SUSY Still in Hiding

Recent rumors supposedly coming from theorists at Harvard indicating that today would be the day that an announcement would be made of first evidence for a superpartner of a top quark have just been shot down. The talk at CERN on recent ATLAS searches for such a signal shows that nothing was found. An example of new limits is that if stops are produced via gluinos, the gluino has to have mass greater that 650 GeV and the stop a mass greater than 450 GeV.

Over the past year the LHC has conclusively falsified pre-LHC predictions that strongly interacting superpartners would easily be seen in the early data, with typical bounds on gluino masses now up to 1 TeV or so. One way to evade this conclusion has been to argue that the first two generations of squarks are quite heavy, with only the sbottoms and stops accessible to the LHC. A typical example of analysis of scenarios of this kind can be found here, where the conclusion is that naturalness requires that the mass of an stop be less than 400 GeV, and the mass of a gluino less than twice the mass of the stop. This is now starting to be in significant disagreement with the data.

The ATLAS analysis uses 2 fb-1 of data, with the promise of updated results using the full 4-5 fb-1 coming soon. The details of the new analyses were made public today here, here and here. For some background, see the latest posting at Resonaances. I hear that similar analyses now completed by CMS, with the full 2011 dataset, also show nothing. This week the earliest of the Winter conferences is going on, at Aspen, and tomorrow there will be talks updating the LHC SUSY situation from ATLAS, CMS, and theorist Matt Reece.

The LHC has done an impressive job of investigating and leaving in tatters the SUSY/extra-dimensional speculative universe that has dominated particle theory for much of the last thirty years, and this is likely to be one of its main legacies. These fields will undoubtedly continue to play a large role in particle theory, no matter how bad the experimental situation gets, as their advocates argue “Never, never, never give up!”, but fewer and fewer people will take them seriously. As always seemed likely, the big mystery the LHC will solve will be that of the Higgs: is it really there, and if so does it behave as the Standard Model predicts, or does it do something more interesting? Unfortunately we’re going to have to wait a while longer for more news on that front.

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57 Responses to SUSY Still in Hiding

  1. manyoso says:

    With so many prominent theorists betting on SUSY over the last few decades and the continued null signal at the LHC… if this continues couldn’t you almost call it ‘New Physics’ discovered by the LHC in that so many expected to see SUSY?

  2. Harry says:

    “Never, never, never give up!”.. Is this supposed to echo Churchill’s “never, never, never […] give in except to convictions of honour and good sense” ? 🙂

  3. physicsphile says:

    Having spoken to someone working at the LHC, apparently crazy seeming results are always turning up but they have always gone away on closer examination. So it would probably be better if the rumor mongers rather wait to get the official word from CERN.

  4. MathPhys says:

    In my humble opinion, the belief that there is susy and it solves many problems, but we don’t see it because it’s softly broken, and if we go to high enough energy, we’ll see it again, is one of the most simple-minded ideas in modern physics.

    I have to believe that God is more imaginative than that.

  5. Peter Woit says:

    physicsphile,

    Or they could get higher-quality rumors from more reliable blogs…

    MathPhys,

    What’s odd is that since following this logic leads you quickly to something quite ugly that explains very little (105 extra parameters???). I’ve never understood why people found that route attractive. There’s some fascinating mathematical structure going on, and I can see why people want to take that seriously, but there’s also clearly some big ideas missing about how to relate this to the real world.

  6. MathPhys says:

    Peter,

    In my very humble opinion, people take the susy road for two reasons

    1. The mathematically-minded types find supersymmetric quantum field theories extremely attractive because you can do some stunning things in them.

    In QCD, you work so hard for so long to compute some radiative correction to low order in perturbation theory, then you go to super YM and use relatively simple arguments to obtain some deeply non perturbative results. It’ hypnotic.

    2. To the rest, it’s a good way to generate a steady stream of papers.

    I think that things are getting really exciting in high energy physics now. I am very curious how things will be like 5 years from now.

    Can such a wonderful, elegant and extremely useful mathematical structure turn out to be physically totally irrelevant? Did the “unreasonable effective of mathematics in the physical world” finally let us down? Very exciting times ahead.

  7. MathPhys says:

    I went to a talk on some topic in a hyperbolic universe. The speaker started by saying that of course we know that the universe is not hyperbolic, but it’s still important to learn as much as we can about that topic regardless of the parameters.

