bluecap said:
What range of energy in TeV do you think the Superpartners can be lurking?
This I am really not the right one to ask or answer.
I do take interest supergravity, on the grounds that it has excellent theoretical motivation, and I appreciate the curious fact that KK-compactifications to 4d that preserve global ##N=1## supersymmetry happen to be those that are
mathematically rich (CY-geometry, ##G_2##-geometry), whatever that may be telling us; but I notice that there seems to be no theoretical reason why these compactifications should be dynamically preferred, and that the folklore of their phenomenological motivations (hierarchy problem, gauge coupling unification, naturalness) is based on an essentially numerological attitude only.
This makes me want to recall that:
"The alternative to naturalness, often neglected as an alternative, is having a theory."
which is a great sentence that one finds in
Kane 17, p. 56 (6-10).
Now Kane of course does assume ##G_2##-compactification, which, while certainly interesting in itself, seems to be lacking a dynamical explanation from within the theory; but that granted then the great achievement of him and his collaborators is that, based on this single assumption, they first of all try to and then to a remarkable extent succeed with working out the theoretical consequences systematically, by analysis of the theory. Even if the result eventually disagrees with experiment, we will have learned what the generic predictions of this model are, hence will have learned something tangible about 11d supergravity and its UV completion, while from much of the unsystematic by-hand susy model building entertained elsewhere we will possibly have to conclude in 50 years time to have learned little, besides the lesson that physics unconstrained by theoretical framework becomes arbitrary.
One of the theoretical insights that Kane and collaborators have been amplifying is that in this model the gravitino mass after susy-breaking sets the scale for the moduli and the superpartners, such that, in the words of
Kane 17, p. 43 (5-1), the upshot is this:
"When supersymmetry is broken the gravitino becomes massive — the splitting between the graviton (always massless) and the gravitino is a measure of the strength of the supersymmetry breaking, and it sets the scale for all the superpartner masses.
"It is important to understand that there are two measures relevant to understanding supersymmetry breaking, one the scale at which it is broken (about ##10^{14}## GeV as described above), and the other the resulting gravitino mass. In the compactified M-theory case the gravitino mass is calculated, and comes out to be about 40 TeV (40 000 GeV). Sometimes even experts confuse these two scales if they are speculating about supersymmetry breaking without a real theory to calculate.
"Thus 40 TeV is the natural scale for superpartner masses. That is not a surprising number in a theory starting with everything at the Planck scale, but it is surprising if one expects the superpartner masses to be near the particle masses (all well below 1 TeV). The squarks and other masses are indeed predicted to be at the gravitino scale, tens of tera-electronvolts."
"The theory has formulas (‘supergravity formulas’) for all the masses. When one calculates carefully the masses of the superpartners of the gauge bosons that mediate the Standard Model forces they turn out to get no contribution from one large source, and the resulting value for the superpartners of the gauge bosons (gauginos) is about 1 TeV, rather than about 40 TeV. They are the gluino, photino, zino, and wino. The strong force gluino is heavier, about 1.5 TeV or somewhat more, and the electroweak ones (photino, zino, wino) are somewhat lighter, about half a tera-electronvolt. The lightest superpartner, which is important for how to detect the signals at the LHC and for understanding dark `matter, will be a combination of the electroweak ones, and thus about half a tera-electronvolt in mass. All of these are observable at the LHC in the run underway through 2018. That run is supposed to collect an amount of data measured in units called inverse femtobarns (##fb^{-1}##). At the time of writing (December 2016) it has collected about ##40 fb^{-1}##, and is into the region where we can hope for signals of gauginos. The goal for the LHC is to collect ##300 fb^{-1}## through 2018. Without a detailed theory to calculate with, we would not have had serious predictions for masses."
(from
Kane 17, chapter 5).
