PoS(CORFU2019)049 http://pos.sissa.it/ ∗ -ray excess. The picture of ours for dark matter has it being cm-size pearls of γ [email protected] [email protected] Speaker. We return to a model of ours forwith what the the Standard dark Model matter alone. can be The with onlyon the genuine property the new that physics parameters/couplings it is is in a compatible principle the imposingbeing Standard restrictions degenerate Model. in energy They density are withfrom required the each to dark other. lead matter, which to We are especially several notexcess look vacua just and for gravitational: further some The 3.55 of keV the X-ray signals radiation, the positron 100000 ton mass in order of magnitude. ∗ Copyright owned by the author(s) under the terms of the Creative Commons c ⃝ Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). Corfu Summer Institute 2019 "School and(CORFU2019) Workshops on Elementary Particle Physics and31 Gravity" August - 25 September 2019 Corfu, Greece Holger Bech Nielsen Colin D. Froggatt Glasgow University E-mail: Niels Bohr Institute, Blegdamsvej 15 -21,E-mail: Copenhagen Several degenerate vacua and a modelMatter for in Dark the pure Standard Model PoS(CORFU2019)049 , 6 , 5 , 4 ]. How- 935 being 12 . , 0 11 = , t g 10 Holger Bech Nielsen , 9 , 8 ]. 3 1 , 2 , 10 GeV 1 ± GeV, but no new physics at the LHC except for non-perturbative ] to be 135 12 14 , 13 ]. 3 , ]. 2 , 15 1 ] = MPP. About 5 anomalies - seeming deviationsof from magnitude the as Standard non-perturbative Model effects, - due are to explainable the in order top Yukawa coupling The Higgs plays a crucial role for our somewhat “complicated” dark-matter speculation. Our “Multiple Point (Criticality) Principle” wasto used predict before the its Higgs mass particle [ was observed Hypothesising the existence of threeMPP), we degenerate obtain vacua the in right thesecond order minimum Standard of in Model magnitude the for Higgs (again effective the from potential,scale weak which [ scale happens(?) relative to to be close the to scale the of Planck the For fine-tuning and the hierarchywhich only problem restricts we the make couplings use andStandard the Model of in Higgs our terms mass, “multiple of but new point gives particles no principle”, say. deviation from the pure We propose a rather complicated speculativeever model it for is dark based matter on [ the“Multiple pure Point Standard (criticality) Principle” Model (MPP), only using with Higgsquarks. the exchange to help bind from top our and fine-tuning anti-top law, the For neutrino oscillations and thesaw scale, baryon presumably excess 10 we haveeffects. to accept new physics at the see- “big” [ 7 For fine tuning problems we introduce/proposeof a the new coupling law of constants nature, andinstance, that masses the restricts in the hierarchy values the problem Standardscale of (or Model. why the GUT the In scale, weak if this it scale way existed) is we [ so explain, lowThe for compared new law: to the Theredensity/cosmological Planck are constant. several We vacua/phases call of it empty the “multiple space, point all (criticality) having principle” the [ same energy No new fundamental particles, except see-sawPlanck neutrinos scale; and but possibly we particles shall almost not at talk the about such high energies today. Several degenerate vacua and a modelWe for believe Dark Matter in in the the pure pure Standard Standard Model Model further up in energy than most physicists, except for • • • • • • • • • • see-saw neutrinos and the baryon number excess for which we accept the need for new physics: Dark matter, pure S.M. 1. Introduction PoS(CORFU2019)049 an energy density Holger Bech Nielsen ∼ ]. 18 2 , 5 keV the pearls will be highly non-transparent. 17 . , 3 16 > ν Positrons relative to gamma-rays from dark matter. The 3.5 keV X-ray radiation [ – – 5 keV. However for frequencies Our pearls - making upto the dark which matter has by been ourpressure hypothesis added from - ordinary the are matter domain bubbles wall. under of this strong new pressure vacuum in order to counteract the Our main new physics assumption (whicheffect is from not really the new Standard but Model): shouldphase be of Higgs a these non-perturbative bosons particles and attractingenergy top density each quarks as other interact the had usual so vacuum. been strongly, fine that tuned a byThis MPP gives to rise to get domain the walls separating same the two phases with a tension which by dimensional arguments is given by the top or Higgs masses. Some non-gravitational dark matter signals support our dark matter pearl model: Multiple Point Principle:tension Several “walls” vacua (surfaces with much like the the surface same of energy a bubble density of separated water). by high Our dark matter model/idea ofby mouse the size effects pearls of of Higgs exchange a binding new top type quarks of and vacuum, anti-top to quarks. be explained . The pearls will be transparent for radiation of frequency less than the homolumo energy gap Our pearls are bubbles of a new vacuum with highly compressed ordinary matter inside Main points of present talk: 3 • • • • • • < Sharp fall in transparency at 3.5 keV ν Dark matter, pure S.M. 2. Dark Matter PoS(CORFU2019)049 3.55 ∼ Holger Bech Nielsen ] approximation. This screening energy 19 3 ], giving a gap in the electron energy spectrum. 20 Homolumo Gap We estimate the screening energy per electron in the highly compressed material in the inside The pearl would have a very high density and therefore also a very high refractive index, which Refracting pearl functions like a homolumo gap effect [ keV. Thus it would make a verythe deformed image and above inverted picture of of the the sun surroundings, and as the illustrated horizon in refracted through the pearl. of our pearls using the semi-classical Thomas Fermi [ of course is only observable in the frequencies below the homolumo gap energy/frequency Dark matter, pure S.M. PoS(CORFU2019)049 ]. 