Monday, October 27, 2014

Tiny dark energy from co-existence of phases

There are some interesting hep-ph articles on the arXiv today. I will mention two of them – both papers are available on owned by Elsevier (so their title pages are almost identical). First, there is the paper
SUSY fits with full LHC Run I data
by the MasterCode Collaboration (represented by Kees Jan de Vries). They present the state-of-the-art fits on simple supersymmetric models. Unless one relies on a significant amount of good luck, the anomalous value of the muon magnetic moment can only be satisfactorily explained by the superpartners – without contradicting the current bounds imposed by the LHC – if one sacrifices the usual grand-unification-inspired relationship between the MSSM couplings.

But I want to spend more time with
On the smallness of the cosmological constant
by Froggatt, Nevzorov, Nielsen, and Thomas (they have written similar papers in the past). They want to explain the small value of the cosmological constant – and perhaps also of the Higgs mass – in the Planck units using their "Multiple Point Principle" (MPP).

The principle first postulated in 1993 or 1995 says that Nature wants to choose the values of some parameters in the theory to allow the co-existence of "phases" with the same value of the energy density. In this particular paper, they study the principle in the context of supergravity models that allow the co-existence of supersymmetry-preserving and supersymmetry-breaking Minkowski (zero cosmological constant) vacua.

The supersymmetry-preserving vacua may have demonstrably vanishing (or tiny?) values of the cosmological constant (or the Higgs mass), and the MPP then implies the same virtues for the supersymmetry-breaking vacua (for which the vanishing or smallness otherwise looks like fine-tuning).

It seems to me that they only use the other vacua to explain the properties of our vacuum – while the other degenerate vacua remain "unused in physics". In this sense, if I understood the paper well, they are not proposing a version of my favorite paradigm of the cosmological constant seesaw mechanism. I am still in love with the latter idea, spending some research time with it. Sometime in the future, I may write some update about it – how it effectively deals with the existence of fields that take values in a discrete set and how calculations may be done with such variables.

These authors are linking the small magnitude of the dark energy and the Higgs boson's lightness to the vanishing of some couplings near the Planck scale which also seems to be equivalent to the bounds on the Higgs stability and to the degeneracy of the vacua, and so on. There are some specific computations concerning the gaugino condensates etc.

The tip of an iceberg swimming in the ocean is likely to be close to 0 °C.

Unfortunately, the principles and logic of the new way of looking at these things aren't spelled out too clearly. In particular, I don't understand whether MPP could be compatible with string theory. String theory dictates the value of couplings in all of its effective field theories. But could the stringy ways to calculate them be (approximately or exactly) equivalent to the MPP, the requirement that phases may co-exist? Why would it work in this way? And if this doesn't work exactly in this way, could there be some room for such a new principle adjusting the effective couplings?

Why should the MPP be true in the first place? In the usual reasoning about naturalness, we allow some otherwise unnatural values of couplings if they are able to increase the amount of symmetry of the physical theory. A theory with a larger symmetry is "qualitatively different", so the probability distribution may have a delta-function-like peak at the loci of the parameter space with enhanced symmetry.

But maybe points of the parameter space that allow the "co-existence" (can they really co-exist!?) of two ore several phases are also "qualitatively different", even if there is no obvious enhanced symmetry, so they may be more likely. Is that what we should believe? And if it is, is there a clearer justification for this belief?

The analogy with the phase transitions of solids, liquids, and gases may be highly attractive. Think about water. The temperature \(T\) is a continuous parameter and all values are equally likely. In particular, you might predict that the percentage of water whose temperature is 0 °C (plus minus 0.01 °C) will be tiny.

Except that when ice is melting or water is freezing, it spends some time exactly at 0 °C (or whatever is the relevant melting point) because heat isn't being spent to change \(T\) at this point; instead, heat is being spent to change the percentage of ice vs liquid water in the mixture. So indeed, you find lots of places on Earth where the temperature of water or ice is almost exactly 0 °C.

However, in that case of water, I actually gave you a mechanism which explains why the probability density for \(T\) gets a delta-function-like peak at \(T=0\) °C. Could there be a similar "melting-like" mechanism if we replaced \(T\) by the energy density \(\rho\)? And if there is no such mechanism (and let's admit, it seems hard to gradually change \(\rho\)), isn't it a problem for the MPP? Shouldn't a similar mechanism or "qualitative change" of the dynamics be a condition if we claim that some regions of the parameter space are much more likely than others?

There are many interesting questions and "incomplete answers" I can give you but I would like to hear some complete answers and I am not sure that these answers are included – explicitly or implicitly – in this very interesting paper.


  1. If it is a second order transition, there is no latent enthalpy nor is there a sudden slope change in a thermodynamic observable (first derivative continuous). Second order transitions display divergent susceptibility, infinite correlation length, and power-law decay of correlations near criticality.

  2. Very interesting papers:
    (1)”Unless one relies on a significant amount of good luck,
    the anomalous value of the muon magnetic moment * can only be* satisfactorily explained by the superpartners – without contradicting the current bounds imposed by the LHC – if one sacrifices the usual grand-unification-inspired relationship between the MSSM couplings.” If this is a fact, it should give
    good boost to SUSY. All of remember that calculation of anomalous magnetic moment of electron gave a big boost to QED.
    (2) I am wondering if there are models (other than MPP) which relate the two great puzzles i.e smallness of CC and smallness of Higgs mass. I have yet to read about your see saw

  3. Off topic, shouldn't the roughly eagg shaped iceberg in the picture above rotate roughly 90 degrees to minimize its gravitational potential energy?

  4. Could the MPP be used of some kind of constraint to find vacua that resemble our universe, if it can be reasonably motivated from string theory? About the motivation for the MPP I am very curious too ... :-)

  5. Aleksandar MikovicOct 30, 2014, 10:44:00 AM

    There is a simpler explanation for the smallness of the cosmological constant which is based on the assumption that spacetime is a simplicial complex and the metric is replaced by the edge lengths, see arxiv:1407.1394, arxiv:1407.1124 and arxiv:1402.4672 . The corresponding path integral is finite for an appropriate choice of the measure and the effective action can be approximated by the usual QFT with a physical UV cutoff which corresponds to a minimal edge length, which must be much greater than the Planck length. The effective CC is given by the sum of the classical CC + quantum gravity CC + matter CC. One can set the sum classical CC + matter CC to zero, so that CC = quantum gravity CC = O(l_P^4/L_0^4), which for L_0 = 10^{-5} m gives the observed value.