Could M_G,79 hadron physics be seen at LHC?

Gaussian Mersennes M_G,n=(1+i)ⁿ-1 (complex primes for complex integers) are much more abundant than ordinary Mersennes and corresponding p-adic time scales seem to define fundamental length scales of cosmology, astrophysics, biology, nuclear physics, and elementary physics. There are as many as 10 Gaussian Mersennes besides 9 Mersennes above LHC energy scale suggesting a lot of new physics in sharp contrast with the GUT dogma that nothing interesting happens above weak boson scale- perhaps copies of hadron physics or weak interaction physics. In the following I consider only those Gaussian Mersennes possibly interesting from the point of view of very high energy particle physics.

n∈{2, 3, 5, 7, 11, 19, 29, 47, 73} correspond to energies not accessible at LHC. n= 79 might define new copy of hadron physics above TeV range - something which I have not considered seriously before. The scaled variants of pion and proton masses (M₁₀₇ hadron physics) are about 2.2 TeV and 16 TeV. Is it visible at LHC is a question mark to me.

Some weeks after writing the last sentence I saw the posting of Lubos suggesting that M_G,79 pion might have been already seen! Lubos tells about a bump around 2(!)TeV energy observed already earlier at ATLAS and now also at CMS. See the article in Something goes bump in Symmetry Magazine. The local signficance is about 3.5 sigma and local significance about 2.5 sigma. Bump decays to weak bosons.

Many interpretations are possible. An interpretation as new Higgs like particle has been suggested. Second interpretation - favored by Lubos - is as right-handed W boson predicted by left-right- symmetric variants of the standard model. If this is correct interpretation, one can forget about TGD since the main victory of TGD is that the very strange looking symmmetries of standrad model have an elegant explanation in terms of CP₂ geometry, which is also twistorially completely unique and geometrizes both electroweak and color quantum numbers.

Note that the masses masses of M_G,79 weak physics would be obtained by scaling the masses of ordinary M₈₉ weak bosons by factor 2^(89-79)/2)= 512. This would give the masses about 2.6 TeV and 2.9 TeV.

There is however an objection. If one applies p-adic scaling 2^(107-89)/2=2⁹ of pion mass in the case of M₈₉ hadron physics, M₈₉ pion should have mass about 69 GeV (this brings in mind the old and forgotten anomaly known as Aleph anomaly at 55 GeV). I proposed that the mass is actually an octave higher and thus around 140 GeV: p-adic length scale hypothesis allows to consider octaves. Could it really be that a pion like state with this mass could have slipped through the sieve of particle physicists? Note that the proton of M₈₉ hadron physics would have mass about .5 TeV.

I have proposed that M₈₉ hadron physics has made itself visible already in heavy ion collisions at RHIC and in proton-heavy ion collisions at LHC as strong deviation from QCD plasma behavior meaning that charged particles tended to be accompanied by particles of opposite charged in opposite direction as if they would be an outcome of a decay of string like objects, perhaps M₈₉ pions. There has been attempts - not very successful - to explain non-QCD type behavior in terms of AdS/CFT. Scaled up variant of QCD would explain them elegantly. Strings would be in D=10. The findings from LHC during this year probably clarify this issue.

Lubos is five days later more enthusiastic about superstring inspired explanation of the bump than the explanation relying on left-right symmetric variant of the standard model. The title of the posting of Lubos is The 2 TeV LHC excess could prove string theory. The superstringy model involves as many as six superstring phenomenologists as chefs and the soup contains intersecting branes and anomalies as ingredients.

The article gives further valuable information about the bump also for those who are not terribly interested on intersecting branes and addition of new anomalous factors to the standard model gauge group. The following arguments show that the information is qualitatively consistent with the TGD based model.

1. Bump is consistent with both ZZ, WZ, and according to Lubos also Zγ final states and is in the range 1.8-2.1 TeV. Therefore bump could involve both charged and neutral states. If the bump corresponds to neutral elementary particle such as new spin 1 boson Z^' as proposed by superstring sextet, the challenge is to explain ZZ and Zγ bumps. WZ pairs cannot result from primary decays.
2. There is dijet excess, which is roughly by a factor of 20 larger than weak boson excesses. This would suggest that some state decays to quarks or their excitations and the large value of QCD coupling strength gives rise to a the larger excess. This also explains also why no lepton excess is observed.

   For the superstring inspired model the large branching fraction to hadronic dijets suggesting the presence of strong interactions is a challenge: Lubos does not comment this problem. Also the absence of leptonic pairs is problematic and model builders deduce that Z^' suffers syndrome known as lepto-phobia.

3. Neutral and charged M_G,79 pions can decay to virtual M_G,79 or M₈₉ quark pair annihilating further to a pair of weak bosons (also γγ pair is predicted) or by exchange of gluon to M_G,79, M₈₉ (or M₁₀₇) quark pair producing eventually the dijet. This would explain the observations qualitatively. If the order of magnitude for the relative mass splitting between neutral and charged M_G,79 pion is same as for ordinary pion one, the relative splitting is of order Δ M/M≈ 1/14 - less that 10 per cent meaning Δ M<.2 TeV. The range for the position of the bump is about .3 TeV.
4. The predictions of TGD model are in principle calculable. The only free parameter is the M_G,79 color coupling strength so that the model is easy to test.