LHC: Higgs mass vs SUSY

The LHC Shows the Way workshop rolls on, looking at the implications of the Higgs at 125-126 GeV for supersymmetry.
I live blog, slowly.

Where are the sparticles.

Coloured supersymmetric partners, the quark and gluon supersymmetric partners, must be massive – greater than ~ 1,000 GeV

in some natural implementation of supersymmetry, natch, clever theorists can of course think of increasingly contrived ways to get around most any limit, at the expense of fewer and fewer people believing them.

Minimal supersymmetric extensions to the standard model, with the Higgs mass assumed to be 126 GeV and allowing the coupling to the supersymmetric sector to float.

Problem is the Higgs physical mass is significantly lower than the “naked” mass of the Higgs, as calculated – this is the problem that as the Higgs “gives mass” to the other particles, this changes the mass of the Higgs.

eg. the supersymmetric partner to the top quark can pull the Higgs mass down significantly, but is one of several offsetting terms shifting the Higgs mass around. Including the lightest supersymmetric particle (LSP), whichever that is.
Mass shift also depends on an energy scale, which is unknown, and could be loosely thought of as the unification energy scale, fortunately it only comes in as a log term.

Either the s-top is more massive than 500 GeV or the LSP is more massive than 150 GeV.
So taking the LSP to lower mass allows the s-top to have higher mass, but then one has to ask if the LSP is so light why haven’t we seen it.

Hence we start squeezing the model.

You can get out of a lot of constraints by abandoning minimal supersymmetry, and, eg. adding more Higgs particles.
You so totally don’t want to know how much you can mess with the mass once you allow 3+ Higgses.

Actually, to be fair, the theory is still squeezed surprisingly tight.
So either there is no supersymmetry, or the data are telling us exactly where the minimal supersummetry theory is, or supersymmetry is messy and just adds more epicycles.

Oh, what SUSY: sounds to me, and I might have missed something, that we’re looking at a strongly coupled (λ ~ 0.7) theory with a low mass LSP and high mass s-top (as the lowest mass coloured sparticle).

What we really care about, of course, is the mass of the LSP and its nature, as it is a prime Cold Dark Matter particle.
It must be weakly coupled and neutral.

Than there are really crazy supersymmetric theories.
Some of which sound like quite a lot of fun.

Real info will be in the ratio of the branching ratios of the decay modes of the Higgs.
Figuring that the big messy perturbation theory calculations of those are reasonably good at the level of approximation being made.

Once you go to complicated theories, any one step is less fine tuned, but then you have to do some tuning of several different steps – so, is the net tuning something like the product of the tuning of the individual steps (ie are the tuning parameters effectively independent)?
If so, the fine tuning problem becomes worse in the complicated theories.

BUT, sometimes what we see as fine tuning to get theories to match experiments, is just the theory being constrained to the true parameter values and we were just wrong about our Bayesian priors.
Or, the theory is just wrong.

Strongly coupled non-minimal supersymmetric models (or at least this variety) have lower branching ratios to b-bbar quark decay mode compared to minimal supersymmetric models.
Should be seen in the detectors with a bit more data.
Some other decay mode(s) must then have higher branching ratios.
(see, this IS still science!).
Enhances photon decay.

Net effect is ~ factor of 2 shift in branching ratios.

So… minimal supersymmetry is now fine tuned at the < 1% level.
Need to find LSP.

Ok, back from coffee - almost ran out, which would be catastrophic, but supply was finely tuned to demand.

First part was Josh Ruderman et al.

Hall, Pinner & Ruderman “A Natural SUSY Higgs Near 125 GeV”
Elor, Hall, Pinner & Ruderman “Yukawa Unification and the Superpartner Mass Scale”

Now, Daniele Alves et al on Sister Higgs: more non-minimal supersymmetry

adds new hidden gauge group with new charge
assume SU(2) new gauge group – so some sort of shadow electroweak charge

Er, too detailed and too many new bits – read the papers if anyone wants to see how this fits in.

Gives a LSiP – Lightest Sister Charged Particle – as Cold Dark mAtter candidate.

Alves, Fox & Weiner “Supersymmetry with a Sister Higgs”