22 , 21 Holger Bech Nielsen 4 The 12 top and anti-toparound 750 ground GeV, similar state to is that bound of the so now strongly dead "F(750)-digamma" that resonance its [ mass is estimated to be The more tops and anti-tops you can put together the stronger they bind. But tops are fermions andsame the geometrical Pauli state principle to limits be the no more number than of 12. tops and anti-tops in the The Higgs field is an evenattraction order between tensor field “everything” tops like the and graviton anti-tops. field and like the latter gives an Diagram giving the binding of 12 top and anti-top quarks to an “F(750)-digamma”. Using this energy gap excitons may be formed as weakly bound states of an electron above the • • • • 3. Higgs boson exchange binds top and anti-top quarks to make a new vacuum gap and a hole below.thus Such produce excitons the are mysterious 3.5 now keV supposed line. to decay under emission of an X-ray and Dark matter, pure S.M. PoS(CORFU2019)049 Holger Bech Nielsen -digamma plus ordinary matter, e.g. carbon ) 5 750 ( F At temperatures above the energy scale of the domain walls there are many many walls around. Inside the pearls: the bound states 4. Formation of our Dark Matter Pearls etc. Dark matter, pure S.M. PoS(CORFU2019)049 Holger Bech Nielsen 6 0) and will attract the baryons say. = > ψ < Pearls which are sufficiently large that thebaryons pressure out is will sufficiently be low stabilized so and as survive not till to today squeeze or its longer. With only degeneracy (MPP)(vacua) and there one is of them some will win/take difference over. betweenOnly the if there two is or some speciala more mechanism, bit which phases of can stabilize both small phases(probably pearls survive of . one phase, In will our case one phase has a smaller Higgs expectation value It is crucial that there is no- symmetry because - such that as causes say a a catastrophic spontaneously broken cosmology. discrete symmetry As times goes on, in the early universe, the walls straighten out and one phase may disappear. • • • • Pearls stabilized by their baryon and electron content become very spherical. Dark matter, pure S.M. PoS(CORFU2019)049 ], where 12 Holger Bech Nielsen is needed [ π 4 √ 9 / 4 2 ’s with 3.5 keV emitted in such γ = ξ of N . . 2 ) , and only thought about it after seeking to fit min R 2 ξ R ( ξ π 7 needed to press a nucleon out of a pearl and the = = R V σ ∆ times the formal minimal size needed for stability π 4 √ 9 / 4 2 ] fitted data on the 3.5 keV X-ray from Dark Matter from the point of view to the fit of Cline and Frey 23 2 σ for stability. M N min R we define the actual pearl radius to be It must of course also be proportional to the number In our model the 3.5the universe, keV and X-ray thus radiation the is intensitycross of emitted section the for when X-rays two two pearls to of colliding be the observed must pearls be collide proportional out to in the the 3.5 keV X-ray radiation intensity.) (In our earlier papers we ignored this factor Assuming that the minimal energy But to avoid breaking up intoa smaller somewhat pieces bigger and size thus is becoming needed. unstable in the lastWe moment estimate that typically an extra reserve radius factor tension in the domain wallradius around the pearl are known, one can estimate the minimal pearl a collision. Comparing Cline and Frey [ Typically the pearl size is Only sufficiently big pearls survive. • • • • • that the line is due to inelasticThe scattering important of feature dark of matter this to model an forfrom excited us a state is that region that, subsequently of as decays. space in is our proportional model, to the the intensity square of radiation of coming the dark matter density. 5. 3.5 keV X-ray radiation from Dark Matter ? Dark matter, pure S.M. PoS(CORFU2019)049 of ρ . 2 σ M N ]. 23 . Holger Bech Nielsen M / ignored ignored Remark in average ∗ 2 ) 2 is calculated as if the density ) > 0.008 0.006 v cm . CF CF 2 ± 27 ± GeV M boost σ σ − ∗ M 10 < v 2.7 - 5.3 / ( N 10 -ray emission must be proportional to the 0.07 - 0.11 0.04 - 0.07 ( 0.037 - 0.09 0.084 - 0.93 γ 0.026 -0.043 0.032 0.016 0.0086 - 0.026 0.00017 - 0,0012 8 5 30 30 30 30 30 10 boost s / v 975 926 116 118 1280 1280 1280 km ∗ 1 5 − 2 > s ) 10 3 v 250 ∗ cm CF ± GeV M σ 22 This table is based on the table 1 of Cine and Frey in reference [ 10 − ( < 480 (1 - 2) 1400 - 3400 2600 - 4100 1200 - 2000 10 10 - 30(NFW) N 0.1 -0.7 (NFW) 30 -50 (Burkert) 50 -550 (Burkert) of the matter density and consequently to 1 Table 1: ] ] ] ] ] ] is the cross section as calculated assuming that there is no boost (see below) for the ] 16 17 24 16 16 17 25 CF N is the number of 3.5 keV photons emitted perσ collision. particles of the dark matter to collide. That is to say Thus the rate to be extracted from the fit to the observations is the combination For a given mass densitynumber of density of of the pearls is dark proportional matter, to as the estimated inverse mass fromSince per its the pearl gravity pearls 1 must of meet course, to the collide the rate of square Units The notation used in Table 1 is as follows: Name • • • • • Average MW[ M31[ CCO[ Perseus[ Perseus[ Perseus[ Clusters[ 3.5 keV Radiation comes after collisions Dark matter, pure S.M. PoS(CORFU2019)049 (5.2) (5.3) (5.1) . The of the dark square Holger Bech Nielsen 2 ]. These papers contain com- 28 /(10 GeV) 2 is . 2 2 σ cm . M N ] and [ 27 /kg 2 − 27 10 cm boost ], [ / ∗ 23 ) 26 ] stand for a couple of different models for the CF 10 σ 9 30 ∗ 006 of the pearl, . ) = 0 3 2 / . 1 σ ± 0 S ± of the 3.5 keV radiation, 032 0 . . 2 σ 0 1 M N = ( = ( ] and “Burkert”[ exp 29 ) 2 σ M N ( . These quantities are: MeV V ∆ 10 is the increase in collision rate due to the clumping of the dark matter into sub-halos, ∗ ξ is the mass of the dark matter particles. is the average velocity dispersion. The frequency of the radiation 3.5 keV, The intensity related quantity The cube root of the surface tension CCO stands for a combination of Coma + Centaurus + Ophiuchus clusters. MW stands for our Milky Way galactic center. M31 is the Andromeda Galaxy. Because of the uncertainty inwhether the it dark be NFW matter or distribution Burkert - inuncertainties we the it left is Milky the quite Milky Way Way consistent center center with (MW) out the of - average. the averaging;The but within notations “NFW”[ which we crudely estimate from references [ boost M Since it looks hopeless to getor a 100, fit we with left values out forthe the the model same Boyarsky used quantity measurement by differing for Cline by the and a Perseus Frey factor cluster. with 50 the It intensity really proportional means to that the v dark matter