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Superbumps, a new (and imminent?) signature of supersymmetry

Pairs of nearby CP-even, CP-odd resonances

I do believe that the main idea is sort of obvious – and had to come to the mind of many particle physicists who were thinking about the possibly emerging new \(750\GeV\) cernette particle – but I also think it is great that Yang Bai and Joshua Berger have posted a special preprint dedicated to this idea, the first (and therefore characteristically bold) preprint of hep-ph today titled

Superbumps (arXiv)
Normally, supersymmetry is a Grassmann-odd continuous symmetry generated by "fermionic" operators \(Q_\alpha\) which transforms bosons to fermions and vice versa. But these infinitesimal generators transform as spinors and the \(d=4\) spinor has at least two complex components.

LHC: a probe beam is already circulating!

That means that you can act with the supersymmetry generators repeatedly and get bosons from bosons or fermions from fermions as well.

Moreover, because the generators are complex, given the fact that \(SO(3,1)\sim SL(2,\CC)\), at least some of the fields mixed by the SUSY transformations must have some complex structure on them, too. This general fact is well-known, of course, and in the early 1990s, Nathan Seiberg (and later he and Ed Witten) provided us with the basic tricks to use the power of "holomorphy" in the calculation of many quantities in supersymmetric theories.

I need to emphasize that this "holomorphy" doesn't generally arise in non-supersymmetric models. In particular, bosonic spinless fields in non-supersymmetric theories may be just "real", one-component fields. On the contrary, in \(\NNN=1\) \(d=4\) SUSY theories, the spinless fields must arise from the chiral multiplets and when they do so, they arise as complex fields. (Spin-1/2 fields are naturally complex even in non-SUSY theories; spin-1 fields are "real" even in SUSY theories, and so on.)

This has consequences for the spectrum. The spin-0 "real" particles just want to come in pairs in SUSY theories because they arise from a complex field, namely from the spin-0 part of the "chiral superfield". For example, the Standard Model has just one spin-0 elementary particle, the single Higgs boson. You may calculate one as \(4-3=1\). Here, four is the number of real components in a doublet of scalar field, and three is the number of components eaten because the 3-dimensional group \(SU(2)\times U(1)\) was broken.

(Holy cow, click at the word "eaten" and after one more click, you will learn that the gay-and-other-letters physicist spamming CERN with obscene posters believed that the Higgs boson didn't exist at all as recently as in Fall 2011. It's hard to get rid of the feeling that he's at CERN not because of what he knows and can do but because of what he would like to have coitus with. Some unsigned CERN apparatchiks posted an outrageous statement yesterday that threatens all CERN employees who disagree with this sick ideology.)

In minimal SUSY cousins of the Standard Model, there are five physical Higgs bosons. Five arises as \(8-3=5\). The number of broken gauge group generator wasn't changed, it's three. But the doublets were doubled. Also, as a result, there are five physical polarizations.

Three of them, usually labeled \(h,H,A\), are electrically neutral, and the remaining two, \(H^\pm\), are antiparticles to each other. The CP conjugation produces \(H^\mp\) from \(H^\pm\) (it permutes them) while \(h,H\) are CP-even and \(A\) is CP-odd.

As model builders know, \(H,A\) have the opposite CP parity but they often have very similar masses (and cross sections). If and when you observe these additional Higgs bosons, you collect positive evidence in favor of SUSY. But Bai and Berger discuss more complex examples (which could also have a higher cross section than \(H,A\)), e.g. involving a 24-dimensional representation of \(SU(5)\) SUSY GUT theories, plus the possibility that the \(750\GeV\) cernette bump is actually a collection of two bumps (which is why the bump looks broad), something that has already appeared in the literature.

They discuss some more complex channels in which the pairs of particles, CP-even and CP-odd, may be seen, as well as some ways to derive their properties by closely looking at the supersymmetry breaking etc.

But in principle, if there are pairs of spin-0 bumps with nearby masses, similar cross sections, and the opposite CP parity, it's quite a strong evidence in favor of SUSY because no other known principle in physics may naturally force us to combine spin-0 fields into complex packages with both signs of CP. The CP may really be flipped in between these two bumps because \(Q_1 Q_2\) has the capability of messing up with CP. That's different than the "usual" bosonic symmetry which commute with (and therefore don't change) the CP of the fields/particles related by the symmetry. One may say that SUSY is special because it can relate particles of different spin; but it is also special because it can relate particles of the same spin but different CP.

Note that the CP parity may be extracted e.g. from the angular distribution of leptons when the particles decay. The cross sections of the two particles should be the same up to small corrections.

SUSY may be defined as a symmetry transforming bosons into fermions and vice versa. But when you actually study what SUSY implies, you realize that it's so much more. It's constraining the theories, giving them great properties, making many "seemingly intractable" questions rather easily calculable, and it may provide us with new signatures by which we may gain confidence that SUSY has been seen in the near future.

The \(750\GeV\) cernette bump, if real and composed of two, may become such evidence in a couple of months. I am not promising anything here but I believe it is totally possible. Incidentally, hours ago, CMS published a top squark search (search for stops) and I do tend to think that the upper left parts of Figures 15 and 16 show a mild excess (a downward wiggle of the black curve) also seen in many other searches that tries to repel the curve from a \(600\GeV\) stop and a \(350\GeV\) LSP, roughly speaking.

A moonshine stringy paper

By the way, I also think that the first paper of hep-th today, a paper on Mathieu and umbral moonshine and 3D heterotic/K3 string theory, is beautiful, too. It's a good idea to place papers that their authors probably love to the top of the lists and I think that this natural bias has existed for years. In this paper, non-monstrous moonshine is studied by looking at (twenty-four, for some reason, linked to the Leech lattice and 23 Niemeier lattices) points in the moduli space of heterotic or K3-compactified string theory compactified to \(d=3\) where the \(24+8\)-dimensional even self-dual lattice decomposes to the \(E_8\) lattice and an even self-dual \(24\)-dimensional ones. The paper is full of hypergeometric functions, theta series, and large integers so don't expect any easy reading.

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