Toponium at 40.4 GeV?

Prof. Matt Strassler tells about a gem found from old data files of ALEPH experiment by Arno Heisner. The 3-sigma bump appears at 30.40 GeV and could be a statistical fluctuation and probably is so. It has been found to decay to muon pairs and b-quark pairs. The particle that Strassler christens V (V for vector) would have spin 1.

Years ago I commented a candidate for scaled down top quark reported by Aleph: this had mass around 55 GeV and the proposal was that it corresponds to p-adically scaled up b quark with estimated mass of 52.3 GeV.

Could TGD allow to identify V as a scaled up variant of some spin 1 meson?

1. p-adic length scale hypothesis states that particle mass scales correspond to certain primes p≈ 2^k, k>0 integer. Prime values of k are of special interest. Ordinary hadronic space-time sheets would correspond to hadronic space-time sheets labelled by Mersenne prime p=M₁₀₇=2¹⁰⁷-1 and quarks would be labelled by corresponding integers k.

2. For low mass mesons the contribution from color magnetic flux tubes to mass dominates whereas for higher mass mesons consisting of heavy quarks heavy quark contribution is dominant. This suggests that the large mass of V must result by an upwards scaling of some light quark mass or downwards scaling of top quark mass by a power of square root of 2.
3. The mass of b quark is around 4.2-4.6 GeV and Upsilon meson has mass about 9.5 GeV so that at most about 1.4 GeV from total mass would correspond to the non-perturbative color contribution partially from the magnetic body. Top quark mass is about 172.4 GeV and p-adic mass calculations suggest k=94 (M₈₉) for top. If the masses for heavy quark mesons are additive as the example of Upsilon suggests, the non-existing top pair vector meson – toponium – would have mass about m= 2× 172.4 GeV =344.8 GeV.
4. Could the observed bump correspond to p-adically scaled down version of toponium with k= 94+7=101, which is prime? The mass of toponium would be 30.47 GeV, which is consistent with the mass of the bump. If this picture is correct, V would be premature toponium able to exist for prime k=101. Its decays to b quark pair are consistent with this.
5. Tony Smith has talked about indications for several mass peaks for top quark. I have discussed this here in terms of p-adic length scale hypothesis. There is evidence for a sharp peak in the mass distribution of the top quark in 140-150 GeV range). There is also a peak slightly below 120 GeV, which could correspond to a p-adically scaled down variant t quark with k=93 having mass 121.6 GeV for (Y_e=0, Y_t=1). There is also a small peak also around 265 GeV which could relate to m(t(95))=243.2 GeV. Therefore top could appear at least at p-adic scales k=93, 94, 95. This argument does not explain the peak in 140-150 GeV range rather near to top quark mass.

What about Aleph anomaly? The value of k(b) somewhat uncertain. k(b)=103 is one possible value. I have considered the explanation of Aleph anomaly in terms of k=96 variant of b quark. The mass scaling would be by factor of 2^7/2, which would assign to mass m_b=4.6 GeV mass of about 52 GeV to be compared with 55 GeV.

For a summary of earlier postings see Latest progress in TGD.

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