Although SUSY is not needed to stabilize Higgs mass in TGD, the anomaly of muonic g-2 requires SUSY. The following strongly symmetry inspired picture is what allows rather precise predictions for sfermion masses.
- In TGD (p-adic thermodynamics) based SUSY mass formulas are same for particles and sparticles and only the p-adic length scale is different. This resolves the extremely problematic massivation issue of supersymmetric QFTs.
- Ordinary leptons are characterized by Mersennes or Gaussian Mersennes: (M127,MG,113, M107) for (e,μ,τ). If also sleptons correspond to Mersennes of Gaussian Mersennes, then (selectron, smuon, stau) should correspond to (M89,MG,79,M61) is one assumes that selectron corresponds to M89. This is of course a prediction assuming additional number theoretic symmetry.
Selectron mass would be 250 GeV and smuon mass 13.9 TeV. g-2 anomaly for muon suggests that the mass of selectron should not be much above .1 TeV and M89 indeed fits the bill. Valence quarks correspond to the primes not smaller than the Gaussian Mersenne k=113, which suggests that squarks have k ≥ 79 so that squark masses should be above 13 TeV. If sneutrinos correspond to Gaussian Mersenne k=167 then sneutrinos could have mass below electron mass scale. Selectron would remain the only experiment signature of TGD SUSY at this moment.
- One decay channel for selectron would be to electron+ sZ or neutrino+ sW. sZ/sW (spartner of weak boson) would eventually decay to possibly virtual Z+ neutrino/W+neutrino: that is weak gauge boson plus missing energy. Neutralino and chargino need not decay in the detection volume. The lower bound for neutralino mass is 46 GeV from intermediate gauge boson decay widths. Hence this option is not excluded by experimental facts.
Muonic g-2 anomaly is an excellent test for this vision. The poor man's calculation (see this) modifying suitably MSSM calculation gives a value consistent with data if the mass of W gauge is twice the mass of W boson and sneutrinos are light in W boson mass scale. The result does not depend in the lowest order appreciably on the mass of muonic sneutrino. 250 GeV selectron remains the prediction testable at LHC.
The basic differences between TGD and MSSM and related approaches deserve to be noticed (for the experimental aspects of MSSM see this). If Higgses and Higgsinos are absent from the spectrum, SUSY in TGD sense does not introduce flavor non-conserving currents (FNCC problem plaguing MSSM type approaches). In MSSM approach the mass spectrum of superpartners can be only guessed using various constraints and in a typical scenario masses of sfermions are assumed to be same in GUT unification scales so that at long length scales the mass spectrum for sfermions is inverted from that for fermions with stop and stau being the lightest superpartners. In TGD framework p-adic thermodynamics and the topological explanation of family replication phenomenon changes the situation completely and the spectrum of sfermions is very naturally qualitatively similar to that of fermions (genus generation correspondence is the SUSY invariant answer to the famous question of Rabi "Who ordered them?" !). This is essential for the explanation of g-2 anomaly for instance. Note that the experimental searches concentrating on finding the production of stop or stau pairs are bound to fail in TGD Universe.
Another key difference is that in TGD the huge number of parameters of MSSM is replaced with a single parameter- the universal coupling characterizing the decay
sparticle→ particle+right handed neutrino,
which by its universality is very "gravitational". The gravitational character suggests that it is small so that SUSY would not be badly broken meaning for instance that sparticles are rather longlived and R-parity is a rather good symmetry.
One can try to fix the coupling by requiring that the decay rate of sfermion is proportional to gravitational constant G or equivalently, to the square of CP2 radius
Sfermion-fermion-neutrino vertex coupling to each other same fermion M4 chiralities involves the gradient of the sfermion field. Yukawa coupling - call it L - would have dimension of length. For massive fermions in M4 it would reduce to dimensionless coupling g different M4 chiralities. In equal mass case g would be proportional to L(m1+m2)/hbar, where mi are the masses of fermions.
- For the simplest option L is expressible in terms of CP geometry alone and corresponds to
L= kR .
k is a numerical constant of order unity. hbar0 denotes the standard value of Planck constant, whose multiple the efffective value of Planck constant is in TGD Universe in dark matter sectors. The decay rate of sfermion would be proportional to k2R2 (M/hbar)3≈ k2107× (G/hbar0)× (M/hbar)3,
where M is the mass scale characterizing the phase space volume for the decays of sfermion. M is the mass of sfermion multiplied by a dimensionless factor depending on mass ratios. The decay rate is extremely low so that R-parity conservation would be an excellent approximate symmetry. In cosmology this could mean that zinos and photinos would decay by an exchange of sfermions rather than directly and could give rise to dark matter like phase as in MSSM.
- Second option carries also information about Kähler action one would have apart from a numerical constant of order unity k= αK. The Kähler coupling strength αK= gK2/4π×hbar0≈ 1/137 is the fundamental dimensionless coupling of TGD analogous to critical temperature.
- For the option which "knows" nothing about CP2 geometry the length scale would be proportional to the Schwartchild radius
In this case the decay rate would be proportional to k2G2M2(M/hbar)3 and extremely low.
- The purely kinematic option which one cannot call "gravitational" "knows" only about sfermion mass and f Planck constant, and one would have
L= k× hbar/M.
Decay rate would be proportional to the naive order of magnitude guess k2(M/hbar) and fast unlike in all "gravitational cases". R-parity would be badly broken. Again k propto αK option can be considered.
Note that also in mSUGRA gravitatational sector in short length scales determines MSSM parameters via flavor blind interactions and also breaking of SUSY via breaking of local SUSY in short scales.
To my opinion the success of TGD using only simple scaling and symmetry arguments instead of heavy computational approach demonstrates how important it is to base the models on a genuine theory. Blind phenomenology can be completely misleading when basic principles are replaced with ad hoc assumptions. Here of course the problem is that super strings and M-theory can provide no principles helping the phenomenologist.
Addition: Tommaso Dorigo mentions the eprint Supersymmetry and Dark Matter in Light of LHC 2010 and XENON 100 Data as one of the first reactions of SUSY specialists to the 2010 LHC data represented in Europhysics 2011. The message is that one can find simple enough variants of MSSM which can cope with the experimental constraints (the number of parameters of MSSM is more than hundred). Authors are however cheating a little bit: they have dropped from their fit the really painful muonic g-2 anomaly requiring light wino or zino scale and/or some light sleptons, say light sneutrino. Taking this contraints into the fit *very* probably kills it. If not, authors would not have forgotten to mention it!;-)
For TGD SUSY see appropriate section in the chapter New Particle Physics Predicted by TGD: Part I of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy".