The simplest identification of the 150 GeV resonance in TGD framework

The picture about CDF resonance has become (see the postings Theorists vs. the CDF bump and More details about the CDF bump by Jester. One of the results is that leptophobic Z' can explain only 60 per cent of the production rate. There is also evidence that Wjj corresponds to a resonance with mass slightly below 300 GeV as naturally predicted by technicolor models.

The simplest TGD based model indeed relies on the assumption that the entire Wjj corresponds to a resonance with mass slightly below 300 GeV for which there is some evidence. If one assume that only neutral pions are produced in strong non-orthogonal electric and magnetic fields of colliding proton and antiproton, the mother particle must be actually second octave of 147 GeV pion and have mass somewhat below 600 GeV producing in its possibly allowed strong decays pions which are almost at rest for kinematic reasons. Therefore the production mechanism could be exactly the same as proposed for two and one half year old CDF anomaly and for the explanation of DAMA events and DAMA-Xenon100 discrepancy,

1. This suggests that the mass of the mother resonance is in a good accuracy two times the mass of 150 GeV bump for which best estimate is 147+/- 5 GeV. This brings in mind the explanation for the two and half year old CDF anomaly in which tau-pions with masses coming as octaves of basic tau-pion played a key role (masses were in good approximation 2^k× m(π_τ), m(π_τ)≈ 2m_τ, k=1,2. The same mechanism would explain the discrepancy between the DAMA and Xenon100 experiments.

2. If this mechanism is at work now, the mass of the lowest M₈₉ pion should be around 73 GeV as the naivest scaling estimate gives. One can however consider first the option for which lightest M₈₉ has mass around 147 GeV so that the 300 GeV resonance could correspond to its first p-adic octave. This pion would decay to W and neutral M₈₉ pion with mass around 147 GeV in turn decaying to two jets. At quark level the simplest diagram would involve the emission of W and exchange of gluon of M₈₉ hadron physics. Also the decay to Z and charged pion is possible but in this case the decay of the final state could not take place via annihilation to gluon so that jet pair need not be produced.

3. One could also imagine the mother particle to be ρ meson of M₈₉ hadron physics with mass in a good approximation equal to pion mass. At the level of mathematics this option is very similar to the technicolor model of CDF bump based also on the decay of ρ meson. In this model the decays of π to heavy quarks have been assumed to dominate. In TGD framework the situation is different. If π consists of scaled up u and d quarks, the decays mediated by boson exchanges would produce light quarks. In the annihilation to quark pair by a box diagram involving two gluons and two quarks at edges the information about the quark content of pion is lost. The decays involving emission of Z boson the resulting pion would be charged and its decays by annihilation to gluon would be forbidden so that Wjj final states would dominate over Zjj final states as observed.

4. The strong decay of scaled up pion to charged and neutral pion are forbidden by parity conservation. The decay can however proceed by via the exchange of intermediate gauge boson as a virtual particle. The first quark would emit virtual W/Z boson and second quark the gluon of the hadron physics. Gluon would decay to a quark pair and second quark would absorb the virtual W boson so that a two-pion final state would be produced. The process would involve same vertices as the decay of ρ meson to W boson and pion. The proposed model of the two and one half year old CDF anomaly and the explanation of DAMA and Xenon100 experiments assumes cascade like decay of pion at given level of hierarchy to two pions at lower level of hierarchy and the mechanism of decay should be this.

Consider next the masses of the M₈₉ mesons. Naive scaling of the mass of ordinary pion gives mass about 71 GeV for M₈₉ pion. One can however argue that color magnetic spin-spin splitting need not obey scaling formula and that it becomes small because if is proportional to eB/m where B denotes typical value of color magnetic field and m quark mass scale which is now large. The mass of pion at the limit of vanishing color magnetic splitting given by m₀ could however obey the naive scaling.

1. For (ρ,π) system the QCD estimate for the color magnetic spin-spin splitting would be

   (m(ρ),m(π))= (m₀+3Δ/4,m₀-Δ/4) .

   p-Adic mass calculations are for mass squared rather than mass and the calculations for the mass splittings of mesons (see this) force to replace this formula with

   (m²(ρ),m²(π))= (m₀² +3Δ²/4,m₀²-Δ²/4) .

   The masses of ρ and ω are very near to each other: (m(ρ),m(ω)=(.770,.782) GeV and obey the same mass formula in good approximation. The same is expected to hold true also for M₈₉.

