The anomaly manifests itself as a bump in the distribution of e^{+}e^{-} pairs in the transitions ^{8}Be*→ ^{8}Be at certain angle between electrons. The theoretical interpretation is in terms of a production of spin 1 boson - christened as X - identified as a carrier of fifth force with range about 12 fm, nuclear length scale. The attribute 6.8σ tells that the probably that the finding is statistical fluctuation is about 10^{-12}: already 5 sigma is regarded as a criterion for discovery.
The assumption about vector boson character looks at first well-motivated: the experimental constraints for the rate to gamma pairs eliminate the interpretation as pseudo-scalar boson whereas spin 1 bosons do not have these decays. In the standard reductionistic spirit it is assumed that X couples to p and n and the coupling is sum for direct couplings to u and d quarks making proton and neutron. The comparison with the experimental constraints forces the coupling to proton to be very small: this is called protophoby. Perhaps it signifies something that many of the exotic particles introduced to explain some bump during last years are assumed to suffer various kinds of phobies. The assumption that X couples directly to quarks and therefore to nucleons is of course well-motivated in standard nuclear physics framework relying on reductionism.
Two observations, and the problems created by them
TGD inspired interpretation based on nuclear string model is based on two observations and potential problems created by them.
- The first observation is that 12 fm range corresponds rather precisely to p-adic length scale for prime p≈ 2^{k}, k=113 assigned to the space-time sheets of atomic nuclei in TGD framework. The estimate comes from L(k)= 2^{(k-151)/2}L(151), L(151) ≈ 10 nm. To be precise, this scale is actually the p-adic Compton length of electron if it where characterized by k instead of k_{0}=127 labelling the largest not super-astrophysical Mersenne prime. k=113 is very special: it labels Gaussian Mersenne prime (1+i)^{k}-1 and also muonic space-time sheet.
- A related observation made few days later is that the p-adic scaling of the ordinary neutral pion mass 135 MeV from k=107 to k=113 by 2^{-(113-107)/2}=1/8 gives 16.88 MeV! That p-adic length scale hypothesis would predict the mass of X with .7 per cent accuracy is hardly an accident. This would strongly suggest that X boson is k=113 pion.
- There is however a problem. The decays to photon pairs producing pion in l=1 partial wave have not been however observed. This creates puzzle. If X is ρ meson like state with spin 1, it should have same mass as pionic X? This is not plausible.
There is however a problem: the estimate for Γ(π, e^{+}e^{-}) obtained by p-adically scaling the model based on decay virtual gamma pair decaying to e^{+}e^{-} pair is by a factor 1/88 too low. One can consider the possibility that the dependence of f_{π} on p-adic length scale is not the naively expected one but this is not an attractive option. The increase of Planck constant seems to worsen the situation.
The dark variants of weak bosons appear in important role in both cold fusion and TGD inspired model for chiral selection. They are effectively massless below the scaled up Compton scale of weak bosons so that weak interactions become strong. Since pion couples to axial current, the decay to e^{+}e^{-} could proceed via annihilation to Z^{0} boson decay to e^{+}e^{-} pair. The estimate for Γ(π(113), e^{+}e^{-}) is in the middle of allowed range. The success suggests that the couplings of mesons to p-adically scaled down weak bosons could describe semileptonic decays of hadrons and explain the somewhat mysterious origin of CVC and PCAC.
Effective action approach
One must construct the effective action for the process using relativistic approach and Poincare invariance.
- The effective action in the fifth force proposal involves the term giving rise to the decay Z→ ^{8}Be+X. ^{8}Be*==Z is treated as effective U(1) gauge field Z_{αβ} = ∂_{α}Z_{β} - ∂_{β}Z_{α} expressible in terms of vector potential Z_{α}. The corresponding term in the effective action density is proportional to ε^{αβγδ} Z_{αβ}∂_{γ}X ∂_{δ}Y. Here X is pseudoscalar meson and ^{8}Be==Y scalar. The coupling constant parameter has dimensions of length squared.
- In the recent case a reduction to the level of single color bond takes place so that Z_{αβ} is replaced with ρ_{αβ} representing spin 1 colored bond and pseudo-scalar X with the colored analog of π(113).
