The discovery of X boson as a further evidence for nuclear string model
Anomalies seem to be popping up everywhere, also in nuclear physics and I have been busily explaining them in the framework provided by TGD. The latest nuclear physics anomaly that I have encountered was discovered in Hungarian physics laboratory in the decays of the excited state ^{8}Be* of an unstable isotope of ^{8}Be (4 protons and 4 neutrons) to ground state ^{8}Be (see this). For the theoretical interpretation of the finding in terms of fifth force mediated by spin 1 boson see this.
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 like 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.
What could TGD say about the situation? First two observations, a puzzle created by them, and the solution of the puzzle.
- 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.
To see this more clearly 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 electron pair. The amplitude for decay to electron pair is completely analogous to for the decay of ordinary pion to electron pair and at microscopic level involves the decay qqbar→ γ*→ e^{+}e^{-} described by QED. The rate for π(113)→ e^{+}e^{-} can be scaled down from the rate π(107)→ e^{+} e^{-} for the decay of ordinary pion.
- In TGD framework the decay of pion like state X=π(113) to gamma pair corresponds microscopically to a radiative process involving a triangle quark loop with gammas at the outgoing vertices. The effective action density is determined by axial anomaly and is proportional to ε^{αβγδ }F_{αβ} F_{γδ} π(113), where F is the electromagnetic field. The coupling constant parameter with dimensions of length is dictated completely by anomaly considerations and the rate can be scaled down from that for the decay of ordinary pion to γ pair (the "Quantum Field Theory of Iztykson-Zuber gives a good account about this). What turns out tobe essential is that the effective action results as a radiative correction and is proportional to α and thus to 1/hbar.
- The crucial point to notice is that the effective action for π(113)→ γγ emerges as a radiative correction being thus proportional to α and therefore to 1/hbar. The contributions of tree diagrams give the classical cross section to the scattering rate and this cannot depend on 1/hbar: Compton length hbar/m is indeed replaced with classical electromagnetic radius e^{2}/m in the rate. One motivation for introducing non-standard value of Planck constant h_{eff}=n× h (see this) was that in this manner Nature would take care that the perturbation series converges: perturbative corrections would come as powers of the scaled down fine structure contant α_{eff}=α/n. Same would apply to all gauge coupling strengths.
- The basic assumption is that dark matter resides at magnetic flux tubes. If the quarks and color magnetic flux tubes connecting nucleons are dark, the scaling h→ h_{eff}/n takes place and the rate for π(113)→ γγ is reduced by factor 1/n^{2} and for sufficiently large n it is possible to obtain rate consistent with the experimental bounds. The rate r(π(113)→ e^{+}e^{-}) is determined by tree diagram and is not reduced. This solution of the puzzle is the only one that I can imagine in TGD framework.
- 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.
- ^{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 Reactor antineutrino anomaly and X boson as indications for new nuclear physics predicted by TGD 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.