condensed matter, particle physics and cosmologyfjeger/krakow_8.pdf · 2014-11-28 · astronomy,...

Lecture 8:the SM as a low energy effective theory and its impact on cosmology

Outline of Lecture 8:

® Summary and outline

Topics:

o The Hierarchy Problem revisitedo a new view on naturalness and physics beyond the SMo an alternate path to new physics?o open problemso how to scrutinize SM Higgs inflationo cold dark matter, what could it be?o quo vadis particle physics?

F. Jegerlehner, IFJ-PAN, Krakow Lectures 2014, —≪x Lect. 8 x≫ 501

http://www-com.physik.hu-berlin.de/~fjeger/Krakow_7.pdf


The Hierarchy Problem revisited

A reminder:“The fate of Infinities”

r Infinities in Physics are the result of idealizations and show up assingularities in formalisms or models.

r A closer look usually reveals infinities to parametrize our ignorance ormark the limitations of our understanding or knowledge.

r My talk is about taming the infinities we encounter in the theory ofelementary particles i.e. quantum field theories.

r I discuss a scenario of the Standard Model (SM) of elementary particles inwhich ultraviolet singularities which plague the precise definitionas well as concrete calculations in quantum field theories are associatedwith a physical cutoff, represented by the Planck length.




r Thus in my talk infinities are replaced by eventually very large but finitenumbers, and I will show that sometimes such huge effects are neededin describing reality. Our example is inflation of the early universe.

Limiting scales from the basic fundamental constants: c, ~,GN

Ü Relativity and Quantum physics married with Gravity yield

Planck length: `Pl =

√~GNc3 = 1.616252(81) × 10−33 cm

Planck time: tPl = `Pl/c = 5.4 × 10−44 sec

Planck (energy) scale: MPl =√

c~GN

= 1.22 × 1019 GeV

Planck temperature: MPlc2

kB=

√~c5

GNk2B

= 1.416786(71) × 1032 K

l shortest distance `Pl and beginning of time tPl

l highest energy EPl = ΛPl ≡ MPl and temperature TPl

tPl < t −∞ < t




One impact of UV divergences in local QTFs: vacuum energy is in fact

ill-defined in a local continuum QFT as it produces quartically divergent

quantum fluctuations.

This is another indication which tells us that local continuum QFT has itslimitation and that the need for regularization is actually the need to look atthe true system behind it, i.e. the cut-off system is more physical and doesnot share the problems with infinities which result from the idealization. Inany case the framework of a renormalizable QFT, which has been extremelysuccessful in particle physics up to highest accessible energies, is not ableto give answers to the questions related to vacuum energy and hence to allquestions related to dark energy, accelerated expansion and inflation of theuniverse.

Such questions can be addressed only in the LEESM “extension” of thelocal QFT SM!




Remember the upshot of renormalizability and renormalized QFTs:

In a renormalizable QFT all renormalized quantities as a function of therenormalized parameters and fields in the limit of a large cut-off are finiteand devoid of any cut-off relicts!

Renormalization Theorem

The Bogoliubov Parasyuk theorem in quantum field theory states thatrenormalized Green’s functions and matrix elements of the scattering matrix(S-matrix) are free of ultraviolet divergencies. The theorem specifies a concreteprocedure (the Bogoliubov Parasyuk R-operation) for subtraction of divergenciesin any order of pertrubation theory, establishes correctness of this procedure, andguarantees the uniqueness of the obtained results.

i.e. in the low energy world cut-off effects are not accessible to experiments!and a “problem” like the hierarchy problem is not a statement which can bechecked to exist in our low energy reality.




What about the hierarchy problem?

The hierarchy problem cannot be adressed within the remormalizable,renormalized (like all observables) SM. In this framework all independentparameters are free and have to be supplied from experiment.

In the LEESM “extension” of the SM bare parameter turn into physicalparameters of the underlying cut-off system as the “true world” at shoertdistances. Then the hierarchy problem is the problem“tuning to criticality” which concerns the dim < 4 relevant operators , in

particular the mass terms:

Our Hierarchy Problem!

