Braibant S., Giacomelli G., Spurio M. Particles and Fundamental Interactions: An Introduction to Particle Physics

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402 13 Microcosm and Macrocosm

energy electron bremsstrahlung or inverse Compton). A clear evidence for

the presence of hadronic processes in astrophysical objects (the “smoking

gun” for the discovery of CR sources) could only come from the observation

of neutrinos from the decay of charged pions. The detection of high energy

neutrinos and antineutrinos is mandatory for a comprehensive understanding

of many astrophysical processes taking place in our Galaxy and particularly

extragalactic objects such as AGNs and those cosmic objects that give rise to

gamma-ray bursts (GRBs).

The small cross-section is the reason for the modest neutrino attenuation

in crossing the dense layers around the astrophysical objects where they

are produced. Neutrinos reach the Earth after traveling enormous galac-

tic/intergalactic distances. A 100 GeV neutrino has a cross-section of 6:7 

7

b, which means that it can travel on average through a thickness of

24 million km of water before undergoing an interaction. The small neutrino

cross-section requires the use of huge detectors, for example, those consisting

of a large volume of water (sea or lake) or even ice. It is estimated that an

instrumented volume of about 1 km

of ice or water is needed to be sensitive

to the neutrino ﬂux from a cosmic source.

The most efﬁcient way to search for astrophysical neutrinos is through the

detection of charged current interactions of muon neutrinos, with a muon in

the ﬁnal state. The muon is the particle with the longest range (Chap.2): a

200 GeV muon can travel about one kilometer of water. Moreover, at high

energies, the muon essentially retains the original direction of the neutrino

(the average deﬂection angle is less than 0:1

for 1 TeV neutrino). A detector

measuring the muon direction can therefore be used to trace back the 

emission source.

The  is detected trough the Cherenkov light produced when the relativistic

particle crosses a transparent and dense medium, as deep sea water or deep

ice. A suitable array of photomultiplier tubes (PMT) can be used for the detec-

tion of photons emitted by the muon; from the PMT positions and photon ar-

rival times, dedicated algorithms can trace back the muon direction. Only up-

ward going muons are unambiguously originated from neutrino interactions.

Neutrinos (in association with charged leptons) produced by CR interactions

with atmospheric nuclei represent an irreducible background for cosmic

neutrinos. Even if a detector is located under 2–3 km of water/ice, the number

of muons produced by cosmic ray interactions in the atmosphere above the

detector is overwhelming by more than ﬁve orders of magnitude than that

produced by atmospheric neutrinos. Unlike traditional astronomy, neutrino

astronomy examines the sky underground, on the other side of the Earth!

A neutrino telescope buried under the Antarctic ice is almost completed

(2010); this telescope will study the northern hemisphere sky. To observe

the southern celestial hemisphere (where the galactic center is located,

with its potentially interesting sources), the construction of a 1 km

-scale

13.5 Dark Matter 403

neutrino telescope in the Mediterranean Sea is planned in the next few years.

The ANTARES neutrino telescope near the French coast is a smaller scale

experiment (1=50 km

) in operation since May of 2008.

Particles and cosmology. The study of the dynamics of the stars in the galac-

tic halos and of galaxies in galaxy groups showed that the quantity of matter

in the Universe must be much larger than that observed with astronomical

instruments. Matter which does not produce any electromagnetic radiation is

denoted as dark matter; its nature is still unknown. It is likely that a part of the

dark matter consists of celestial bodies like the planet Jupiter and gas clouds

(baryonic dark matter); another part could consist of a “gas” of cold, weakly

interacting and massive particles, see Sect. 13.5.

The knowledge of the fundamental interactions between particles is needed

to understand the dynamics of the ﬁrst moments of the Universe (Sect. 13.6).

As a result of what happened in the early moments, different types of “relic”

particles may be now present in the Universe (as for the case of magnetic

monopoles, Sect. 13.1.2). After the phase transition corresponding to the

formation of atoms (about 300,000 years after the Big Bang), the decoupling

of electromagnetic radiation and matter took place. The Universe is uniformly

ﬁlled with a microwave electromagnetic radiation, the cosmic microwave

background, with a frequency spectrum typical of that of a 3 K blackbody

radiation [W08].

