant independent of \(n\) and fully determined by \(\sum P_n = 1\). Instead, the probabilities \(P_n\) must be allowed to depend on some features of the \(n\)-th vacuum that could have reasonably and strongly affected the vacuum selection process, some very obvious "innate or historical group differences".

For example, \(P_n\) may be extremely small if \(n\) is a Calabi-Yau compactification with very high Hodge numbers – when a highly complex Calabi-Yau manifold is used for the hidden dimensions. Maybe, the evolution of the early Universe demanded such a complex Calabi-Yau manifold to "evolve" and this achievement may be much more likely for Calabi-Yaus with low Hodge numbers – and those may very well be favored, despite the small number of elements in this set.

However, the property that Acharya et al. "derive" by their quasi-anthropic argument is a "consequence" of some "technical details" describing each vacuum and not a reasonable cause affecting the likelihood of a particular vacuum selection. They are comparing "patricians with other patricians" that have comparable Hodge numbers and other characteristics that are obvious to the naked eye.

And that's why I find it reasonable to assign comparable probabilities \(P_n\) to all elements in the set of vacua that Acharya et al. are comparing – and why I tend to be sympathetic to their argumentation and conclusions, too. The vacua just look like citizens in an "innately or historically uniform nation" and when a large majority of elements in such a set have a certain property, one may believe that this property is likely to hold for "you" when you want to know "who you are" and "where you come from".

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