String phenomenology 2011: Gordon Kane

Francis Emule News (Spanish) direct our attention to a very interesting conference that took place in Madison, Wisconsin last week:

String Phenomenology 2011 (talks)

There are many interesting talks in heterotic string theory model building, F-theory model building (which became dominant these days, partly because it was absent as recently as a decade ago: there are lots of entries about it on TRF), and some type IIA string theory quivers. You learn about SUSY in the early Universe, exophobia, leptophobia, other manias, mu-problem and the proton decay, robust stringy electroweak similar breaking, and so on.

The composition of the topics suggests that this sub-discipline of string theory is very healthy these days. The mathematically rich features of the theories rooted in actual detailed observed properties of particle physics are the central players once again. In particular, there seems to be no anthropic metaphysics and dogmatic egalitarianism or mediocrity on these conferences anymore.



Every proper American capital has a Capitol. I have only seen those in D.C. and Austin.

Together with Francis, however, I will choose the singular \(G_2\) holonomy manifolds compactifications of M-theory - the second newest player in stringy phenomenology that was added around 2000 in papers by Witten and others.




The relevant talk was delivered by Gordon Kane:

String theory and generic predictions for our world – superpartner masses, LHC signatures, dark matter, EWSB, cosmological history of universe, etc

An ambitious title. While Gordy Kane may be considered the main source of excitement and testosterone in the M-theory model building, he couldn't do his work without collaborators. Bobby Acharya is arguably the most famous and deepest among them - but there are other young people who work in this business.

They have decided that they have understood lots of very characteristic predictions of the \(G_2\) vacua of M-theory. Sometimes I am not sure which of the properties are actually derived from the models and which of them follow from observational constraints but they surely do seem certain that there's something very special about the predictions they're making.

Most importantly, the masses of the moduli - the scalar fields remembering the shape of the compactified dimensions - should be "somewhat larger" than 30 TeV; the same inequality holds for the gravitinos. This cosmological constraint goes back to a 2000 paper by Moroi and Randall; and was revisited in a 2008 paper by Acharya, Kumar, Bobkov, Kane, Shao, and Watson (now you know the names of many of the bright folks).

The 2008 paper makes it clear that there are some cosmological constraints that were assumed to hold; and some other conditions that were satisfied by the \(G_2\) compactifications as a bonus (a nontrivial check of the theory). The precise attribution which of the claims about the solved problems and numerical results follow from which assumptions - or the theory - is somewhat complex.

At any rate, here is their new picture of the superpartner and other new particles' masses:



Click to zoom in.

That looks pretty different from all the "behind the corner" SUSY model building - and in some sense, it even resembles split supersymmetry. Let us go through this diagram. ;-)

You see that 4 out of 5 of the MSSM Higgs bosons have masses around 50 TeV; only one Higgs boson is light - and Standard-Model-like - and will be discussed later. The same mass of 50 TeV also holds for all squarks and sleptons; only a stop sits at 30 TeV and a sbottom at 45 TeV or so. Things are very busy near 50 TeV. If I became convinced that this prediction is very likely (which requires some other successes of these ideas as well as my own hard "rediscovery" of those things), I would become a huge advocate of a future 50+ TeV collider. Note that the SSC was supposed to collide 2 beams of 20 TeV protons (40 TeV in total) - it's not that far but you would still need an edge to actually see 50 TeV particles.

There is an "intermediate" range - around 4-5 TeV - where you find the 3rd and 4th neutralino (there are four neutralinos in MSSM - superpartners of the photon, Z-boson, and two neutral Higgs components: well, I mean their linear combinations that are mass eigenstates) and the 2nd chargino and its antiparticle (there are 2 charginos in MSSM: superpartners of the W-boson and the charged Higgs components). This 4-5 TeV energy interval may potentially be reached by the LHC but don't expect it much.

The rest is light and directly observable.

That includes a less than 700 GeV gluino - which is not excluded by the LHC so far because the limits for the gluino mass get much more tolerant if the squarks are heavier and they're damn too heavy here, indeed.