    I think that that’s how people will continue to work on many topics long after LHC discredits them. My point of view is that, if it’s harmless and makes you happy, go for it.

  8. Pingback: My own private I dunno | Emanuel Derman

  9. Cesar Laia says:

    I don’t understand why they used only 2 fb-1 of data, when they have already 5 fb-1. If the 5 fb-1 data will come soon, I guess they already have an idea of it’s coming. So… would it make any sense to announce now they saw notting just to say a few months later that actually there is something new?

  10. Peter Woit says:

    Cesar,

    It takes a lot of work to analyze this data. They need to completely understand the behavior of their detector and all the possible sources of background. And the data was gathered over 2011 under changing conditions (luminosity was increasing, triggers changing). So, possibly quite a lot more work is needed to analyze the rest of the data set.

    Right now ATLAS has the best bounds on SUSY of this kind, which is presumably why they announced now. They’re in a competition with CMS, which provides pressure to release results once they have confidence in them, not wait for something better.

  11. Angel Naydenov says:

    Dear Peter,
    I am currently reading Chapter 12 of your book and to be honest, I was hesitating to continue once the stop rumour surfaced.
    However, it looks as if apologies are in order for letting you down. All seems so logical when you explain it, it’s fascinating that your view is not shared by the majority of scientists.
    Do you believe a paradigm shift is on its way? Which direction shall we choose to make a step forward?
    Thanks, and please blog more! 🙂

  12. Eric says:

    There are actually two separate issues which are being confused here, the rumors regarding the stop having been seen at the LHC and the speculation of one blogger that these rumors were to be addressed in a seminar this past Tuesday. The speculation regarding the Tuesday seminar did not pan out, however it does not then follow that there is nothing to the rumors. Be patient and let the experimenters complete their analyses.

  13. Anonyrat says:

    Eric, Tuesday’s seminar set more stringent bounds on sTops, so……

  14. Eric says:

    Anonyrat, this is only with 2 fb-1 of data, whereas 5 fb-1 of data has been collected, so…

  15. Anonyrat says:

    sigh, if the 2 fb-1 showed some hint of something, then its strengthening in 3 additional fb-1 of data would be plausible.

  16. MathPhys says:

    Is there a way to put money on whether susy will or will not discovered, let’s say by end of 2012?

    I want to bet $100.00 that there will be NO evidence of susy by end of 2012. `Evidence’ here means an official announcement from LHC. Rumours do not count.

  17. Peter Woit says:

    Angel,

    Thanks, though I should point out though that my views about SUSY, string theory, extra dimensions, etc. have never really been minority ones, and definitely aren’t now. I think MathPhys is going to have trouble finding anyone willing to bet $100 on SUSY this year, or maybe even on SUSY this decade.

    One big lesson of the LHC I think is going to be that the Standard Model is just too good. None of the ideas of dramatically adding lots of complicated structure to it are having any success. It would be a good idea to concentrate on what we don’t understand about the Standard Model itself (one example: how to formulate chiral gauge theories non-perturbatively). Personally I’m enthusiastic about new ideas I’m working on about how to handle gauge symmetry with a variant of BRST called Dirac cohomology, as well as related ideas about the relationship of QFT and Langlands theory in math. But, people should work on whatever they enjoy and think is promising. It’s getting harder and harder though to claim that SUSY ideas like the MSSM are in any sense “promising” these days.

  18. anon. says:

    Two brief comments:

    * The original rumors I heard, at least, were about CMS, not ATLAS. Further attempts to ferret out what’s going on haven’t turned up anything, and the rumors exist in several contradictory strains, so I doubt there was any substance to them.

    * Tuesday’s seminar didn’t set more stringent limits on stops, it set limits on gluinos decaying to stops, and not really more stringent ones than previous same-sign dilepton analyses had set.

  19. sUP says:

    Dear Peter,

    if there is no SUSY out there, what would be most promissing explanations for so called dark matter/energy puzzle?

  20. Peter Woit says:

    anon.,

    I’m still curious about where these supposed Harvard-originated rumors came from. I’ve seen one soon-to-be-released CMS SUSY analysis very similar to the new ATLAS ones, and they see nada.

