^{0}charges of elementary particles are screened in electro-weak length scale or not. The hypothesis has been that the charges are feeded to larger space-time sheets in this length scale rather than screened by vacuum charges so that an effective screening results in electro-weak length scale.

A more promising approach inspired by the TGD based view about dark matter assumes that weak charges are indeed screened for ordinary matter in electro-weak length scale but that dark electro-weak bosons correspond to much longer symmetry breaking length scale.

The large value of hbar in dark matter phase implies that Compton lengths and -times are scaled up. In particular, the sizes of nucleons and nuclei become of order atom size so that dark nuclear physics would have direct relevance for condensed matter physics. It becomes impossible to make a reductionistic separation between nuclear physics and condensed matter physics and chemistry anymore. This view forces a profound re-consideration of the earlier ideas in nuclear and condensed physics context. It however seems that most of the earlier ideas related to the classical Z^{0} force and inspired by anomaly considerations survive in a modified form.

### How to characterize dark matter?

The identification of the precise criterion characterizing dark matter phase is far from obvious. TGD actually suggests an infinite number of phases which are dark relative to each other in the sense that the particles of different phases cannot appear in the same vertex and a phase transition changing the particles to each other analogous to de-coherence is necessary.

The assumption has been that macroscopically quantum coherent dark matter corresponds to a large hbar. This characterization relies on intuition that only space-time sheets with same size interact quantum coherently. This intuition generalizes to the hypothesis that only space-time sheets with the same p-adic prime and same value of hbar, be it small or large, have direct quantum coherent interactions and that incoherent interaction involve a phase transition changing the value of p-adic prime and hbar. Infinite number of relatively dark phases is predicted.

Furthermore, each particle is characterized by a a collection of p-adic primes characterizing the space-time sheets at which it feeds its gauge fluxes and particles can interact only via their common space-time sheets and are otherwise dark with respect to each other. This allows to resolve objections against p-adic hierarchies of color and ew physics.

A particular kind of dark matter corresponds to conformally confined matter with particles having complex conformal weights such that the net conformal weight is real. In this case hbar need not be large. If particles of given phase have a fixed conformal weight corresponding to a multiple of a non-trivial zero of Zeta or its conjugate, there is no effective violation of Fermi statistics. The space-time correlate for the complexity of conformal weights would be Gaussian primeness but also other extensions of p-adic numbers can be considered and zeros of Zeta could map to Gaussian Mersennes in the case of gauge bosons if they quite generally correspond to Mersennes.

The chiral selection in living matter suggest large
parity breaking and presence of light dark weak
bosons with complex conformal weights corresponding
to increasing values for the zeros of Zeta. The
Gaussian Mersennes (1+i)^{k-1}for k=113,151,157
163,167 correspond to nuclear length scale and
four biologically important length scales in the
range 10 nm-25 μm, which seem to relate
directly to the coiling hierarchy of DNA double
strands.

For a given prime, TGD predicts actually an entire hierarchy of dark matters corresponding to varying values of hbar such that the many particle states at previous level become particles at the next level. The hierarchy for large values of hbar would provide a concrete physical identification for the hierarchy of infinite primes identifiable in terms of a repeated second quantization of an arithmetic super-symmetric QFT. The finite primes about infinite prime is in a well defined sense a composite would correspond to the particles in the state forming a unit of dark matter.