Similarly, about 1 s after the Big Bang, the decoupling of neutrinos from

the rest of matter and radiation occurred. These relic neutrinos should

have a temperature of about 2 K and the density number would be about

300 cm

3

(50 for each neutrino and antineutrino type). Relic neutrinos are

not currently observable. As discussed in Sect. 12.9, cosmology allows one

to set upper limits to the neutrino masses. Neutrinos with a very small mass

should be distributed almost uniformly in the Universe; on the contrary, if

the  mass is of the order of a few eV, they would form halos around galaxy

groups. This has consequences regarding the dynamics of galaxy formations,

and the limit on the  mass is derived from the observed distributions.

13.5 Dark Matter

The Universe is observed using electromagnetic waves of different frequencies

emitted by celestial bodies (in the optical band ﬁrst, then in the radio, infrared,

X-rays and -rays). It is very likely that a majority of the matter in the Universe

does not emit electromagnetic radiation. The existence of this invisible matter, the

404 13 Microcosm and Macrocosm

dark matter (DM), was indirectly highlighted through its gravitational interaction

with ordinary matter, which emits electromagnetic radiation.

Evidence for the existence of dark matter in spiral galaxies emerges from the

analysis of the revolution speeds of stars and gas clouds in the galactic halo as a

function of the distance from the center of the galaxy. Spiral galaxies, like our own

galaxy, contain 10

stars, arranged in the form of a central nucleus and a ﬂattened

rotating disk. The revolution speed of a mass m star around the center of the galaxy

is determined by the condition of stable orbits, equating the gravitational force with

the centrifugal force, that is,

(13.17)

from which:

v.r/ D

: (13.18)

is the total mass of stars and interstellar material within the distance r from the

center of the galaxy. Most of the stars of a spiral galaxy are located in the central

spherical bulge with radius r

.If is the average density of stars in the bulge, we

have M

D  

r

for r<r

; it follows that

v.r/ D

G

r  r for r<r

: (13.19a)

If all the galaxy mass is assumed inside the bulge, then M

' constant for r>r

and

v.r/  1=

r for r>r

: (13.19b)

The observed matter distribution in the bulge and disk leads to a revolution speed of

the stars as shown by the dashed line in Fig. 13.8 for the spiral galaxy NGC3198. The

ﬁgure also shows the contribution of a possible dark matter halo. The experimental

data obtained using the Doppler effect are indicated with black dots. From the ﬁgure

it is evident that at high r, the measured velocities v ' 200 km s

1

are larger than

those obtained using (13.18), also including the additional contribution of stars in

the disk. There must be a contribution from a halo of dark matter. Similar results are

obtained by measuring the speed of stars in other spiral galaxies. Evidence for the

presence of dark matter also exists for elliptical galaxies and for galaxy clusters.

One of the major achievements of “experimental cosmology” is the series of

precision measurements of cosmic microwave background (CMB). In 1992, the

COBE satellite measured the black body spectrum (at a temperature of 2.725K)

of the background radiation. The measurements conﬁrmed that any deviation

from a Planck curve was smaller than 1/10,000, as expected (J.C. Mather and

G.F. Smoot, Nobel laureates in 2006). The deviations from a perfect black body

13.5 Dark Matter 405

0510

100

200

300

15 20 25

v (km s

–1

)

r (kpc)

halo

bulge

+ disk

Fig. 13.8 The points indicate the measured rotation speeds of stars in the spiral galaxy NGC3198,

versus their distance r from the galactic center. The dashed line represents the expected

contribution based on the visible matter in the galactic nucleus (bulge) and in the galactic disk;

the dotted-dashed line includes the contribution of a halo of dark matter. The solid line is a ﬁt to

experimental data assuming visible matter in the bulge and disk and dark matter in the halo

spectrum were measured with experiments placed on balloons (BOOMERanG

[13B00], MAXIMA). Recently, the WMAP experiment on a satellite measured the

temperature differences in the CMB radiation with high precision. The measured

anisotropies are used to estimate the Universe’s geometry, content, and evolution;

test the Big Bang model and the cosmic inﬂation theory. Cosmology closely

connects the curvature of the Universe with its matter density ˝ D =

,where



is the critical density of the Universe:



8G

3.100 h

km s

1

Mpc

1

8G

' 1:9  10

29

gcm

3

(13.20)

where H D 100h

km/s/Megaparsec is the Hubble constant, h

' 0:71.