    It always seems to be though that as new ATLAS/CMS analyses are released, we hear “move along, nothing new to see here”. Is there an analysis to be released at Moriond that SUSY proponents can point to as likely to provide a signal according to one of their favorite scenarios? If not, what is the time scale for such an analysis: Summer 2012? Winter 2013? Winter 2016?

    sUP,

    SUSY never gave an explanation of dark energy. For dark matter, I know of no explanation that could be called “promising”, SUSY or otherwise.

  21. Shantanu says:

    suP, dark energy could be a plain cold cosmological constant or just back reaction
    due to density inhomogeneties (which has nothing to do with SUSY)

    Also dark matter could be axion or primordial black holes (nothing to do with
    SUSY) or massive graviton and many other such candidates nothing to do with SUSY.
    none of these are ruled out.
    Or maybe dark matter also could be due to modified gravity (yes, people
    always cite bullet cluster as a counter-evidence against this, but that is oversold
    and bullet cluster observations pose problems for dark matter).

  22. anon. says:

    Rumors I heard originated with CERN theorists.

    A few results so far that were not “nothing to see here,” in my idiosyncratic opinion:
    * First 1/fb jets+MET results
    * First 1/fb same-sign dilepton results
    * ATLAS limit on sbottom -> bottom + invisible
    * Limits on R-hadrons
    * The potential Higgs signal

    All of these wiped out huge chunks of parameter space. I don’t know if Moriond will give us anything as dramatic or not. Direct stop searches are more difficult, but will be very interesting, whenever they start to appear.

  23. harryb says:

    @MathPhys

    “Is there a way to put money on whether susy will or will not discovered, let’s say by end of 2012?”

    Yes. Go to Intrade.com and you will find a potential market there. I raised this before in this blog a month ago, and was chastised for leading people to a market that is too thin for real gains. Whatever, acorns, oaks etc.

    I still believe that if there was an active “market” for current theories then as in sports that were latterly opened up to proper markets, interesting bets might take place. (Who would believe a left tackle is the second highest paid position in American football etc).

    If capitalism / market theory (flawed or nor depending on your political flavour) is essentially a human endeavour, as is science, then a consilience between the two ought to be at least explored. If nothing else it would take esoterica more mainstream and if String Theory stock fell miserably, we all might feel a bit more comforted (and if it rose, then we would have explaining to do).

    Anyway – I think the market test you propose is very good. Good luck at Intrade.

  24. SpearMarktheSecond says:

    Well, if there is thermal equilibrium between quarks/leptons and the dark matter, a weak interaction cross section between quarks/leptons and the dark matter is indicated. Hence the promising WIMP conjecture.

    That SUSY implementations got this right along with detailed Big Bang modeling was also promising.

    But SUSY has lots of nutty adaptations in it… like 5 squarks degenerate in mass. Also… left handed scalars and right handed scalars. Lots of people have trashed SUSY for a long, long time.

  25. MathPhys says:

    @SpearMarkTheSecond,

    Can you give us more details of how susy model building was abused? This has always been my impression as well, but I don’t know enough phenomenology to say something meaningful. I go to their talks and I hear what I consider to be unimaginative science fiction, but everyone else sits there nodding.

    @harryb

    Thank you. I will.

  26. Cesar Laia says:

    I would like to make a question. Everyone seems focused on the LHC results, but what are the chances in the near future that other experiments could give hints about SUSY and other theories? E.g., I wonder what relevance the results from the Planck Telescope will have, but being a laymen I am not aware of other promising experiments. It seems to me that what you need are clever experiments right now.

  27. Shantanu says:

    Cesar, short answer is no. Planck can only potentially detect tensor modes, from
    which you can potentially say something about inflaton potential. but susy says nothing about it.
    In theory if proton decay is detected that could be an indication for SUSY. but again
    the current limits have already ruled out many promising models and I doubt even the SUSY enthusiasts who post on this blog are sanguine about proton decay been detected.

  28. anonymous says:

    Planck is likely to nail 2 important and largely unknown parameters, N_eff and n_s, and is likely to observe f_NL. N_eff is the effective number of neutrino species, which is 3.04 in the standard model. Other CMB experiments (ACT/SPT/WMAP) have been reporting a higher value, albeit with large error bars. Higher N_eff could be evidence for sterile neutrinos. The other two parameters, n_s and f_NL, are important for understanding cosmic inflation or alternative theories. Planck is probably not sensitive to the other inflation parameter, r, although BICEP2/Keck Array or some of their up-and-coming competitors may have something to say about it in a couple years. Cosmic inflation is thought to occur around the GUT scale — a lot of new physics to learn there.

