The Dark Matter in the Approach Unifying Spin and Charges Analysis of the Cosmological Evolution

Postgraduate Seminar Author: Gregor Bregar Mentor: prof. Norma Mankoč Borštnik 3.3.2009

Presentation Plan:

      introduction experimental restrictions for cosmological scenarios of the dark matter the dark matter in the approach unifying spin and charges - particle candidates basics of the expansion of the early universe analysis of the proposed scenario conclusion

Introduction

Evidences for the dark matter:

– rotation velocities of stars in galaxies + measurements of the amount of H, He and stars – rotation of galaxies in clusters of galaxies – measurements of the distribution of mass in the universe + models of structure formation with dark matter and ordinary matter – analysis of a collision of two galaxy clusters – direct measurements (DAMA) (in disagreement with similar smaller experiments (CDMS, Zepplin, CREST ...) therefore nonconclusive)

Some other information about the dark matter:

– – – – Modification of general relativity is unsuccessful.

A very big part of the dark matter is not made of neutrons, protons and electrons.

It is not known if the dark matter consists of macroscopic objects or of elementary particles (or bound systems of a few elementary particles).

The dark matter can have many components (a small part are neutrinos).

General requirements for dark matter particles

− − − − − − decay time >> age of the universe zero electric charge mass density today must fit 0.3 critical density cross section for all scatterings is very small – only gravitational interaction can play a role after the nucleosynthesis (for our case) if the particles carry EM or color charge they should form neutral clusters before the nucleosynthesis at the time of galaxy formation the particles were nonrelativistic

Particle candidates in the approach unifying spin and charges (1)

More than 3 families: 4+4 decoupled families.

The lightest (the fifth) family is stable.

The fifth family particles have identical quantum numbers to the first 3 families except for the masses.

Two particles: one quark and one lepton are stable depending on the masses m u5 , m d5 , m e5 , m ν5 .

The dark matter particles are

neutral bound systems

quarks and leptons.

of the fifth family Scenario with mixed systems of fifth and first family particles is unlikely.

The aim of this seminar is to answer the question:

(No CP asymmetry and quark Are there such masses of the particles of the new family that just the fact that these particles are stable fulfills quantitative and qualitative constraints put by the cosmology of the early universe. lepton transitions are included.)

Particle candidates in the approach unifying spin and charges (2)

There are 2 options: a) neutrino is stable b) electron is stable.

Consequences: a) DAMA experiment (if true) excludes neutrinos as dominant DM content.

(1 TeV neutrinos are not excluded from cosmological analysis.) neutral heavy baryons are needed: n 5 =u 5 d 5 d 5 |m u5 /m d5 – 1| < 10 -3 or 10 -4 We have n 5 and the heavy neutrino.

b) All heavy electrons must bind on heavy baryons d 5 d 5 d 5 or u 5 u 5 u 5 .

We have bound systems of heavy baryons and heavy electrons.

The remaining unbound heavy particles can bind with ordinary matter afterwards and form anomalous hydrogen and helium which is severely constrained !

Particle candidates in the approach unifying spin and charges (3)

Properties of the heavy baryons u 5 u 5 u 5 , u 5 u 5 d 5 , u 5 d 5 d 5 , d 5 d 5 d 5 : - the mass range we are interested in is 10 TeV < m < 10000 TeV QCD is perturbative Coulomb-like potential: the binding energy and typical size is estimated within Bohr’s approximation: The neutral u 5 d 5 d 5 behaves as a weakly interacting particle soon after it is formed. (for m > 1 TeV).

The bound systems of heavy baryons and heavy electrons can be treated similarly.

Basics of expansion of the early universe (1)

The early universe was homogeneous, dense and the particles were in thermodynamical equilibrium. This is the first approximation, we will start with it.

Hubble expansion: - the relative velocity of distant objects in space is proportional to their separation - the comoving coordinates and the scale factor: - the metric: - the universe is close to being flat the expansion is described by Einstein’s equations of GR in this case called the Friedmann equation. For flat spacetime it is: This equation connects time and the scale factor.

Basics of the expansion of the early universe (2)

The energy density: - massless bosons with zero chemical potential – each spin state: - massless fermions with zero chemical potential – each spin state 7/8 of this.

( ħ=c=k B ) The entropy: The entropy of all physical content in a fixed comoving volume is constant.

The total entropy density scales as 1/a 3 .

- massless bosons with zero chemical potential – each spin state: - massless fermions with zero chemical potential – each spin state 7/8 of this.

The entropy conservation connects temperature and the scale factor.

