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H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

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Met and Not Meeting Profesor Nambu

Once he - in Paris - invited me out for a dinner.
Did not meet Nambu san, in the conference in Copenhagen,where we ought to have met, because he had the bad luck ofgetting stuck in a desert and could not reach out. (A famous
bad luck story.) But I was participating in just the conference
he missed. Major subject was indeed the string, and professor
Nambu had written about string, “The Nambu -Goto action”( but no Goto at that stage).

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

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Yoichiro slept in laboratory and were disturbed by
Ziro Koba in the early morning.
After the war, Nambu and Hida married, whereupon he left forTokyo to take up a long-promised research position. (Hida stayedon in Osaka to look after her mother.) Housing was scarce, andNambu moved into his laboratory for three years. Gas andelectricity were free, and he could bathe in the water basin
intended for extinguishing air-raid fires. But his officemate, Ziro
Koba, a diligent young man (he once shaved his head for missing acalculation), would come in early and often embarrassed Nambu,
who was sleeping across both their desks.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

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Isolation from West”I was hungry all the time,” Nambu says. Finding food took upmost of the week. For the rest, he thought about physics,
calculating on rolls of cashregister paper. Koba, a student ofTomonaga, kept Nambu informed about the latter’s work. A groupof solid-state physicists in a neighboring office also provided
stimulating company.
All that these researchers knew of scientific developments in theWest came from sporadic issues of Time magazine. Later, journals
in a library set up by the Occupation forces helped to fill in thegaps. Yet much had to be reinvented by the Japanese physicists.
Sometimes they got there first. After moving to Osaka City
University in 1949, Nambu published a formula describing how twoparticles bind, now known as the Bethe-Salpeter equation.
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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Further from early times

Along with others, he also predicted that strange particles shouldbe created in pairs, a discovery usually attributed to Abraham Pais.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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There are several arguments for that there should be several vacua
with the same energy densities. There is in fact - tiny ? but some experimental evidence for such a principle. We speculate that dark
matter consists of cm-size bubbles of a second type of vacuum (“condensate vacuum”)on top of which is ordinary matter underenormous pressure inside the bubble.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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I liked physics because it was a way of studying fundamental
problems in natural sciences, Nambu.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

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Dark Matter and the Standard Model Vacua
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D.
Froggatt

Osaka City U. , December 12 , 2018
Unlike most colleagues believing in the application ofsuper string theory to the whole of physics - rather than just to
hadrons - as model beyond the Standard model, and thus
super symmetric partners of e.g. photons and Z zero being
candidates for dark matter, we shall use another of the ideas
brought to our understanding by Yoichiro as being behind the atpresent mysterious dark matter, namely the idea of degenerate
different vacua (similar to spontaneous breaking).
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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Main Topics: 1) (Standard Model) Vacua, 2) Dark
Matter Bubbles
Vacua We suggest a new law of Nature: Multiple Point
Principle: There are several vacua - not neccessarily
connected by symmetry - but nevertheless they all have thesame energy density (or in modern version they all have verysmall energy density of the order of the energy density of thevacuum in the universe).
Dark matter For the mysterious missing matter / dark matterin the universe we propose that it consists of cm-size bubbles
of one of the alternative vacua with in addition inside highly
compressed ordinary matter, say carbon etc.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

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Crucial to the Nambu-Goldstone Theorem is the
Idea of Non-trivial Vacuum, Lacking some of theSymmetries of Laws of Nature
To day I shall talk about the idea of there being several vacua,
but not connected by any symmetry.
Our main postulate is what we call “Multiple Point Principle”(MPP), and it says: The different vacua all have the same (or innewer version very small) energy densitites.
If the different vacua were connected by symmetry, it would follow
from the symmetry that they would have the same energy density,
but when they are not, this is ana priori strange postulate.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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Vacuum Non-trivial.

In physics, vacuum is the name given to nothing. How can asymmetry be broken even spontaneously when there is nothingaround? The radical nature of this idea has been best described byPhil Anderson: To me and perhaps more to his fellow particle
theorists this seemed like a fantastic stretch of imagination. The
vacuum, to us, was and always had been, a vacuum it had, since
Einstein got rid of the aether, been the epitome of emptiness... I,at least, had my mind encumbered with the idea that if there wasa condensate, there was something there ... This is why it took aNambu to break the first symmetry.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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Vacuum Analogous to Sea, Matter Waves on Top

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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Our Multiple Point (Criticallity) Principle as
Spontaneous Breaking Without Symmetry.
Comparing to the famous spontaneous break down by Nambu, one
could say that our “Multiple Point Criticallity Principle” (MPP) is
MPP = Spontaneous breakdown

Without any

symmetry to break down

In the most interesting case, where one gets the
Nambu-Goldstone-boson one has a spontaneous break down of a
Lie group. But a spontaneous breakdown of a discrete symmetrygroup like Z2 is highly possible, although cosmologicallydisfavoured.
Since we in our MPP have no symmetry involved at all, we tend to
think on just a discrete set of vacua with the same energy
density(=cosmological constant), more like the discrete group case.
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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Non-symmetry-related Vacua are Very Different
WorldsSince we in MPP have no symmetry the vacua are different inalmost all respects: In one vacuum most particles would be muchheavier (or much lighter) than in the other one.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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Several not quite convincing arguments for Multiple
Point Principle
Like to postpone arguing for why we should believe in our new lawof nature: Multiple Point Principle.
If one in say baby universe theory or antropic principle cansolve cosmological constant problem, then the multiple point
principle is to put the cosmological constant problem solution
in plural.
In theories without true locallity, but rather so that the(effective) couplings are functions of what happens in spcetime all over, you may easily derive MPP.
Fixing extensive quantities rather that intesive gives a way toderive MPP.
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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Spontaneously Broken Discrete Symmetry Not
Good Phenomenologically.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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But Without Symmetry the Extension of One
Vacuum Would be Only Seldomly Comparable tothat of the Other one