    Direct dark matter searches often say they’re in the business of looking for SUSY. These experiments usually postulate the existence of a WIMP and try to observe it scattering off a nucleus. Ones that use aggressive cuts to make sure that all they ever see is WIMPs tend to report negative results (e.g. Xenon-100). Ones that just look for seasonal variations in signal tend to report positive results (e.g. DAMA). Some theories say dark matter annihilation can give excess background in the Fermi telescope, which looks at gamma rays although you shouldn’t take a result based on a too-high background all that seriously.

    One of the more interesting but ignored experiments I see coming together soon is AEGIS, which wants to look at the effect of gravity on antihydrogen. Any surprises there would tell us a lot about the equivalence principle and basic assumptions of particle physics.

  29. Shantanu says:

    anonymous, does super-symmetry actually predict the existence of a sterile neutrino?
    (and conversely if no sterile neutrino is found, does that mean SUSY is ruled out?).
    from what I understand non-0 neutino mass, whether sterile neutrinos exist,
    whether theta_13 is zero or not is completely decoupled from TeV scale physics
    and models for EW symmetry breaking.
    Also I disagree with
    “Cosmic inflation is thought to occur around the GUT scale — a lot of new physics to learn there.”
    This may have been true before WMAP results. but current limits on energy scale of inflation have already ruled out GUT models as I understand.

  30. Rick Ryals says:

    MathPhys,

    If harryb’s market doesn’t do it for you, try Longbets, “The Arena For Accountable Predictions”:

    http://longbets.org/

    You may or may not find a taker, but it’ll be on record, regardless. John Horgan, and more notably, Martin Reese, have predictions there. So do I:

    http://longbets.org/476/

  31. anonymous says:

    Yes, those properties of neutrinos should be independent of most SUSY theories. However, neutrino oscillation is the one piece of “Beyond the Standard Model” physics that has been observed concretely.

    As for the GUT comment, nobody really knows for sure. There’s a lot of parameter space that experiments are actively exploring. The state of the art is the SPT+WMAP+H_0+BAO result at http://arxiv.org/abs/1105.3182 , which has a solid 3.6 sigma evidence of n_s < 1 and the best published upper limit on the tensor-to-scalar ratio (r < 0.21), with figure 8 showing how some of the more optimistic models are getting ruled out. You need to measure r, though, if you really want to learn the energy scale of inflation. With r~0.2, the energy scale of inflation still could be as high as ~10^15 to 10^16 GeV (very approximately), which SUSY people will tell you is the GUT scale. These SPT+WMAP attempts to measure r through CMB temperature only (as opposed to polarization) are running out of steam because cosmic variance ultimately gets in the way ( http://arxiv.org/abs/astro-ph/9407037 ). If r<0.01, then polarization experiments will also start running into lensing and galactic foregrounds. Hopefully an exciting signal gets discovered before then…

  32. Shantanu says:

    Anonymous, you said

    “However, neutrino oscillation is the one piece of “Beyond the Standard Model” physics that has been observed concretely.”
    This is what everyone says in any neutrino talk, but that’s incorrect.
    PDG lists it as part of standard model.

    See the discussion between me, Tomasso and Andrea here on this in the comment section. (At that time this was news to me also).

    Plus as you yourself agree models of neutrino mass such as seesaw mechanism are completely decoupled from BSM physics.

  33. MathPhys says:

    Okay, so even neutrino oscillations are part and parcel of the standard model. Is it safe to say that we don’t know of anything, anything at all, that requires ‘beyond standard model’ physics?

  34. Thomas Larsson says:

    I gave an undergradutate seminar about neutrino oscillations in the spring of 1981, as part of course which nominally was about nuclear physics, but which we students generally called CERN physics because of the trip that ended the course (Cernphysik statt Kernphysik, same thing in Swedish). Assuming that I did not originally came up with the idea of neutrino oscillations, it must have been pretty mainstream at that time.

  35. Ravi K says:

    Shantanu — I think there is no “standard” model for the neutrinos yet. If there is one what is it?

  36. Ravi K says:

    Cesar — I am looking forward to the neutron edm experiments — for a good recent update please see this http://www.nature.com/news/dipole-hunt-stuck-in-neutral-1.9943 I hope they will provide clues as to how P and CP symmetries got violated in nature…..