The recent WMAP results have shown that (1) the Universe is 13.7 billion years

old (with 1% margin of error); (2) the cosmological scenario which includes a period

of cosmic inﬂation is in agreement with the observations; (3) the Hubble constant is

H D 100h

D 71 ˙ 4 km/s/Megaparsec; (4) ˝

tot

D 1.

In particular, the matter density ˝ can be expressed as the sum of different

density terms:

1. Visible baryonic matter: ˝

vis

' 0:005:

2. Nonvisible baryonic matter: ˝

' 0:046:

3. Nonbaryonic dark matter: ˝

 0:23:

4. (from which neutrinos: ˝



 0:003  0:1/:

5. “Quintessence”(dark energy) ˝

 0:72:

406 13 Microcosm and Macrocosm

The “Quintessence” (or dark energy) is still an unknown form of energy that

permeates the space and tends to increase the expansion rate of the Universe. We

will return to this topic at the end of this chapter.

No experiment has ever provided direct information on the nature of dark matter.

The baryonic fraction of DM could be astrophysical bodies in their terminal phase

(remnants) as white dwarfs, neutron stars and black holes. They could also be

smaller objects, with insufﬁcient mass (0.1 m

,wherem

indicates the mass of

the Sun) to become stars (Jupiter-like planets); these massive compact objects are

called MACHO. The research in galactic halos (via effects like gravitationallensing)

indicates that such objects with m < 0:1m

exist, but that their total mass is much

smaller than that of the dark matter halo. MACHOs are probably not important at

the cosmological level, and they are almost certainly negligible even at the level of

the internal dynamics of galaxy structure and formation.

There are other arguments in favor of the existence of nonbaryonic DM. For

example, the study of nucleosynthesis of light nuclei at the cosmic time t ' 200 s

leads to the value ˝ < 0:02 if only baryonic matter is considered. It is noteworthy

that without nonbaryonic DM, it is difﬁcult to construct models of galaxy formation

starting from small ﬂuctuations, like those observed in the cosmic microwave

background. The nonbaryonic DM could be a gas of weakly interacting particles,

classiﬁed as hot or cold particles depending on whether they were relativistic or not

at the time of galaxy formation. If these DM particles are in thermal equilibrium with

baryons and radiation, they are classiﬁed as hot or cold DM if their mass is smaller

or larger than 1 keV, respectively. Models with cold DM are better reproducers of

the observed large scale structure of our Universe.

An interesting candidate for cold DM is the stable SUSY particle, the lightest

neutralino, with a mass of the order of 100 GeV; it manifests itself as a Weakly

Interacting Massive Particle (WIMP). A WIMP can be directly detected through

elastic interaction with nuclei in scintillators, solid state detectors, etc.; the recoil

nucleus will deposit a few keV of energy large enough to be measured.

There is currently a continuous development of larger and more sophisticated

detectors (particularly cryogenic detectors) that can provide accurate measurements

of temperature rise due to WIMP energy loss by ionization or excitation. The main

problem is to distinguish genuine WIMPs interaction from background due to the

ambient radioactivity. To unambiguously distinguish a possible WIMP signal from

the background, the DAMA experiment [13B08] at the Gran Sasso Laboratory

exploits the peculiarities of the “wind” which produces a WIMP annual modulation.

Our galaxy should be surrounded by a WIMPs halo and our solar system (which is

moving at a speed of about 230 km/s compared to the galactic system) should be

continuously hit by a WIMPs “wind.” As the Earth moves around the Sun, the ﬂux

of WIMPs, if any, should be maximum in June (when the revolution speed of the

Earth adds to the speed of the solar system in the galaxy) and minimum in December

(when the two velocities have opposite directions). Data collected for 7 years

suggest the presence of an annual modulation. This modulation can be explained

by a contribution of WIMPs with mass of about 10 GeV. Other experiments (using

different experimental techniques) do not conﬁrm this signal, but the discussion is

still open.

13.6 The Big Bang and the Primordial Universe 407

WIMPs are also searched for by using indirect methods: massive WIMPs can

be slowed down by elastic collisions and captured by a celestial body (like the

Earth or the Sun). If WIMPs collect in the nuclei of these celestial bodies, a higher

concentration is expected, and WIMP–antiWIMP annihilation can take place. This

annihilation would produce particles that decay into high energy 



that could be

detected in large underground detectors and in neutrino telescopes, resulting in high

energy muons from 



N ! 