### Evidence for long range weak forces and new nuclear physics

There is a lot of experimental evidence for long range electro-weak forces, dark matter, and exotic nuclear physics giving valuable guidelines in the attempts to build a coherent theoretical scenario.- Cold fusion [9] is a phenomenon involving new nuclear physics and the known selection rules give strong constraints when one tries to understand the character of dark nuclear matter. In particular, the model discussed here requires that only nuclear protons are in dark phase.
- Large parity breaking effects in living matter indicate the presence of long ranged weak forces, and the reported nuclear transmutations in living matter [18,19] suggest that new nuclear physics plays a role also now.
- The physics of water involves a large number of anomalies and life depends in an essential manner on them. As many as 41 anomalies are discussed in the excellent web page "Water Structure and Behavior" of M. Chaplin [1]. The transparency of water is still a mystery for science [8]. The fact that the physics of heavy water differs much more from that of ordinary water as one might expect on basis of different masses of water molecules suggests that dark nuclear physics is involved. The finding that one hydrogen atom per two water molecules remain effectively invisible in neutron and electron interactions in attosecond time scale [1,2] suggests that water is partially dark. These findings have been questioned in [3] and thought to be erroneous in [4]. If the findings are real, dark matter phase made of super-nuclei consisting of dark protons could explain them as also the clustering of water molecules predicting magic numbers of water molecules in clusters. If so, dark nuclear physics could be an essential part of condensed matter physics and biochemistry. For instance, the condensate of dark protons might be essential for understanding the properties of bio-molecules and even the physical origin of van der Waals radius of atom in van der Waals equation of state.
- The scaling law of homeopathy suggests that the scalings associated with the transitions to dark matter correspond to scalings by powers n/v
_{0}, n=3, and that a hierarchy of dark matters is involved (dark matter, dark dark matter, etc...) - Exotic chemistries [10] in which clusters of atoms of given given type mimic the chemistry of another element. These systems behave as if nuclei would form a jellium (constant charge density) defining a harmonic oscillator potential for electrons. Magic numbers correspond to full electron shells analogous to noble gas elements. It is difficult to understand why the constant charge density approximation works so well. If nuclear protons are in large hbar with n=3 state the electromagnetic sizes of nuclei would be about 2.4 Angstroms and the approximation would be natural.
- The anomalies reported by free energy researchers such as over unity energy production in devices involving repeated formation and dissociation of H
_{2}molecules based on the original discovery of Nobelist Irwing Langmuir [14] (see for instance [15]) suggest that part of H atoms might end up to dark matter phase liberating additional energy. The "mono-atomic" elements of Hudson suggest also dark nuclear physics [7]. There is even evidence for macroscopic transitions to dark phase [12,13,11]. - Tritium beta decay anomaly [5,17,18]. suggests exotic nuclear physics related to weak interactions and that dark anti-neutrino density at the orbit of Earth around Sun oscillating with one year period is involved. This kind of remnant of dark matter would be consistent with the model for the formation of planets from dark matter. The evidence for the variation of the rates of nuclear and chemical processes correlating with astrophysical periods [16] could be understood in terms of weak fields of astrophysical range created by dark matter.

### k=113 dark nuclear physics

k=113 characterizes electromagnetic size of u and d quarks, of nucleons, and nuclei. k=107 characterizes the QCD size of quarks and hadrons and valence quarks could be actually be in dark matter phase as far as QCD is considered, which would mean that their QCD size (k=107) is of order electron Compton length. These surprisingly long length scales have a natural interpretation as the height of the magnetic/color-magnetic body of nucleon.

The basic criterion for the transition to dark matter phase is that perturbation theory for gauge interacting system ceases to converge. A more practical criterion in terms of two particle gauge interactions reads as Q_{1}Q2α≈ 1. The criterion suggests that all quarks make a transition to dark matter phase meaning that real p-adic prime p≈ 2^{113} is replaced by Gaussian Mersenne M^{G}_{113}. The electromagnetic size L(113) of u and d quarks would increase by a factor n/v_{0}≈ 2^{11}n, where n is integer, for n=3 this would give size of 1.2 Angstroms, order of magnitude for a typical van der Waals radius.

Although the phase transition occurs for both neutrons and protons, it is possible to understand the selection rules of cold fusion. The point is that Coulomb repulsion makes the rate for the fusion of p and p resulting in the phase transition of dark p slow. If conformal weights remain real and large hbar phase transition occurs for k=113 sheet only, the lifetimes of nuclei are not changed and nuclear physics is not affected as far as classical lowest order in hbar predictions are considered. The basic effects come from the dramatic lowering of Coulomb wall by the increase of the nuclear size.

The phase transition increasing only hbar must
be distinguished from a phase transition making
conformal weights complex. In this phase transition
the real prime corresponding to k=113 would
become Gaussian Mersenne. This would bring in
conformally non-trivial weak bosons with k=113
with mass scaled down by a factor 2^{-12}. The
lifetime of neutrons would become very short unless
the mass difference is below electron mass and this
condition would serve as a criterion for the
stability of the resulting exotic nuclei.

If both of these phase transitions occur k=113 weak bosons would have a Compton length of order atomic size scale. This could allow to understand the large parity breaking effects in living matter..

### Water and k=113 exotic nuclear physics

There is evidence for two kinds of hydrogen bonds [21,20]: a possible identification is in terms of ordinary and dark proton. Tedrahedral water clusters consisting of 14 water molecules would contain 8 dark protons which corresponds to magic number for dark nucleus consisting of protons. Icosahedral water clusters in turn consist of 20 tedrahedral clusters and the interpretation would be as magic dark dark nucleus associated with k=151 dark dark electro-weak bosons. The appearance of the dark dark hierarchy level could make water completely exceptional and make it unique from the point of view of living matter in which also higher hierarchy levels would be present and correspond quite concretely to the coiling hierarchy of DNA at the level of ordinary matter. For more details see the new chapter*Dark Nuclear Physics and Living Matter*which can be found either here here or here .

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