2. One obtains for the parameters Δ and m₀ the formulas

   Δ= [mⁿ(ρ)-mⁿ(π)]^1/n , m₀= [(m²(ρ)+3m(π)²)/4]^1/n .

   Here n=1 corresponds to ordinary QCD and n=2 to p-adic mass calculations.

3. Assuming that m₀ experiences an exact scaling by a factor 512, one can deduce the value of the parameter Δ from the mass 147 GeV of M₈₉ pion and therefore predict the mass of ρ₈₉. The results are following

   m₀=152.3 GeV , Δ= 21.3 GeV , m(ρ₈₉)=168.28 GeV

   for QCD model for spin-spin splitting and

   m₀=206.7 GeV , Δ= 290.5 GeV , m(ρ₈₉)=325.6 GeV .

   for TGD model for spin-spin splitting.

4. Rather remarkably, there are indications from D0 for charged and from CDF for neutral resonances with masses around 325 GeV such that the neutral one is split by .2 GeV: the splitting could correspond to ρ-ω mass splitting. Hence one obtains support for both M₈₉ hadron physics and p-adic formulas for color magnetic spin-spin splitting. Note that the result excludes also the interpretation of the nearly 300 GeV resonance as ρ₈₉ in TGD framework.

5. This scenario allows to make estimates also for the masses other resonances and naive scaling argument is expected to improve as the mass increases. For (K₈₉,K^*₈₉) system this would predict mass m(K₈₉)>256 GeV and m(K^*₈₉)<456.7 GeV.

The nasty question is why the octaves of pion are not realized as a resonances in ordinary hadron physics. If they were there, their decays to ordinary pion pairs by this mechanism would very slow.

1. Could it be that also ordinary pion has these octaves but are not produced by ordinary strong interactions in nucleon collisions since the nucleons do not contain the p-adically scaled up quarks fusing to form the higher octave of the pion. Also the fusion rate for two pions to higher octave of pion would be rather small by parity breaking requiring weak interactions.

2. The production mechanism for the octaves of ordinary pions, for M₈₉ pions in the collisions of ordinary nucleons, and for leptohadrons would be universal, namely the collision of charged particles with cm kinetic energy above the octave of pion. The presence of strong non-orthogonal electric and magnetic fields varying considerably in the time scale defined by the Compton time of the pion is necessary since the interaction Lagrangian density is essentially the product of the abelian instanton density and pion field. In fact, in technicolor article it is mentioned that 300 GeV particle candidate is indeed created at rest in Tevatron lab -in other words in the cm system of colliding proton and antiproton beams.

3. The question is whether the preoduction of the octaves of scaled up pions could have been missed in proton-proton and proton antiproton collisions due to the very peculiar kinematics: pions would be created almost at rest in cm system (see this). Whether or not this is the case should be easy to test. For a theorists this kind of scenario does not look impossible but at the era of LHC it would require a diplomatic genius and authority of Witten to persuade experimentalists to check whether low energy collisions of protons produce octaves of pions!

There is also the question about the general production mechanisms for M₈₉ hadrons.

1. Besides the production of scalar mesons in strong non-orthogonal magnetic and electric fields also the production via annihilation of quark pairs to photon and weak bosons in turn decaying to the quarks of M₈₉ hadron physics serves as a possible production mechanism. These production mechanisms do not give much hopes about the production of nucleons of M₈₉ physics.

2. If ordinary gluons couple to M₈₉ quarks, also the production via fusion to gluons is possible. If the transition from M₁₀₇ hadron physics corresponds to a phase transition transforming M₁₀₇ hadronic space-time sheets/gluons to M₈₉ space-time sheets/gluons, M₁₀₇ gluons do not couple directly to M₈₉ gluons. In this case however color spin glass phase for M₁₀₇ gluons could decay to M₈₉ gluons in turn producing also M₈₉ nucleons. Recall that naive scalings for M₈₉ nucleon the mass 481 GeV. The actual mass is expected to be higher but below the scaled up Δ resonance mass predicted to be below 631 GeV.

For more about new physics predicted by TGD see the chapter New Particle Physics Predicted by TGD: Part I of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy". For reader's convenience I have added a short pdf article Is the new boson reported by CDF pion of M89 hadron physics? at my homepage.