were given just by thewithout model any for clumping dark further matter distribution than usedestimated the by true galaxies Cline cross and themselves section Frey, having is been thus included rather puter simulations of gravitational interactionshalos forming between clumps dark of matter much higher constituentsously density in enhances than the the galactic true average average density. square Such density compared clumping to obvi- the square of the average density. matter density is disfavored by the Perseus cluster analysis. distribution of dark matter inthe a center galaxy of mainly the deviating galaxy. by “NFW” having a strong peak at It turns out that the quantities whose values we use as tests of our model depend on the single From Table 1 it follows that the experimental value of • • • • • • • • • • • • parameter Dark matter, pure S.M. PoS(CORFU2019)049 . (5.4) (5.5) (5.6) (5.7) (5.8) (5.9) spread S t radiation t Holger Bech Nielsen , 2 , /kg 2 keV cm 19 7 + − 22 on which the quantities happen to l.b. . 10 10 6 5 2 . . ∗ 0 0 = 9 8 MeV + − V . . /kg ∆ 6 2 8 2 10 . ∗ + − 1 ξ 7 cm . theory 4

22 90% 40% 40% 80% 3 ′′ ) = 100% 100% . = 0 10 57 Uncertainty . ∗ keV ± 0 ) 5 ( . 2 95 (for 4 degrees of freedom) 57 theory 10 . .

± 4 0 exp 2 MeV V σ ∆ 10 10 0 M = = = N ∗ 1.3 1.4 . -1.3 1.61 0.88 ξ 2 V > > = ( χ ∆ ln exp

and MeV MeV . The fourth column contains crudely estimated uncertainties of the 2 V V σ to be. The third column is the natural logarithm of that required value ξ ∆ ∆ MeV V M 10 10 N 1 4 ∆ MeV 5.0 3.8 2.4 V 10 ∗ ∗ 0.28 ∆ ∗ 10 MeV V ξ ∗ ξ ξ ∆ 10 ξ ∗ ln ξ < V < ] for a discussion of this ratio and of our two theories for the surface tension ∆ The frequency predicted “3 , 12 ⇒ , i.e. ln ξ The intensity predicted 2 =1 σ M N MeV V ∆ 10 spread ∗ t radiation ξ t theory 1) theory 2) Name 3 3 Table of four theoretical predictions of the parameter / / 1 1 Intensity S S Theoretical values of both Ratio This our best fit including everything gives the following overall fitted values for the experi- Using our theory 2) for the surface tension we obtained the following fit: • Frequency “3.5keV” Combined theory with l.b. to stress thatWe it refer is to only our a paper lower [ bound and shall not be considered a great agreement for our theory. which is to be compared with and mental quantities mainly depend. The first column denotestal the value quantities for to which be we expected can forthe provide our a parameter theoretical fit combination or to experimen- that quantity. The next column gives whatparameter these expected thus values fitted need counted in this natural logarithm. In the last column we just marked the ratio Table 2: for the ratio Dark matter, pure S.M. Our calculations are almost just order ofof magnitude the estimates above and quantities so as we given make in fits Table to 2. the logarithms PoS(CORFU2019)049 (7.1) Holger Bech Nielsen 2 GeV 1 − ster − s 2 − m 3 − E 11 150 ) = − e + + e ( f lux ]! 31 Very strangely: If 3.5 keV radiationNOT should come come from from a big supernova-remnant; clustersremnant of but [ dark it matter, was it seen should from the Thyco Brahe’s supernova The speculation now could be that the dark matter could itself produce these excess positrons To estimate the absolute amount of positrons needed to be explained as coming from the dark One of the hopes for seeing something other than gravitational effects from dark matter is the • either by decay or by annihilationpearls or, with in each our other. model of dark matter, via collisions of thematter dark let matter us first,electron for around 10 normalization GeV purposes, the flux remark of positrons that or in electrons counted the together energy is of range the per order positron or 7. Positrons from dark Matter ? observation that above 9 GeVof or electrons so plus the positrons ratio in cosmic ofshould radiation the fall goes if number up the of with standard positrons energy. secondary This toin production is the of the unexpected positrons galaxy combined as during is number the the alone ratio propagation responsible of for cosmic the rays positrons. In our model this maysupernova be provides explained our pearls by with the energy. fact Theradiation that pearls of then the frequency radiate 3.5 cosmic that keV, radiation due energy to out from the as the excitons characteristic remnant formed of in the their interior. Dark matter, pure S.M. 6. Other heating of Pearls PoS(CORFU2019)049 ]. 14 33 (7.2) (7.3) (7.4) (7.5) (7.6) 3 m / Holger Bech Nielsen 1 − GeV 1 π . This means that very − ster 4 3 1 ∗ − ) cm s ster to the third power fall off, it 8 2 1 / − − E 10 s 2 ∗ . GeV − 3 3 3 ( m 3 . GeVm / cm − / 02 . 02 02 . . 0 0 0 ∗ ∗ ∗ GeV 2 GeVm 8 14 20 20 20 − − / / / 1 1 1 10 10 ∗ ∗ ∗ 12 ∗ ∗ 6 6 . . 150 0 0 150 150 , we may imagine integrating up over the spectrum in 2 ≈ ≈ = ≈ ≈ ) ′′ ′′ + GeV e 1 ] it is found that the ratio of positrons to (electrons plus positrons) in ( − 32 f lux ster 1 − s GeV energy f lux 2 “ 20 − energy density ∼ m 3 − E region giving an energy flux ∫ meaning “ ], the ratio of positrons to the sum of both positrons and electrons is about 0.05, while In the Pamela experiment [ 32 The dark matter density in our solar neighborhood is 0 When rather seldomly two of our dark matter pearls collide with each other and unite their Taking very crudely the result at 20 GeV that there is an (absolute) excess of positrons of Taking 20 GeV as a typical energy of the positron we have, according to the PAMELA obser- common skin is contracted to form the smaller surface of bubble skin around the two united pearls. (0.05 - 0.03) *150 Figure 1: cosmic rays does not follow the theoretical expectation, which is here shown by the continuous curve [ the neighborhood of the energyof 20 positrons: GeV or 10 GeV to obtain for the order of magnitude of a flux crudely around us thesmaller suspected than the excess energy of density of positrons the has dark matter an from energy which we density suspect about it to a come. factor 10 vation [ Dark matter, pure S.M. per GeV in the spectrum. the expected value with onlylooks the higher “normal” up in production energy mechanism towardsand would 100 more rather GeV copious. be where But 0.03. the data of As stop, course the one on positrons the get background relatively of more an energy The