Basics of the expansion of the early universe (3)

Reactions of particles The expansion causes the cosmic plasma to become more and more dilute.

Therefore it can occur that the particles virtually stop interacting and fall out of chemical equilibrium – freeze out.

This is possible if the ratio of typical time for two particles to react and the Hubble time goes to infinity when time passes.

Basics of the expansion of the early universe (4)

The Boltzmann equations 4 types of particles and a reaction 1+2

↔

3+4 each particle species

i

has

g i

internal states classical (nonquantum) gas the gas is in kinetical equilibrium but not in chemical – the chemical potentials are not the same for 4 particles: for example due to low densities or low cross section for the above reaction in comparison with elastic scattering How do number densities change with time?

Analysis of the proposed scenario (1)

The freeze out of free quarks -

The situation at temperature when the 5 th family quarks were ultrarelativistic:

the quark-gluon plasma was perturbative; thus similar to EM plasma the cross section for annihilation of heavy quarks to all light particles scales as 1/E 2 the ultrarelativistic heavy quarks can not freeze out the freeze out of free quarks is possible at the nonrealativistic stage -

The situation at the nonrelativistic stage:

to solve the Boltzmann equations for free quarks the connections between

t

and

a

and also between

a

and

T

are needed (and the cross section) most of the energy density comes from: 4 families of massles quarks and leptons (without the righthanded neutrino) and photons, weak bosons and gluons most of the entropy comes from these same particles If we do not include the entropy of the Higgs field (which is unknown) we obtain:

Analysis of the proposed scenario (2)

The freeze out of free quarks We take m u5 =m d5 and write the Boltzmann equation for number density of quarks u 5 . The cross section (first order) for annihilation of u 5 into all 4 families of quarks and into gluons is: The next formulas are: the thermally averaged cross section, equilibrium number density, the Boltzmann equation, introduction of new variables and the dimensionless Boltzmann equation: We assumed that the annihilations affect the number density of the massless particles negligibly.

Analysis of the proposed scenario (3)

The freeze out of free quarks Evolution of Z with x=m/T for m=3 TeV:

Z

at freeze out in the case if all free quarks formed neutral baryons is connected to the present day dark matter density via This is nonrealistic because at the formation of bound states a lot of quarks annihilate through an intermediate bound state of a quark and an antiquark.

giving the lower limit for the mass of the heavy quarks

m > 2 TeV

since it turns out that

Analysis of the proposed scenario (4)

The formation of bound states

Only a qalitative anylysis based on calculations will be presented.

- The freeze out of free quarks is completed within 30 % at T=m/100.

The baryons are kinematically ‘allowed ‘ at T=m/20 but are practically not formed before T=m/300.

- The annihilations through a very fast decaying quark-antiquark state compete with the formation of bound states.

- If these thermally averaged cross sections are the same only 5 % of the initial quarks form bound states for m=10 TeV.

A relative small difference in these cross sections in favor of annihilations causes significant amount of annihilations.

- The gluons from annihilations of the decaying quark antiquark states ionise the already formed baryons. (probably negligibly because of low number densities of quarks 10 -10 relative to number density of massless quarks).

A more precise calculation (estimation) of the mass of heavy quarks demands a calculation of thermally averaged cross sections for formation of bound states and the annihilation of decaying states.

Analysis of the proposed scenario (5)

The formation of bound states The nonperturbative effects need to be examined if the mass turns out to be too low.

When the neutral baryons form and the heavy quarks stop annihilating the baryons decouple from the plasma due to their small size and acts as a weakly interacting particles.

The remaining free unannihilated free quarks must annihilate at QCD nonperturbative phase transition within 10 -30 efficiency otherwise the scenario fails due to anomalous hydrogen.

The scenario with the heavy electrons stable does not have a chance because the remaining free heavy electrons surely do not annihilate and therefore bind with ordinary matter and form anomalous matter at easily detectable quantities.

Conclusions

If there is a stable family of particles with identical quantum numbers as the known 3 families with the only difference in the masses and if we do not include any asymmetry in the number of these particles and forbid quark-lepton transitions, the scenario of the dark matter being composed of neutral baryons u 5 d 5 d 5 and heavy neutrinos is the only option .

Therefore the relative difference in masses of u 5 than 10 -3 or 10 -4 .

and d 5 is less The high confidence level lower limit of these masses is 2 TeV .

The scenario can be realistic only if practically all (10 -30 ) the unbound u 5 and d 5 get annihilated at quark confinement stage (T=300 MeV). This must still be investigated.

(A more involved calculation can yield a narrow inteval of masses.)