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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If something gets collected inside the contracting
phase,that stuff could keep the otherwise
disappearing pearls from collapsing.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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Main Point: The mysterious Dark Matter madefrom Pieces of an otherwise contracting phasepumped up by ordinary matter, atoms.
One of the two phases / vacua attrackts ordinary matter(electrons and nuclei) because the Higgs field expectation
value inside this phase is lower than in the other one.
This phase happens also to be the one that - for some may becomplicated reason - becomes the minority phase at somestage and therefore contrackts so as to almost disappear,...
but then it collect nucleons and electrons and stop
contracting at some stage if these materials can carry thecontraction pressure.
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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Forming a Picture of Our Dark Matter Model, Pearls
They are really bubles - with the vacuum being in two
different phases, the normal vacuum outside the pearl, and a“condensate vacuum” inside. Like water-droplets have water
inside and air outside.
The surface tension - being of weak interaction scale 100 GeV- is exceedingly high from dayly life scale point of view.
“surface tension” = 1011 kg /m2 = 1028 N/m
An atom-broad strip provides 1018 N ∼ the weight of
1017 kg =1014 ton.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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Picturing Our Pearls (continued)

To keep the extremely strong surface tension from collapsing
the pearl away, it must be filled with, say, ordinary matter,under extreme pressure. So there is ordinary matter insidethe dark matter in our model. Like in a white dwarf say.
If you feed a pearl with neutrons it can take them up underrelease of about 10 MeV energy per neutron. Protons would
have to be shot in with big speed.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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Picturing Our Pearls (continued)
In the inside phase, “condensate vacuum”, we have in ourmodel estimated that the Higgs field expectation value isabout half the outside value and the quarks and the nucleons
therefore lighter inside than outside by about 10 MeV.
Nucleons are atrackted towards the inside phase by a ca 10
MeV potential. For electrons this attracktion is less.
Some electrons are bound electrically, but some a bit outside
the surface with the strong tension.
Over-dimensioned “nucleus” is not a nucleus but rather
ordniary matter compressed.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

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H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

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H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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Wide Range for the Masses of the Particles making
up the Dark MatterOn the plot over the exclusion of the possible masses forprimordial black holes identified with dark matter there seems
not many possibilities for the primordial black holes being thedominant component of dark matter below a mass MDM > 1
to 100 M⊙ where it may be controversial, but really up to1013 M⊙ it is excluded on the figure.
But the exclusion observations for black holes up to ∼ 1024 g∼ 10−9 M⊙ are special for black holes such as their Hawking
radiation evaporation, and neutron star capture, or explosionof white dwarfs. So a similar mass particle, that was not a
black hole, such as our pearl-sized bubbles of new vacuum
would not be excluded up to 1024 g ∼ 10−9 M⊙ .
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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Bounds on masses of Dark Matter Particles(continued)
From this 1024 g ∼ 10−9 M⊙ and upward, however, themicrolensing lack of observing enough microlensings exclude
that dark matter could be dominated by MACHOS ( such
macroscopic particles).
For our pearl we propose a mass of the order of
108 kg = 1011 g = 1/2 ∗ 10−22 M⊙ or 500000 tons there is no
problem!. Our particle mass 500000 ton is safely under thelimit for gravitational lensing by 16 orders of magnitude. This
mass is fitted to:
Number of Tunguska events taken to one every century.
Very crude estimate of probability for that we see the volkanosof the type kimberlite pipes, from which one gets diamonds,
supposed to have been produced through the history of theearth by impacts of our pearls.
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

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A crude agreement with Dimensional Argument forthe size of the pearls if top quark relevant.
The weight of our pearls as estimated from the expected density ofdark matter and the falls of Tunguska events or number ofkimberlite pipe vokanos of say 500000 ton matches with assuming:
Inside density is - by our new law of nature multiple point
principle - the same as out side i.e. essentially 0.
The surface tension is of the order of magnitude given by
dimensional arguments from assuming top-quark mass or
weak scale being decicive for the surface tension.
the pearls are only of order unity bigger than the borderline
size, at which they would collaps, by spitting out thenucleons, that keep them pumped up. Stability border.
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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Further Successes of Our Dark Matter Model
3.55 keV line We get reasonable estimates for both the energy
per photon 3.55 keV for this -generally assumed dark matterradiation - and for the rate, provided we hypotesize that theenergy for the radiation comes from the surface contracktion
when two of our pearls collide. ( a factor 50 may be wrong forthe radiation intensity, but quite fine for the radiation fromthe galactic center in our own milky way.)
A story estimating the ratio of dark to ordinary matter.
and about supernova 1987A: Two strong neutrino bursts, one
hours before the real explosion.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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New Law of Nature: Multiple Point
Principle.
There are several phases of
vacuum(having relativity principles) and they
all have very very small energy
densities(like the astronomically determined one for ourpresent vacuum).
This principle is analogous to the having a specific temperature - ina microcanonical ensemble - when there are say both water and ice
present.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

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The Analogy:
The analogy between the triplepoint in the vapor- water-ice
combination at (T , p) = “tripelpoint ′′ = (273.16K , 0.6117kPa)
and “Multipel Point Principle” is:
The intensive quantities, temperature T and pressure p are
analogous to the kobling constants and the parameters, suche2
,etc.
as gt , α = 4π
The extensive quantities such as energy of the content of thebottle E , the amount (measured in mol e.g.) ofwater-molekyles N, the volume V are analogous to some
integrals, which could include
space-time-volume = lifetime of universe multiplied by its
volumeE.g. an integral over the square of the Higgs-field = theaverage value of the Higgsfield squared and multiplied with thejust mentioned spacetime volume.
But it could be something similar but based on other fields.
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

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H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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Must tell about that: We predicted the Higgs-Mass
We used what we call Multiple Point Principle (with Don
Bennett,...), which means that we assume, that the
coupling-constants - as e.g. the top-Yukawa-coupling related tothe top-quark mass - and other parameters in the field-theory (saythe Standard-Model) - such as the Higgs mass square - arefinetuned to have just such values that one ensures: Several
Vacua with the same energy density approximately so.
That we proposed (C.D.Froggatt and I under use of Bennetts andmine MPP) and thus we PREdicted - long befor the Higgs wasfound - the mass af the Higgs.
In a paper (with Froggatt and Takanishi, Meta-MPP) 121.8 GeV± 10 GeV; I have been painted together with Mogens Lykketoft
with 135 GeV ± 10 GeV(behind Lykketofts head). Higgs recently
confirmed with mass 125.09 ± 0.21(stat.) ± 0.11 (syst.) GeV/c 2 .
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

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H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

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H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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Three Agreeing Fits of the Bound State Mass:

In this way we got even two calculations for the bound state mass using in addition crude estimation mF (from “high field vacuum”) ≈ 850GeV ± 30%with ∼ 2(2)

mF (from “high field vacuum”) ≈ 710GeV ± 30%without ∼ 2 (3)mF (“condensate vac.”) ≈ 692GeV ± 40%(4)mF (“bag estimate”) ≈ 5mt = 865GeV (veryuncertain).
(5)