- Second term in the effective action describes decays of pseudoscalar X to gamma pair and electron pairs. The scaling of standard model produces gamma+gamma decay rate below the experimental upper limit. The scaling of standard model produces a rate which is by a factor about 1/100 too small. The description in terms of coupling to p-adically scaled down variant of Z boson via axial current leads to a prediction consistent with experimental limits. Also the dark variant of Z boson can be considered as a model but now the rate is by order of magnitude smaller than the lower limit proposed in the article. Also the decay of ordinary pion could proceed by same mechanism.
Model for color bonds of nuclear strings
One should also construct a model for color bonds connecting nucleons to nuclear strings.
- In nuclear string model nuclei are identified as nuclear strings with nucleons connected by color flux tubes, which can be neutral or charged and can have net color so that color confinement would be in question in nuclear length scale. The possibility of charged color flux tubes predicts the existence of exotic nuclei with some neutrons replaced by proton plus negatively charged color flux tube looking like neuron from the point of view of chemistry or some protons replaced with neutron plus positively charged flux tube. Nuclear excitation with energy determined buy the difference of initial and final color bond energies is in question.
- The color magnetic flux tubes are analogous to mesons of hadron physics except that they can be colored and are naturally pseudo-scalars in the ground state. These pion like colored flux tube can be excited to a colored state analogous to ρ meson with spin 1 and net color. Color bonds would be rather long flux loops with size scale determined by the mass scale of color bond: 17 MeV gives estimate which as electron Compton length divided by 34 and would correspond to p-adic length scale k=121>113 so that length would be about 2^{(121-113)/2}=16 times longer than nuclear length scale.
- If the color bonds (cb) are indeed colored, the mass ratio m(ρ,cb)/m(π,cb) need not be equal to m(ρ,107)/m(π,107)=5.74. If the ρ and π type closed string states are closed string like objects in the sense as elementary particles are so that there is a closed magnetic monopole flux tube along first sheet going through wormhole contact to another space-time sheet and returning back, the scaling m(ρ/π,107)/m(ρ/π,113)= 8 should hold true.
Model for ^{8}Be* → ^{8}Be +X
With these ingredients one can construct a model for the decay ^{8}Be* → ^{8}Be +X.
- ^{8}Be* could correspond to a state for which pionic color(ed) bond is excited to ρ type color(ed) bond. The decay of ^{8}Be* → ^{8}Be +X would mean a snipping of a color singlet π meson type closed flux tube from the color bond and leaving pion type color bond. The reaction would be analogous to an emission of closed string from open string. m(X)=17 MeV would be the mass of the color-singled closed string emitted equal to m(π,113)=17 MeV. The emitted π would be in l=1 partial wave so that resonant decay to gamma pair would not occur but decay to e^{+}e^{-} pairs is possible just like for the ordinary pion.
- Energy conservation suggests the identification of the excitation energy of ^{8}Be* as the mass difference of ρ and π type colored bonds (cb): E_{ex}(^{8}Be*)=m(ρ,cb)-m(π,cb)= m(π,113)= 17 MeV in the approximation that X is created at rest. If one has m(ρ,cb)/m(π,cb)= m(ρ)/m(π) - this is not necessary - this gives m(ρ,cb)≈ 20.6 MeV and m(π,cb)≈ 3.5 MeV.
- This estimate is based on mass differences and says nothing about nuclear binding energy. If the color bonds carry positive energy, the binding energy should be localizable to the interaction of quarks at the ends of color bonds with nucleons. The model clearly assumes that the dynamics of color bonds separates from the dynamics of nuclei in the case of the anomaly.
- The assumption about direct coupling of X to quarks and therefore to nucleons does not makes sense in this framework. Hence protophoby does not hold true in TGD and this is due to the presence of long color bonds in nuclear strings. Also the spin 1 assignment would be wrong.
For details see the article X boson as evidence for nuclear string model or the chapter Nuclear string model of "Hyper-finite factors, p-adic length scale hypothesis, and dark matter hierarchy".
For a summary of earlier postings see Latest progress in TGD.
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