A personal addendum to the cast of the 750 GeV episode of Game ofThrones

July 01, 2016

A personal addendum to the cast of the 750 GeV episode of Game ofThrones

Since I am no longer bound by my vow of silence about the 750 GeV "inconclusive hint" (dixit Fabiola Gianotti at 30:40 of this video at the Lindau Nobel Laureates Meeting 2016) of a new particle in the first data of LHC run 2, I decide to indulge myself with a follow-up to the last very commented post written by Jester on his famous blog Résonaances.

Starring as Jon Snow and his companions:

Ufuk Aydemir and his collaborators for the following published article ;-)

Recently, ATLAS [14] and CMS [15] have both reported a resonance in the diphoton channel with an invariant mass around 750 GeV. The local significances were respectively 3.6σ and 2.6σ, assuming a narrow width resonance. These signals may be the first hint associated with the long-anticipated physics beyond the SM. The 95% CL cross section upper limit around 750 GeV set by ATLAS (CMS) is roughly 10±2.8 fb (6.5±3.5 fb) using 3.2 fb^-1 (2.6 fb^-1 ) of data at √s = 13 TeV, assuming the resonance is a scalar produced through gluon-gluon fusion. When the width of the resonance is allowed to vary, a maximum local significance of 3.9σ is attained by ATLAS at a width of 45 GeV. On the other hand, the local significance attains its maximum for a narrow width resonance in the CMS results. Therefore, at this stage, given these preliminary analyses, it is difficult to infer conclusively whether the width of the resonance is wide or narrow.

The Feynman diagram of the production and decay of the SM-singlet scalar S
at the LHC through colored-scalar χ in the loop.

In this letter, we discuss a possible identification of this resonance with SM singlet scalars in the NCG motivated unified G₂₂₄ models. A plausible and economical way to realize the LHC diphoton signal in the unified G₂₂₄context is to couple this SM-singlet scalar to gluons and photons via loops of colored scalars, as recently discussed in Ref. 17 in the context of SO(10) GUT, cf. Fig {above}... We list the three unified G₂₂₄models proposed by Chamseddine, Connes, and van Suijlekom in Refs. 4 and 5, and specify how we fit the diphoton resonance into their particle content. These models emerge from an underlying NCG, which is an extension of the NCG of the SM to that of left-right symmetric models. The three versions differ in the scalar sector content, and the unbroken symmetry structure as listed in Table {below}...

We use the following notation for the symmetries:

where D in G_224D refers to the left-right symmetry, a Z2 symmetry which keeps the left and the right sectors equivalent. The last row of Table 1 lists the scalar content of an SO(10) based G₂₂₄ model studied in Ref. 17, below its unification scale where the SO(10) had broken to G₂₂₄. The scalars φ(2,2,1), ∆R(1,3,10), Σ(1,1,15) are respectively obtained from the SO(10) multiplets 10 (or 120), 126, and 210. The 210 also includes a (1,1,1) representation, whose VEV breaks SO(10) down to G_224.

The distinguishing feature of noncommutative geometric (NCG) motivated versions of the standard model (SM) [2, 3] as well as its G₂₂₄ completion discussed here is that they come with GUT-like coupling unification conditions, due to the underlying spectral action having only one overall coupling. This is not the case for the canonical G224 constructions found in the literature...

Our framework is a grand unified version of G₂₂₄ models, within which the corresponding Higgs content is restrictively determined (or uniquely determined for each model) from the underlying non-commutative geometry. This should be contrasted to the regular G₂₂₄ models, discussed in the literature, in which the corresponding Higgs context is arbitrarily selected.

The symmetry breaking chain of the model considered in this letter has been discussed in detail in our previous papers [11, 26]. The ordering of the breaking scales must be strictly maintained in the computations, i.e.

M_U ≥ M_C ≥ M_Z . (3)

We label the energy intervals in between symmetry breaking scales [M_Z, M_C] and [M_C, M_U] with Roman numerals as

I: [M_Z, M_C], G₂₁₃ (SM) , II : [M_C, M_U], G₂₂₄or G_224D...

The particle content and the renormalization group coefficients for the three models in the two energy intervals are listed in Tables. 3, 4, and 5. As stated above, though S survives in the energy interval I, being an SM singlet, it does not contribute to the RG coefficients...