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

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H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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Scale problem ?
In Nambus book Quarks we learn that God was a bit drunk,when he wrote the weak interactions.
In our days one of the problems getting more and more severe is
the hierarchy problem, that calculating loop corrections to themasss-square of the Higgs particle leads to much bigger corrections
than the final renormalized Higgs mass square of (125GeV )2 weshall end up with !
Strange.
But it is strange that the Higgs mass was so small in the firstplace! This is the scale problem.
We want to say that Multiple Point Principle can enforce an
exponentially small Higgs mass (in the first place)!
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

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With MPP you have several vacua. In S.M.: 3 vacua
To describe our vacua for the Standard Model we speculate aneffective field describing a bound state we call F (750) or just F ,which is a bound from 6 top quarks and 6 antitop quarks (a closed
shell). Call this effective field for the bound state φF , while we callthe Higgs field φH . There are then 3 vacua:
The present vacuum, with φF = 0 and φH = 246GeV . This
the vacuum we live in so to speak.
Condensate vacuum with a condensate of the bound state F
and thus non-zero φF 6= 0. And φH a bit smaller than for thepresent one. This we hope to find inside the dark matter
pearls.
High field vacuum with a Higgs field expectation close to
the Planck scale, but zero bound state field.
There should be minima of the effective potential Veff (φH , φF ) asa function of the two variables (φH , φF ) at all the three vacua,
H.B. Nielsen,
Niels Bohr theyInstitutet(givingColinotherwise
wouldtalk),
notbeD. Froggattstable. We assume a bottom in the
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The running top-yukawa-coupling gt (µ)
MPP-specified both at high energy µ = EPl and at
the weak scale.
For vacua with small energy density as required by Multiple Point
Principle (=MPP) running top-yukawa-coupling needed:
At the High field vacuum gt (EPl ) = 0.4.
At the weak scale gt (µ ≈ MH ) = 1.02, a value estimated formaking the condensate vacuum have zero energy.
The running beta-function is known if couplings except Higgs mass
thought known.
To make the two running gt values compatible we need an
exponentially large ratio between the Planck scale and the weak
scale. But that can be considered a solution of the scale problem!
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

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In what way did we solve the scale problem ?
Imposing the MPP assumption you cannot avoid getting the
Higgs mass small compared to Planck scale unless thecoupling changed appreciably away from their experimentally
known values. So you get in a stable way the very small Higgs
mass, the fine tuned mass one would say.
With the values of finestructure constants etc. complimented
with the MPP resrtictions the logarithm of the mass of the
Higgs scale comes out very well. So MPP even tell the weak
scale in this way.
we would say the MPP is a finetuning mechanism, that leads
to the exponentially small weak scale value.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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The Hierarchy Problem proper ?
The most seriously problem is the hierarchy problem:
Each time one goes up in perturbation order the Higgs masssquare gets a correction which is typically huge compared to thefinal renormalized Higgs mass square.
In our MPP-scheme: One must adjust the bare couplings especiallythe bare Higgsmass squared to fullfill the vacuum energies being
small/zero.
The mysterious adjustment need to keep the Higgs mass small
while increasing the order to which one calculates will still be there
in the calculation, but now the finetuned bare masses appear as aresult of finetuning to fullfill the zero vacuum energy conditions of
MPP rather than just fitting to experiment as one would have to
do without any solution to the fine tuning problem.
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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Cosmolgical Constant Problem
Asymptotically Vanishing Cosmological Constant in the Multiverse
Hikaru Kawai, Takashi Okada Department of Physics, Kyoto
university, Kyoto 606-8502, Japan Abstract:
We study the problem of the cosmological constant in the context
of the multi- verse in Lorentzian spacetime, and show that thecosmological constant will vanish in the future.
This sort of argument was started from Coleman in 1989, and heargued that the Euclidean wormholes make the multiverse partitiona superposition of various values of the cosmological constant ,which has a sharp peak at = 0. However, the implication of the
Euclidean analysis to our Lorentzian spacetime is unclear. With
this motivation, we analyze the quantum state of the multiverse in
Lorentzian spacetime by the WKB method, and calculate thedensity matrix of our universe by tracing out the other universes.
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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Kawai and Okada, Colemann Cosmological Constant(continued)

Our result predicts vanishing cosmological constant.
While Coleman obtained the enhancement at = 0 through theaction itself, in our Lorentzian analysis the similar enhancementarises from the front factor of e iS in the universe wave function,
which is in the next leading order in the WKB approximation.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

Once having such solving cosmological constantproblem getting MPP is very close.

Crudely: Our “Multiple Point Principle” (in modern version) is theplural of what is needed for getting the surprisingly small energy
density (= cosmological constant).
But if we have as Kawai and Okada gave us (following Coleman,
Hawking, Banks) a mechanism explaining the small cosmological,
we should immediately think of using their mechanism to derivealso Multiple Point Principle.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

Dark Matter, Mystery, What it is
Most Popular The dark matter consists of supersymmetricpartners of some known particle such as a photino or a Zino
(or best a superposition of such suspersymmetric partners).
Supersymmetry being inspired via string theory this is apossibility inheriting from Nambu.
Nambu-Goldstone Dark Matter (I shall skip that)
Bubbles of Alternative Vacuum This is our own - Froggattand mine - model for the mysterious dark matter being
bubbles of a speculated vacuum strongly inheriting fromtaking vacuum seriously from Nambu.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

Personally I believe Several Vacua more likely thanString Theory Based Dark Matter because...

Vacua can be thought to be
there in Only Standard Model,
while String theory must inpractice be strongly improved
with many parametrs.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

Conclusion
We have proposed a ”New Law of Nature” Mutiple Point(Crticallity) Principle which has two versions:
Several vacua have same energy density.
Several vacua have (almost) zero energy densities(=cosmological constants).