  37. Shantanu says:

    Ravi, for some reason the link I pointed to did not come out well.
    See the comment section of
    http://dorigo.wordpress.com/2008/10/31/cdf-publishes-multi-muons/

    esp. comments by Tomasso and Andrea Giammanco
    Also as mentioned above seesaw mechanism (or whatever other mehanisms
    you invoke to give neutrino mass) is completely decoupled from TeV scale physics,
    ew symmetry breaking.

  38. Ravi K says:

    Hi Shantanu,

    I think the argument by Andrea in that link that neutrino mass is like any other particle’s small mass, only smaller, is not quite right.

    Basically there is new physics because the standard model has only one mass scale — the Higgs VEV. I dont think you can get the neutrino mass from this single mass scale by multiplying it with a small dimensionless number. The problem is not that the number is too small — the problem is that such a procedure will also make the right handed neutrino light. We need to introduce a second mass scale — large or small — to explain the neutrino mass.

    The mechanism may be decoupled from EW symmetry breaking — but so what? why should that not make it BSM. However nothing really is decoupled from anything as we have the hierarchy problem…..

  39. Shantanu says:

    Ravi, I disagree, but let’s agree to disagree. I have yet to see a single prediction from
    any of the BSM theories about theta_13, whether sterile neutrinos exist or not etc.
    (Note also that by this logic do you consider existence of gravity
    is also beyond the standard model physics).

  40. Ravi K says:

    Agreed! — and anyway whether it is SM or BSM its just a name.

    You dont have a single more or less agreed upon prediction because there is no consensus on the model with neutrinos. But each model by itself would have some predictions for example on whether sterile neutrinos exist or not. Also some of these models have gotten ruled out (or constrained) because of their predictions.

    But what is the standard model prediction for neutrino mass/mixing scale — that is a question that should have an agreed upon answer, and any deviation from it can be attributed to BSM.

    Quantum treatment of gravity would be BSM in my view — If gravitons are found would that be considered SM physics? Currently there are two parallel standard models – one for the quantized forces and one for gravity.

  41. David Broadhurst says:

    > neutrino oscillation is the one piece of “Beyond the
    > Standard Model” physics that has been observed concretely
    Neutrino oscillations were envisaged before the standard model.
    Bruno Pontecorvo [JETP 33 (1957) 549; 34 (1958) 247]
    originally suggested oscillation between \nu{e} and
    \bar{\nu}e. Later he suggested [JETP 53 (1967) 1717]
    oscillations between \nu{e} and \nu{\mu}, before Ray Davis
    had firmly established a deficit in the solar neutrino flux.
    This was elaborated with Gribov [Phys. Lett. B28 (1969) 493].
    Reading this as student, I found it natural to assume
    that all quarks and leptons are massive and that neutrinos,
    like quarks, may mix. Growing up along side the SM, I saw
    no reason to exclude that possibility and, when I started
    teaching the SM, I used to remind students that the number
    of its free parameters had (then) been underestimated.
    I find it odd to read, nearly 40 years on, that neutrino
    mixing is now supposed to be BSM.
    David Broadhurst

  42. Ravi K says:

    I guess what I am trying to say is that there are two ways of extending the standard model to accommodate the observed neutrino physics. One way is by adding 2 or 3 right handed singlet neutrinos to the standard model quark and leptons and providing them with a very heavy mass — maybe even like at the GUT scale — which will in turn see-saw into the observed small masses of the already known neutrinos. The other way is to not add any right-handed neutrinos keeping the usual fermion content of the standard model with only the left-handed neutrino and try to accommodate the neutrino masses.

    Until one of these ways is experimentally ruled out it may be difficult to claim there is a standard way of dealing with the neutrinos though theoretically the see-saw way seems to be the more standard way.

    However in either way of doing things a new mass scale for quantized forces is implicated by the neutrino data.

