The implications of .5 MeV and 3.5 keV monochromatic lines for TGD based nuclear model

Very interesting popular article in Nature tells about very interesting new results found by Safti et al. The findings challenge the prevailing particle physics view about existence of galactic dark matter halo and consisting of some exotic new particles behaving like dark matter. These findings add to a long list of negative results related to the existence of dark matter halo and the attempts to find predicted dark matter particles.

There are two observed candidates for ford particles what would form the speculative galactic dark matter halo. They would have as decay products monochromatic gamma rays at energy of around .5 MeV and 3.5-keV X rays having no standard identification. The recent findings exclude the possibility that these particles reside in the conjectured galactic dark matter halo. They could however reside in galactic centers so that their existence is not challenged.

A. .5 MeV gamma ray signal

There is an old gamma ray signal from Milky Way at gamma ray energy of slightly more than electron mass. It has been proposed that it results as dark particle and antiparticle almost at res with respect to each other annihilate. Now it seems that the interpretation as in the proposed sense seems to be excluded.

One can of course, why not a particle which has mass nearly twice the electron mass could not decay to two gamma rays. For some reason this option haven not been experienced as interesting.

  1. Support from the existence of pseudo-scalar with this mass emerged already at seventies but because it did not fit witht he standard model picture it was forgotten. Later evidence for a particle with masses twice the mass of muon and tau lepton with similar interpretation emerged. For the same reason also these pieces of evidence were forgotten.
  2. TGD led long time ago to what I call lepto-pion hypothesis (see this). In TGD color is not spin-like but angular momentum-like quantum number. Color correspond to the analog of angular momentum for the analog of rigid body rotation in CP_2 degrees freedom. In particular, TGD allows colored excitations of leptons: for instance, electron could appear in color octet state. Color excited electron and positron might form a pion-like color confined pion with mass very nearly 2 times electron mass. Same for muon and tau.
  3. These states could be dark in the sense that they have non-standard value of effective Planck constant heff=n×h0. This would explain why they are not produced in the decays of Z0 boson and therefore do not affect its decay rate. Otherwise Z0 and W decays widths exclude leptopions.
  4. This darkness has however nothing to do with the darkness of galactic matter, which reside as energy and possibly dark matter at long very cosmic strings to which linear structures formed by galaxies can be assigned. These cosmic strings can locally thicken to flux tubes and liberate energy as particles forming galaxies. They generate radial gravitational force predicting the flat velocity spectrum of distant stars.
TGD picture would explain why these particles have not been observed outside galactic nucleus.

B. 3.5-keV X ray signal

Can one imagine any standard physics identification for the 3.5-keV line?. An interesting atomic physics based identification is as as X ray emitted in the capture of electron by sulphur ion with principal quantum number n≥9, which is rather high (see this and this ). This requires plasma at temperature of order 3 keV plus cold dense cloud moving at few hundred km/s .

3.5-keV X rays appearing as an un-identified mono-chromatic line in X ray spectrum have been proposed to result from the annihilation of dark particles having mass about 7 keV: annihilation of inert neutrinos is one proposal. The experimental findings exclude the possibility that these X rays are produced in the proposed galactic halo. TGD suggests two alternative explanations based on the notion of monopole flux tube.

  1. In TGD framework also 3.5-keV X rays could result in a decay of pion-like state with mass of 7 keV. TGD indeed predicts new nuclear physics in keV scale. As a matter fact, TGD leads to a new vision about nuclear physics on basis of model of "cold fusion" (see this) . Magnetic flux carrying monopole flux serve as basic building bricks also now: TGD Universe is indeed fractal.
  2. Nuclear string model relies on the assumption that nuclei are sequences of nucleons connected by pionlike bonds - loopy flux tubes much longer than the M4 distance between nucleons. These loopy flux tubes have length of order electron Compton length are essential for the TGD based model of nuclear reactions and also of "cold fusion".
  3. This model allows to consider two options concerning the interpretation of 3.5-keV line.

    Option I:

    These flux tubes would be like pions with mass about 7 keV decaying to two X rays with energy 3.5-keV. They might be produced even in nuclear physics laboratory. Also now darkness in TGD sense (heff =n×h0>h) is essential and one can talk about dark nuclei.

    In the annihilation of pion like bond to X ray pair, fission of the nucleus would take place. There is no dependence on environmental parameters like temperature.

    Option II:

    The 3.5-keV energy could correspond to a cyclotron transition of for a light quark with mass scale of E=7 MeV assignable to the flux tube having cyclotron energy of this order of magnitude. Recall that cyclotron frequency is determined by the radius of the monopole flux tube and from the quantization of magnetic flux assumed to be minimal plus the from the fact that Bend= .2 Gauss for electron is .6 MHz.

