\(E_6\) Yard Unification, F-Theory Prevail Inwards The \(750\Gev\) Phenomenology Today

Models of numerous kinds accept been proposed inward most 130 model builder papers then far that endeavour to explicate the diphoton resonance of invariant majority some \(750\GeV\) seen at the LHC – which may plough out to live a manifestation of novel physics or a fluke.

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

The bump may really live due to Loch Ness as well as Mickey Mouse assuming that both of them cooperate as well as Loch Ness is properly twisted past times the Donald Duck. Dorigo has overlooked that model.

More seriously, inward the existent world, the bumps may live existent as well as many of the explanations are feasible if non highly intriguing. I've discussed sgoldstinos, radions, D3-branes as well as closed strings, sbinos as well as NMSSM, as well as a few other generic options.

But today, nosotros accept a clear novel winner, the \(E_6\) grand unified theories.

On the hep-ph arXiv, nosotros were shown the outset dose of new papers submitted inward 2016. There are 84 entries on the hep-ph arXiv today. 33 of them are novel papers primarily classified equally hep-ph articles. I believe that xi of them are dedicated to the novel diphoton resonance: 2, 9, 12, 17, 24, 28-33.

Previously, the total release of hep-ph papers most the resonance was 118 on Dec 29th. I believe that xi were added on Dec 31st but exclusively 2 on Jan 1st. So equally of now, the release of papers should live 118+11+2+11=142 but I promise you lot empathise that it volition live increasingly hard to live whatever for certain most the total release (the papers can't live constitute past times whatever piece of cake reliable "reference"). See this page amongst a graph as well as hyperlinks claiming that the electrical current release is 146 (thanks, Djack).

At the terminate of the year, I could call a fun Chilean paper that claims to explicate the patterns inward quark as well as lepton masses, on top of the diphoton resonance, from a scalar amongst a \(\ZZ_{14}\times\ZZ_2\) grouping as well as a novel quark of accuse \(+8/3\); as well as Ian Low's as well as Joe Lykken's newspaper imposing model-independent bounds on the branching ratios.

But amidst the xi novel papers today, at that topographic point is 1 rather specific sort of models that dominate. 4 out of xi papers (36%) debate that the diphoton resonance may live obtained from the grand unified theories whose estimate grouping is \(E_6\), the exclusively uncomplicated exceptional compact Lie grouping that has complex representations as well as is so conduct feasible equally the estimate grouping of grand unified acre theories. It is non quite a novel category – I've reminded you lot of some \(E_6\) model edifice e.g. inward the context of the paper [25] here, marketed equally an extension of NMSSM. (Maybe I was the outset 1 to verbalise most \(E_6\) inward the context of the diphoton resonance as well as the novel papers accept copied me – as well as I am non upset at all if that is the case.)

But the "synergy" amongst which the today's authors write most \(E_6\) is sort of remarkable.

The \(E_6\) Dynkin diagram is left-right-symmetric, much similar the \(SO(2N)\) as well as \(SU({}^\geq 3)\) diagrams (\(SO(8)\) has the higher \(S_3\) triality symmetry). This \(\ZZ_2\) symmetry is what exchanges the representations amongst their inequivalent complex conjugate friends. The existence of this left-right symmetry as well as so these complex representations (reps inequivalent to their complex conjugates) is ironically needed to explicate the left-right-asymmetric grapheme of the electroweak forcefulness which is why \(E_6\) is the exclusively exceptional grouping that may live conduct used equally a grand unified estimate group.

We are talking most 4 papers

Palti: Vector-Like Exotics inward F-Theory as well as \(750\GeV\) Diphotons

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

Chao: The Diphoton Excess from an Exceptional Supersymmetric Standard Model

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

Bonus from terminate of Jan 2016:
King+Nevzorov: \(750\GeV\) Diphoton Resonance from Singlets inward an Exceptional Supersymmetric Standard Model

Three papers amidst the 4 (except for Ko+2) verbalise most the stringy source of these effective acre theories. The outset as well as the lastly 1 explicitly verbalise most F-theory, Vafa's geometric generalized nonperturbative description of type IIB string vacua, piece the 3rd newspaper past times Chao envisions a heterotic string model equally the source (there be heterotic-F-theory dualities then a model may oft accept both descriptions at the same moment).