C X, with direction coming from the center of the

Earth (or the Sun).

Another searched particle is the axion,that is, a particle theoretically predicted

in models beyond the SM whose mass should be 10

5

eV. Axions would be

nonrelativistic even if they have low mass. They are searched through their

conversion into photons in a nonuniform magnetic ﬁeld.

13.6 The Big Bang and the Primordial Universe

According to the Big Bang model, the expansion of the Universe originated

from a “primordial explosion,” from a space-time singularity of very high density

and temperature. Starting from the Big Bang, the Universe can be considered

as a gas of particles rapidly expanding. Our knowledge on particle physics,

fundamental constituents and interactions, helps us to understand what probably

happened. Theories on the uniﬁcation of fundamental interactions have been

applied to describe the evolution of the Universe immediately following the

Big Bang.

To imagine the nature of the expansion, the example of the swell of a balloon

is used. Inﬂating the balloon, the distance between any pair of points drawn on its

surface increases. A hypothetical two-dimensional observer located at one point on

the balloon surface would see all other points moving away from his position in all

directions. Other observers on the balloon surface will observe the same recession.

There is no privileged point: the expansion has no center within the two-dimensional

surface. For two-dimensional observers on a spherical surface, the Universe is ﬁnite

and unrestricted in the sense that a ﬂat individual can move in a ﬁxed direction

and, continuing, will return to the starting point. According to general relativity, the

Universe expansion happens in four dimensions; it is difﬁcult for us to see the fourth

dimension, as it is difﬁcult for the two-dimension observers to visualize their third

dimension.

The Big Bang model is mainly based on three experimental facts: (1) the

recession of galaxies; (2) the cosmic microwave background and (3) the ratio of

helium–hydrogen abundance.

Cosmic microwave background radiation. The Universe is uniformly ﬁlled with

a cosmic microwave background radiation generated at the time of H and He atoms

formation, when the temperature of the Universe had dropped to 4,000K (time of

atoms formation). As the radiation no longer had enough energy to further ionize the

408 13 Microcosm and Macrocosm

atoms, the Universe became transparent and from that moment, matter (i.e., atoms)

and electromagnetic radiation were independent. The corresponding present number

density of photons, about 400 cm

3

, represents the largest number of particles in

the Universe. When increasing time, the Universe expanded and cooled down to

its present status. The expansion causes an increase in the distance between two

successive wave crests. A longer wavelength corresponds to lower photon energy.

Helium abundance in the Universe. Direct observation indicates that the helium

present in every galaxy, in any direction and at any distance, corresponds to 20–24%

of the visible baryonic mass. This is explained assuming that helium (and other light

elements, for example, D;

He;

Li;

Be) was produced in the early moments of

the Universe. Heavier nuclei have been synthesized in heavy stars, see Sect. 14.10.

The picture of the Universe before the helium formation (200 s after the Big

Bang) was as follows: the temperature was about 10

K and a large number of

photons, a relatively small number of protons, neutrons and electrons were in

statistical equilibrium. A large number of neutrinos were also present, but with

negligible inﬂuence because of the low neutrino interaction cross-section with

matter. The interaction between neutrons and protons formed deuteron nuclei

with energy release; but deuteron were dissociated through  C d collisions and

immediately split into their constituents n and p. When the temperature fell below

one billion degrees, the photon energy kT was no longer able to break the deuteron

nuclei. Then, a series of nuclear reactions undisturbed by the photons began; the

reactions led to the formation of helium, the more stable between light nuclei, and

of a relatively small number of other light nuclei elements. The time at which they

were produced is called the nucleosynthesis phase of light elements.

The evolution after the Big Bang. As for the above description of the nucleosyn-

thesis of light elements, the state of the Universe at any given moment is determined

by statistical mechanics laws. Additional information exists regarding the number

density of particles present, their temperature (i.e., their average kinetic energy),

and how they interact. This information can be obtained by making extrapolations

based on the knowledge of the interactions among particles at lower energies, and

assuming conservation laws. It is assumed that all the conserved physical quantities

(charge, baryonic and leptonic numbers, :::) were zero at the beginning. At some

point, during a phase transition, some process (yet unknown) which allowed the

matter to dominate over antimatter must have occurred.