This MPP can be considered ”spontaneous breaking without
any symmetry”.
It leads to a few phenomenologically promissing
consequencies: PREdicted Higgs mass; PREdicted number offamilies in an ANTI-GUT model; ”solve” the scale problem
and in a sense even hierarchy problem; suggest a possible
picture for dark matter in Standard Model alone; even one
model calculate the vacuum energy.
Provided some assumption restricting all space time - like
extensive quantities or baby universe theory, ...- someH.B. Nielsen, Niels
Bohr Institutet(givingtalk), Colin
D. Froggattderivationsof MPPlookpossible. ( but with full causality it
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

X-ray Line 3.55 keV from Dark
Matter, Our Glass Pearls

Mainly work with Colin D. Froggatt, Glasgow but also work with
Ivan Andric, Larisa Jonke and especially Danijel Jurman from
Rudjer Boskovic is mentioned, major basics for our picture goes toalso Larisa Laperashvili, Don Bennett, ...
Talk is presented by Holger Bech Nielsen.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

Forming a Picture of Our Dark Matter Model, Pearls
They are really bubles - with the vacuum being in two
different phases, the normal vacuum outside the pearl, and a“condensate vacuum” inside. Like water-droplets have water
inside and air outside.
The surface tension - being of weak interaction scale 100 GeV- is exceedingly high from dayly life scale point of view.
“surface tension” = 1011 kg /m2 = 1028 N/m
An atom-broad strip provides 1018 N ∼ the weight of
1017 kg =1014 ton.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua(6)

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

Picturing Our Pearls (continued)

To keep the extremely strong surface tension from collapsing
the pearl away, it must be filled with, say, ordinary matter,under extreme pressure. So there is ordinary matter insidethe dark matter in our model. Like in a white dwarf say.
If you feed a pearl with neutrons it can take them up underrelease of about 10 MeV energy per neutron. Protons would
have to be shot in with big speed.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

Picturing Our Pearls (continued)
In the inside phase, “condensate vacuum”, we have in ourmodel estimated that the Higgs field expectation value isabout half the outside value and the quarks and the nucleons
therefore lighter inside than outside by about 10 MeV.
Nucleons are atrackted towards the inside phase by a ca 10
MeV potential. For electrons this attracktion is less.
Some electrons are bound electrically, but some a bit outside
the surface with the strong tension.
Over-dimensioned “nucleus” is not a nucleus but rather
ordniary matter compressed.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

Pearl Picture, Hope for the 3.5 keV LineFor the purpose of explaining the unidentified X-ray line withenergy 3.5 keV in our dark matter model we hope that the matter
inside the pearl - where the vacuum is in the “condensate vacuum”
phase - is an insulator with a gap between the filled and empty
electron levels being of order 3.5 keV, since then:After excitation and some relaxation we could have a lot ofelectrons in the states which should be empty(in ground state)- especially the lowest enrgy ones among these -, and a lot ofholes -especially also close to the fermi surface.
This really means a lot of excitons(=pairs of hole andelectron) in their low energy state.
Finally the excitons decay under emmission of light of theenergy corresponding to the energy released by the electron
falling into the hole. The gap hoped to be 3.5 keV.
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

Order of Magnitude of the Gap (Homolumo-gap)
That the gap (homolumo-gap) should be of order a few keV is
not so unreasonable, because the ordinary matter inside the“condensate vacuum phase” in our dark matter according toour fits is compressed to to a density of the order 1014 kg /m3 ,meaning a compression in each of the three dimensions by a1
factor (1011 ) 3 ∼ 5000, and we expect the homolumo gap tobe crudely proportional to the inverse of the distance ofneighboring atoms.
We shall argue for a homolumo-gap ≈ pfermi α2 , which withpfermi ∼ 10MeV can give “homolumo − gap ′′ ∼ 1keV .

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus“Pedagogical Model” Merle and Schneider.
Merle and Schneider propose the simple model that the dark
matter consists of “sterile neutrinoes” (or other particles) withmass 7.1 keV decaying then very slowly
νst

→ ν+γ

(7)

Since this is into two massless particles, a neutrino ν and a γ theyeach get the half energy 3.55 keV.
We may represent the rate information by fitting the lifetime ofthis model -which I mainly consider pedagogical to describe e.g.
the rate of radiation -:“life time” = 1028 s
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua(8)Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

About the rate of 3.5 keV
The energy release into the 3.5 keV line corresponding to theMerle Schneider model fit of life time 1028 s means(3 ∗ 108 m/s)2(9)“Radiation per mass”=
2 ∗ 1028 skg=
0.5 ∗ 10−11 W /kg (10)mpWith ρDM
=
(11)
3m3
=
10−27 kg /m3 ,(12)“Radiation per vol.”=For cube 8kpc sides having“From “galaxy cube””
Compare: “luminocity Galaxy”
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

10−38 W /m3
16 3(8 ∗ 3 ∗ 10 ) m
52

3

=

10 m ,

comes

25

=

(13)
3

(14)
(15)

10 W (3.55 radiation)(16)
5 ∗ 1036 W(17)

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

K. J. H. Phillips , B. Sylwester , J. Sylwester
criticize: In Solar flare can be 9 to 11 times higher
K abundance.
Recent work by Bulbul et al. and Boyarsky et al. has suggested
that a line feature at 3.5 keV in the X-ray spectra of galaxy
clusters and individual galax- ies seen with XMM-Newton is due tothe decay of sterile neutrinos, a dark matter candidate. This
identification has been criticized by Jeltema and Profumo on the
grounds that model spectra suggest that atomic transitions inhelium-like potas- sium (K xviii) and chlorine (Cl xvi) are more
likely to be the emitters. Here it is pointed out that the K xviii lines
have been observed in numerous solar flare spectra at high spectral
resolution with the RESIK crystal spectrometer and also appear in
Chandra HETG spectra of the coronally active star σ Gem.
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

Continue of Critisism: Due to K-line from Higher
Abundace

In addition, the solar flare spectra at least indicate a mean coronalpotassium abundance which is a factor of between 9 and 11 higher
than the solar photo- spheric abundance. This fact, together withthe low statistical quality of the XMM-Newton spectra, completely
accounts for the 3.5 keV feature and there is therefore no need to
invoke a sterile neutrino interpretation of the observed line feature
at 3.5 keV.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

Hitomi does NOT find the 3.5 keV

Hitomi malfunctioned just over a month after launch in February
last year, but managed to collect enough data to disprove a
previously claimed sighting of the 3.5 keV line in the Perseus
galaxy cluster.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

Draco Dwarf Only has Upper Limit for 3.5 keV LineIn spite of the fact that the Draco Dwarf (galaxy) 80 ± 10kpc away
holds so much dark matter that its ratio of mass to luminocity is
440Msun /Lsun it was found that it has no 3.5 keV line with a 90 %confidence 20 times smaller than expected, if it were radiation
simply from dark matter decay.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

Any Hope for Rescuing a Connection to Dark
Matter??