data seem to increase with the9 energy GeV. of The the idea positron is and that become this bigger excess than above the 9 expectation from GeV about could be due to dark matter. means that the positron rate falls off a bit slower than the one of the electrons. PoS(CORFU2019)049 times the Einstein Holger Bech Nielsen 14 − 13 , a region is heated to about MeV temperatures and large amounts S -rays from Dark matter. γ On the figure we seek to illustrate that the electrons have been slung far away and produced an -rays/light. In “usual” dark matter models -is a particle accelerated decaying over and a producing the veryquantum positron mechanics. short - the distance, positron effectively given by the massIn of our model the the particle acceleration and takescloud from place the over explosion. a distance At least given it by is the “macroscopic”. extent of the electron γ The emission of such lightthe has charged an particle, intensity here proportional the to positron. the square of the acceleration of of the degenerate electrons in the pearl are spit out. Some of the electrons may run outcreate to an a electric long field distance from able the toin two some accelerate united amount) positrons pearls at (which and first they are will estimate probably up also to being a produced fewIn MeV any energies, model but a with few positrons will being get produced much more. and accelerated, such positrons will shake off When two of our dark matterwith pearls high collide surface tension and the skin/domain wall around them contracts Positrons and • • • • • • Figure 2: electric field that potentially could drive e.g. the positrons. Dark matter, pure S.M. We imagine that part of the energyaccelerating released positrons by as the well skin as contraction to acceleratepositrons is mainly produced transformed electrons. and into accelerated making We must in and now this estimateannihilating way, and whether with having the electrons not yet around, disappeared could byrest have losing mass an energy energy energy or of of the the dark matter order from of which 10 it comes. PoS(CORFU2019)049 . s 17 (7.7) 10 -ray flux ∗ γ 3 . 4 = , i.e. an effective s Holger Bech Nielsen 28 10 ∗ 63 . s 0 15 = 100. So, thinking in terms of the 10 s / 8 ∗ . 1 times as much energy in positrons as 3 27 . ≈ 6 14 ) − = 2 -ray flux. It may be quite complicated and / s γ 1 30 ( / needed for the positrons to come from the dark 10 s ∗ 4% 15 . 14 63 . 10 0 ∗ ∗ 3 . 6 14 -ray prediction relative to the positron production. How- − = γ 10 ]. This means that half the (Einstein) energy of the dark matter 4% of the (Einstein) energy of these dark matter pearls actually = . 34 needed [ t s 3 . needed 0 t ± 8 . 27 10 . Thus the time needed to produce 10 s ∼ 30 70, then the observed positron excess could match our dark matter model. 10 / DM ∗ τ 1 ∼ 63 . than in the “usual” type of model. ever the positrons in ourdistances model than are in accelerated simple over WIMPs much orget longer a the - much like basically smaller decaying acceleration macroscopic or squared - annihilating for type the of positrons models. and thus So a we much smaller The usual dark matter decayproblem of or predicting annihilation a models too large of accompanying the positron excess suffer from the If the “fraction ofuniverse energy age the going positrons to can positronsthan keep on in running the around collisions” in times the neighborhood” “the can fraction be of bigger the model dependent to obtain our Propaganda for “Multiple Point (Criticality) Principle”(=MPP). This “multiple point (criticality) principle” is really a new law of nature, which we want to Positron Excess could be realized in Our Model for Dark Matter. But this means the survival time for positrons having been produced by the collisions of the Time needed for positron production In the simple model of a sterile neutrino of mass two times 3.5 keV decaying into a photon • • propose and argue for inall different these ways. vacua have The very law small energy saysThese densities that (or “vacua” “there in are the are older several to version: differentmolecules, the be vacua, same say, and thought energy can density)”. of be in as a phases phase of of space, fluid much water, water like vapor that or space ice. filled When with we water talk about vacua 8. Multiple Point Principle (our only new physics) dark matter should be atthe the collisions very should least go into 1/70 positrons, of it the should age be of even longer! the universe. If not all the energy from Luckily for our model, this time plus a normal neutrino, one fitsparticle to the be life-time of the sterile neutrino supposed to be the dark matter Dark matter, pure S.M. would go into the 3.5 keVwhen X-ray our line pearls with collide a and decayto produce rate our a model given lot only as of of the the 3.5 inversegoes order of keV of into this X-rays 0 the life-time. from X-rays. Now theinto energy So X-ray released, counted energy according in in terms the 3.5 ofsterile keV neutrino how line, model much our by of model a the is factor energy less of of effective the - the order having dark a 0 matter smaller decays rate - than the mass or energy decaying, thethan effective that life-time for in the our sterilelife-time model 0 neutrino is model about mentioned one abovethe hundred 10 energy times of longer the dark matter itself is matter is 70 times smaller than the age of the universe, which is 13.7 milliard years PoS(CORFU2019)049 Planck 14 agrees . Celsius. It << 0 0 ± 00 . 1 Holger Bech Nielsen = t g 15 ]. Scale problem: Why is the Higgs mass 21 935 [ . ]. The predicted top-Yukawa coupling 0 ]. 