We see that for all three models, M_U is below the Planck scale and {the unified coupling} α_U is perturbative, as are all the gauge couplings during their course of running. The value of the symmetry breaking scale M_C is high in the 10^10∼13GeV range, suggesting that providing S and χ = ∆−2/3 R3 (1, −4/3, 3) with TeV scale masses, and the TeV scale coupling κMRSχ †χ between them would involve fine tuning.

In this note, we have argued that the observed cross sections involving the 750 GeV diphoton resonance could be realized through a SM singlet scalar field and colored scalars in the NCG of unified G₂₂₄ models. However the color scalars are light and thus fine tuned from the usual effective field theory point of view. This indicates a certain rigidity of the NCG approach to the Standard Model and its natural completion in the context of the unified G₂₂₄models. As already emphasized, this conclusion is based on the effective field theory reasoning, which might fail in the NCG framework due to the possible mixing between the short-distance and long distance physics as we have discussed in our previous papers Ref. 11, as well as Refs. 12, 13. In this paper we have discussed three different scenarios and their implications for the physics beyond the Standard Model. We have concentrated on the purely phenomenological aspects of the NCG unified G₂₂₄ models without relying on their deep mathematical structure or various novel physics aspects that go beyond the effective field theory framework. We believe that the discussion presented in this note gives extra evidence to the underlying phenomenological rigidity of the NCG approach towards understanding of the origins of the Standard Model and the physics beyond the Standard Model. However, this phenomenological rigidity might be the price one has to pay for the non-commutative nature of the approach, and it might be indicative of a possibly exciting relation to the non-particle sector of high energy physics, that is to be found in the context of the underlying quantum structure of space and time.

The 750 GeV diphoton excess in unified SU(2)_L×SU(2)_R×SU(4) models from noncommutative geometry

Ufuk Aydemir, Djordje Minic, Chen Sun, Tatsu Takeuchi

(Submitted on 5 Mar 2016 (v1), last revised 7 Jun 2016 (this version, v2))

This very article has ~~not~~ been eventually quoted in the (last version of the) last review (see below) about the 750 GeV possible resonance named digamma (label F) by Alessandro Strumia. Nevertheless it is interesting to note that the well known italian physicist from CERN has chosen to quote the young post-doc Ufuk Aydemir but for another paper (not published yet) who focused on an interpretation with colored scalars in SO(10) grand unification but its phenomenology was similar to the former paper as far as I can tell, both belonging to the "everybody's model" emphasized by Strumia :

... we include dimension 5 non-renormalizable interactions, which are a good approximation to a generic unknown more complete theory with extra particles that mediate F → γγ, provided that such extra particles are much heavier than M_F...

Many renormalizable models can realise one or more of the effective operators: for example couplings to fermions can be mediated at tree level by one extra Higgs doublet or by extra vector-like fermions. A different class of models attracted most attention: those where the new particles that mediate F → γγ (the only process mandated by data) also mediate gg → F. Such renormalizable models are obtained adding to the SM a neutral scalar z and extra charged fermions or scalars Q in order to mediate the effective z couplings to vectors in the following way:

The role of Q cannot be played by SM particles, because F would also decay into them at tree level, violating the bounds in eq ...

We summarised plausible, creative, wild, bizarre, delusional, grandiose speculations. Experimental testability is what differentiates scientific thinking from paranoid thinking. Hopefully we are seeing the tip of an iceberg and, although it’s too early to infer what lies behind, new features will emerge thanks to new data, eliminating the wrong ideas and bringing us closer to the right theory.

Interpreting the 750 GeV digamma excess: a review

Alessandro Strumia

(Submitted on 30 May 2016)

Reading thoroughly the work of Aydemir and collaborators (and more posts in this blog ;-), I wish it helps the reader to forge an opinion about the noncommutative geometric version is worth just as much as the older SO(10) grand unified theories. This is one lesson one could learn from this 750 GeV bump in the long rutted road to higher energy scales!

//update 8 August 2016

The finale

The above discussion is a disproportionate amplification of a quantum fluctuation: no 750 GeV γγ excess is present in the first (12.2 + 12.9) fb−1 of new 2016 LHC data [see figures below], which confirm the Standardissimo Model and the bad reputation of the digamma symbol F