As I accept previously mentioned, relatively to the 16-dimensional representation for fermions inward \(SO(10)\) grand unified model edifice (the sixteen components include the right-handed neutrino, different the 5+10-dimensional representation inward \(SU(5)\) models), the fundamental representation of \(E_6\) is 27-dimensional as well as decomposes equally \[

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

\] nether the \(SO(10)\) subgroup. The extra 10-dimensional representation behaves equally \({\bf 5}\oplus \bar{\bf 5}\) nether the \(SU(5)\) subgroup. Because nosotros teach both the representation as well as its complex conjugate, it way that the fermions volition transform equally total uniform Dirac spinors nether the \(SU(5)\) group. So the estimate couplings volition live non-chiral i.e. vector-like, equally people telephone phone it. In the Dirac spinor notation, you lot won't quest whatever \(\gamma_5\) to write the Lagrangian for those fields.

The chiral interactions are the cornerstone of the electroweak theory, equally you lot know (only the left-handed fermions as well as right-handed antifermions interact weakly) but to explicate the diphoton resonance, nosotros quest the couplings to the pairs of gluons (initial state) as well as pairs of photons (final state) as well as non-chiral interactions are expert for that.

However, equally most of the 4 papers notice, the novel vector-like quarks interact chirally amongst a novel \(U(1)'\) estimate grouping that arises out of the \(E_6\). At to the lowest degree the outset 2 papers amidst the 4 papers higher upwardly explicate that this is keen because this non-chiral interaction of the novel exotic quarks guarantees that they accept masses linked to the Higgs that breaks this \(U(1)'\) symmetry – which they set unopen to \(1\TeV\). This scale used to live expected to live close the GUT scale instead. The outset newspaper claims that past times reducing this scale, nosotros teach an extra bonus: the proton decay slows down!

Note that inward the original "normal" 2013 TRF text most the basic GUT embeddings.

Off-topic: 21 days are left to the global destruction.

At whatever rate, the today's papers assume the original Georgi-Glashow embedding. Because the novel exotic vector-like fermions coming from the \(E_6\) models transform equally a 5-dimensional representation of \(SU(5)\) addition its complex conjugate, the exclusively color-charged states they incorporate are those resembling the down-quark.

So these \(E_6\) models accept novel Dirac spinors that facial expression similar the down-quark – the same electrical charge, 3 colors, but no chiral (left-right-asymmetric) electroweak interactions. It's this novel exotic quark that runs inward the loop (triangle) that produces the intermediate scalar – as well as that allows it to decay, too. The intermediate scalar is the novel Higgs that breaks the \(U(1)'\) symmetry inward these models; as well as it has an fifty-fifty CP-even "real part" which is said to live the \(750\GeV\) novel particle allegedly observed past times the LHC.

This model makes a lot of sense. The \(E_6\) grand unification has predicted the extra states. There were no experimental signs of them – which was 1 argue why people preferred to assume that all of them were heavy. But aside from the "absence of experimental evidence" which is non the "evidence of absence", at that topographic point has never been whatever expert argue to live convinced that the "rest of the 27-dimensional representation" must live GUT-scale heavy.

In 2016, the LHC may really good start to regain the novel exotic down-quarks, 3 generations of them, which combine to the 27-dimensional representation along amongst the known quarks as well as leptons. That would live genuinely remarkable.

Supersymmetry as well as grand unification are 2 of the beautiful principles inward the beyond-the-standard-model model building. It's somewhat hard to tell which of them is to a greater extent than radical – the outset as well as exclusively non-bosonic symmetry; or a consummate unification of all non-gravitational estimate groups? Well, SUSY would however win. But 1 argue why it was considered "hotter" was the supposition that SUSY must emerge earlier grand unification because SUSY has some expert reasons (an explanation of the hierarchy problem) to appear close the Higgs majority scale; piece the residuum of the GUT model edifice is probable to accept masses close the GUT scale.