We will show the evolution of the early moments of the Universe using a set

of “snapshots” taken at increasing times. We must remember that our knowledge

decreases when approaching the Big Bang. The broad outlines of the Universe

history, illustrated in Fig. 13.9 and described below, are clear, but perhaps many

“details” remain to be deﬁned.

1. Cosmic time t

D 0, about 13.7 billion years ago. The Big Bang happens, i.e.,

the singularity at the origin of the Universe. From this moment, the Universe

expands. All conserved quantum numbers are equal to zero. Probably, the total

energy is also equal to zero because the kinetic energy, i.e., the energy of

motion, is equal and opposite to the gravitational potential energy.

13.6 The Big Bang and the Primordial Universe 409

Structures (Galaxies, galaxy clusters, ....)

Matter and radiation decoupling

Primordial nucleosynthesis

Quarks confinement

Quark gluon plasma

Inflation

GUTs

Quantum gravity

2.7

T (∞K)

+15

+40

–40

010

–40

–5

–15

–25

–35

–45

Radius (cm)

Present

Time (sec)

Fig. 13.9 One possible way to describe the evolution of the Universe: temperature (T ) and time .t/

versus the parameter R

that can be identiﬁed as the “radius” of the Universe. Note the inﬂationary

phase, when the Universe expanded exponentially

2. First phase transition at t

D 10

43

s (Planck time). The temperature is T

5  10

K; the average kinetic energy of each particle is E

' 10

GeV. It is

the moment when particles are generated. For times smaller than the Planck

time, quantum mechanical ﬂuctuations did not allow one to consider particles

as separate entities and the gravitation was uniﬁed with the Grand Uniﬁed

interaction. Up to this moment, the emitted gravitational waves were absorbed;

from this time, they are free to propagate.

3. From 10

43

to 10

35

s. The Universe (if quarks and leptons are the ulti-

mate constituents of matter) is a gas of quarks and leptons, antiquarks and

antileptons, and of X; Y bosons, the mediators of the Grand Uniﬁcation

interaction (if they exist). In this case, leptons and quarks behave like members

of the same family; a quark can transform into a lepton (or vice versa).

4. Second phase transition at t

' 10

35

s. The temperature is T

' 5  10

' 10

GeV per particle. The era of the Grand Uniﬁcation of the

strong with the electroweak interaction (from t

to t

) ends with a phase

transition. Transitions from a quark to a lepton (or vice versa) are no longer

possible. Interactions of quarks became very different from those of the leptons.

This is the GUT transition, during which new particles can be created, for

example, the magnetic monopoles.Att D t

,theelectroweak era started.

According to some models, the phase transition at t D t

began with a hyper-

410 13 Microcosm and Macrocosm

expansion (or inﬂation) of the Universe. Inﬂation is expected to have reduced

the number of magnetic monopoles, and made the Universe “ﬂat,” isotropic

and causally connected. Inﬂation has increased with a superluminal speed at a

region of about 10

25

cm to 100 m in a very small fraction of time.

5. From 10

35

to 10

10

s. Strong and electroweak interactions are different,

and quarks and leptons behave as different objects; the X; Y bosons decay

into quarks and leptons. Their decay leads to an asymmetry between matter

and antimatter, with a slight predominance of the former. During this period

(electroweak era), it seems that nothing happens: it is a short time interval

that corresponds to a large energy range. Many physicists deﬁned this time

interval as the desert. Maybe the desert will “ﬂourish,” if new particles (e.g.,

supersymmetric particles) with masses of the TeV order are discovered.

6. Third phase transition at t

D 10

10

s. The temperature is T

' 1:5 

K, E

' 200 GeV. The electroweak era ends: after this moment, the

electromagnetic and weak forces are different from each other.

7. Fourth phase transition at t

D 10

6

s. Particle–antiparticle annihilations

begin. As a result of q

q and e



annihilations, there is the disappearance of

antimatter, leaving a number (relatively limited) of quarks and electrons. Before

, there was a plasma of q; q, gluons (quark-gluon plasma), plus electrons.

