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Tuesday, March 14, 2017 9:35

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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 M_{89} have scaled up copies assignable to Gaussian Mersenne M_{79}. 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.

- TGD based explanation of family replication phenomenon in terms of genus-generation correspondence forces to ask whether gauge bosons identifiable as pairs of fermion and antifermion at opposite throats of wormhole contact could have bosonic counterpart for family replication. Dynamical SU(3) assignable to three lowest fermion generations labelled by the genus of partonic 2-surface (wormhole throat) means that fermions are combinatorially SU(3) triplets. Could 2.9 TeV state – if it would exist – correspond to this kind of state in the tensor product of triplet and antitriplet? The mass of the state should depend besides p-adic mass scale also on the structure of SU(3) state so that the mass would be different. This difference should be very small.
- Dynamical SU(3) could be broken so that wormhole contacts with different genera for the throats would be more massive than those with the same genera. This would give SU(3) singlet and two neutral states, which are analogs of η' and η and π
^{0}in Gell-Mann's quark model. The masses of the analogs of η and π^{0}and the the analog of η', which I have identified as standard weak boson would have different masses. But how large is the mass difference? - These 3 states are expected top have identical mass for the same p-adic mass scale, if the mass comes mostly from the analog of hadronic string tension assignable to magnetic flux tube. connecting the two wormhole contacts associates with any elementary particle in TGD framework (this is forced by the condition that the flux tube carrying monopole flux is closed and makes a very flattened square shaped structure with the long sides of the square at different space-time sheets). p-Adic thermodynamics would give a very small contribution genus dependent contribution to mass if p-adic temperature is T=1/2 as one must assume for gauge bosons (T=1 for fermions). Hence 2.95 TeV state could indeed correspond to this kind of state.

Could the exchange of massive M_{G,79} photon and Z^{0} give rise to additional electromagnetic interaction inducing the breaking of Universality?

- The additional contribution in the effective Coulomb potential is Yukawa potential. In S-wave state this would give a contribution to the binding energy in a good approximation given by the expectation value of the Yukawa potential, which can be parameterized as

V(r)= g^{2} e^{-Mr}/r ,&g^{2} = 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= g^{2}| Ψ(0)|^{2} × I ,

Ψ(0) ^{2} =[2^{2}/n^{2}]×(1/a_{0}^{3}) ,

a_{0}= 1/(mα) ,

I= ∫ (e^{-Mr}/r) r^{2}drdΩ =4π/M^{2}.

For the energy shift and its ratio to ground state energy

E_{n}= α^{2}/2n^{2}× m

one obtains the expression

Δ E_{n}= 64π^{2} α/n^{2} α^{3} (m/M)^{2} × m ,

Δ E_{n}/E_{n}= 2^{7} π^{2}α^{2} k^{2}(m/M)^{2} .

For k=1 and M=2.9 one has Δ E_{n}/E_{n} ≈ 8.9× 10^{-11} for muon.

Consider next Lamb shift.

- Lamb shift as difference of energies between S and P wave states (see this) is approximately given by

Δ_{n} (Lamb)/E_{n}= 13α^{3}/2n .

For n=2 this gives Δ_{2} (Lamb)/E_{2}= 4.9× 10^{-7}.

Δ E(r_{p}) =a – br_{p}^{2} +cr_{p}^{3}

= 209.968(5) – 5.2248 × r^{2}_{p} + 0.0347 × r^{3}_{p} meV ,

where the charge radius r_{p}=.8750 is expressed in femtometers and energy in meVs.

x=[Δ E(r_{p}))-Δ E(r_{p}(exp))]/Δ E(r_{p})

= [- 5.2248 × (r^{2}_{p}- r^{2}_{p}(exp)) + 0.0347 × ( r^{3}_{p}-r^{3}_{p}(exp))]/[209.968(5) - 5.2248 × r^{2}_{p} + 0.0347 × r^{3}_{p}(th)] .

The estimate gives x= 1.2× 10^{-3}.

This value can be compared with the prediction. For n=2 ratio of Δ E_{n}/Δ E_{n}(Lamb) is

x=Δ E_{n}/Δ E_{n} (Lamb)= k^{2} × [2^{9}π^{2}/13α] × (m/M)^{2} .

For M=2.9 TeV the numerical estimate gives x≈ k^{2} × 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 background see the chapters New Physics Predicted by TGD: Part I and New Physics Predicted by TGD: Part II.

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

Articles and other material related to TGD.

Source: http://matpitka.blogspot.com/2017/03/could-second-generation-of-weak-bosons.html