But this supposition may accept been incorrect as well as the GUT multiplets may present upwardly inward front end of our eyes really soon. Imagine that. Imagine that the LHC volition rather shortly regain 3 generations of fermions that consummate the 3 generations transforming inward the 27-dimensional representation (probably merely 25 of 27 because the 2 singlets at 2 levels are equally good weakly interacting; but nosotros should also watch 3 generations of the novel vector-like lepton doublet). The LHC folks may deserve a Nobel prize but then tin the theorists.

Who should teach a Nobel prize for the \(E_6\) model building? The to a greater extent than full general idea, the grand unification initiated past times the \(SU(5)\) group, was started past times Georgi as well as Glashow. They're keen physicists as well as entertaining men. But to some extent, they accept abandoned their spiritual pocket-size similar an Islamic begetter who (fortunately non-lethally) stabs his offspring because he's upset that it's a girl. I accept a work to consider Georgi as well as peculiarly Glashow equally flagships of grand unification today. The physicists celebrated for something shouldn't live "accidental encounterers" of something but folks who were convinced that the regain is existent as well as of import as well as who kept on pushing it for years, mayhap despite some opposition. Georgi as well as Glashow (who basically abandoned GUT model edifice later on the outset simple-minded prediction of the proton decay was falsified) are non examples of that.

Moreover, it's the \(E_6\) grouping that is needed. The possibility to supervene upon \(SU(5)\) past times \(SO(10)\) or \(E_6\) was somewhat obvious. I acknowledge that I don't know who wrote the outset papers on grand unification involving these larger groups. But I retrieve it's truthful that the exceptional groups are sufficiently exotic for most non-stringy particle physicists then that a huge percentage of the \(E_6\) grand unified literature is really stringy or at to the lowest degree string-inspired.

\(E_6\) as well as the beauty of string theory

As I merely hinted, I desire to terminate upwardly amongst a department emphasizing how terribly unopen \(E_6\) – which may teach experimentally discovered – would live to some key aspects of the beauty hiding inward string theory model building. The largest compact exceptional uncomplicated Lie grouping is \(E_8\). It can't live used equally a starting indicate (gauge group) inward acre theory because it has no complex representations. But it does work equally the starting indicate inward string theory because strings accept new, intrinsically stringy ways to interruption the estimate symmetry.

And indeed, at that topographic point exists a beautiful geometric description of this \(E_8\) starting point, the \(E_8\times E_8\) heterotic string, the master copy "detailed candidate for a stringy TOE" of the 1980s (and for some, including your humble correspondent, fifty-fifty today). The \(E_8\) estimate grouping may also live shown (and Hořava+Witten did it) to arise on the boundaries of the spacetime inward the 11-dimensional M-theory on spaces amongst boundaries. Influenza A virus subtype H5N1 "board" of the 11-dimensional spacetime has 2 boundaries (upper as well as lower; the vertical dimension is a business interval) which is why nosotros teach 2 \(E_8\) factors inward the dual heterotic string at each indicate of the 10 "horizontal" spacetime dimensions.

Also, F-theory equally good equally M-theory may live shown to acknowledge codimension-4 singularities amongst the \(E_8\) estimate supermultiplet living on them. Such M/F-theoretical vacua amongst singularities may live shown dual (equivalent) to the heterotic string, at to the lowest degree inward some uncomplicated (and some hard) cases. It's really interesting to know which singularities create the \(E_6,E_7,E_8\) estimate group. The response is given past times the ADE classification. They arise from \(\CC^2/\Gamma\) where \(\Gamma\) is a finite subgroup of \(SU(2)\), basically a subgroup of \(SO(3)\) translated to its activeness on the 2-dimensional spinor. If \(\Gamma\) is the symmetry grouping of the tetrahedron, you lot teach an \(E_6\); if you lot pick a cube or an octahedron instead, you lot obtain \(E_7\); for a dodecahedron or the dual icosahedron, 1 ends upwardly amongst the \(E_8\). Many of these facts are well-known as well as rigorous mathematical as well as physical facts. Some of them are intriguing speculations. For example, nosotros may teach an \(E_6\) from the orbifold past times the tetrahedron isometry grouping which resembles an \(A_4\) or an \(S_4\). It's really tempting to seat this grouping amongst 1 of the most realistic choices of the "family groups" that create realistic spectra of fermion masses!

