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The \(2\TeV\) LHC excess could prove string theory

On Friday, I praised the beauty of the left-right-symmetric models that replace the hypercharge \(U(1)_Y\) by a new \(SU(2)_R\) group. They could explain the excess that especially ATLAS but also (in a different search) CMS seems to be seeing at the invariant mass around \(1.9\TeV\), an excess that I placed at the first place of attractiveness among the known bumps at the LHC.

A random picture of intersecting D-branes

Alternatively, if that bump were real, it could have been a sign of compositeness, a heavy scalar (instead of a spin-one boson), or a triboson pretending to be a diboson. However, on Sunday, six string phenomenologists proposed a much more exciting explanation:

Stringy origin of diboson and dijet excesses at the LHC
The multinational corporation (SUNY, Paris, Munich, Taiwan, Bern, Boston) consisting of Anchordoqui, Antoniadis, Goldberg, Huang, Lüst, and Taylor argues that the bump has the required features to grow into the first package of exclusive collider evidence in favor of string theory – yes, I mean the theory that stinky brainless chimps yell to be disconnected from experiments.

Why would such an ambitious conclusion follow from such a seemingly innocent bump on the road? We need just a little bit of patience to understand this point.

They agree with the defenders of the left-right-symmetric explanation of the bump that the particle that decays in order to manifest itself as the bump is a new spin-one boson, namely a \(Z'\). But its corresponding \(U(1)_a\) symmetry may be anomalous: there may exist a mixed anomaly in the triangle\[

U(1)_a SU(2)_L SU(2)_L

\] with two copies of the regular electroweak \(SU(2)\) gauge group. An anomaly in the gauge group would mean that the field theory is inconsistent. In the characteristic field theory constructions, the right multiplicities and charges of the spectrum are needed to cancel the anomaly. However, string theory has one more trick that may cancel gauge anomalies. It's a trick that actually launched the First Superstring Revolution in 1984.

It's the Green-Schwarz mechanism.

In 1984, Green and Schwarz figured out how the anomaly works in type I superstring theory with the \(SO(32)\) gauge group – which is given by a hexagon diagram in \(d=10\) much like it needs a triangle in \(d=4\) – but the same trick may apply even after compactification. The new spin-one gauge field is told to transform surprisingly nontrivially under a gauge invariance of a seemingly independent field, a two-index field, and the hexagon is then cancelled against a 2+4 tree diagram with the exchange of the two-index field.

In the \(d=4\) case, we may see that this Green-Schwarz mechanism makes the previously anomalous \(U(1)_a\) gauge boson massive – and the "Stückelberg" mass is just an order of magnitude or so lower than the string scale (which they therefore assume to be \(M_s\approx 20\TeV\)). This is normally viewed as an extremely high energy scale which is why these possibilities don't enter the conventional quantum field theoretical models.

But string theory may also be around the corner – in the case of some stringy braneworld models, particularly the intersecting braneworlds. In these braneworlds, which are very concrete stringy realizations of the "old large dimensions" paradigm, the Standard Model fields live on stacks of branes, they have the form of open strings whose basic duty is to stay attached to a D-brane. Some string modes (particles) live near the intersections of the D-brane stacks because one of their endpoint is attached to one stack and the other to the other stack and the strings always want to be stringy short, not to carry insanely high energy.

To make the story short, the anomaly-producing triangle diagram may also be interpreted as the Feynman diagram for a decay of the new \(Z'\) boson of the \(U(1)_a\) groups into two \(SU(2)_L\) gauge bosons. When the latter pair is decomposed into the basis of the usual particles we know, the decays may be\[

Z' &\to W^+ W^-,\\
Z' &\to Z^0 Z^0,\\
Z' &\to Z^0 \gamma

\] All these three decays are made unavoidable in the Green-Schwarz-mechanism-based models – and the relative branching ratios are pretty much given. Note that \(W^0\equiv W_3\) is a mixture of \(Z^0\) and \(\gamma\) so all three pairs created from \(Z^0\) and \(\gamma\) would be possible but the Landau-Yang theorem implies that the \(\gamma\gamma\) decay of \(Z'\) is forbidden (the rate is zero) for symmetry reasons.

Their storyline is so predictive that then may tell you that the new coupling constant is \(g_a\approx 0.36\), too.

So if their explanation is right, the bump near \(2\TeV\) will be growing – it may already be growing now: the first Run II results will be announced on EPS-HEP in Vienna, a meeting that starts tomorrow (follow the conference website)! Only about 1 inverse femtobarn of \(13\TeV\) data has been accumulated in 2015 so far – much less than 20-30/fb at \(8\TeV\) in 2012. And if the authors of the paper discussed here are right, one more thing is true. The decay channel \(Z\gamma\) of the new particle will soon be detected as well – and it will be a smoking gun for low-scale string theory!

No known consistent field theory predicts a nonzero \(Z\gamma\) decay rate of the new massive gauge boson. The string-theoretical Green-Schwarz mechanism mixes what looks like a field-theoretical tree-level diagram with a one-loop diagram. Their being on equal footing implies that the regular QFT-like perturbation theory breaks down and instead, there is a hidden loop inside a vertex of the would-be tree-level diagram. This loop can't be expanded in terms of regular particles in a loop, however: it implies some stringy compositeness of the particles and processes.

A smoking gun. This particular one is a smoking gun of someone else than string theory, however.

This sounds to good to be true but it may be true. I still think it's very unlikely but these smart authors obviously think it's a totally sensible scenario. It's hard to figure out whether they really impartially believe that these low-scale intersecting braneworlds are likely; or their belief mostly boils down to a wishful thinking.

If these ideas were right, we could observe megatons of stringy physics with finite-price colliders!

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