  43. David Broadhurst says:

    Ravi K wrote, on February 19, 2012 at 11:40 pm:
    > a new mass scale for quantized forces is implicated
    > by the neutrino data
    Yes, I tend to agree with that, if one regards the SM as an
    effective theory. Yet, if one adopts the R-G viewpoint that
    no term in the Lagrangian density can have its coefficient
    specified a priori; rather it must be taken from experiment
    (as in pure QED), then the SM may still be regarded as
    formally complete. I guess that we all hope that the SM is
    merely an “effective theory”, with something (as yet utterly
    unknown) lying above it, at some (as yet utterly unknown)
    energy scale. But that is, at present, pure hope. All we
    know, at present, is that, within the rigid formalism of
    renormalizable QFT and the discipline of experiment, the
    standard model is theoretically and empirically flawless.
    It seems to me that only experiment can modify that strange
    success. Else, I can only agree with Hamlet that “there is
    nothing either good or bad, but thinking makes it so”.

  44. Mark says:

    I just went through Matt Reece’s slides and was a bit surprised to see the claim that in Type IIB the tree-level gauginos are down by the Log[M_Pl/m_32] relative to the scalars, which is not the conclusion of the paper he is referring to. Has he actually checked the reference http://arxiv.org/abs/hep-th/0610129 that he is citing? At the bottom of page 24 it clearly states that because parameter p=1 for bifundamental matter, which is what the MSSM scalars are, “the scalar masses are comparable to the gaugino masses rather than logarithmically larger”. There is even a sample spectrum for the this Large Volume scenario on page 30 and for the KKLT type scenarios on pages 31 and 32 where one clearly sees that in these Type IIB vacua the squarks and sleptons are as light as the gauginos. It’s disappointing to see incorrect information presented in such important review talks.

  45. Mark says:

    I just realised that Matt is actually referring to an earlier paper of Conlon and Quevedo, http://arxiv.org/abs/hep-th/0605141 where the computation of the scalar masses was estimated before the authors found the form of the Kahler potential for bifundamentals. Sorry Matt, I guess you were a bit misled by that earlier paper, but I hope you’ll take the time to read the subsequent paper as well.

  46. Henry Bolden says:

    At least we finally have definitive news on the Higgs:

    Dilbert discovers the Higgs.

  47. Matt Reece says:

    Sorry for the sloppiness, Mark. I’m not an expert on string constructions. A later reference, 0906.3297, also makes the claim that there may be “a minor version of split supersymmetry,” and I was trying to grab the earliest such claim in the literature. Looks like I picked the wrong one. (The ’06 references, as far as I understand, all suffer from the chirality vs moduli stabilization problem pointed out in 0711.3389, so I probably should have stuck with just citing the later one.)

    Anyway, the point wasn’t to single out a specific construction so much as to observe that these small hierarchies often fall out of models, and that we should maybe understand a little better precisely when it does or doesn’t happen. Your later reference reinforces that point, I think—it seems to me that there should be a 4d effective field theory explanation of why, on doing a more careful calculation, they found the expected leading term ~m_{3/2} canceled.

  48. Joseph Conlon says:

    Matt,

    One comment to make here is that many of these cancellations of terms of order M_{3/2 } relate to an underlying no-scale susy breaking structure. No-scale has many neat features: it cancels both tree-level and loop corrections to soft masses (such as arise in anomaly mediation). The fact that no-scale also arises naturally in string constructions further marks it out as a very special structure.

    There should be a right way of looking at supergravity so that the no-scale cancellations all become obvious. Unfortunately I don’t know what that way is, but there is manifestly a structure present in no-scale models that is obscured by the conventional presentation of supergravity, where these cancellations appear just as a series of terms that happen to add up to zero.

  49. Marko says:

    Thank you for your reply, Matt! I see Joe has already tried to answer your question. As far as I understand, in the KKLT case the suppression of the scalar masses relative to m_3/2 is due to warped sequestering, which does have a 4D interpretation as conformal sequestering, as explained here: http://arxiv.org/abs/hep-th/0703105 . In the LV scenario of Joe et al, the no-scale structure does play the crucial role and specifically arises in Type IIB due to the particular scaling of the Kahler potential. However, the LV scenario is also unique because SUSY breaking there is moduli-dominated. So, these two properties, when combined, lead to the above cancellation. This remarkable property disappears in, e.g. G2 vacua, where the scaling of the Kahler potential wrt to the moduli is completely different and even if one could construct a G2 analogue of Joe’s LV vacua with moduli-dominated SUSY breaking, the corresponding scalar masses would look like m_i^2=[(1-7/3)+\epsilon_i^2]*m_32 so the scalars would remain as heavy as m_3/2. As for the reference for string models with slightly split spectra, check the papers of Acharya et al.

  50. Marko says:

    the m_32 should be m_32^2

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