It has become clear that the anomalously small proton charge radius is here to state. I have considered earlier a model for the observation, which however failed to predict the size of the effect.
The anomaly could be explained also as breaking of the universality of weak interactions. Also other anomalies challenging the universality exists. The decays of neutral B-meson to lepton pairs should be same apart from corrections coming from different lepton masses by universality but this does not seem to be the case (see this). There is also anomaly in muon's magnetic moment discussed briefly here. This leads to ask whether the breaking of universality could be due to the failure of universality of electroweak interactions.
The proposal for the explanation of the muon's anomalous magnetic moment and anomaly in the decays of B-meson is inspired by a recent very special di-electron event and involves higher generations of weak bosons predicted by TGD leading to a breaking of lepton universality. Both Tommaso Dorigo (see this) and Lubos Motl (see this) tell about a spectacular 2.9 TeV di-electron event not observed in previous LHC runs. Single event of this kind is of course most probably just a fluctuation but human mind is such that it tries to see something deeper in it – even if practically all trials of this kind are chasing of mirages.
Since the decay is leptonic, the typical question is whether the dreamed for state could be an exotic Z boson. This is also the reaction in TGD framework. The first question to ask is whether weak bosons assignable to Mersenne prime M89 have scaled up copies assignable to Gaussian Mersenne M79. The scaling factor for mass would be 2(89-89)/2= 32. When applied to Z mass equal to about .09 TeV one obtains 2.88 TeV, not far from 2.9 TeV. Eureka!? Looks like a direct scaled up version of Z!? W should have similar variant around 2.6 TeV.
TGD indeed predicts exotic weak bosons and also gluons.
Could the exchange of massive MG,79 photon and Z0 give rise to additional electromagnetic interaction inducing the breaking of Universality?
V(r)= g2 e-Mr/r ,&g2 = 4π kα .
The expectation differs from zero significantly only in S-wave state characterized by principal quantum number n. Since the exponent function goes exponentially to zero in the p-adic length scale associated with 2.9 TeV mass, which is roughly by a factor 32 times shorter than intermediate boson mass scale, hydrogen atom wave function is constant in excellent approximation in the effective integration volume. This gives for the energy shift
Δ E= g2| Ψ(0)|2 × I ,
Ψ(0) 2 =[22/n2]×(1/a03) ,
a0= 1/(mα) ,
I= ∫ (e-Mr/r) r2drdΩ =4π/M2.
For the energy shift and its ratio to ground state energy
En= α2/2n2× m
one obtains the expression
Δ En= 64π2 α/n2 α3 (m/M)2 × m ,
Δ En/En= 27 π2α2 k2(m/M)2 .
For k=1 and M=2.9 one has Δ En/En ≈ 8.9× 10-11 for muon.
Consider next Lamb shift.
Δn (Lamb)/En= 13α3/2n .
For n=2 this gives Δ2 (Lamb)/E2= 4.9× 10-7.
Δ E(rp) =a – brp2 +crp3
= 209.968(5) – 5.2248 × r2p + 0.0347 × r3p meV ,
where the charge radius rp=.8750 is expressed in femtometers and energy in meVs.
x=[Δ E(rp))-Δ E(rp(exp))]/Δ E(rp)
= [- 5.2248 × (r2p- r2p(exp)) + 0.0347 × ( r3p-r3p(exp))]/[209.968(5) - 5.2248 × r2p + 0.0347 × r3p(th)] .
The estimate gives x= 1.2× 10-3.
This value can be compared with the prediction. For n=2 ratio of Δ En/Δ En(Lamb) is
x=Δ En/Δ En (Lamb)= k2 × [29π2/13α] × (m/M)2 .
For M=2.9 TeV the numerical estimate gives x≈ k2 × 10-4. The value of x deduced from experimental data is x≈ 1.2× 10-3. For k=3 a correct order of magnitude is obtained. There are thus good hopes that the model works.
For a summary of earlier postings see Latest progress in TGD.