*A scheme of the Randall-Sundrum spacetime.*

**As Numcracker pointed out, the most revolutionary paper in this third wave claims that the \(750\GeV\) resonance is a Higgs-radion, a particle signaling an extra dimension of the spacetime.**

The last among the three previous TRF blog posts mentioning a radion discussed a proposed interpretation of the \(125\GeV\) boson as a radion. It was in April 2012, before the Higgs boson was officially discovered – and before we were clearly shown that its properties are boringly Standard-Model-like. So extra-dimensional or extra-terrestrial speculations could have been a bit more appropriate but I didn't believe that the Higgs boson would turn out to be too different from the Standard Model, anyway.

You may still want to read that text from 2012, however. But you don't need to. In theories with a fifth spacetime dimension, the radion is basically the component \(g_{55}\) of the metric tensor: both indices are chosen along the new dimension of the spacetime.

String theory generally predicts more than one hidden dimension. There may be one special dimension among them, however. This is e.g. the case of Hořava-Witten "heterotic M-theory" which is M-theory on a spacetime whose one dimension has the shape of a line interval or, equivalently, the \(S^1/\ZZ_2\) orbifold. This line interval has two end points – or fixed points of the orbifold group – and those end points give rise to the 10-dimensional "end-of-the-spacetime" branes which carry the \(E_8\) gauge bosons and their superpartners.

Heterotic M-theory may very well be the right description of Nature. The extra Hořava-Witten dimension (there are six more extra dimensions that we neglect) may be nearly "flat". However, there exists a very interesting possibility that the extra dimension makes the spacetime highly curved, warped, like the anti de Sitter space, and this possibility is known as the Randall-Sundrum models.

A component of the metric tensor \(g_{55}\) still exists and is known as the radion. To change its expectation value means to adjust the proper distance between the two "end-of-the-world" branes which are known as the Randall-Sundrum IR and UV branes. In the Randall-Sundrum case, the two ends-of-the-world have very different values of the usual components of \(g_{\mu\nu}\) which allows you to label them with asymmetric names, UV and IR.

In a new paper on the resonance,

Higgs-radion interpretation of \(750\GeV\) di-photon excess at the LHC,Aqeel Ahmed along with four infidels study the possibility that the Randall-Sundrum radion is what the ATLAS and CMS experiments were seeing – if they are going to see it again in 2016. ;-) More precisely, the particle with mass \(750\GeV\) should be mixed with the known particle at \(125\GeV\), the Higgs boson. So you need to study the 2-dimensional space generated by the "usual Higgs" and the "radion" and diagonalize the mass matrix in this 2-dimensional space. The two mass eigenvalues are supposed to be \(125\GeV\) and \(750\GeV\). Because of this "mixing business", they talk about the Higgs-radion but the new particle is "mostly" the radion. They also use the word "dilaton" for the same object; they reserve the word "radion" for the bulk interpretation of the mode and the word "dilaton" for the description of the same object in terms of the holographic boundary CFT (where the mode "expands" i.e. "dilates" the spacetime).

Well, their Lagrangian for the Higgs and the radion is the following one:\[

\eq{

{\mathcal L}_{\rm eff} &=

-\frac 12 \phi_0[(1+6\xi\ell^2)\square + m_{\phi_0}^2] \phi_0

\\

&+6 \xi \ell h_0 \phi_0\square \phi_0- \frac 12 h_0 (\square+m_{h_0}^2) h_0

}

\] The first line is mostly the Klein-Gordon Lagrangian for the radion derived from 5D general relativity; the second line is mostly the Klein-Gordon Lagrangian for the Higgs boson taken from the Standard Model. But you see the additional \(\xi\) terms that mix the Higgs with the radion (and with the geometry – which is why one kinetic term is affected as well). The \(\xi\) terms ultimately arise from the\[

\xi{\mathcal R}_4 H^\dagger H

\] term before some change of the variables. The parameter \(\xi\) is adjustable. But something special happens for \(\xi=1/6\): the theory becomes conformal. This value is known as the conformal limit of the Higgs-radion theory.

Shockingly enough, this value seems to be pretty much exactly the right value that they need to get realistic properties of the two scalar particles. What's nice about this value is that the coupling of the "mostly radion" to the particle pairs vanishes except for the coupling to \(gg\) and \(\gamma\gamma\) – exactly what we need to produce the resonance out of two gluons; and to allow it to decay to two photons.

Is it a coincidence that the Higgs boson mass \(125\GeV\) is \(1/6\) of the radion mass \(750\GeV\) while \(\xi=1/6\)? I couldn't see an answer in the paper. Maybe it is a coincidence. They seem to say that \(\xi\to 1/6\) implies \(m_\phi\gg m_{h}\).

Their model predicts a tiny partial width of the \(750\GeV\) to the two photons, not much more than \(0.1\GeV\) – even less than in the sgoldstino models. So they would face trouble if they wanted to describe a large width, which is weakly indicated by the (especially ATLAS) data, especially if they would like to keep the branching ratio of the diphoton channel high.

Like other models, this model predicts other decay channels for the new particle. In particular, I think that the decay to two gluons \(gg\) is virtually unavoidable because that's how the particle is created at the beginning, too. That's why their model predicts that there should exist two-jet decays of the new particle, too. My understanding is that those are dominant; but they're not too visible because dijets have a higher background.

I think that the probability of extra-dimensional scenarios like that is small but not ludicrously small, perhaps 0.5% or so, and the probability that the RS extra dimension exists and affects this resonance is just a little bit lower, perhaps 0.3%.

The discovery of an extra dimension through these resonances would be a more radical revolution than the sgoldstino revolution and others, I think. It could be expected that other signs of the extra dimension would be around the corner, too. For example, they assume that the first Kaluza-Klein mode of a gluon moving in the extra dimension wouldn't be far from \(3\TeV\). Well, they say so because they want to be as close to the current exclusion limits as possible – and there's really no reason why Nature should try to be so close to them – but to say the least, extra-dimensional particles that are as light as \(3\TeV\) are still conceivable and the \(750\GeV\) particle could be the first step towards making the new dimension visible.

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