36 = 40 , t , g 35 14 , , 6 13 ] In some models we have success phenomenologically: E.g. PREdicted the 3 , 2 ]. , We - CDF and HBN - PREdicted the mass of the Higgs boson from MPP, before 1 37 one even sees that the value for the Higgs mass was painted long before the Higgs , 3 14 Theoretical predictions are made in a global time perspective , 7 , 5 , 4 scale, say? [ number of families [ Theory By this rather cryptic statement ofthe “global usual time perspective” locality, is but meant that thatour we at typical do model least not say coupling assume functions constants[ of can integrals feel over all even space-time the of future some by field being combinations in Phenomenology: PREdiction : it was discovered [ In figure particle was found. with the observed value Thinking of the multiple point principle as concerning just some special phases, one may There are actually several points which encourage us to believe that nature indeed satisfies this As just stated we talked about two versions: the old version in which the statement of the law of So our postulated new law of nature states that whenever you find such a phase with a valid • • • be encouraged by theDenmark analogous and Scotland situation - what that in English one isat called actually the slush, same namely sees that time. you quite see Then, bothis often by ice namely seeing and - only fluid that, at water especially you this in in temperatureboth fact that e.g. ice know there and that can fluid be the water a temperature at balancephases is in we the just pressure can usual 0 and so pressure temperature to of between speak one extract atmosphere. knowledge of From one the parameter, coexistence as of here the said two the temperature. law of nature, the multiple point principle: nature is only that the different Lorentza invariant phases, - vacua, we have can the call same - energy newer densities,that version, and says for that which all we vacua thank have Leonard veryis Susskind small that for or a zero then private energy you communication, density. can (Thespecial advantage consider case of of the this our latter smallness new version of version of the the cosmological multiple constant point - principle.) a great mystery - as a relativity principle on it, so thatenergy it density can be as considered all a the vacuum,called then other vacua. this phases phase of shall this have the relativistic same invariant type, deserving therefore to be Dark matter, pure S.M. instead of just phases wethat mean if that you we imagine think movingrelative inside of to such phases the vacuum, a which without vacuum observing are you something Lorentzlike else. cannot invariant, in There determine in is the in so the theory any to sense speak of way acourse relativity, your relativity such is principle, velocity that contrary the to velocity ifsense of you to one were ask of moving for the the through vacuacall velocity a makes a relative no phase vacuum, to sense. but of the if water; This water. ithave of in had So called that been it the completely case a phase impossible vacuum. it of to makes e.g. define perfect a fluid velocity water relative is to it not we what would we PoS(CORFU2019)049 ) 14 10 . 0 ± ± 135 38 ( . [h] Holger Bech Nielsen ] we would have predicted 38 GeV, which is also shown in the ) 5 ± 174 ( (Dansk Kunst 1998) the Higgs particle was found 16 long before ] we assumed the Higgs field expectation value in the second vacuum to be equal to the Planck 8 GeV for the Higgs mass to be compared with the actually found one 125 13 . This painting by Lars Andersen, belonging to Frederiksborg Museet, shows that one of us (HBN) ]. 1 39 ± Since our principle is so similar to requiring the coexistence of different phases, as is what This was what we did when we PREdicted the Higgs mass: We postulated that a vacuum phase The main application of the multiple point principle is precisely of this type also: by assuming 4 . painting. Had we insteadand used obtained the a top Higgs vacuum quark expectation mass value as of the input, order we of would the still Planck have scale. predicted the Higgs mass 129 happens in the situation of the“slush-principle”. existence of slush, you could be tempted to even call our principle a (i.e. a relativistic invariant phase) withwas a degenerate very (had high the Higgs same field energy (close densitypresent to and vacuum the thus surrounding Planck could us. scale coexist in of Then, a energy) as considering rather all already stable way) the given, with other we the parameters took inthe the the right Higgs Standard value mass later Model to on be for this adjusted Higgs to mass. the With degeneracy. today’s This knowledge [ turned out being the coexistence of different vacua (phases)we with can the deduce a same relation coupling between constant these and couplings mass and parameters, mass parameters. Figure 3: was even painted and the painting exhibited energy and predicted the then poorly known top quark mass to be GeV [ Dark matter, pure S.M. in CERN in 2012,GeV so is that visible except nobody for could theLykketoft. 1 at Notice behind the that the name time head ofour of know another paper the the one [ previous of mass. member us of C. the Nevertheless D. cabinet the Froggatt in mass on Denmark Mogens the top of the painting. We note that in PoS(CORFU2019)049 Holger Bech Nielsen (when the pressure is one atmosphere). 0 17 ] "Safety of Minkowski Vacuum" states: We give a simple 41 This picture should illustrate that just by looking at it and seeing slush (both ice and fluid water) Fixing Extensive Quantities (say energy) The abstract of Dvali’s paper [ However, it seems that Gia Dvali has found a derivation of the multiple point principle, in We therefore tend to think that in order to make a theoretical “derivation” in some way of our Usually we think that, since the coupling constants and the other parameters in the Lagrangian argument suggesting that in a consistent quantumto field a theory lower tunneling energy from vacuum a must Minkowskifor vacuum be localized impossible. states Theories of negative that mass, allow and for therefore, such should a be tunneling inconsistent. also allow which it appears that hepoint did is not that assume Lorentz any invariance breaking wouldwhen of enforce the the some different divergent usual vacua terms, principles have which of the could same locality. only energy His be densities. main avoided new law of nature, the multiple pointis principle, not one full should at causality. the Then outsetwhat at take goes least a model on coupling in in constants which the and there future. massaccept parameters there We have can can worked be be on influence influenced some from from future, such it very is speculative models much easier and, to once derive you the multiple point principle. density have been the samethe forever, big they bang had when the samefound a values astronomically piece even today, of far would relatively back hardly emptythe in be sameness space, time