Aleph anomaly just refuses to disappear

From FB I learned about evidence for a bump around 28 GeV ). The title of the preprint is " Search for resonances in the mass spectrum of muon pairs produced in association with b quark jets in proton-proton collisions at s^1/2 = 8 and 13 TeV. Thanks to Ulla for the link.

An excess of events above the background near a dimuon mass of 28 GeV is observed in the 8 TeV data, corresponding to local significances of 4.2 and 2.9 standard deviations for the first and second event categories, respectively. At 13 TeV data the excess is milder. This induced two dejavu experiences.

1. First dejavu

Last year (2018) came a report from Aleph titled " Observation of an excess at 30 GeV in the opposite sign di-muon spectra of Z→ bbbar+X events recorded by the ALEPH experiment at LEP" . The preprint represents re-analysis of data from 1991-1992. The energy brings strongly in mind 28 GeV bump.

TGD - or more precisely p-adic fractality - suggests the existence of p-adically scaled variants of quarks and leptons with masses coming as powers of 2 (or perhaps even 2^1/2. They would be like octaves of a fundamental tone represented by the particle. Neutrino physics is plagued by anomalies and octaves of neutrino could resolve these problems.

Could one understand 30 GeV bump - possibly same as 28 GeV bump in TGD framework? b quark has mass 4.12 GeV or 4.65 GeV depending on the scheme used to estimate it. b quark could correspond to to p-adic length scale L(k) for k=103 but the identification of the p-adic scale is not quite clear. p-Adically scaling b-quark mass taken to be 4.12 GeV by factor 4 gives about 16.5 GeV (k= 103-4= 99), which is one half of 32 GeV: could this correspond to the proposed 30 GeV resonance or even 28 GeV resonance? One must remember that these estimates are rough since already QCD estimates for b quark mass vary about 10 per cent.

28 GeV bump could correspond to p-adically scaled variant of b with k=99. b quark would indeed appear as octaves. But how to understand the discrepancy: could one imagine that there are actually two mesons involved and analogous to pion and rho meson?

2. Second dejavu

Concerning quarks, I remember an old anomaly reported by Aleph at 56 GeV. This anomaly is mentioned in a preprint published last year and there is reference to old paper by ALEPH Collaboration, D. Buskulic et al., CERN preprint PPE/96-052. What was observed was 4-jet events consisting of dijets with invariant mass around 55 GeV. What makes this interesting is that the mass of 28 GeV particle candidate would be one half of the mass of a particle with mass of mass of 56 GeV particle, quite near to 55 GeV.

My proposal for the identification of the 55 GeV bump was as a meson formed from scaled variants b and bbar corresponding to p-adic prime p≈ 2^k, k=96. The above argument suggests k=99-2=97. Note that the production of the 28 GeV bump decaying to muon pair is associated with production of b quark and second jet.

3. What the resonance are and how could they be produced?

The troubling question is why the two masses around 28 GeV ad 30 GeV? Even worse: for 30 GeV candidate a dip is reported in at 28 GeV! Could the two candidates correspond to π(28) and ρ(30) having slightly different masses by color-magnetc spin-spin splitting?

The production mechanism should explain why the resonance is associated with b-quark and jet and also why two different mass values suggest themselves.

1. If one has 56 GeV pseudo-scalar resonance consisting mostly of bbbar - call it π(56), it could couple to Z⁰ by standard instanton density coupling, and one could have the decay Z→ Z+π(56). The final state virtual Z would produce the b-tag in its decay.
   
   
2. π(56) in turn would decay strongly to π(28)+ρ(30) with spin 1 and analogous to the rho meson partner of ordinary pion. Masses would be naturally different for π and ρ.
   
   

It is easy to check that the observed spin-spin splitting is consistent with the simplest model for the spin-spin splitting obtained by extrapolating the for ordinary π-ρ system.

1. At these mass scales the spin-spin splitting proportional to color magnetic moments and thus to inverses of the b quark masses should be small and indeed is.
   
   
2. Consider first ordinary π-ρ system. The predicted masses due to spin-spin splitting are m(π)= m-Δ/2 and m(ρ)= m+ 3Δ/2), where one has m= (3m(π)+ m(ρ))/4 and Δ= (m(ρ)-m(π))/2. For π-ρ system one has r₁= Δ m/m≈ .5.
   

   Δ m/m is due to the interaction of color magnetic moments and proportional to r₂=α_s² m²(π)/m²(d). The small masses of u and d quarks - m(d)≈ 4.8 MeV (Wikipedia value, the estimate vary widely) - implies that m(π)/m(d)≈ 28.2 is rather large. The value of α_s is larger than α_s=.1 achieved at higher energies, which gives r₂= α_s² m²(π)/m²(d)>.28. One has r₁/r₂≈ .57.
   
   

3. For π(28)-ρ(30) system the values of the parameters are m≈ 29 GeV and Δ m=2 GeV and r₁= Δ m/m≈ .07. The mass ratio is roughly m(π)/m(b) = 2 for heavy mesons for which quark mass dominates in the meson mass. For α_s=.1 the order of magnitude for r₂=α_s² m²(π(28))/m²(b) is r₂≈ .04 and one has r₁/r₂=.57 to be compared with r₁/r₂=.56 for ordinary π(28)-ρ(30) system so that the model looks realistic.
   

   Interestingly, the same value of α_s works in both cases: does this provide support for the TGD view about renormalization group invariance of coupling strengths? This invariance is not global but implies discrete coupling constant evolution.
   
   

See the chapter New Physics predicted by TGD: part I.

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

Articles and other material related to TGD.