If there should be any hope for that the line 3.5 keV should comefrom dark matter it looks needed that it is produced by someinteraction so that the line signal gets produced mostly fromregions with bf lots of e.g. ordinary matter, that e.g. could throw
some radiation on the dark matter (or perhaps interaction withdark matter itself).

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

Searching for the 3.5 keV Line in the Deep Fields
with Chandra: the 10 Ms observations Nico
Cappelluti, Esra Bulbul, Adam Foster, Priyamvada
Natarajan, Megan C. Urry, Mark W. Bautz,
Francesca Civano, Eric Miller, Randall K. Smith(Submitted on 27 Jan 2017)
In this paper we report a 3 detection of an emission line at 3.5 keVin the spectrum of the Cosmic X-ray Background using a total of
10 Ms Chandra observations towards the COSMOS Legacy and
CDFS survey fields.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

Deep Fields (Continued)
The line is detected with an intensity is (8.8 ± 2.9)10−7 phcm2 s 1 .
Based on our knowledge of Chandra, and the reported detection of
the line by other instruments, we can rule out an instrumental
origin for the line. We cannot though rule out a backgroundfluctuation, in that case, with the current data, we place a 3σ
upper limit at 10−6 ph cm−2 s −1 . We discuss the interpretation ofthis observed line in terms of the iron line background, S XVIcharge exchange, as well as arising from sterile neutrino decay. We
note that our detection is consistent with previous measurementsof this line toward the Galactic center, and can be modeled as theresult of sterile neutrino decay from the Milky Way when the dark
matter distribution is modeled with an NFW profile. In this event,
we estimate a mass ms ∼ 7.02 keV and a mixing angle
sin2 (2θ) = (0.69 to 2.29) ∗ 10−10 . These derived values of theneutrino mass are in agreement with independent measurements
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
towardclusters,
Dark Matterand thegalaxy
Standard Model
Vacua the Galactic center and M31.

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

SEARCHING FOR THE 3.5 keV LINE IN THE STACKEDSUZAKU OBSERVATIONS OF GALAXY CLUSTERS
Esra Bulbul, Maxim Markevitch, Adam Foster, Eric Miller, MarkBautz, Mike Loewenstein, Scott W. Randall, and Randall K. Smith
Published 2016 October 26 2016. The American Astronomical
Society. All rights reserved. The Astrophysical Journal, Volume831, Number 1
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Article information Abstract
We perform a detailed study of the stacked Suzaku observations of
47 galaxy clusters, spanning a redshift range of 0.010.45, to search
for the unidentified 3.5 keV line. This sample provides an
independent test for the previously detected line. We detect a
2σ-significant spectral feature at 3.5 keV in the spectrum of the
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
full sample. When the sample is divided into two subsamples
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

7.1 keV sterile neutrino constraints from X-ray observations of 33
clusters of galaxies with Chandra ACIS
F. Hofmann, J. S. Sanders, K. Nandra, N. Clerc and M. Gaspari
1 Max-Planck-Institut fr extraterrestrische Physik,
Giessenbachstrae, 85748 Garching, Germany e-mail:fhofmann@mpe.mpg.de 2 Department of Astrophysical Sciences,
Princeton University, Princeton, NJ 08544, USA 3 Einstein andSpitzer Fellow
Received: 16 December 2015 Accepted: 13 June 2016
Abstract
Context. Recently an unidentified emission line at 3.55 keV has
been detected in X-ray spectra of clusters of galaxies. The line has
been discussed as a possible decay signature of 7.1 keV sterile
neutrinos, which have been proposed as a dark matter (DM)candidate.
Aims. We aim to put constraints on the proposed line emission ina large sample of Chandra-observed clusters and obtain limits on
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
the mixing angle in a 7.1 keV sterile neutrino DM scenario.
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

Is Dark Matter the Source of a Mysterious X-ray Emission Line?
April 01, 2016 The nature of dark matter is still unknown, but one
potential candidate is a theoretical particle known as the sterile
neutrino. In 2014, two independent groups of astronomers
detected an unknown X-ray emission line around an energy of 3.5
keV in stacked X-ray spectra of galaxy clusters and in the centre of
the Andromeda galaxy. The properties of this emission line areconsistent with many of the expectations for the decay of sterile
neutrino dark matter. However, if this hypothesis is correct, allmassive objects in the Universe should exhibit this spectral feature.
To test this intriguing possibility, scientists at MPA and the
University of Michigan examined two large samples of galaxies,
finding no evidence for the line in their stacked galaxy spectra.
This strongly suggests that the mysterious 3.5 keV emission line
does not originate from decaying dark matter. The nature of dark
matter, and the origin of this emission line, both remain unknown.
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

For MOS, the flux in the 3.57 keV line was
6
2 1
4.0+0.8
0.8 (1.2) × 10 photonscm s , where the errors are 68% (90%).
For PN, at the best-fit energy of 3.51 keV, the line flux is +1.0 6
3.9 +0.6 photons cm2 s 1 . If we fix the line 1.0 ( 1.6 ) 10 energy
from the MOS fit, for PN
 we obtain the flux 2.5 + 0.6to0.7 6+1.0photonscm2 s 1 .1.1 × 10

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus...The best-fit flux at +3.7 5 3.57 keV was 5.2 +2.4 photons cm 2
s 1 . 1.5 ( 2.1 ) 10 This flux corresponds to a mixing angle of sin 2(2 ) = +3.9 10 5.5 +2.6 . This angle not only is an outlier in our
1.6 ( 2.3 ) 10 measurements from the other samples but is also
not coH.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

A 3.55 keV Line from Exciting Dark Matter without
a Hidden Sector Asher Berlin, Anthony DiFranzo,
Dan Hooper(Submitted on 14 Jan 2015)
Models in which dark matter particles can scatter into a slightly
heavier state which promptly decays to the lighter state and aphoton (known as eXciting Dark Matter, or XDM) have beenshown to be capable of generating the 3.55 keV line observed fromgalaxy clusters, while suppressing the flux of such a line fromsmaller halos, including dwarf galaxies. In most of the XDM
models discussed in the literature, this up-scattering is mediated bya new light particle, and dark matter annihilations proceed into
pairs of this same light state. In these models, the dark matter andmediator effectively reside within a hidden sector, without sizable
couplings to the Standard Model. In this paper, we explore a
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggattmodel of XDM that does not include a hidden sector. Instead, theDark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

Carlson Jeltena Profumo :The clumped nature of this residual is difficult to reconcile with the much smoother
distribution expected from dark matter as is the radial profile which has a muchsharper gradient at the edge of the core than what expected from a decaying dark
matter profile .