of or with shortly any smallness a after significance. ofcould cosmological energy have But constant densities had if of of any so significance. the the it But orderLagrangian order is if density of could so, hard cosmological only then to have constants the taken see at on couplingthey their that constants how multiple got and time point them mass principle via parameters adjusted a values in mechanism provided the some which way. was precognizant, i.e. which was influenced by the future in Figure 4: the reader should be soe.g. experienced what that clothes he the intuitively people - inprinciple: by the ice experience picture and - should water feels wear. together how This give cold is a namely special it the temperature must main 0 be point and for thus the multiple point Dark matter, pure S.M. PoS(CORFU2019)049 Holger Bech Nielsen , N 2 1 fixed fixed fixed · = = = x x x 18 4 4 4 d d d ) ) ) x x x ( ( ( 2 1 N L L L ∫ ∫ ∫ , ) x ( i L This kind of mathematical problem of determining relations between the coupling constants So the hope in our model is that several phases - several vacua - may be needed and they have The extensive quantities are integrals over the whole sample, while the intensive quantitiesOur are analogy to this distinction between intensive and extensive quantities deviates a little bit The “derivation” of our new law, the multiple point principle, which we wouldWe now know like these different to possibilities from chemistry or thermodynamics: One can put some and mass parameters from thethe specification determination of of the the extensive pressureof integrals and mol is temperature of very in water much a moleculesextensive analogous and bottle quantities to energy. with which pre-specified is This not volume, specificationpressure of can number must null lead, be measure, in at to a the the rangewater, critical requirement ice of point! that and values vapor. the That for The temperature is idea these and the isother that the point model - of - supposing coexistence we we of can know the all calculatethree form the the phases of meeting, analogue three the so of phases Standard that such Model fluid it or a should some critical be point called (possibly “multi-critical”) with and then even more that is than our multiple point to coexist. This coexistence means thatthe they same should coupling be realized constants in andconstants the should mass same so parameters physics, to meaning in speak with be the the Lagrangian same density. all over The the space-time. bare coupling If nature specifies thesestants four-dimensional and integrals, mass instead parameters ofadjusted in specifying by the first nature Lagrangian, the to then coupling giveBut the con- the then pre-specified couplings our extensive and hope integrals mass is overseveral that parameters four-dimensional achieving vacua space-time. must this say. be adjustment This turns is outyou specify to analogous the require to energy there the in to a situation bepresent. sample, in several This very phases, a often situation you where microcanonical cannot two ensemble achieve phasesin a where, are say solution in when temperature unless equilibrium (if two corresponds phases we to are fixedin. a the phase If transition energy slush point of is the present, the whole temperature sample) must and be this zero. is where the slush comes locally observable. from the usual chemical oneanalogues by to seeking the to extensive make quantities our areexpressions discussion integrals four over dimensional both so space and that time e.g. of our Lagrange-like field give is based on the crucialthan assumption on that intensive somehow quantities Nature to settles be given on a extensive priori. quantities rather specified amounts of various types ofgiven molecules size. and Quantities a like specified the amount amount ofare of energy called molecules into extensive, (measured a contrary in bottle mol) to of of quantities a which a like are substance the called or temperature intensive. the or energy pressure, or chemical potentials Dark matter, pure S.M. PoS(CORFU2019)049 Holger Bech Nielsen 19 than the supposedly fundamental scale given by the Planck 17 GeV. Even if one does not accept the Planck scale as the fundamental one, 19 This way of looking at our principle as a law of fine-tuningIndeed opens it up turns the out possibility that that the it scaling can problem we mentioned above can be solved by the multiple But SUSY particles have yet to be found and supersymmetry must be broken. So the correction Using the multiple point principle we take a somewhat different point of view: Supersymmetry Often one discusses the hierarchy problem in which one then accepts, as being more admissi- One of the great mysteries or fine tuning problems is the question of why the weak energy Say the Planck Scale help to solve some of the fine-tuning problems in physics. point principle, in thelow sense compared that to the our Planck principlevacuum scale can with or a some explain high other why Higgs fundamental thesay, field scale. turns out weak that Actually from comes scale measured it in. values is is of the thescale. This so gauge scale In high coupling extremely of any constants Higgs case to the field be it approximately scale, is the accidentally a Planck very you high may scale, essentially the Planck scale. that cannot be suppressed by supersymmetyWe gets must bigger already as put experiments the continue SUSY tomay breaking exclude even scale SUSY. be so required high one that could it say, is then a to bit get accidental, such a a bitcannot small of leave Higgs fine-tuning us mass without as fine-tuning, oneas even finds. if acceptable. we So took there the isprinciple assumption comes no of in a way as small except a bare by fine-tuningmultiple mass accepting law! point squared some We principle can fine-tuning! as look a at Now kind the the of coupling multiple fine-tuning. constant point restrictions from the ble, the fact that theBut bare then Higgs mass one squared has wasunderstood, the tuned wrong hierarchy in or problem, to rotten: be whichsquared very makes The to small calculation it the or of even renormalized even maybe the more HiggsGUT-scale, zero. mass correction clear very squared to that big. is get something divergent from So is or,such the it if a