Wednesday, October 03, 2012

SUSY with a colored adjoint chiral multiplet

I discussed the same exciting possibility in November 2011 and May 2012 but because there's a new paper on the arXiv, I won't resist to make another comment.

The paper is called
Pushing the SUSY Higgs mass towards \(125\GeV\) with a color adjoint
and it was written by Gautam Bhattacharyya and Tirtha Sankar Ray. Even though the names may look like two names of the same ethnic origin, the paper is actually an outcome of an Indian-German-French-Australian collaboration. ;-)

Steven Weinberg has said many nontrivial propositions I fully subscribe to and one of them is
"Our mistake is not that we take our theories too seriously, but that we do not take them seriously enough."
What could it mean in the case of supersymmetry? Well, it could mean that we're not trying to incorporate enough supersymmetry into our theories. The new Indian paper is another example showing why this criticism could be valid.

String/M-theory admits lots of vacua with 32 real supercharges; this "maximum" amount of supersymmetry is also referred to as \(\NNN=8\) in the four-dimensional notation. However, even 16 and 8 supercharges i.e. \(\NNN=4\) and \(\NNN=2\) is too many (too many new particles, too constrained interactions, no left-right asymmetry) so whenever physicists try to describe the world around us, they talk about models with 4 supercharges, i.e. \(\NNN=1\) supersymmetric theories.

That's fine but the reduction all the way down to 4 supercharges is only necessary because of some "problems" that are really problems for the matter fields – leptons and quarks (and perhaps the Higgs field) – only. For the gauge fields, one could perhaps survive a larger amount of supersymmetry.

Somewhat more elementary: Don Lincoln of Fermilab explains the Standard Model in 8 minutes. A new video.

The new Indian paper is another way to formulate a theory of this kind; they are adding a "chiral multiplet" transforming in the adjoint of the gauge group. Well, they mean the QCD \(SU(3)\) group only so they're cousins of the gluon and the gluino. What does it mean? It means that they are adding a complex scalar field and a Weyl fermion that transform in the same way as the gluons and gluinos and that mix with each other under the minimal \(\NNN=1\) supersymmetry.

A funny thing is that their charges and colors are the same as those of the gauge bosons' vector supermultiplets. And if you combine a vector multiplet and a chiral multiplet with the same charges and related quantum numbers, you may get an \(\NNN=2\) vector multiplet – a vector multiplet under a larger supersymmetry group, one that has 8 real supercharges.

Of course, the main reasons why I find this possibility attractive are
  • the more supersymmetry, the better;
  • the fact that string theory may make gauge fields live on branes that may preserve a higher amount of SUSY than the "brane intersections" where the matter fields live.
Those are theorists' reasons to be intrigued by the possibility. But the phenomenologists' reasons are cool, too. With the new chiral multiplet, one may predict the observed Higgs boson mass around \(125.7\GeV\) much more naturally than without it (aside from the new multiplet, they try to follow the rules of the cMSSM, so they are working within the so-called cMSSM+ framework where the plus sign represents the new multiplet).

Even more importantly, look at this graph of the predicted gluino (\(x\)-axis) and stop squark (\(y\)-axis) masses:

The blue region is the prediction from an ensemble of cMSSM models and they really want the gluino to start at \(2\TeV\) and the stop squark around \(1\TeV\). However, the red cMSSM+ regions nicely allow both superpartners to be as light as \(0.5\TeV\) or so. And that's quite something.

While I have never liked the wishful thinking of the model builders who always expected new physics right behind corner (they looked to me like if they tried to have a chance to get a Nobel prize as soon as possible which is not a legit motivation to direct physics research, I think), I do feel that a model that still allows the new particles to be this light – given the available data – is more natural, both in a vague and in the technical sense.

These models with some impressively light superpartners and "even more supersymmetry than we thought" remain viable and that's quite something. Maybe if the gauge fields come up with all the light superpartners of an \(\NNN=2\) multiplet, something even more dramatic awaits us in the gravitational sector. What about models with an \(\NNN=4\) graviton supermultiplet, to make it really ambitious? Maybe with such enhanced supermultiplets, we could get new tools and new cancellations to address some annoying problems including the cosmological constant problem.