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

The Power in the Unidentified Line 3.5 keV

ObjectCounts4π ∗ dist 2
ph s −1 cm−2
m2
Unit:
−5
Galactic Center
2.2*106*1041−6
Perseus cluster (6 to 7)10
0.6*1050
3.5keV = 3500 ∗ 1.6 ∗ 10−19 J = 6 ∗ 10−16 J

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

PowerW
7*1025
2*1029Per galaxyW
7*1025<2*1026

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

Typical Value for σ/m for Dark Matter ?

Our model
Bound from Lux...
Atom

σ/m
10−12 to −13 m2 /kg
10−13 m2 /kg
106 m2 /kg

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua(not good for dark matter!)Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

Any Hope for Florescence-type Dark Matter ?
Perseus cl.:
FormulaOur p.’s:P3.51032 W

=
>

“eff”
0.2

Hope

1031 W=

0.5

Bounds1031 W

;

<1

Other

1031 W

>

low

σ
m



10−12 m2kg
102 m2kg<<106 m2kg<<106 m2kg
10−13 m2kg

ρDM
5∗10−28 kg
m3
10−26 kgm3
10−26 kgm3
10−26 kgm3
10−26 kgm3

tsp
1016 sPrad1037 W

1017 s1038 W< 1017 s

1038 W

1017 s1038 W

Lux-big
1031 W > low
1017 s1038 W
The radiation in the line 3.5 keV from Perseus cluster P3.5 .
The radiation of say cosmic ray hope to provide the energy Prad .
The effectivity of a piece of darkmatter to convert the energy “eff”.
Density of dark matter in the region where this convertion goes on
ρDM .
σ
.
The ratio of the cross-section to the mass of the dark matter m
H.B. Nielsen,
Niels
Bohr
Institutet(givingtalk),Colin
D.
Froggatt
The time the radiation runs arround tsp .
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

New Law of Nature: Multiple Point
Principle.
There are several phases of
vacuum(having relativity principles) and they
all have very very small energy
densities(like the astronomically determined one for ourpresent vacuum).
This principle is analogous to the having a specific temperature - ina microcanonical ensemble - when there are say both water and ice
present.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

The Analogy:
The analogy between the triplepoint in the vapor- water-ice
combination at (T , p) = “tripelpoint ′′ = (273.16K , 0.6117kPa)
and “Multipel Point Principle” is:
The intensive quantities, temperature T and pressure p are
analogous to the kobling constants and the parameters, suche2
,etc.
as gt , α = 4π
The extensive quantities such as energy of the content of thebottle E , the amount (measured in mol e.g.) ofwater-molekyles N, the volume V are analogous to some
integrals, which could include
space-time-volume = lifetime of universe multiplied by its
volumeE.g. an integral over the square of the Higgs-field = theaverage value of the Higgsfield squared and multiplied with thejust mentioned spacetime volume.
But it could be something similar but based on other fields.
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

Må fortælle om at:
Vi forudsagde Higgs-Massen
Vi brugte, hvad vi kalder Multiple Point Principle (med Don
Bennett,...), hvilket betyder, at vi antager, at koblings-konstanterne- som f. eks. top-Yukawa-koblingen relaterede til top-quark massen- og andre parametre i felt-teorien (lad os sige Standard-Modellen)- sådan som Higgsens massekvadrat - er finindstillede til at havejust sådanne værdier at der sikres: Flere Vacua med Samme
Energi- tæthed eller tilnærmelsesvis sådan.
Det foreslog vi (C.D.Froggatt og jeg under brug af Bennetts og
min MPP) og dermed FORudsagde vi - længe før Higgsen blev
fundet - massen af Higgsen.
I et papir (med Froggatt and Takanishi, Meta-MPP) 121.8 GeV ±10 GeV; jeg er blevet malet med Mogens Lykketoft med 135 GeV± 10 GeV(bag Lykketofts hoved). Higgs nyligt bekræftet med
massen 125.09 ± 0.21(stat.) ± 0.11 (syst.) GeV/c 2 .
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

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Three Agreeing Fits of the Bound State Mass:

In this way we got even two calculations for the bound state mass using in addition crude estimation mF (from “high field vacuum”) ≈ 850GeV ± 30%with ∼ 2(18)mF (from “high field vacuum”) ≈ 710GeV ± 30%without ∼ 2(19)mF (“condensate vac.”) ≈ 692GeV ± 40%(20)mF (“bag estimate”) ≈ 5mt = 865GeV (veryuncertain).
(21)

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

Det Kolde Mørke/sorte stof ude
i rummet mellem stjernerne
Mine kollegaer mener, at det sorte stof, som er nødvendigt at havemellem stjernerne, for at disse kan løbe så hurtigt rundt om
galaksen, som de måles at løbe, ikke kan fås, hvis Standard
Modellen er den endelige teori. Man har brug for mindst en anden
slags partikel, som kan udgøre det sorte stof! Kun Colin Froggattog jeg har en teori, efter hvilken, det er muligt - om end lidt
kompliceret - at få det sorte stof ud af Standard Modellen alene!
Lad mig dog tilstå at vi dog har brug for et særligt
finindstillingss-princip, som sørger for at koblings-konstanterne iStandard Modellen tager værdier, som sørger for at der bliver flerevacua/tomrumstilstande med samme energitæthed. Koblingerne
har altså meget specielle værdier, eller rettere relationer mellem
deres værdier.
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

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Collissions of Our Pearls as Source of Energy for e.g.
the 3.5 keV line.

