Models of numerous kinds have been proposed in about 130 model builder papers so far that try to explain the diphoton resonance of invariant mass around \(750\GeV\) seen at the LHC – which may turn out to be a manifestation of new physics or a fluke.

Tommaso Dorigo is a cynic but I found his recent comment amusing, even if it is wrong. He claims that the \(750\GeV\) bump can be neither the Loch Ness Monster nor Mickey Mouse, because of some differences in the shape. Otherwise, the bump can be anything.

*The bump may actually be due to Loch Ness and Mickey Mouse assuming that both of them cooperate and Loch Ness is properly twisted by the Donald Duck. Dorigo has overlooked that model.*

More seriously, in the real world, the bumps may be real and many of the explanations are viable if not highly intriguing. I've discussed sgoldstinos, radions, D3-branes and closed strings, sbinos and NMSSM, and a few other generic options.

But today, we have a clear new winner, the \(E_6\) grand unified theories.

On the hep-ph arXiv, we were shown the first dose of new papers submitted in 2016. There are 84 entries on the hep-ph arXiv today. 33 of them are new papers primarily classified as hep-ph articles. I believe that 11 of them are dedicated to the new diphoton resonance: 2, 9, 12, 17, 24, 28-33.

Previously, the total number of hep-ph papers about the resonance was 118 on December 29th. I believe that 11 were added on December 31st but only 2 on January 1st. So as of now, the number of papers should be 118+11+2+11=142 but I hope you understand that it will be increasingly difficult to be any certain about the total number (the papers can't be found by any easy reliable "reference"). See this page with a graph and hyperlinks claiming that the current number is 146 (thanks, Djack).

At the end of the year, I could mention a fun Chilean paper that claims to explain the patterns in quark and lepton masses, on top of the diphoton resonance, from a scalar with a \(\ZZ_{14}\times\ZZ_2\) group and a new quark of charge \(+8/3\); and Ian Low's and Joe Lykken's paper imposing model-independent bounds on the branching ratios.

But among the 11 new papers today, there is one rather specific kind of models that dominate. 4 out of 11 papers (36%) argue that the diphoton resonance may be obtained from the grand unified theories whose gauge group is \(E_6\), the only simple exceptional compact Lie group that has complex representations and is therefore directly viable as the gauge group of grand unified field theories. It is not quite a new category – I've reminded you of some \(E_6\) model building e.g. in the context of the paper [25] here, marketed as an extension of NMSSM. (Maybe I was the first one to talk about \(E_6\) in the context of the diphoton resonance and the new papers have copied me – and I am not upset at all if that is the case.)

But the "synergy" with which the today's authors write about \(E_6\) is kind of remarkable.

*The \(E_6\) Dynkin diagram is left-right-symmetric, much like the \(SO(2N)\) and \(SU({}^\geq 3)\) diagrams (\(SO(8)\) has the higher \(S_3\) triality symmetry). This \(\ZZ_2\) symmetry is what exchanges the representations with their inequivalent complex conjugate friends. The existence of this left-right symmetry and therefore these complex representations (reps inequivalent to their complex conjugates) is ironically needed to explain the left-right-asymmetric character of the electroweak force which is why \(E_6\) is the only exceptional group that may be directly used as a grand unified gauge group.*

We are talking about four papers

Palti: Vector-Like Exotics in F-Theory and \(750\GeV\) DiphotonsThree papers among the four (except for Ko+2) talk about the stringy origin of these effective field theories. The first and the last one explicitly talk about F-theory, Vafa's geometric generalized nonperturbative description of type IIB string vacua, while the third paper by Chao envisions a heterotic string model as the origin (there exist heterotic-F-theory dualities so a model may often have both descriptions at the same moment).

Ko+2: Diphoton Excess at \(750\GeV\) in leptophobic \(U(1)'\) model inspired by \(E_6\) GUT

Chao: The Diphoton Excess from an Exceptional Supersymmetric Standard Model

Karozas+3: Diphoton excess from \(E_6\) in F-theory GUTs

Bonus from end of January 2016:

King+Nevzorov: \(750\GeV\) Diphoton Resonance from Singlets in an Exceptional Supersymmetric Standard Model

As I have previously mentioned, relatively to the 16-dimensional representation for fermions in \(SO(10)\) grand unified model building (the 16 components include the right-handed neutrino, unlike the 5+10-dimensional representation in \(SU(5)\) models), the fundamental representation of \(E_6\) is 27-dimensional and decomposes as \[

{\bf 27} = {\bf 16}\oplus {\bf 10}\oplus {\bf 1}

\] under the \(SO(10)\) subgroup. The extra 10-dimensional representation behaves as \({\bf 5}\oplus \bar{\bf 5}\) under the \(SU(5)\) subgroup. Because we get both the representation and its complex conjugate, it means that the fermions will transform as full uniform Dirac spinors under the \(SU(5)\) group. So the gauge couplings will be non-chiral i.e. vector-like, as people call it. In the Dirac spinor notation, you won't need any \(\gamma_5\) to write the Lagrangian for those fields.

The chiral interactions are the cornerstone of the electroweak theory, as you know (only the left-handed fermions and right-handed antifermions interact weakly) but to explain the diphoton resonance, we need the couplings to the pairs of gluons (initial state) and pairs of photons (final state) and non-chiral interactions are good for that.

However, as most of the 4 papers notice, the new vector-like quarks interact chirally with a new \(U(1)'\) gauge group that arises out of the \(E_6\). At least the first two papers among the four papers above explain that this is great because this non-chiral interaction of the new exotic quarks guarantees that they have masses linked to the Higgs that breaks this \(U(1)'\) symmetry – which they put close to \(1\TeV\). This scale used to be expected to be near the GUT scale instead. The first paper claims that by reducing this scale, we get an extra bonus: the proton decay slows down!

Note that in the original "normal" Georgi-Glashow \(SU(5)\) grand unified models, we need fermions in \({\bf 5}\oplus \bar{\bf 10}\) under \(SU(5)\) and the known leptons and quarks are organized so that the five-dimensional representation contains a lepton doublet and a right-handed

*down-quark*which is an electroweak singlet. The identity \(3+2=5\) is helpful here. In the "flipped" \(SU(5)\) models (Barr 1982; Nanopoulos et al. 1984; Antoniadis, Ellis, Hagelin for the supersymmetric, string-inspired version), the assignments of the charges are switched to another possible solution and the 5-dimensional representation contains a lepton doublet plus the right-handed

*up-quark*instead. See a 2013 TRF text about the basic GUT embeddings.

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