Then it includes the 1st (lightest) and 2nd (heavier) neutralinos at 200 GeV and 500 GeV, respectively. The lightest superpartner (LSP) is mostly wino, the superpartner of the \(z\)-component (the neutral one) of the electroweak SU(2) gauge boson. Well, the LSP may also be something else than wino depending on the mu parameter etc.

Finally, what about the light Higgs? The Higgs mass pretty much depends on \(\tan\beta\) and nothing else. This pattern is arguably derivable not only in M-theory in \(G_2\)-holonomy compactifications but in any theory with this kind of split spectrum: RG flows play an important role. The dependence looks like this:



You see that for \(\tan\beta=3\) or so, the Higgs mass starts at 114 GeV, the lower bound imposed by LEP. It initially grows more quickly, reaches 119 GeV (my new favorite value) for \(\tan\beta=4\) and then it grows less quickly. For \(\tan\beta=15\) or so - which seems to be the upper bound according to various recent measurements - the mass stabilizes near 127 GeV or so (which is Kane's favorite mass).

So these models constrain the Higgs mass between 114 and 128 GeV or so which seems perfectly compatible with the measurements at the LHC so far: a Standard-Model-like Higgs boson which is this light requires 10-20 inverse femtobarns to be discovered so we will only get it next year.



A SUSY-friendly Higgs below 130 GeV is pretty much guaranteed by the newest informal exclusions by combined ATLAS+CMS data. Picture via Phil Gibbs taken from a fresh talk by Eilam Gross. I also recommend you to see slide #60 in the talk - what a deja vu: where have you seen the beautiful dark green background color? :-)

You see that the model still plays with fire - it is very boldly predictive. Kane tells you what the gluino will decay into - stop and antitop or sbotton and antibottom; stop or sbottom will instantly decay into a top and bottom (not necessarily in this order) and a neutralino or a chargino. The branching ratios are known, they should tell us additional things, and the decay has a low background and should be nicely accessible by the LHC.

Well, things are less clear when it comes to the gaugino masses: Kane indicates that the light gauginos could be partly due to wishful thinking and they could be at those 30 TeV or so, too. At another point, he suggests that some compactifications have light gauginos and some of them don't. His talk makes it rather clear that they're not certain about these matters because e.g. he talks about KKLT D3-branes - there are no D3-branes in M-theory so this "hybridization" of ideas involving type IIB/F landscape seems confusing to a reader who expects precision.

Concerning dark matter, PAMELA (and Fermi) are supposed to observe a pair-wise annihilation of two winos via a chargino in the \(t\)-channel into a W-boson pair. Kane seems confident that the observations are consistent with their models and they may extract one parameter out of them.

For decades, people tried to make all superpartners and other particles as light as possible to maximally solve the (little) hierarchy problem. 

In May 2011, Kane and 3 collaborators pointed out that even if the gravitino mass and other masses are in the 10-50 TeV range, there's a huge portion of the parameter space where the electroweak symmetry breaking induces mass splittings below 1 TeV. One must be a bit more careful about the measure for the fundamental parameters - and realize that e.g. the light Higgs mass isn't quite a fundamental parameter so its relatively low value doesn't immediately imply fine-tuning.

Kane mentions the cosmological constant problem as an open issue but probably not the most serious problem in physics - I agree - and he says that an analogous apparent fine-tuning in the case of the strong CP-problem is being successfully ignored. There are other things he has said but you should go through the talk yourself.

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If you got up to this point, you're among the exceptional, TRFic readers. What follows is an everyday life story unrelated to science. In the morning, I had two funny minor expenses.

After many years, I met 3 municipal cops - 1 man and 2 women - and discussed whether one may ride one's bike on the sidewalk. Because of their weapons and a sophisticated nation-wide system to strengthen this mafia, they won the debate against your humble correspondent and I had to pay. ;-)

Then I bought a 1 GB RAM memory to speed up my aging desktop but some detailed properties - going beyond it's being DDR2 and 553 MHz - didn't match so mixing with the old chip didn't work and I possess a useless $15 chip. ;-)