# I What follows after SUSY

#### kelly0303

Hello! I am really not an expert in this so please correct me if I say something stupid. I read a few articles (e.g. https://journals.aps.org/rmp/pdf/10.1103/RevModPhys.90.025008) in which there are presented the implications of low energy physics on high energy physics. In the electric dipole moment (EDM) of fundamental particles section it is said that the limits on the electron EDM (eEDM) implies that possible SUSY particles should have a mass greater than 10 TeV. Also an improvement in the eEDM measurements sensitivity by 1 or 2 order of magnitudes (which is not an easy task experimentally by any means), with a null result, would rule out SUSY (almost) completely, in the sense that the masses of the particles needed to explain the value of the EDM would be too large for SUSY to be able to solve the problems it was originally created for (e.g. Higgs mass, baryon asymmetry). So, assuming I didn't missunderstand what I read, I have a few questions. I hear over and over again that CERN is still trying, as one of its main objectives to search for SUSY. Yet if the masses of the particles are bigger than 10 TeV they wouldn't be able to find it at the current energies, and the HL-LHC, will just give more statistics, but not more energy to produce these particles. So, what do they mean when they say they are searching for SUSY particles? Are there some loopholes that allow such a small EDM and yet small mass SUSY particles at the same time? And a second question, assuming the EDM will not be found after the sensitivity improvement, hence most of the SUSY models ruled out, what are the most viable models available at our energy level that the physics community is most likely to start to look for? Thank you!

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#### phyzguy

I'm far from an expert in this area, but it seems to me that the ν-MSM is a very promising extension to the standard model that potentially addresses all of the issue we know about. I'd be interested to hear the comments of the people on this forum who know a lot more about high-energy physics than I do.

#### mitchell porter

too large for SUSY to be able to solve the problems it was originally created for (e.g. Higgs mass, baryon asymmetry)
As far as I know, the first supersymmetry in physics was proposed by Miyazawa in 1966, to place mesons (bosons) and baryons (fermions) in the same multiplet. Then at the start of the 1970s, it was found mathematically within string theory and field theory, but not yet with any application in mind. The standard phenomenological applications (hierarchy problem, gauge unification, dark matter) only came as people studied what it could do. To this narrative I would add the construction of the mature forms of string theory - superstring theory, M theory - as the apex of supersymmetric theory development. String theory opened a new frontier, possibly a final frontier, for model-building, as significant as the 1970s revolution in renormalizable quantum field theory.

If you ask particle physicists, what comes next, if the paradigm of weak-scale supersymmetry hasn't worked out, most of the theorists will still say that the hierarchy problem remains the outstanding problem to solve. The standard way to solve it, supersymmetric or otherwise, is still to have extra particles that cancel most of the divergences, and with them the need for tuning; and so all such frameworks face the same problem, that the new particles are hiding away. There are longstanding deviations from the standard model (B decays, g-2), and I suppose natural model builders now focus on models that would produce those effects.

There are other proposals for how to solve the hierarchy problem. Some people have anthropic arguments. These can lead to extra predictions if the anthropic framework is sufficiently detailed. For example, you might think you know that the string theory landscape is dominated by certain versions of MSSM, and tuning the Higgs like so, implies a certain mass spectrum for all the superpartners. I suppose "split supersymmetry" is an example of this.

Then you have mechanisms in which the Higgs vev evolves over cosmological time, and gets pinned at its current value by some mechanism. The "relaxion" paper from a few years ago pioneered this. I have seen a few papers lately which try to deal with tuning of Higgs vev and cosmological constant at the same time, with both being the product of the same trip through a series of vacua or local minima during the early universe. The extra predictions of such models would mostly be cosmological.

The fact that the Higgs mass places the standard model on the boundary of stability and metastability often sounds like a clue to new physics, though it's bad for phenomenology in the sense that it implies any new physics comes only at very high energy scales. I think it's a clue that theorists have yet to interpret correctly - there's work on it, but none of it has achieved its final form.

