Contents

supersymmetry

# Contents

## Idea

In particle physics phenomenology, the term split supersymmetry refers to models of supersymmetric extensions of the standard model of particle physics (MSSM or other) whose supersymmetry breaking-scale is very high (for instance at GUT-scale of about $10^{15}$ GeV), much higher than the electroweak symmetry breaking-scale (of about 246 GeV) hence violating the idea of “naturalness”, but such that approximate chiral symmetry protects the masses of the fermionic superpartners.

As a result, in such models there is a “split” of the mass scales of the superpartner particles:

1. the scalar superpartners (the sfermions, hence the squarks and sleptons) have high rest masses, from tens of TeV (mass scale of the gravitino) up to the supersymmetry breaking-scale many order of magnitudes higher;

2. the fermionic superpartners (gauginos and higgsino) have masses much closer to the electroweak symmetry breaking scale, at about a few TeV.

Therefore one speaks of “split supersymmetry” (Giudice-Romanino 04).

Historically, the consideration of split supersymmetry (Arkani-Hamed, Dimopoulos 04) was in contrast to the folklore of “naturalness” which governed supersymmetry model-building. Split supersymmetry was motivated by the observation that many other theoretical problems of low-scale susy models disappear if one does not insist on “naturalness”. Indeed, after the LHC experiment produced first observational results, susy models exhibiting “naturalness” were ruled out, while only split supersymmetry models remained viable (this as of beginning of 2018).

## Examples

### $G_2$-MSSM

The class of physics called G2-MSSM generically exhibits “slightly” split supersymmetry.

It is important to understand that there are two measures relevant to understanding supersymmetry breaking, one the scale at which it is broken (about $10^{14}$ GeV as described above), and the other the resulting gravitino mass. In the compactified M-theory case the gravitino mass is calculated, and comes out to be about 40 TeV (40 000 GeV). Sometimes even experts confuse these two scales if they are speculating about supersymmetry breaking without a real theory to calculate.

Thus 40 TeV is the natural scale for superpartner masses. That is not a surprising number in a theory starting with everything at the Planck scale, but it is surprising if one expects the superpartner masses to be near the particle masses (all well below 1 TeV). The squarks and other masses are indeed predicted to be at the gravitino scale, tens of tera-electronvolts.

The theory has formulas (‘supergravity formulas’) for all the masses. When one calculates carefully the masses of the superpartners of the gauge bosons that mediate the Standard Model forces they turn out to get no contribution from one large source, and the resulting value for the superpartners of the gauge bosons (gauginos) is about 1 TeV, rather than about 40 TeV. They are the gluino, photino, zino, and wino. The strong force gluino is heavier, about 1.5 TeV or somewhat more, and the electroweak ones (photino, zino, wino) are somewhat lighter, about half a tera-electronvolt.

## References

The idea originates with

Further discussion includes

Popular discussion of the “slightly split” G2-MSSM is in

Discussion of phenomenology in view of the observed near-criticality of the Higgs field vacuum stability:

• Gian Giudice, Alessandro Strumia, Probing High-Scale and Split Supersymmetry with Higgs Mass Measurements, Nuclear Physics B Volume 858, Issue 1, 1 May 2012, Pages 63-83 (arXiv:1108.6077)

• Gino Isidori, Andrea Pattori, On the tuning in the $(m_h, m_t)$ plane: Standard Model criticality vs. High-scale SUSY, Physics Letters B Volume 782, 10 July 2018, Pages 551-558 (arXiv:1710.11060)