    In this case however the pion-like loopy flux tube bonds between nucleons would have mass about 2mu, which would be of the order of nuclear binding energy of order E rather than being in keV range. The energy differences for subsequent states at nuclear IR Regge trajectories assignable to nucleons are predicted also to have energy of order E. Both the intra-nucleon bonds and inter-nucleon bonds would have the same mass scale. The model for nucleus constructed recently however assumed that the mass scale for the bond is keV. The masses of bonds ncreasing mass could be compensated by downwards shifts at IR Regge trajectories of nucleons.

    The cyclotron transitions would naturally correspond to the return to the ground state after thermal excitation. Temperature would correspond to thermal energy of order 3 keV. The line intensity depends on the temperature of environment.

    Remark: For Option I the cyclotron energies for quarks with masses in keV range would be of order eV, which is also predicted to be a nuclear energy scale in the proposal for TGD based nuclear physics.

  4. The intensity of 3.5-keV lines depends on environment. This excludes Option I but saves Option II. For instance, it is known that 3.5-keV line is associated with galactic clusters and galactic nuclei but not with spheroidal dwarf galaxies with little or no star dust, no recent star formation, and low luminocity (see this). The presence of plasma at temperature of order 3 keV distinguishing between these options seems necessary. This temperature is possible for several astrophysical X-ray sources (see this). Also celestial sources such as the surfaces of stars with surface temperature of this order of magnitude are possible (for Sun the surface temperature is 3 orders of magnitude lower).

    The temperature of order 3.5-keV makes possible for hot fusion to start- in solar core the temperature is 1.5 keV) so that 3.5-keV line could serve as a signature for regions, where star formation is beginning. In TGD framework, where dark fusion explaining "cold fusion" serves as a "warm-up band" for hot fusion, this correlation is especially natural.

  5. One should be able to predict correct value of the cyclotron energy with natural assumptions. The loopy flux tube would correspond to k=127 for electron. The endogenous magnetic field carrying monopole flux corresponds to Bend= .2 Gauss assignable to k=167 flux tube. The cyclotron of fe= Bend/me of is electron fJ=6× 105 Hz for heff=h . fe is scaled up by a factor 240≈ 1012 in the replacement k=167→ 127.

    Proton cyclotron frequency is scaled fp=(me/mp)fe. For proton cyclotron energy one obtains (heff/h) × (me/mp)× (gp/2)× fJ. Proton has magnetic oment μp= 2.79 e/2mp . For heff/h=211 this gives Ec,p) ≈ 3.78 keV, which is sligthly higher than 3.5 keV. If one has heff/h≈ mp/me≈ 1876 one obtains 3.46 keV quite near to 3.5 keV! For heff=h one have in this case 1.8 eV so that eV scale emerges and would correspond to the cyclotron energy of single sheet of covering. Therefore proton's cyclotron energy for heff/h≈ mp/me or electron's cyclotron frequency for heff=h could be in question in Bend scaled up from k=167 to k=127.

    For neutron the dipole momenta is μn=-1.91× e/2mp and cyclotron energy would be Ec,n=2.46 keV, which might be a testable prediction. Cyclotron energy per single sheet would be Ec,n=1.31 eV.

C. Questions raised by the interpretation of 3.5-keV signal

These interpretation of 3.5-keV signal raises several questions.

  1. The earlier proposal has been that nuclear neutrons could correspond to pairs of proton and pion-like flux tube carrying negative charge. The observation above forces to ask whether the intra-nucleon flux tubes carry electrons and have heff=h. Could nuclear proton transform effectively to neutron by the presence of flux tube carrying electron so that the idea about neutrons as pairs of proton and electron-neutrino pair could make sense inside nuclei.
  2. Could also interpret the bonds as scaled down analogs of weak bosons? I have actually considered the possibility of scaled down variants of electroweak gauge bosons earlier in the model (see this) for the so called X boson anomaly. The inspiration for this came from CVC resp. PCAC hypothesis relates the conserved vectorial resp. partially conserved axial electroweak currents to strong interactions. This hypothesis is encouraged also by M8-H duality strongly suggesting that QCD type description provides the quark-gluon description at high energies at the level of H=M4× CP2 and M8= M4 × E4 description provides the description of hadron physics in terms of O(4)= SU(2)× SO(3) symmetry group acting as isometries of E4 of old-fashioned hadron physics appearing in CVC and PCAC.

    What is important is that weak bosons would be effectively massless below the scaled up weak scale L(127), and depending on the situation also to some other scales as p-adic length scale hypothesis suggests, and being as strong as electromagnetic interactions below this scale. Could one interpret strong interactions in hadronic and nuclear scales as scaled-down weak interactions?

