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Sgoldstino at \(750\GeV\) prevails in second theorists' bump day

Yesterday, there were 10 pheno papers trying to explain the bump near \(750\GeV\) if the bump is not just a deceitful fluke. Three preprints mentioned supersymmetry, mostly suggesting that the minimal supersymmetric standard model (MSSM) doesn't look quite compatible with the data.

SSM wasn't a supersymmetric standard model when I was a teenager. It was the Socialist Youth Union whose membership offer I had to refuse. ;-)

Today, the number of papers on the bump decreased by 20%, to eight. And they have a rather different focus. I won't discuss all the papers one by one anymore because it would be a full-time job. Instead, let me mention that two papers identify the bump as something very specific and supersymmetric.

It's the sgoldstino, stupid. I believe that the term sgoldstino has only been around since 2000 and the paper only has 50+ cits. Nevertheless, it's the #1 candidate explanation in two today's papers by

Brando Bellazzini, Roberto Franceschini, Filippo Sala, Javi Serra

Christoffer Petersson, Riccardo Torre

Tomorrow, bonus:
Demidov, Gorbunov (two sgoldstino veterans were scooped)
You don't hear about goldstinos too often, let alone sgoldstinos. Not even model builders use this term too often – if you compare it to the neutralinos such as wino or bino (or higgsino), the gluino as the other gaugino, or even the gravitino, not to mention squarks and sleptons and stop and sbottom.

But for these two papers, the sgoldstino is the primary suspect. Let's first analyze the word as if we were stupid linguists.

The primary root of the word is Goldstone which is either a rock created out of a precious metal; or Jeffrey Goldstone, a retired MIT physicist (who has switched to quantum information along with Preskill at some point and was an important chap in funding agencies). Choose your favorite answer. If you picked the latter, the Goldstone bosons were bosons that inevitably arise whenever you break a continuous symmetry. Goldstone has proven their existence and the reason of their existence is very simple.

If you spontaneously break a symmetry, it means that the vacuum state is no longer invariant under the symmetry. So if you infinitesimally transform the vacuum, you get another, nearby state (which is physically "equivalent" due to the symmetry but not equal in the sense of equal vectors). And the difference between these two vacuum states must correspond to an excited state in either vacuum. It is an excited state with zero momentum and zero spin which is however nonzero. So it must correspond to a massless scalar excitation! There must be something to excite and if you make the symmetry transformation spacetime-dependent, you may actually discover the nonzero-momentum modes of the same field, too.

When you break supersymmetry, the situation is analogous except that the symmetry generator carries \(j=1/2\), and that must be the spin of the new particles, too. So the spontaneously broken supersymmetry must produce new fermionic particles, the goldstinos. The -ino suffix generally denotes that the new particle is a fermion that is a superpartner of a similarly named bosonic particle.

Similarly, the prefix s- denotes a scalar, bosonic particle that is the superpartner of a similarly named "ordinary" fermion. So a sgoldstino should be a \(j=0\), scalar superpartner of a goldstino. And the goldstino should be a fermionic mode associated with the spontaneously broken supersymmetry. Here, however, the goldstino isn't a superpartner of any "specific" preexisting boson. It is just the Goldstone particle associated with the supersymmetric partner of the general notion of a (bosonic) symmetry, and the supersymmetric partner of the notion of a bosonic symmetry is a/the supersymmetry generator, of course. ;-)

The existence of these massless particles is this simple when the broken symmetry is a global one. When you break a local symmetry, the Goldstone modes ultimately become the new, longitudinal modes of the (now massive) gauge boson associated with the gauge symmetry. We say that "gauge bosons have eaten the Goldstone modes". This dinner terminology has two justifications: the gauge bosons were massless but become massive after the symmetry breaking, so it seems that they have eaten somebody because of the counting of the mass. Second, the gauge bosons have a higher number of polarizations that also suggests that they have eaten another degree of freedom. From both perspectives, the Goldstone boson may be identified as the dinner.

Similarly, you could say that supersymmetry is a local symmetry – because we ultimately embed the whole theory in a supergravity theory. That should mean that the goldstinos should be eaten by the "gauge bosons" (which are now fermions) associated with the supersymmetry (because it's a fermionic symmetry). And these "gauge bosons" (fermions) are the gravitinos. So the new modes of the gravitinos should be made out of the goldstinos. The polarization \(j_z\) for a gravitino may be \(\pm 3/2\) but when the particle gets massive, \(j=\pm 1/2\) become possible as well and the new degrees of freedom arise from the goldstinos.

What is the superpartner of the goldstino? Now, things are subtle. Supersymmetry only carries \(j=\pm 1/2\). So you can't say that the superpartner of all polarizations of the gravitino is the graviton: the graviton remains massless which only has \(j=\pm 2\). By supersymmetry, you may only get to \(j=\pm 3/2\). So by the supersymmetry transformation, you can't get from the graviton to \(j=1/2\). It means that the "less spinning" components of the gravitino – which came from the goldstino – must also have a new superpartner. It has \(j=0\) and is called the sgoldstino. Microscopically, such a particle is excited by the fields responsible for the SUSY breaking: it's the F-term part of the \(X\) superfield whose vev breaks supersymmetry. The mass of the sgoldstino is about \(\langle F \rangle / M\) with the just mentioned vev where \(M\) is the mass scale of the SUSY-breaking sector.

Both papers analyze some possibilities to explain the resonance in terms of Goldstone-like degrees of freedom (the four-author paper talks about some Goldstone associated with another symmetry as well) and both (especially the two-author paper) conclude that the sgoldstino is the most promising one. The two-author paper says that the sgoldstino superfield \(X\) has the real (\(\phi\) or \(\sigma\)) and imaginary (\(a\)) part which are interpreted as CP-even and CP-odd bosons in four dimensions. Their masses are nearly degenerate – the masses may be \(745\GeV\) and \(760\GeV\), for example – and that's why the width of the bumps seems to be nonzero (even though the sgoldstino width is said not to exceed \(1\GeV\) by both papers). There are actually two nearby bumps! I think that ATLAS and CMS should actually be able to say "something" about the possibility that what they're seeing are actually two narrow peaks rather than one broad one.

The two-author paper points out that the tree-level terms including the Higgs and the sgoldstino add a small amount to the Higgs mass which can make it more natural – \(125\GeV\) usually looks a "little bit" higher than natural in the minimal supersymmetric theories. So the sgoldstino could have some extra nice implications aside from explaining a bump. Note that the sgoldstino must be R-parity-even because along with the R-parity-even graviton, they're the superpartners of components of a gravitino (which must therefore be R-parity-odd).

It would surely be fun if the resonance existed and were not only connected to supersymmetry but if it were one of the "most systemic" yet overlooked particles associated with supersymmetry breaking – a superpartner of the superpartner of the graviton which isn't a graviton. ;-)

As the bonus (Russian) paper suggests, in these models with a sgoldstino, the gravitino should be very light and the lightest superpartner – between 1 and 10 millielectronvolts. It's allowed by cosmology. And if the cosmological constant could be simply the gravitino mass to the fourth, it would have the observed value.

P.S.: I really haven't heard about sgoldstinos too many times in my life. So I've searched for some sensible quick introduction to that. But look what text from 2001 I found LOL. This planet is just too small. ;-) I don't really remember having explained those things in the past – it must be easy to forget such things in the absence of conversations. Delphi at that time was reporting a search for sgoldstinos around \(200\GeV\).

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