I am thinking about brane worlds that make such things pretty natural. In fact, they're extremely close to the "toy theories of everything" that Barton Zwiebach uses in his textbook based on his lectures of string theory for the undergraduates. Wouldn't it be fun if the stuff taught to the youngest kids was actually the most physically relevant one? ;-)


  1. N=2 supersymmetry? Does that mean there will be new particles called sgluinos an squakinos ;_)? I did find one thing confusing. How does N=1 supersymmetry give 4 supercharges? If R symmetry is N=1 supersymmetry and doubles the known particles, isn't that just 2 supercharges or am I counting wrong. Maybe I need to include chirality or something.

  2. OT(prompted by final P and ad for text): I have Barton Zwiebach's book on my shelf, but need time and motivation to launch into it----maybe MIT opencourseware will provide it----it offers a course that he and Alan Guth taught in 2007 (Alan must have absorbed stringy knowledge when he slept through Lubos' string course :))

    The MIT courses offer the materials and transcriptions of the lectures----no certificates or credits

    There is also something called Coursera (started by AI and Machine Learning Andrew Ng and Daphne Koller from Stanford). It offers many courses for free online from top universities when the instuctors are teaching the courses. There are assignments and exams, and if one passes, a signed certificate of achievement from the instructor....the world is changing.

  3. Hi Gordon,

    should there be video lectures of the Zwiebach / Guth course? I did not find them, I saw only the PDF lecture notes. Such videos would be motivating indeed ... :-D

  4. Thanks for explaining this paper Lumo, you know I alway like such things :-)

    I dont know how the full N=2 SUSY spectrum would look like (my demystified book contains only the MSSM :-P ...) but would one not need a mechanism to explain why only this particular new multiplet should be there and the rest of the N=2 spectrum is absent / at higher energies / or ...?


  5. Hi Dilaton,

    in the braneworlds, the gauge fields often live on certain higher-dimensional branes – imagine open strings whose both endpoints are attached to a D4-branes. D-branes in flat space preserve 1/2 of supersymmetry - which is 8 supercharges at some simple enough geometries, like orientifold of a torus. So gauge fields may come in full N=2 supermultiplets.
    On the other hand, leptons and quarks and Higgs are confined to intersections of branes - they're open strings attached to 2 different branes by the endpoints - so they naturally have a lower amount of supersymmetry and they only arrive in N=1 supermultiplets.
    The general conclusion is that string theory has reasons why these different kinds of fields "see" a different fraction of the total SUSY, that SUSY is broken to different extents for them. The phenomenological papers don't discuss this "natural stringy justification" at all. They find purely phenomenological reasons why this scenario is good, so one may view the stringy argument as an "independent confirmation that the concept makes sense".


  6. Dear Physics Junkie, there would be no squarkinos because quarks only arrive in N=1 supermultiplets. But yes, there are new partners of the gluon - the new chiral multiplet is the main hero of this paper and you may call its fermionic and bosonic components sgluons and sgluinos, indeed. ;-)

  7. Thanks for these further explanations Lumo, that was exactly what I needed :-)

    I dont know why this is, but purely phenomenological reason often dont satisfy me, in my opinion they are too similar to pulling an ace (or a new supermultiplet) out of one's sleeve or thin air ...

    (The paper is cool, but I always like it better when things can be more fundamentally motivated)

  8. Thank you Lumo. I am still wondering how 4 supercharges gives R symmetry which seems like two charges. If you have some time I would love an answer to that question. Thanks for pointing out the book. I may finally be able to learn string theory from it with my undergraduate physics degree.

  9. the guy from rhinocerosOct 4, 2012, 4:50:00 AM

    Dear Lubos, Advance apologies for bringing in an off-topic subject, but if it isn't too dumb for you, I'd like to read your response:

    Demolishing Heisenberg with clever math and experimentsGood, general measurement choices eliminate uncertainty.

    by Chris Lee - Sept 29 2012, 9:00am PDT

  10. Hi! Non-destructive measurements is being used in the same bogus way as "weak measurement", they just differ in details.

    I will probably write another blog about it. So far see:

  11. It's pretty straightforward, really. Supersymmetry is an extension of the Lorentz (well, Poincaré) group by spinorial generators. The minimal spinor in 3+1 dimensions has two complex components, i.e., four real components.