First rumors about super partners in LHC

Lubos reports the first rumors from LHC concerning super-partners. The estimates for the masses are 200 GeV for scalar super partner (higgsino) and 160 GeV for fermion superpartner (I guess selectron). Being an incurable optimist I suppose that the rumors from LHC are more trustworthy than the physics blog rumors usually. If so, can one understand these masses in TGD framework and what can one conclude about them? Also this posting has been replaced with a new one since I finally ended up with the understaning of how the TGD based variant of gauge boson massivation could explain how gauge bosons get their longitudinal components and how the ratio of W and Z masses could result in this framework in terms of weak string picture.

Consider first the theoretical background in light p-adic mass calculations, the weak form of electric-magnetic duality, and TGD based view about supersymmetry.

1. 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.

2. If the p-adic prime p≈ 2^k 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.

3. 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.

4. 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.

1. 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.
2. If one gives up the upper bound m_Z=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.

One can of course forget the upper bound on mass and give up the horror scenario for a moment and look what one obtains.

1. 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.
2. 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.

I have already earlier considered the predictions of p-adic length scale hypothesis for super partners on basis of single very strange scattering event (see the section "Experimental indication for space-time supersymmetry"). This kind of considerations must of course be taken as a mere blog entertainment. The hypothesis assuming that the mass formulas for particles and sparticles are same but p-adic length scale is possibly different, combined with kinematical constraints fixes the masses of TGD counterparts of selectron, higgsino, and Z⁰-gluino to be 131 GeV (just at the upper bound allowed kinematically), 45.6 GeV, and 91.2 GeV (Z⁰ mass) respectively. The masses are consistent with the bounds predicted by the MSSM inspired model. Selectron mass would be by a factor factor 2^-1/2 smaller than 177 GeV and presumably consistent with the 160 GeV rumor. Higgsino mass would be one half of Z⁰ mass and would satisfy the proposed constraint k< 89. Z⁰ gluino mass would be equal to Z⁰ mass also in accordance with the proposed constraint. W gluino is predicted to have same mass as W. In the case of photino the upper bound to the mass would be given by weak boson mass scale. Could it be that the life would be so simple? Could these predictions make it easy to discover super partners at LHC? Well-informed reader might be able to answer these questions.

For background see the new section of p-Adic Mass Calculations: New Physics.