This hypothesis combined with p-adic length scale hypothesis is very powerful and can be tested.
  1. Higgs boson with mass 125 GeV would correspond to k=89. Higgs mass would be minimal possible if p-adic mass squared is of order O(p) so that real mass squared is m2R= 1/p. Contrary to the long-held expectations W and Z bosons with standard values of Weinberg angle naturally correspond to k=90 if pure U(1) boson would have Higgs mass.

    TGD predicts also pseudo-scalar variant of Higgs. For k=90 the minimal mass would be 88 GeV. LHC has observed a bump at about 96 GeV (see this), and this could correspond to pseudo-scalar Higgs, call it P, and assume its mass is indeed 96 GeV. The masses of weak bosons would be therefore (m(H),m(P),m(W),m(Z))= (125 ,96, 80.4, 91.2) GeV and masses for other p-adic length scales follow by simple scaling.

  2. The masses of Higgs and W and Z bosons with same Weinberg angle for k=127 would be obtained by scaling with a factor 2(-127+k)/2, k= 89 for Higgs and k=90 for P, W and Z. This would give (m(H),m(P),m(W),m(Z))= (.238 ,.129 , .11, .12) MeV. What is nice is that these scales are considerably below the nuclear binding energy scale about 7-8 MeV per nucleon for heavier and 1.1 MeV for D so that one could indeed assign nuclear binding and excitation energies to the nucleon flux tubes as proposed.
This raises questions.
  1. Could also the intra-nuclear flux tube bonds have scaled-down weak boson masses but with different p-adic length scale? Can one regard the electrons in these bonds effectively as free electrons as far as cyclotron energies are considered? Could the old-fashioned hadron physics at least partially reduce to weak interaction physics below electron Compton length and possible other p-adic length scales assignable to the flux tubes involved?
  2. Intra-nucleon flux tubes have been assumed to have intra-nucleon binding energy scale about 7-8 MeV (1.1 MeV for neutron-proton pair)? The proposal is that binding energy scale corresponds to the energy scale of IR Regge trajectories for nucleons and is thus single nucleon property (or that of the MB of nucleon). Nuclear strings would be strings formed from 4He strings a units, possible D type string, and lonely nucleons (protons or neutrons depending on the sign of Z-N.

    Nuclear binding energy scale 7-8 MeV would be assignable to the MB of nucleons of 4He and of heavier nuclei and 1 MeV energy scale to the MBs of p and n in D. The binding energy scale and energy scale of excitations would be determined by the p-adic length scale assignable to the intra-nucleon flux tubes and depending on environment via the value of k defining the p-adic lengths scale.

  3. What would this mean p-adically? The scaling of weak boson masses with mass scale .1 MeV to larger mass scale should correspond to that for the binding energy scale and give binding energy scale 1 MeV for D and 8 MeV for 4He.
    1. Consider first 1 MeV scale assignable to intra-nucleon flux tubes in D. k=127-6=121 would give (mH,mP,mW,mZ)=(1.90,1.06,.877, .8) MeV. The mass of P is quite near the the D binding energy 1.11 MeV.

      A connection with lepto-hadron hypothesis suggests itself. For k= 121=112 the mass of P would be 1.06 MeV and very nearly twice the electron mass 1.022 MeV. The mass of the electro-pion proposed to explain the pseudo-scalar resonance observed in heavy ion collisions is very very near to 2me. Could electro-pion identified as a pair of color octet leptons correspond scaled down P? Also evidence for muon-pion and tau-pion exists. Could these correspond to higher generations of weak bosons predicted by TGD?

    2. What about 7-8 MeV scale? k=113 is basic candidate for nuclear scale and the corresponding masses would be scaled by factor 27=128 giving (mH,mP,mW,mZ)=(30.5,16.5,14.1,15.4) MeV. These scales are too large by a factor of order 2 that k=111 looks more appropriate.
  4. There exists evidence for what is called X boson with mass of 17 MeV. One interpretation would be in terms of pion like state which could corresponds to the electroweak pseudo-scalar predicted by TGD. The mass of k=113 P-boson would be 16.5 MeV and quite near to X boson mass. This would suggest that several p-adic length scales are indeed possible. This interpretation can be tested by checking whether other exotic bosons in this range exist.
To sum up, the TGD inspired model for nucleus predicts correctly the 3.5-eV X ray energy as cyclotron energy with using the earlier assumptions of the model. Also other predictions and tests follow. For instance, the model could be tested by irradiating nuclei in laboratory using 3.5 eV X rays and looking whether this has effects. For instance, nuclear decay rates could be affected.

What M8-H duality together with CVC and PCAC suggests and the above observations quantitatively support is that p-adic length scale hierarchy could allow a description of hadronic and nuclear physics in terms of p-adically scaled down variants of weak interactions such that the value of k for weak bosons would depend on the energy scale of the strong interactions.

See the chapter Could TGD provide new solutions to the energy problem? or the article The implications of .5 MeV and 3.5 keV monochromatic lines for TGD based nuclear model.