In the symmetric phase of the SM, where there is only one mass (the othersare forbidden by the known chiral and gauge symmetries), the one in front ofthe Potential of the Higgs doublet field, the fine tuning to criticality has theform




m20(µ = MPl) = m2(µ = MH) + δm2(µ = MPl) ; δm2 = Λ2

16π2 C

with a coefficient typically C = O(1). To keep the renormalized mass at somesmall value, which can be seen at low energy, m2

0 has to be adjusted to

compensate the huge number δm2 such that about 35 digits must beadjusted in order to get the observed value around the electroweak scale.

One thing is apparent: our fine-tuning relation exhibits quantities (in theLEESM all observable in principle) at very differnt scales, the renormalizedat low energy and the bare at the Planck scale.

r In the Higgs phase:

There is no hierarchy problem in the SM!




It is true that in the relation

m2H bare = m2

H ren + δm2H

both m2H bare and δm2

H are many many orders of magnitude larger than m2H ren .

However, in the broken phase m2H ren ∝ v

2(µ0) is O(v2) not O(M2Planck), i.e. in the

broken phase the Higgs is naturally light. That the Higgs mass likely isO(MPlanck) in the symmetric phase is what realistic inflation scenarios favor.

In the broken phase, characterized by the non-vanishing Higgs field vacuumexpectation value (VEV) v(µ), all the masses are determined by the wellknown mass-coupling relations

m2W

(µ) = 14 g

2(µ) u2(µ) ; m2Z(µ) = 1

4 (g2(µ) + g′2(µ)) u2(µ) ;m2

f(µ) = 1

2 y2f(µ) u2(µ) ; m2

H(µ) = 1

3 λ(µ) u2(µ) .

Funny enough, the Higgs get its mass from its interaction with its owncondensate! and thus gets masses in the same way and in the same




ballpark as the other SM species.

r Higgs mass cannot by much heavier than the other heavier particles!

r Extreme point of view: all particles have masses O(MPl) i.e. v = O(MPl).This would mean the symmetry is not recovered at the high scale,notion of SSB obsolete! Of course this makes no sense.

r since v ≡ 0 above the EW phase transition point, it makes no sense to saythat one naturally has to expect v(µ = MPl) = O(MPl)

l Higgs VEV v is an order parameter resulting form long rangecollective behavior, can be as small as we like.

Prototype: magnetization in a ferromagnetic spin system




M = M(T ) and actually M(T ) ≡ 0 for T > Tc furthermore M(T )→ 0 as T <→Tc

l v/MPl 1 just means we are close to a 2nd order phase transition point.

r In the symmetric phase at very high energy we see the bare system:




the Higgs field is a collective field exhibiting an effective massgenerated by radiative effects

m2bare ≈ δm

2 at MPl

eliminates fine-tuning problem at all scales!

Many example in condensed matter systems.

Astronomy, Astrophysics are unthinkable without the input from laboratoryphysics

now we are at a stage where particle physics has to learn form cosmology

In contrast to an old paradigm: the ground state of the world is filled withdark energy, Higgs condensate, quark and gluon condensates They play akey role in the evolution of the universe




l in fact by reparametrization the cut-off dependence of the preasymptotictheory (renormalizable tail) is completely removed. This implies that from arenormalizable low energy effective theory a cut-off dependence cannot beobservable (renormalized theory parametrized in terms of observedparameters)

l in that sense it is nonsensical to say that in the LEET we would naturallyexpect the Higgs mass to be of the order of the cut-off.

All those working on SM physics, in particular high precision physics andhigher order corrections are finally contributing a big deal to a betterunderstanding of the physics of the universe and in particular to theemergence of the early cosmos.




