Consider first the theoretical background in light p-adic mass calculations, the weak form of electric-magnetic duality, and TGD based view about supersymmetry.
- The simplest possibility is that the p-adic length scale of the super-partner differs from that of partner but the p-adic thermodynamical contributions to the mass squared obey the same formula.
- If the p-adic prime p≈ 2k of super-partner is smaller than M89=289-1, the weak length scale must be scaled down and M61=289-1 is the next Mersenne prime. Scaled up variant of QCD for M89 would naturally correspond to M61 weak physics and would have hadronic string tension about 218 GeV2 by scaling the ordinary hadronic string tension of about 1 GeV2. This scaled up variant of hadronic physics is an old prediction of TGD. As noticed, also weak string tension could have the same value. Quite generally, the pairs of weak and hadronic scales predicted to form a hierarchy could correspond to pairs of subsequent (possibly Gaussian) Mersenne primes.
- What happens for k=89? Can the particle topologically condense at the same p-adic scale that characterizes its weak flux tube? Or should one assume that the p-adic prime corresponds to k< 89 assuming that the particle has standard weak interactions. If so then the superpartners of light fermions would have k< 89. This is a strong prediction if superpartners obey the same mass formula as particles. In the case of weak gluinos and
also QCD gluinos the bound would be k≤ 89 and even stronger bound would be k=89 so that the masses of
wino and zino would be same as W and Z.
One must be however very cautious with this kind of arguments since one is dealing with quantum theory. For instance, quarks inside proton have masses in 10 MeV scale and their Compton lengths are much larger than the Compton size of proton and even atomic nucleus. The interpretation is that for the corresponding space-time sheets is in terms of the color magnetic body of quark. These large space-time sheets are essential in the model of the Lamb shift anomaly of muonic hydrogen.
- In TGD framework Higgs and its pseudo-scalar companion define electroweak triplet and singlet and Higgs could be eaten completely by electro-weak gauge bosons if the TGD based mechanism of massivation is correct. The condition of exact Yangian symmetry demands the cancellation of IR divergences requiring a small mass for all gauge bosons and graviton. The twistorially natural assumption that gauge bosons are bound states of massless fermion and antifermion implies that the three-momenta of fermion and antifermion are in opposite directions so that all gauge bosons -even photon- and graviton would be massive. Super-symmetry strongly suggests that gauginos eat Higgsinos as they become massive so that only massive gauge bosons and gauginos and possible pseudoscalar Higgs and its superpartner would remain to be discovered at LHC. Similar mechanism can indeed work also in the case of gluons expected to have colored scalar counterparts. Gluon would be massless below the scale corresponding to QCD Λ and massive above this scale.
What does this picture give when compared with the rumors about super-partners of fermion and scalar. If selectron corresponds to the not necessarily allowed M89=289-1, and obeys otherwise the same mass formula as electron, the mass should be 250 GeV, which is too large. For k=88 which is the smallest value allowed by the above argument, one would obtain 177 GeV not far from 160 GeV. Therefore the interpretation as selectron could make sense. In the case of super-partner of scalar one can consider several options.
- The first observation is that 200 GeV mass does not satisfy the proposed upper bound k> 89 for higgsinos and gauginos suggested by the condition that the weak string cannot have p-adic length scale longer than the p-adic length scale at which the particle condensed topologically. Hence neither higgsino nor longitudinal polarization of gaugino can be in question.
- If one gives up the upper bound mZ=91.2 GeV on mass but takes the twistorially motivated and mathematically beautiful horror scenario for LHC seriously, the 200 GeV particle can only correspond to a longitudinal polarization of Zino or photino.
- If photonic Higgs is not eaten by photon, one would obtain k(Higgs)= k(Higgsino)+n. n=1,2,3 would give Higgs mass equal to (141,100, 71) GeV for m(Higgsino)= 200 GeV. On basis of experimental data mildly suggesting that neutral Higgs appears in two mass scales I have considered the possibility that Higgs indeed appears at two p-adic length scales corresponding to about 130 GeV and 92 GeV related by square root of two factor. 130 GeV would give m(Higgsino)= 184 GeV: I dare guess that this is consistent with the estimate 200 GeV.
- For W and Z0 Higgsinos the mass mass would be p-adically scaled up variant of W or Z0 mass and for Z0 mass about 91.2 GeV Z0 Higgsino mass would be 182.4 GeV for n=2. For W Higgsino the mass would be around 160.8 GeV.
For background see the new section of p-Adic Mass Calculations: New Physics.