Somewhat analogous to annihilation there can in our pearl model
be released a lot of energy when the dark matter particles
meet/collide:
We expect them to unite and then the surface / the skin (can)contract and thereby release energy, in fact a lot, about the
Einstein energy of a tenth of the mass of the pearl.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

DM Collissions Homolumo Conclus

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

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Self Interaction of Our Pearls
We fitted our model parameters to match that the rate of theearth being hit by one of our dark-matter pearls was about once
every 100 years or 200 years.
Now the ratio of the radius of our pearl 0.6cm to the radius of theearth isrpearlrearth0.6cm
6000km= 10−9=givingareapearl=areaearth

(23)
(24)

2
10−9 = 10−18

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

(22)

(25)

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Estimating Rate of 3.5-line from Pearl Colissions

Becase the area for hitting another pearl is 10−18 times that for thearth, a pearl -a selected one, we think of - will hit another pearl
every:“hitting interval” = 100years ∗ 1018 = 1020 years = 3 ∗ 1027 s. (26)When a colission between two our pearls occurs an energy of theorder of the energy in buble surface is released, and likely a large
fraction of that becomes excitons and thereby gives the 3.5 keVradiation.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

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Ratio of Surface to Bulk Energy
The surface tension of our pearls was supposed to be of the orderof magnitude as given by the weak interaction physics, say given interms of W-masses by dimensional arguments. By the unification
after colission of two pearls the total surface area for the uniting
bubles get reduced by of order unity. Taking crudely the weakinteraction length scale to be 10−18 m = 10−16 cm and the energy
to be 100GeV = 100 ∗ 109 ∗ 1.6 ∗ 10−19 J ∼ 10−8 J the energy inthe tension of the pearl surface becomes“surface energy” =

1016
24

2

∗ 10−8 J(27)= 10 J
24

(28)
17

7

∼ 10 /10 kg = 10 kg
1
This is about 10of the mass of the whole pearl 108 kg.
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua(29)

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Simulated Life- time 1028 s.

Since about one tenth of the Einstein energy of the pearl sits inthe surface tension and gets released by colission of two balls, thelife time of a simulating sterile neutrino model particle would be 10
times the “hitting time” =1027 s, i.e 1028 s simulated life time.
agreeing fine with the earlier fits!

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

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The Energy Comes in Bunches of ∼ 107 kg *c 2
With our story that the dark matter consists of pearls with asurface energy getting released when two of them collide and unite
to one we have got the dark matter pearls function as bombs
releasing 105 times more energy than the one from justcolliding.
By the pure collission one only gets the energy of the event in
Tunguska, which lead down the trees in a region of order of 70 km,
but with the unification of droplets we get with the enormous
surface tension about 100000 times as much energy release !
The temperature may raise to ∼ 50 MeV and corresponding γ-rays
would be emitted, a candidate for a gamma-ray burst?
That the radiation from the dark matter in this way comes inpulses, may be experimentally accessible.
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

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Homolumo-gap-effect
What we here call homolumo-gap-effect is the effect of increasingor producing the gap between the highest occupied (ho) single
electron state (=molecular orbit=mo) and the lowest unoccupied(lu) single electron state (mo) originating from the elctrons acting
back on say the positions of the ions in the material considered.
One shall have in mind that increasing the homolumo-gap lowers
the energy of the system of single electrons, and thus the ions are
driven in the direction by which they can increase this gap.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

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Crude Ideas about Homolumo gap Effect in Very
Dense Mater (inside our pearls)
Expectations for very highly compressed matter:
We expect that the kinetic energy of the electrons will
dominate over the potential energy. (The inverse lattice
momentum scales inversely with lattice constant a,i.e. as 1/a,and thus the kinetic energy with the inverse square kinetic
energy ∝ 1/a2 , while the potential energy ∝ 1/a.
Still if the material is a glas say, a homolumo gap effect could
be there, close to the fermisurface.
Shall argue for the homolumo gap to be crudely of the orderpfermi α2 , where α is the fine structure constant and pfermi issome characteristic momentum for the electrons, the fermi
momentum say
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

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Statistical Simple Calculation of Homolumo-gap inMatrix Model

I. Andric, L. Jonke, D. Jurman, and myself calculated thehomolumo gap in a relativly simple matrix model, although it has
both quenched random and quantum mechanical adjustable
contributions to the single fermion hamiltonian.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

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Our - Andric, Jonke, Jurman, HBN - Matrix Modelfor Homolumo-gap EffectIvan Andri et al, Int. J. Mod. Phys. A 32, 1750046 (2017) [16pages] https://doi.org/10.1142/S0217751X17500464

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

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Adjusting the ω’s of Our Matrix Model to Realistic
Materials
There is one little problem with our general calculation in the work
Ivan Andri et al, Int. J. Mod. Phys. A 32, 1750046 (2017) [16pages] https://doi.org/10.1142/S0217751X17500464, namely thatfor a macroscopic piece of material the number of single eletronstates N say in a specified set of bands will grow with the volume
V proportionally and thus the number of matrix elements will growlike N 2 ∝ V 2 ; but now there cannot reasonable be a number ofdegrees of freedom of the material growing like this square. Any
number of degrees of freedom in the material should grow only as
N ∝ V and NOT like the square!

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

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How to Approximate Functions of Some Variables
by Harmonic Oscillators
In the work by Andric et al. we calculated as if the matrix
elements of the single fermion Hamiltonian were independent
harmonic oscillators - each matric element (M − M0 )ij was an(A)
independent degree of freedom variable ql , where then of course
the index l run over N (A) = N 2 values, where N is the order of thematrix Mij for the single fermion (say electrons in case of ordinary
matterials) states relevant (we imagine the very highest energy
electron states twrown out as an ultraviolet cut off, say).
But now these N (A) dynamical variables are all described interms of the “fundamental”/true variables of the say crystal
ions, of which there are only N (F ) .
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

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Approximate Description of Only N (F ) True Variables
as a Larger Number N (A) >> N (F ) of Formal
Variables
We want to approximate statistically a system of N (F ) hamonic
oscillators with HamiltonianX  1 (F ) 2 1(F ) 2H (F ) =(30)pn+ ω 2 qn22nih(F ) (F )= i~(F ) δnm(31)
qm , pn
by a system of N (A) >> N(F ) harmonic oscillators, with variables(A) (A)ql , plthat are in reality just functions - say linear functions- of the set of N (F ) variables, as if this “formal system” of N (A)(A)
variables ql formed an indepent set of N (A) harmonic oscillators.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

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Identifying a Couple of Sets of Harmonic Oscillators
We want to approximate

the“fundamental”:(F )NX  1 (F ) 2 1
2 (F ) 2pn+ ω qn(32)
22n

H (F )=hi(F ) (F )qm , pn=i~(F ) δnm

by

the

H (A)

=

“formal approximation”(A)N
X  1 (A) 2 1
2 (A) 2p
+ ω ql
(34)
2 l
2

(33)

l

h
i
(A) (A)qk , plwhere we have relations
(A)

ql

=
of

the form

=

(F )
N
X

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

i~(A) δkln(F )(q) (F )Bln qn(35)(36)

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Our Relation between Two Systems of Degrees ofFreedom of Different Numbers (Continued)(F ) (F )(A) (A)We have two systems of d.o.f. qn , pn
and ql , plwhich
we want to treat as harmonic oscillators connected by relations of
the form
(A)
ql