not funny bare you now way Higgs renormalize becomes that to it mass therenormalized just e.g. mystery compensates Higgs the of some mass huge squared? how corrections the to Forhelp, produce, bare this because in problem mass it the converts it sum, can the a has adjust corrections, veryand been small which itself therefore claimed a much in that priori smaller. supersymmetry are can quadratic, into logarithmic corrections scale is so low by a factorenergy of scale about of 10 10 9. The Problem of why the Weak Interaction Energy Scale is so Small Compared to but use instead e.g. grandthe unification weak models energy one scale tendsthe of to Higgs only get mass-parameter, of scales which of the determines the energyconnected order weak much with of scale, the higher 100 ever fact than got GeV. that In toPlanck the be scale this renormalized so or (dressed) light low. unified Higgs it scale. It mass becomes is Sofine-tuned is of to it a very be course is small mystery so a compared how small fine-tuning to compared problem: the to Why the is Planck this mass, renormalized say? Higgs mass Dark matter, pure S.M. principle prediction. That is whatcoexisting we vacuum-phases claim to have to the have same hadthe energy some principle. densities, success as with. stated in Really the we above expect formulation the of PoS(CORFU2019)049 ) = = 0.4 at the ) ϕ ( t run Holger Bech Nielsen g condensate scale ( t run g taken at the scale given by ) ϕ ( 4. . run 0 λ ) = is of the order of the Planck scale. for the electro-weak gauge fields as given, ϕ ) ϕ ( 2 α 20 Plank scale get their masses from the Higgs expectation value. 0 ∼ and ( Z ) ϕ t run ( g and 1 α ± W . In order to have a vacuum at high Higgs field with a small energy density, we ϕ 14 was needed. . 0 At the scale of the highrunning Higgs top-Yukawa coupling field is vacuum (essentially the Planck scale) one needs that the 3) The vacuum with the highscale. Higgs (It field was expectation by value using beingpresent the of one, requirement that the we of order derived the of the same the Higgs energy Planck mass density prior for to the this Higgs vacuum discovery.) and the 1) The vacuum in which we live called the “present vacuum”. 2) The vacuum inside thespeculate dark that this matter vacuum pearls, has a called bosonfloating condensate the of in “condensate some it. bound vacuum”, state because of 6 we top and 6 anti-top ± The above use of the multiple point principle twice gives rise to the two important require- On the other hand: Our bound state of the 6 top + 6 anti-top quarks is bound by Higgs exchange between the Now the energy density for high Higgs fields - the effective potential for the Higgs field for Let us explain this in a bit more detail. We assume that in the pure StandardWe already Model talked there about are these three vacua: Now our main point is: Requiring the existence of three degenerate vacua imposes such re- • • • • ], including a lot of corrections, that a running top-Yukawa coupling 00 . 21 1 Therefore the weak scale mustanti-top be quarks at bind least so lowerBut strongly than now that or to the the have same vacuum such[ as inside a the the strong scale dark binding where matter as the pearls to top can produce and the be condensate achieved. phase we calculated in ref. ments: constituent top quarks.requires Thus that the the physics Higgs ofwe is the call not “condensate the heavier vacuum” weak than needing scale, this this since scale. bound the state The Higgs mass scale is essentially what require this running self coupling tosidering be the very small fine-structure at constants that scale and to have a minimum there. Con- high Higgs values - isa dominated by good the approximation Higgs to self calculatethe interaction the renormalization term effective in group potential the running for energy value athe density. of high Higgs So this Higgs field it self field is coupling by just putting in high Higgs field vacuum scale, where the Higgs field three vacua, which then by ourto multiple be point very principle small, must essentially have zero. their energy densities fine-tuned strictions on the coupling“exponentially constants small” that compared to indeed the theof scale the renormalized of Planck the Higgs scale. vacuum mass with squared the high becomes Higgs field of the order Dark matter, pure S.M. the presence of such a needed minimum implies that the top Yukawa coupling PoS(CORFU2019)049 . ϕ = µ 0, in order . 1 ) = Holger Bech Nielsen as a function of the logarithmic ) t ( condensate scale ( t run g t run over the scale range between the high g ) µ ( t run g 21 -functions describing the running are of the order of 4 and at the scale of the “condensate vacuum”, which we . β 0 to "run” from 0.4 to 1.0. This takes then relatively many = t ) g µ is the quantity we have chosen to represent the energy scale ( ϕ 0. . t run 1 g = t g hierarchy problem ?) ∼ , where the Higgs field ) ϕ ( On this figure we see the running top-Yukawa coupling ln ∼ Also in our picturesquared including obtains huge the quadratically divergent “multiple and/or point finite terms, (criticality) when loops principle”, are the evaluated! Higgs mass At the scale of ‘condensatescale, vacuum”, this which same we running take coupling to shouldthat be be the of higher binding order than be or sufficient equal to to have the the “condensate weak vacuum” at all. t Scale problem ( So we even obtained an approximate numerically correct prediction for the logarithm of the These two requirements, both coming from the multiple point principle, obviously call for a But now the couplings going into the • • scale presume to be the weak scale, Figure 5: weak scale of energy from the multiple point principle theory. The point is thatcoupling: we At have essentially obtained the Planck two scale requirements from the multiple point principle for this running significant running of the top-Yukawa coupling Dark matter, pure S.M. orders of magnitude in energyvery close scale. to post-dicting In the factthe scale a weak of scale numerical the is! estimate “condensate gets vacuum” to order be of very magnitude-wise near to what we know the electroweak fine structure constantssmall. and (One actually could give say rise thatwould to give the rise beta smallness to beta of functions functions the which ofmagnitude coupling order are compared unity constants rather is to compared a the to small scale fine-tuning the problem; problemand values but we need which it discuss the is very here). Yukawa coupling small So in we have a relatively slow running Higgs field vacuum scale and thebe scale as connected high to as the the “condensate vacuum”, weak which scale. must at least PoS(CORFU2019)049 γ = V ∆ 8 GeV to . 