The fundamental representation of \(E_8\) is 248-dimensional as well as coincides amongst the adjoint representation (the exclusively uncomplicated Lie grouping where it's true). The exclusively smaller representation is the trivially transforming 1-dimensional singlet! Under the maximum \(E_6\times SU(3)\) subgroup, \({\bf 248}\) decomposes as\[

({\bf 78},{\bf 1}) \oplus (1,{\bf 8}) \oplus ({\bf 27},{\bf 3}) \oplus (\bar{\bf 27},\bar{\bf 3})

\] It's really intriguing. Aside from the adjoint representation of the subgroup, nosotros teach 3 copies of the 27-dimensional representation of \(E_6\) – it almost looks similar the \(E_8\) has the correct content for 3 families of the correct \(E_6\) type. Some orbifolds link this release 3 to the release of "complex hidden dimensions" as well as inward this sense, they naturally explicate why the release of generations is three.

It's also interesting to watch how the \(E_8\) representation \({\bf 248}\) decomposes nether some other maximal subgroup, \(G_2\times F_4\).\[

({\bf 14}, {\bf 1}) \oplus
({\bf 1}, {\bf 52}) \oplus
({\bf 7}, {\bf 26})

\] Here, \(G_2\) is the automorphism grouping of the octonions (the pure imaginary octonions cast a 7-dimensional existent space); \(F_4\) ends upwardly existence a centralizer of a \(G_2\) within \(E_8\) as well as it's also the automorphism grouping of the "Hermitian" \(3\times 3\) octonion matrices equipped amongst the "anticommutator" binary operation. There is also an interesting human relationship betwixt \(F_4\) as well as \(E_6\): \(F_4\) may live obtained equally a \(\ZZ_2\) orbifold from \(E_6\). Well, if you lot "divide" the \(E_6\) Dynkin diagram past times a \(\ZZ_2\) reflecting the left as well as correct sides, you lot teach the \(F_4\) Dynkin diagram.

All these facts accept some beautiful geometric explanations inward string theory. The grapheme of as well as relationships betwixt the exceptional estimate grouping may facial expression similar some artificially added mathematics inward the context of quantum acre theories. But inward the context of string theory, they're unavoidable as well as "obvious" geometric properties of the possible shapes of extra dimensions. String theory loves to create the correct equations whose solutions comprehend the boring, systematic cases equally good equally the exceptional ones. The fact that nosotros accept a rather clever estimate grouping – such equally the Standard Model estimate grouping or, ideally inward 2016, the \(E_6\) grouping – may live attributed to the extra dimensions. The extra dimensions are what "produces" the complexity as well as construction of these groups as well as the representations inward which the affair fields transform.

If the LHC happened to regain the \(750\GeV\) particle as good as some novel particles predicted past times the \(E_6\) models, that would live spectacular. It wouldn't convey the grand unification scale closer to our experiments. But it would convey some scales ("aspects of the GUT scale") that were assumed to coincide amongst the GUT scale closer.

That would plainly modify the globe when it comes to the "testability" of different claims. If some novel particles implied past times the \(E_6\)-related structures of extra dimensions inward string theory top observable, nosotros may compare lots of the natural predictions of the stringy models amongst the reality. We would start to live seeing some novel aspects of the stringy physics.

I am really intrigued past times many clever ideas that could explicate the excess – sgoldstinos, sbinos, mayhap fifty-fifty radions etc. But if I were to pick the most "conservative" or "obvious" or "natural" or "economic" (according to my previous evaluation of the explanations of the observed complexity of the Standard Model) model, I would likely terminate upwardly picking the (supersymmetric, but inward this instance it's non the most essential thing) models built out of the \(E_6\) GUT, i.e. the \(E_6 SSM\). Go, e-six-es-es-em, go. (ESSM: this 1 from 2013 as well as the pre-rumor, November 2015 text most the LHC's going to show \(E_6\) SUSY GUT.. ;-)