In March, ATLAS has moderately excited us with a 3-sigma SUSY-like excess in final states with a lepton pair, jets, and MET. At the end of another blog post, I mentioned a paper explaining it in terms of a light sbottom.

There's a different explanation on the arXiv now, extending the proposal by Ullwanger 3 weeks ago. It's been a lot of time after the Big Bang so Shang, Yang, Yang Zhang, and Cao (no kidding) have hung a new

Explanation of the ATLAS Z-peaked excess in the NMSSMFortunately, the author names haven't been sung which could make your face blank and unless you're a monk, you would stink link a skunk.

As I mentioned in the context of the sub-10-GeV, (after LUX) no longer convincing dark matter particle, the NMSSM is the "second simplest" realistic supersymmetric quantum field theory.

The acronym stands for the Next to Minimal Supersymmetric Standard Model – next to MSSM. Recall that the MSSM adds superpartners to all known particles. On top of that, it has to double the number of Higgs doublets – two doublets instead of one doublet – to cancel the new anomalies from the higgsinos and to allow masses for both types of quarks (in agreement with SUSY).

Consequently, there are (eight minus three) five Higgs scalars instead of one (four minus three) Higgs scalar we know from the Standard Model. Also, there has to be a new interaction between the two Higgs doublets, namely the quadratic superpotential\[

W = \mu H_u H_d

\] which couples the up-type and down-type Higgs doublets. Superpotentials in \(d=4\) have the units of "cubic mass" so you see that each factor, including \(\mu\) itself, has to have the units of mass. For naturalness, this Higgsino \(\mu\) parameter should be comparable to the electroweak scale.

One may argue that such superrenormalizable interactions – multiplicative coefficients with the units of positive powers of mass – are unnatural if treated as perfect constants. For a similar example, note that \(m\bar\psi \psi\) are the mass terms for the leptons and quarks but we know that these mass terms actually arise from the cubic (Yukawa) interactions with the Higgs field, via \(m=y v=y\langle h\rangle\). The Higgs field "secretly" sits in the coefficient \(m\) for the mass.

You could say that in analogy with that, there should be a field hiding in the constant parameter \(\mu\), too. Well, that's exactly what the NMSSM does. It promotes \(\mu\) into a new electroweak "singlet" superfield called \(S\) which contains one complex scalar (bosonic) field (which may be split to one new real CP-even mode and one new real CP-odd mode) as well as a new fermionic field, the singlino. The boson in \(S\) gets a vev and it behaves like \(\mu\). But we also have the new particle species from the chiral multiplet with their new interactions.

The replacement of the constant \(\mu\) by the field \(S\) with a vev is also natural if you are attracted by the idea of some "scale/conformal invariance" of the right quantum field theory that is only broken dynamically. Note that similar explanations have been proposed for the observation that the Higgs boson mass is on the verge of the instability, too.

For some time, it's been pointed out by some people that the NMSSM may also make superpartners lighter – and therefore more natural – without contradicting the (almost completely) null results from the LHC so far. See e.g. this paper. SUSY is able to hide more easily mainly because the lightest superpartner, the LSP, is the singlino and there are longer decay chains which distribute the energy to various intermediate products in the chain and leave less energy for the singlino (for the missing transverse energy) at the end of the decay chain. Most search strategies for superpartners are based on assuming "lots of missing transverse energy" which is why they may be failing.

At any rate, their NMSSM explanation of the ATLAS excess seems simple. ATLAS is actually producing gluino pairs where the gluino mass is just \(650\GeV\) in the optimum case. And each gluino decays to\[

\tilde g \to q\bar q \tilde \chi^0_2

\] where the second lightest superpartner \(\tilde\chi^0_2\) is mostly bino and its mass is \(565\GeV\) in the optimum case. This bino usually decays to\[

\tilde\chi^0_2 \to Z \tilde \chi^0_1

\] the mostly singlino \(\tilde \chi^0_1\) lightest superpartner of (optimum) mass \(465\GeV\) and a Z-boson. That's why we get some additional final states with the Z-boson, and therefore the excess. One should better avoid a similar decay with a Higgs boson replacing Z above – because the correspondingly enhanced Higgs peak isn't seen. This unwanted decay of \(\tilde \chi^0_2\) to a Higgs boson may be avoided if the mass difference\[

m(\tilde \chi^0_2) - m(\tilde \chi^0_1)

\] is strictly between the Z-boson mass and the (larger) Higgs boson mass.

All these things are pretty cute and natural. The second simplest supersymmetric model – which may be the most natural one at low energies, for various reasons – may explain an excess and keep almost all the superpartners below \(1\TeV\), too.

Those readers who like numerology may be intrigued by the numbers (sligtly more than) \(560\GeV\) and \(650\GeV\) above. If you read all 2014 TRF articles, you will see that CMS saw a hint of \(650\GeV\) leptoquarks and a \(560\GeV\) CP-odd Higgs boson.

Such numerical agreements look cool but I believe that the NMSSM neutralinos and gluinos which would explain the ATLAS excess can't leave the same traces as the leptoquarks and CP-odd bosons from the CMS excesses so the agreements are coincidences. Well, most likely, all these excesses are coincidences by themselves. But we may always be surprised.

If you fall in love with the NMSSM, you may also want to hear that CMS has seen traces of a second Higgs boson at \(136.5\GeV\).

## snail feedback (3) :

Dear Lubos , may I send you my new poster book on Quantum FFF theory please? LeoVuyk@gmail.com for the address

I've very often heard of MSSM explanations for observations at the LHC, interesting to see a few from the NMSSM lately.

Thanks for this nice explanation of how the NMSSM is motivated :-)

And I would love that explanation for the Z excess ...

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