=

(F )
N
X

Bln qn(F )NXBln pn(q) (F )(38)(p) (F )

(39)

n

(A)
pl

=

n

(q)

(p)

where the non-diagonal matrices Bln and Bln are transition
matrices between the two differnt systems of oscillators; they willbe treated only statistically as being for our purpose random.
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
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Our Relation between Two Systems of Degrees ofFreedom of Different Numbers (Continued)
If we simply played the game, that our two sets of degrees of
freedom each had only one single mass for all the d.o.f. in the set,so that(A)= m(A) q̇l(F )= m(F ) q̇l

pl
pl

(A)
(F )

(40)
,

(41)

m(A) (q)Bm(F ) ln(42)

we would obtain the relation
(p)

Bln

=

P (A) (A) 2
for theBut if wants the kinetic term form simply 21 N
l=1 pl“formal”set of systems, say the matrix elements, and
1 PN (F ) (F ) 2
for the “fundamental” set, we must taken=1 pn2(A)(F)
m = m = 1.
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

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Relations between the ω-Parameters
That the two systems of sets of harmonic oscillator related by
(A)
ql

=

(F )
N
X

Bln qn(F )NXBln pn(q) (F )(43)(p) (F )

(44)

n

(A)
pl

=

n

shall represent the same physics, we take to at least imply, thatthey have the same total kinetic and the same total potential
energies.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

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Identifying Potential and Kinetic Energies for the
Two Systems:
N (A)

1 X (A) 2
pl
=
2
l=1

N (A)

1 (A) 2 X (A) 2
ω
ql
=
2
l=1

N (F )

1 X (F ) 2
pn
2

(45)

n=1

N (F )

1 (F ) 2 X (F ) 2
ωqn , which implies (46)
2
n=1

N (A)

X

Bln Blm(p)(p)= δnm and

(47)

(q)

(q)

= ω (f ) 2 δnm

(48)

l=1

ω

(A) 2

(A)
N
X

Bln Blm

l=1

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

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We get a Normalized Bln

P (A) (p) (p)Taken this we obtain especially that N
l=1 Bln Blm is zero for
n 6= m, while it for all cases of n = m (but fixed) has the samevalue, so that we can call it
P (A) (p) (p)B= N
l=1 Bln Bln (no summation over n). Actually we find fromidentical kinetic energies that B=1.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

DM Collissions Homolumo Conclus

Relations to Approximately Identify Two Systems
with Different Numbers of Degrees of Freedom.

Using the definition B =get:

PN (A)(p) (p)l=1 Bln Bln (no summation over n) we

From same kinetic energies:B = 1
From same potential energies:ω
or simply the ω’s must be the same.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

(A) 2

B = ω

(49)
(F ) 2(50)

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How are the Commutators Connected?
(a)

The commutators for a qlhi(A) (A)ql , pk=≈(A)and a pk(F )N
X

is evaluated as
(q)

(p)

Bln Bkm ≈

(51)

n,m=1

BN (F )
,
N (A)

(52)

which is very small if N (F ) << N (A) !
~(A) = ~(F ) ∗H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

N (F )
.
N (A)

(53)

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Effective Classical Approximation for
Homolumo-gap-effect.
The result

N (F ).
(54)
N (A)is very welcome/useful for justifying the calculational technology in
our Homolumo gap paper with Andric, Jonke Jurman and HBN,
because we effectively in order to come through the calculation
have to use what corresponds to ignoring the quantum fluctuations
and so using a classical approximation. In this article we take all
matrix elements in a somehow chopped off matrix single particle
Hamiltonian for the electron/fermion as independent Harmonic
oscillator variables.
~(A) = ~(F ) ∗H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

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Our Homolumo-gap Paper uses Too Many
Variables, Thus goes to ClassicalBut that is far too many variables in a genuine macroscopic pieceof matter, which should have only a number of bosonic d.o.f.
going up with increasing the size of the piece of matter only as
proportional to the volume (to the first power, NOT to thesecond!)H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

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Conclusion
Our “old” model, in which dark matter consists of cm-big
pearls with masses of the order of 100 thausend ton to half amillion ton was suggested to be able to provide the“unidentified”X-ray line of 3.5 keV in fact by:
Providing the line as a result of excititons (= a pair of anelectron and a hole) annihilating, the homolumo-gap should
then be essentially 3.5 keV.
The distribution of the 3.5 keV signal over the sky did not fit
exactly the distribution of dark matter, but rather is moreconcentrated around the centers of big galaxies or galaxy
clusters.This suggests that the 3.5keV-radiation does not
simply come equally strongly from all dark matter!
For instance a production of the 3.5 keV radiation inconnection with collision(e.g. annihilation) of dark matterwithwouldtalk),beColinmorefavoured as the source.
H.B. Nielsen, Niels
Bohritself
Institutet(giving
D. Froggatt
Dark Matter andthe Standard Model“ourVacua pearl model” produces by collission of theRemarkably

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Other Achievements of Our Dark Matter Model
In addition to the wellfitting of the 3.5 keV-line, we claim a goodfitting when we identify our pearl with the object that fell in
Tunguska in 1908 and made the trees fell in an 70 km extended
region and produced huge “fire” on the sky...:The rate of there falling one on earth about once every 100
years fit well with the surface tension being of the order given- by dimensional arguments - from the weak interaction
scale∼ 100GeV.
And with it producing Kimberlite Pipes, of which one found∼ 6500 on the earth. (You find them on old cratoins, where
you have the oldest geological layers.)

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

Nambu Introduction Dark Matter Model MPP Conclusion Model 3.5keV MPP Dark

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Multiple Point Principle among other saying: Inside
pearl and Outside Pearl Phases have Same Energy
Density, if no matter
This new law of Nature - a fine tuning model - has its own
successes:
We - Froggatt and me - PREdicted the Higgs mass to 135
GeV ± 10 GeV long before the Higgs was foundexperimentally.
It “solves” the hierarchy problem in the sense that it says Let
us fine tune! Make a finetuning theory and then an
exponentially low Higgs or weak scale comes out relative to
say the Planck scale.
H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua

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Conclusion onSuccesses of the Multiple Point
Principle(continued)

We could get three independent estimates for the mass of thebound state of 6 top + 6 anti top, which we expect, andwhich fill the vacuum inside the dark matter, and they all
turned out order of magnitudewise to be 750 GeV.

H.B. Nielsen, Niels Bohr Institutet(giving talk), Colin D. Froggatt
Dark Matter and the Standard Model Vacua