My approach to these matters is definitely theory-centric, in the following sense: If we never had another scrap of new data, there are still plenty of things that theorists should be trying to explain. They need to account for the apparent tuning of the Higgs, the QCD theta parameter, and the cosmological constant; they should be hoping to explain where the fundamental constants get their values (and where the qualitative features of fundamental physics come from too, like the symmetry groups; but the unexplained numbers have the most bits of information); and then there's all the astronomical and cosmological data.

Hopefully someone else will give us an experimenter's perspective.

#### Elias1960

String theory opened a new frontier, possibly a final frontier, for model-building, as significant as the 1970s revolution in renormalizable quantum field theory.
It indeed opened a new frontier, but not yet of physics, but up to now only of speculation.

This is very different from what the Wilsonian revolution has given. It has clarified, in particular, that the non-renormalizability of gravity is not a serious problem, given that it does not prevent to use gravity as an effective field theory down to the Planck scale without any problems, and by the way explains why gravity is so weak (because it is non-renormalizable, thus, its large distance limit decreases much faster than that of renormalizable theories).

If you ask particle physicists, what comes next, if the paradigm of weak-scale supersymmetry hasn't worked out, most of the theorists will still say that the hierarchy problem remains the outstanding problem to solve.
And here, the Wilsonian revolution also opens a lot of alternatives. Namely, non-renormalizable variants.

In the past, they were rejected as a no-go. Massive gauge theories without Higgs mechanism? Anomalous gauge theories? A no-go from the start, because of non-renormalizable.

With Wilsonian effective field theory, this looks differently. Non-renormalizable? So what, the non-renormalizable parts will effectively decrease much faster than the renormalizable ones, thus, will be suppressed automatically, down to the power of gravity or so. So, this opens the way to use non-renormalizability of some parts as a mechanism to suppress some parts of a GUT without any additional constructions.

I give you a suggestion for free: Extend the SM to $U(3)_c \otimes U(2)_L \otimes U(1)_R$. Here, $U(3)_c$ acts only on the color, nothing else, independent of electroweak charges, and $U(2)_L \otimes U(1)_R$ only inside electroweak doublets, nothing else, independent of color or baryon charge. Greater but obviously simpler than the SM, given this split of the gauge action into a part acting on color only and an electroweak only part. The additional fields are anomalous, thus, the non-renormalizability of anomalous gauge fields will suppress them without the necessity of any further suppression mechanism.

Moreover, the color only part can be easily implemented as a Wilsonian gauge field, thus, with exact lattice gauge symmetry, while this fails for the electroweak part which is chiral. So, exact gauge symmetry on a lattice regularization will be $U(3)$ (like the $SU(3)_c \otimes U(1)_{\gamma}$ part of the SM, which is in reality a $U(3)$ symmetry too), while everything else is not exact gauge symmetry on a lattice regularization, thus, would be massive.
The standard way to solve it, supersymmetric or otherwise, is still to have extra particles that cancel most of the divergences, and with them the need for tuning; and so all such frameworks face the same problem, that the new particles are hiding away.
What I propose here gives additional particles where the standard Wilsonian approach hides them automatically, given that they are non-renormalizable.
The fact that the Higgs mass places the standard model on the boundary of stability and metastability often sounds like a clue to new physics, though it's bad for phenomenology in the sense that it implies any new physics comes only at very high energy scales.
I would agree.

I would seriously like to understand what would be the problems if one starts without exact gauge symmetry on the fundamental level (or at the critical length where the effective field theory becomes invalid).

Naive counting of degrees of freedom does not make a difference between massive gauge theories without fundamental gauge invariance and Higgs models where the gauge degrees have been factored out with a quite complicate and artificial (negative norms) BRST mechanism and then effectively added again by reintroducing them with a Higgs mechanism. For the really massive gauge fields, we could have the same degrees of freedom from the start, and for the EM field, there would be one additional scalar degree of freedom, the gauge degree of freedom, in comparison the scalar Higgs field.

The only objection I see is that there would be no base to motivate those interactions with this degree of freedom which give the mass of the particles. But here I have to admit that I have never understood the motivation of introducing these terms instead of simply leaving them as mass terms too. Here I would seriously need some help.

"What follows after SUSY"

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