1 ± and thus 4 . 3 − by a compensating rays relative to the Holger Bech Nielsen 10 γ V ∗ ∆ so that only in one (or 1 . 1 MeV V = ∆ 10 ∗ NN ξ ϕ 14 GeV. . g 0 separately, is it relevant that we have ± V 38 . ∆ and ξ 22 14 MeV was not correct. In fact, including the effect of heavier virtual 270MeV. This is about 13 times larger than the value we used above. ± = 20 = 10 GeV. The updated MPP prediction for the Higgs mass is 129 estimate. In the other cases we can absorb the change in V ± diction in 1995 of the Higgs mass (in terms of the vacuum expectation value) to be ∆ V = the ratio of the actual pearl radius to the critical radius being the smallest one for ∆ 246GeV The 3.5 keV X-ray radiation in intensityThe and positron frequency. emission. Especially the problemdark that matter a standard model elementary tends particle tonumber type of give positrons. too This much problem continuum wouldrays be spectrum compared solved to in positrons. our model, which gives fewer Explanation of the ratio of the weakPre scale to the “Planck scale”. 135 Dark Matter as 100000 ton, cm big pearls. be compared with the experimental value 125 ∗ ξ 3 – – – – – − using only the Standard Modeladds and information the about “Multiple the Point parameters of (Criticality) the Principle”, Standard which Model. The only dark matter model is very successfulastronomical being observations able in to addition reproduce to the the following gravitational controversial effects: We have presented a picture/model for It is not the samemakes as the getting getting rid rid of of them, them superfluous. as would say SUSY, but it has the same effect and But these terms are renormalized toate. a theoretical requirement of keeping the vacua degener- So the bare Higgs mass squaredpoint is principle”. tuned in exactly to cancel the corrections by the “multiple 10 After the submission of this paper to the proceedings a referee for another article pointed out • • • • • ∗ 1 . two) of the quantities we fit, wherein we estimate which the pearls are stillradius has stable. to Very be likely taken the as radius an varies average from one. pearl If to we pearl take, and as the we actual must when we consider the 3.5 keV that our value 11. Note added in Proof Luckily, however, our fits used mainly the combined parameter quarks in the nucleonsWei and Chiang, the “Revisiting more Scalar detailed and[hep-ph] Pseudoscalar calculation 18 Couplings in Jun with 2012, e.g. Nucleons” we1 rather arXiv:1202.1292v2 Hai-Yang get Cheng, a and Higgs Cheng- nucleon coupling 10. Conclusion Dark matter, pure S.M. changed the change in PoS(CORFU2019)049 1 13, ; in = 5 V √ (11.1) ∆ spread t radiation t which we should comes to the fifth Holger Bech Nielsen separately, then our MeV V only by a factor V MeV ∆ V 10 ∆ ∆ ∗ 10 ∗ ξ . ξ 4 corresponding to ) keV MeV V 4 for our parameter: the intensity ∆ 10 55 and not on ∗ . , 55-75 (2003); arXiv:hep-ph/0308144. 4, which should now be replaced by = ξ . 3 ( 18 4. It is still in the range allowed by the ∗ . MeV . So we should just drop this restriction V MeV 2 V ∆ V 10 V ∆ 10 ∗ ∆ ∆ ∗ = ξ ∗ ξ 7 5 . axis by this correction is used in this paper is for pearl sizes, without any 1 ) 4 and was described as a lower bound assuming / π 4 4 = 23 dependent, is below unity the contribution to the MeV V = √ ∆ 10 MeV ξ 9 V ∗ / MeV ξ ∆ 4 V 13 10 ∆ 2 5 10 ∗ √ ∗ / is only raised to the first power. Therefore replacing the = ξ ξ , given in Table 2 to be 2 ξ ( V : The time ratio, which we put equal to unity for the 3.5 keV ∆ ∝ MeV factor occurring inside our parameter V by a 13 times bigger value only increases the time ratio by such a ∆ 10 V V ∗ ξ ∆ ∆ spread t radiation t , which is strongly spread t radiation t only approximately true C.D. Froggatt, H.B. Nielsen, Proc. top.73, the (DMFA, Euroconference Zaloznistvo, on 2003); Symmetries arXiv:hep-ph/0312218. Beyond the Standard Model, C.D. Froggatt and H.B. Nielsen, Surveys High Energy Phys. Actually the two experimental quantities fit extremely well to the now most trustable theoreti- If indeed all the quantities giving rise to the fit - after throwing out “the combined theoretical However the theoretical estimate [2] [1] power, the separate occurrence of separately occurring quantity factor 13. Thus the shift in the point on the thus give up including insignificantly modified our by fit; the it correction is of the the value only of one of our fitting ingredients which actually gets of the radiation fitted to thethe radiation 3.5 from keV galaxy frequency clusters requires etc the requires value the 5 parameter (see value Table 3.8 2). and fit would only have changed bythat one this of is the items havingradiation been weighted thrown distribution out. of radii, But indeed now hasfact we a it must relatively behaves weak admit as explicit follows dependence on which is not so great a shift. In fact the value of our parameter on the value of our parameter Note however, that while the that the ratio is aboveemission unity rate (see of Table 3.5 2). keV radiation, Using we the thus distribution get of this pearl value as sizes a weighted reasonable with prediction. the cal prediction from the lower bound giving the value predictions” - just depended on our chosen parameter is shifted from the previous value 4 to 4 3.5 keV radiation is suppressed.radiation Thus just where it this is ratio very equalsratio likely unity. requires that According that to there our our will fitting fits be parameter above a this unity peaking point of for the the 3.5 time keV Dark matter, pure S.M. radiation, the average weightedratio with of the the emission times rate of the 3.5 keV radiation, then when the weighting with the radiation intensity, andun-weighted and will therefore thus not not so relevant be determination relevant. of our It parameter is this theoretical radiation a value 13 times smaller. 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