## Monday, June 17, 2019 ... //

### μνSSM produces nice neutrino masses, new 96 GeV Higgs

The most interesting new hep-ph preprint is

Precise prediction for the Higgs-Boson Masses in the μνSSM with three right-handed neutrino superfields (58 pages)
by Sven Heinemeyer (CERN) and Biekötter+Muñoz (Spain) – BHM. They discuss some remarkable combined virtues of a non-minimal supersymmetric model of particle physics.

Note that none of the so far observed elementary particles – bosons or fermions – seems to be a superpartner of another observed fermion or boson, respectively. But for theoretical reasons, it is more likely that these superpartners exist and a supersymmetric Standard Model is a more accurate description of Nature than the Standard Model – the minimum model encompassing the currently observed particles.

From a string theorist's, top down perspective, there may exist many different supersymmetric models that are relevant at low energies (energies accessible by colliders), with or without grand unification, with or without various hidden sectors. String theory or more generally quantum gravity surely guarantees an infinite number of very massive particle species – that gradually become generic black hole microstates once their mass is above or well above the Planck mass.

But from a bottom-up perspective, what are the first new particles that are likely to be observed? The golden standard extension of the Standard Model is the MSSM, the Minimal Supersymmetric Standard Model. Take all particles of the Standard Model, extend them to a superfield (the superpartner has a spin lower by 1/2, except for the superpartners of scalars that need to go to +1/2, of course), and add all the new couplings compatible with supersymmetry.

Because you find out that the Higgs superfield is chiral, you will need to double the number of Higgs fields – to have two doublets, each of which is also a superfield – to produce the masses for up-type as well as down-type quarks. This doubling of the Higgses is also necessary to cancel some anomalies that would otherwise arise from the new chiral higgsinos. As far as physical particles go, you will get 5 Higgses (8-3, 3 are eaten by the gauge bosons to become massive and gain a longitudinal polarization): the normal CP-even Higgs, its lighter sibling, the CP-odd neutral boson, and a particle-antiparticle pair of charged Higgses. The higgsinos are mixed with photinos and zinos to give you four neutralinos; while the charged higgsinos mix with the winos to produce two charginos.

Aside from other virtues, the MSSM is better (because less unnaturally fine-tuned) than the Standard Model because it eliminates all of the hierarchy problem or most of it – if the superpartners are light enough, they cancel the potentially huge loop corrections to the Higgs mass, with some precision. Also, MSSM is usually (but not always) considered with an unbroken R-parity (the number of new superpartners modulo two) which makes the lightest superpartner, the LSP, stable and an excellent candidate for dark matter.

In the MSSM, the self-interaction of the Higgses arises due to a cubic superpotential which has a coefficient $\mu$. This $\mu$ could also be expected to be large and there's a milder, new hierarchy-like problem, the $\mu$-problem. The most trusted supersymmetric model beyond the MSSM is the NMSSM, the Next-To-Minimal Supersymmetric Standard Model which upgrades this parameter $\mu$ into a new superfield $S$, a new singlet Higgs superfield. The $\mu$-problem is avoided and the NMSSM has some other advantages.

BHM argue that another supersymmetric extension of the Standard Model, the mu-from-nu SSM or μνSSM, should be considered the "third most canonical" supersymmetric extension of the Standard Model if not better. The μνSSM also has a new superfield $\mu$ which plays the same role as $\mu$ in NMSSM. However, in μνSSM, the fermionic components of this new field is simultaneously the right-handed neutrino. So the new singlet Higgses and right-handed neutrinos are unified into a superfield, a nice and economic choice to exploit the available chairs in the superfields – it's nice if it can be compatible with observations. And it can, they argue.

The neutrino masses have the right magnitude because the electroweak seesaw mechanism naturally follows from the equations. The R-parity is broken but a long-lived gravitino seems like a good dark matter candidate (which is invisible to the direct searches). Also, BHM seem convinced by the mathematics that there is no reason for a "flavor blindness" of the parameters in this model. You might be afraid of flavor-changing predictions but they say that with the constraints on the neutrino mass matrices, these FCNC-like predictions are within the experimental bounds.

Because we have three generations of neutrinos, it's natural to have three new $\mu$-like superfields with three right-handed neutrinos and three new singlet Higgs fields. In this new paper, for the first time, BHM consider the full model with three such new $\mu$-fields. And with the help of some software, they also analyze the full one-loop diagrams and the equally accurate renormalization group flows to say something about the masses. Note that the loop diagrams matter in supersymmetric models – for example, even in the MSSM, they are vital to increase the tree-level prediction of the Higgs mass from $83\GeV$ to $125\GeV$. The loop diagrams fulfill some additional tasks in the μνSSM.

As a great by-product, the preliminary $96\GeV$ Higgs boson indicated by some diphoton and bottom-pair excesses at LEP and CMS, may be one of the mass bosonic eigenstates of these new $\mu$-fields (sneutrinos). In some other section, they discuss quite a precise setup with sneutrino masses near $1235\GeV$, this precision is sort of intriguing. I didn't understand whether these very different values of the sneutrino masses follow from one scenario or two.

The folks seem genuinely excited about the $96\GeV$ excess and waiting for new clues about these experimental hints. I am somewhat excited, too – but they're excited enough to find the energy to write 58 pages on calculations in a potentially relevant model.

Because we discussed fake Spaniards with Erwin, here is a Czech remake "A lamb and a wolf" of a random medieval Spanish Christmas carol Riu Riu Chiu – which, as you will probably agree, is better than the Spanish original song. From the 1990 album "You have to insist on your truth" – byt the Spiritual Quintet band, when brothers Nedvěd were members (the membership seems frequently changing). This band isn't quite mainstream on radios but most Czechs are familiar with this kind of music which dominates the campfires (although the Spiritual Quintet clearly sings more religious music than the most famous songs by the Nedvěd brothers and similar musicians).