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Excess at \(2\TeV\) may be due to sleptons, staus

One of the most eye-catching bumps glimpsed by the LHC is the ATLAS' apparently new \(W_R^\pm\)-boson whose mass is about \(2\TeV\) and that seems to decay to \(WW\), \(WZ\), or \(ZZ\): excesses are seen in all these three final states. Moreover, the CMS also sees an excess in a different channel that could result from the same \(2\TeV\) particle.

We've discussed the explanations in terms of new bosons coupled to right-handed fermions (see also the 2-3-5 text) or new intrinsically stringy bosons. There exist papers involving the Higgs compositeness, too. But the most supersymmetric explanation so far has been presented by Ben Allanach and 2 co-authors on the arXiv today: an R-parity-violating di-stau excess.

Tau is the heaviest sibling of the electron and the muon, a charged lepton. Central European approximately 40-year-old kids such as your humble correspondent know Mr Tau, a weirdly elegant magic man with a hat. The music from the Czechoslovak-West-German co-production Tau-related movies was consolidated above. It's been composed by Mr Jaromír Vomáčka and played by Mr Jiří Malásek whenever the piano may be heard.

The superpartner of tau, the scalar tau or stau, may be seen along with tau at 3:05. Both of them are able to shrink and completely disappear, too. They appear in both sizes, with the correct tau-stau mass ratio, around 10:32. You may compare the Lesser Town Square at 11:01 with the current appearance. The guy at 11:10 was a villain. Not only the actor, Mr Miloš Kopecký, has slept with 365 women but he drove Ford, violated the traffic regulations, and spoke English. ;-)

According to Allanach et al., the \(WW\) or \(WZ\) or \(ZZ\) bosons seen in the excesses are actually not the electroweak gauge bosons at all. The particles have been misidentified, they say!

Instead, there exists a new particle, namely stau, whose mass is between \(80\GeV\) and \(105\GeV\). And it has been confused with the \(W\)-bosons and \(Z\)-bosons whose mass is \(80\GeV\) or \(90\GeV\), respectively.

Also, the heavy particle that is produced as a resonance and whose mass is about \(2\TeV\) isn't a new gauge boson. Instead, it is the selectron \(\tilde e^\pm\), smuon \(\tilde \mu^\pm\), or perhaps a sneutrino \(\tilde\nu_\ell\). And it decays to the stau pair, or a pair of one stau \(\tilde \tau^\pm\) and one tau sneutrino \(\tilde \nu_\tau\), depending on the charge of the initial particle.

The decay violates the R-parity so that the three authors have to write an R-parity-violating, lepton-violating superpotential. Well, it's not quite enough for the processes they need so they also need to add a non-supersymmetric term (outside superpotentials) to the Lagrangian, a direct coupling between three sleptons. The coefficient \(A_{j33}\) of this tri-scalar term has the dimension of mass so it may still occur as a soft supersymmetry breaking term (it also violates the R-parity).

I feel that this soft supersymmetric cubic scalar interaction is clever and may have been undeservedly overlooked in the literature. Via the rules of SUSY breaking, this term is bound to appear in the effective theory.

At any rate, it is funny that the superpartners that are as light as the \(W\)-bosons or \(Z\)-bosons may still exist. Colliders may have been looking in their direction for over 30 years and everyone has overlooked them so far. If they do exist, the LHC is bound to prove their existence in the near future.

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