Inflation works

Flatness, Causality, primordial Fluctuations Ü Solution:

Inflate the universe

Add an “Inflation term” to the r.h.s of the Friedmann equation, whichdominates the very early universe blowing it up such that it looks flatafterwards

Need scalar field φ(x) ≡ “inflaton” : Ü inflation term

8π3 M2

Pl

(V(φ) + 1

2 φ2)

Means: switch on strong anti-gravitation for an instant [sounds crazy]

Inflation: a(t) ∝ eHt ; H = H(t) Hubble constant = escape velocity v/distance D

à N ≡ ln aendainitial

= H (te − ti)




ρφ = 12 φ

2 + V(φ)pφ = 1

2 φ2 − V(φ)

Equation of state: w =pρ

=12 φ

2−V(φ)12 φ

2+V(φ)

l small kinetic energy à w→ −1

Friedmann equation: H2 =8πGN

3

[V(φ) + 1

2 φ2]

Field equation: φ + 3Hφ = −V ′(φ)

r Substitute energy density and pressure into Friedmann and fluid equation

r Expansion when potential term dominatesa > 0⇐⇒ p < −ρ3 ⇐⇒ φ2 < V(φ)




N ≡ lna(tend)

a(tinitial)=

∫ te

tiH(t)dt ' −

8πM2

Pl

∫ φe

φi

VV ′

dφ

l need N >∼ 60

Key object of our interest: the Higgs potential

V = m2

2 H2 + λ24H4

r Higgs mechanism

v when m2 changes sign and λ stays positive Ü first order phase transition

v vacuum jumps from v = 0 to v , 0




V (H)V (H)

HH

µ2b < 0µ2

s > 0

+v

µ2s

m2H

Spontaneous breaking of the Z2 symmetry H ↔ −H. Ground state jumpsfrom 〈H〉 = 0 to 〈H〉 = v




The issue of quadratic divergences in the SM

Veltman 1978 [NP 1999] modulo small lighter fermion contributions,one-loop coefficient function C1 is given by

δm2H =

Λ2Pl

16π2C1 ; C1 =

6u2

(M2H + M2

Z + 2M2W − 4M2

t ) = 2 λ +32g′2 +

92g2− 12 y2

t

Key points:à C1 is universal and depends on dimensionless gauge, Yukawa

and Higgs self-coupling only, the RGs of which are unambiguous.

à Couplings are running!

à the SM for the given running parameters makes a prediction for thebare effective mass parameter in the Higgs potential:




The phase transition in the SM. Left: the zero in C1 and C2 forMH = 125.9 ± 0.4 GeV. Right: shown is X = sign(m2

bare) × log10(|m2bare|), which

represents m2bare = sign(m2

bare) × 10X.Jump in vacuum energy: wrong sign and 50 orders of magnitude off ΛCMB !!!

V(φ0) = −m2

effv2

8 = −λ v4

24 ∼ −9.6 × 108 GeV4




q in the broken phase m2bare = 1

2 m2H bare, which is calculable!

à the coefficient Cn(µ) exhibits a zero, for MH = 126 GeV at aboutµ0 ∼ 1.4 × 1016 GeV, not far below µ = MPlanck !!!

à at the zero of the coefficient function the counterterm δm2 = m2bare − m2 = 0

(m the MS mass) vanishes and the bare mass changes sign

à this represents a phase transition (PT), which triggers the

Higgs mechanism as well as cosmic inflation

à at the transition point µ0 we have

vbare = v(µ2

0) ,

where v(µ) is the MS renormalized VEV

In any case at the zero of the coefficient function there is a phase transition,

which corresponds to a restoration of the symmetry in the early universe.




Hot universe Ü finite temperature effects:

r finite temperature effective potential V(φ,T ):

T , 0: V(φ,T ) = 12

(gT T 2 − µ2

)φ2 + λ

24 φ4 + · · ·

Usual assumption: Higgs is in the broken phase µ2 > 0

EW phase transition is taking place when the universe is cooling downbelow the critical temperature Tc =

√µ2/gT .

My scenario: above PT at µ0 SM in symmetric phase −µ2 → m2 = (m2H + δm2

H)/2

m2 ∼ δm2 'M2

Pl

32π2 C(µ = MPl) ' (0.0295 MPl)2 , or m2(MPl)/M2Pl ≈ 0.87 × 10−3 .