8. Fifth phase transition at t

D 10

4

s. The temperature is T

D 1:5  10

' 0:2 GeV. This phase transition corresponds to quarks conﬁnement to

form baryons. Leading up to this moment, quarks are free particles. Now, u;d-

type quarks combine in triplets to form protons and neutrons (maybe also the

few remaining

q join in triplets to form p and n). The difference in the number

of quarks and antiquarks is now a difference between the number of p and

(and between n and

n).

9. From 10

4

to 1:1s. The Universe is dominated by particles with masses smaller

than 6 MeV: electrons, positrons, neutrinos, antineutrinos and photons. The

Universe is still so hot and dense that neutrinos interact quickly and are in

thermodynamic equilibrium with e;. Their abundances are almost equal. The

number of p and n is instead very small, about one in every billion of  (or e



or ). The number of n is almost equal to that of p.

10. Sixth phase transition at t

D 1:1s. The temperature is T

' 1:4  10

' 2 MeV; the neutrino decoupling happens. The average energy of

neutrinos, as that of any other particle, and the neutrino interaction probability

(cross-section) decrease; the matter density decreases as well with increasing

time. As a result, the neutrinos at t D t

do not interact frequently with the rest

of the matter and become independent.

The neutron has a mass slightly larger than that of the proton: this did not

play a role when the typical energies were high. In the collisions, a neutron

could transform into a proton with an equal probability than that for the reverse

reaction. The mass difference between n and p produces a difference in the

reaction probabilities at the kinetic energies of this period. Just before neutrino

decoupling, the reaction 

n ! e



p was more likely than the reverse reaction.

There was therefore a relative increases in the number of protons. At t D 1:1 s,

13.6 The Big Bang and the Primordial Universe 411

there is about 24% of neutrons and 76% of protons. In a pn collision, a

deuterium nucleus can be formed: np ! d. The deuteron is rapidly broken

into its constituents by a photon interaction d ! np .

11. Seventh phase transition at t

D 4s. The temperature is T

' 4  10

'0:5 MeV per particle: the e



pair annihilation begins. Photons have

an energy below the energy required to produce e



pairs. There is no

compensation for electron and positron losses due to their annihilation. The



and e

disappear rapidly, only a small number of electrons, the excess over

the e

, remains. The number of remaining electrons is exactly equal to that of

protons. The released energy in the annihilation process heats the particles that

are coupled together (photons, but not neutrinos). The photons reach an average

temperature 35% higher than that of neutrinos.

12. From 4 to 200 s. Positrons disappear from the Universe. The number of

neutrons relative to that of protons continues to decrease, due to their ˇ-decay

(n ! pe





). At this stage, the main components of the Universe are ; ; 

with a (relatively) small percentage of e



;p;n (an electron/proton for every

billion photons.)

13. Eighth phase transition at t

' 200 s. The temperature is T

' 10

' 140 keV per particle: it is the phase when the nucleosynthesis of

deuterium, helium and other light elements (which have already been discussed

above) takes place. From this moment, there is nuclear matter, with 24% helium

and 76% of protons (in weights).

14. From t

D 200 s to t

' 10;000 years. The Universe mainly contains pho-

tons and neutrinos. There is a (relatively) small amount of matter. There are

no more free neutrons. The radiation continues to cool down as well as matter.

Matter is in the form of a gas of electrically charged particles (protons and

electrons). A plasma of electrons and protons is the fourth state of matter (after

solid, liquid and gaseous states). It is still abundant today because it is the

dominant state inside the stars.

15. t

' 10; 000 years. Matter and radiation energy densities are equal: 

mat ter



radiation

.Theradiation era, which had originated just after the Big Bang,

ends and the matter era (that continues today) begins. In the era of matter,

energy is dominated by matter, i.e., the energy associated with the rest mass

. However, in the radiation era, the particle kinetic energies were much

higher than the energy associated with the mass. Atoms cannot form yet: if a

proton captures an electron to form a hydrogen atom, shortly after, a collision

with a photon breaks the binding.

16. Ninth phase transition at t

' 300;000 years. The temperature is T

4;000 K,

'0:5 eV per particle: this is the time of atom formation.The

photon energy is so low that photons are no longer able to break atoms.

In a relatively short time, electrons combine with protons to form hydrogen

atoms, and with helium nuclei to form helium atoms. As the photons are no

longer absorbed by atoms, the Universe becomes transparent to electromagnetic

radiation, which is now decoupled from the matter and has an “independent