Bonus: An ATLAS \(\mu\mu j\) event with \(m=2.9\TeV\) will be discussed at the end of this blog post.

**A model with exactly this prediction was published in June**

Two days ago, I discussed four LHC collisions suggesting a particle of mass \(5.2\TeV\). Today, just two days later, Tommaso Dorigo described a spectacular dielectron event seen by CMS on August 22nd. See also the CERN document server; CERN graduate students have to prepare a PDF file for each of the several quadrillion collisions. ;-)

On that Tuesday, the world stock markets were just recovering from the two previous cataclysmic days while the CMS detector enjoyed a more pleasing day with one of the \(13\TeV\) collisions that have turned the LHC into a rather new kind of a toy.

This is how the outcome of the collision looked from the direction of the beam. The electron and positron were flying almost exactly in the opposite direction, each having about \(1.25\TeV\) of transverse energy. A perfectly balanced picture.

You may see the collision from another angle, too:

The electron-positron pair is the only notable thing that is going on.

The fun is that no such high-energy collision has been seen at the \(8\TeV\) run – even though it has performed more than 100 times greater a number of collisions than the ongoing \(13\TeV\) run in 2015. When you demand truly highly energetic particles in the final state, the weakness of the \(8\TeV\) run in 2012 becomes self-evident.

The expected number of similar collisions with the invariant mass\[

M_{e^+e^-}\gt 2.5\TeV

\] seen in the CMS dataset of 2015 (so far) has been estimated as \(\langle N \rangle =0.002\). Clearly, this number – because it is so small that we may neglect the possibility that more than 1 such event arises – may be interpreted as the probability that one event (and not zero events) take place. For the mass above \(2.85\TeV\), you would almost certainly get a probability \(0.001\) or less.

If you take the estimate \(p=0.002\) seriously, it means that either the CMS detector has been 1:500 "lucky" to see a high-energy event that is actually noise; or it is seeing a new particle that may decay to the electron-positron pair.

Such a new particle would probably be neutral from all points of view. It could be a heavier cousin of the \(Z\)-boson, a \(Z'\)-boson. That would be the gauge boson associated with a new \(U(1)_{\rm new}\) gauge symmetry. Most types of vacua in string theory tend to predict lots of these additional \(U(1)\) groups.

And your humble correspondent can even offer you a paper that predicts a \(Z'\)-boson of mass \(2.9\TeV\). See the bottom of page 10 here. (Sadly, they made the prediction less accurate in v2 of their preprint.) The left-right-symmetric model in the paper also intends to explain the excesses near \(2\TeV\) – as a \(W'\)-boson. The model is lepto-phobic (LP) which means that only right-handed quarks are arranged to doublets of \(SU(2)_R\) while the right-handed leptons remain \(SU(2)_R\) singlets. It's the model with the Higgs triplet (LPT) that gives the right \(Z'\)-boson mass.

Just for fun, let me show you the calculation of the invariant mass. The coordinates of the two electron-like particles are written as\[

\eq{

p_T &= 1.27863\TeV\\

\eta &= - 1.312\\

\phi &= 0.420

}

\] and \[

\eq{

p_T &= 1.25620\TeV\\

\eta &= - 0.239\\

\phi &= -2.741

}

\] One may convert these coordinates to the Cartesian coordinates\[

\eq{

p_x &= p_T\cos \phi\\

p_y &= p_T\sin \phi\\

p_z &= p_T \sinh \eta \\

E &= p_T \cosh \eta

}

\] in the approximation \(m_e\ll E\) i.e. \(m_e\sim 0\): feel free to check that the 4-vector above is identically light-like. The two 4-vectors (in the order I chose above) are therefore\[

\eq{

\frac{p_A^\mu }{ {\rm TeV}}&= (1.16750, 0.521375, -2.20200, 2.54631) \\

\frac{p_B^\mu }{ {\rm TeV}}&= (-1.15675, -0.48987, -0.30310, 1.29225)

}

\] where the last coordinate is the energy. Now, because these 4-vectors are null, \[

(p_A^\mu+p_B^\mu)^2 = 2p_A^\mu p_{B,\mu} = (2.908\TeV)^2

\] in the West Coast metric convention. You're invited to check it. Thanks to the Higgs Kaggle contest, I gained some intuition for the \((p_T,\eta,\phi)\) coordinates. ;-)

In a few more weeks, we should see whether this highly energetic electron-positron event was a fluke or something much more interesting... You know, the progress on the energy frontier has been rather substantial. Note that \(13/8=1.625\), an increase by 62.5%.

Lots of particles – the \(W\)-bosons, the \(Z\)-boson, the Higgs boson, and the top quark – are confined in the interval \(70\GeV,210\GeV\) – safely four types of particles in an interval whose upper bound is thrice the lower bound. Now, we can produce particles with masses up to \(5\TeV\) or so. Why shouldn't we find any new particles with masses between \(175\GeV\) and \(4,900\GeV\) – an interval whose ratio of limiting energies is twenty-eight?

It's quite some jump, isn't it? ;-) It could harbor lots of so far secret and elusive animals.

Next Monday, the full-fledged physics collisions should resume and continue through the early November.

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