In fact with our value of µ0 almost no change of phase transition point (seePlot below)




The cosmological constant in the SM

l in symmetric phase Z2 is a symmetry: Φ→ −Φ and Φ+Φ singlet;

〈0|Φ+Φ|0〉 = 12〈0|H

2|0〉 ≡ 12 Ξ ; Ξ =

Λ2Pl

16π2 .

just Higgs self-loops

〈H2〉 =: ; 〈H4〉 = 3 (〈H2〉)2 =:

Ü vacuum energy V(0) = 〈V(φ)〉 = m2

2 Ξ + λ8 Ξ2; mass shift m′2 = m2 + λ

2 Ξ

r for our values of the MS input parametersµ0 ≈ 1.4 × 1016 GeV→ µ′0 ≈ 7.7 × 1014 GeV ,

l potential of the fluctuation field ∆V(φ) .

Ü quasi-constant vacuum density V(0) representing the cosmological




constant

r fluctuation field eq. 3Hφ ≈ −(m′2 + λ6 φ

2) φ , φ decays exponentially,

must have been very large in the early phase of inflation

l we adopt φ0 ≈ 4.51MPl , big enough to provide sufficient inflation

r V(0) very weakly scale dependent (running couplings): how to get ride of?

r intriguing structure again: the effective CC counterterm has a zero, whichagain is a point where renormalized and bare quantities are in agreement:

ρΛ bare = ρΛ ren +M4

Pl

(16π2)2 X(µ)

with X(µ) ' 2C(µ) + λ(µ) which has a zero close to the zero of C(µ)when 2 C(µ) = −λ(µ).




Effect of finite temperature on the phase transition: bare [m2,C1 ] vs effectivefrom vacuum rearrangement [m′2,C′1 = C1 + λ ] in case µ0 sufficiently below

MPl finite temperature effects affect little position of PT; vacuumrearrangement is more efficient:

µ0 ≈ 1.4 × 1016 GeV→ µ′0 ≈ 7.7 × 1014 GeV ,




r SM predicts huge CC at MPl: ρφ ' V(φ) ∼ 2.77 M4Pl ∼ 6.13 × 1076 GeV4

how to tame it?

At Higgs transition: m′2(µ < µ′0) < 0 vacuum rearrangement of Higgspotential

V (0)∆V

V (φ)

φ

µ2s

m2H

How can it be: V(0) + V(φ0) ∼ (0.002 eV)4??? Ü the zero of X(µ) makes

ρΛ bare = ρΛ ren to be identified with observed value!




The Higgs is the inflaton!

r after electroweak PT, at the zeros of quadratic and quartic “divergences”,memory of cutoff lost: renormalized low energy parameters match bareparameters

r in symmetric phase (early universe) bare effective mass and vacuumenergy dramatically enhanced by quadratic and quartic cutoff effects

à slow-roll inflation condition 12φ

2 V(φ) satisfied

à Higgs potential provides huge dark energy in early universe whichtriggers inflation

The SM predicts dark energy and inflation!!!

dark energy and inflation are unavoidable consequences of the SM Higgs(provided new physics does not disturb it substantially)




The evolution of the universe before the EW phase transition:

Inflation Times: the mass-, interaction- and kinetic-term of the bareLagrangian in units of M4

Pl as a function of time.




The evolution of the universe before the EW phase transition:

Evolution until symmetry breakdown and vanishing of the CC. After inflationthe scene is characterized by a free damped harmonic oscillator behavior.




m The inflated expansion in the LEESM

Expansion before the Higgs transition: the FRW radius and its derivativesfor k = 1 as a function of time, all in units of the Planck mass, i.e. for MPl = 1.Here LEESM versus Artwork.




Reheating and Baryogenesis

r inflation: exponential growth = exponential cooling

r reheating: pair created heavy states X, X in originally hot radiationdominated universe decay into lighter matter states whichreheat the universe

r baryogenesis: X particles produce particles of different baryon-number Band/or different lepton-number L




“Annihilation Drama of Matter”

10−35 sec.

X

X

???

· · ·

· · ·

q

q

e−

e+

ν

νγ

X, X–Decay: ⇒ q : q = 1,000 000 001:1e− : e+ = 1,000 000 001:1

10−30 sec.

W

W

q

q

e−

e+

ν

νγ

0.3× 10−10 sec. LEP events

qq → γγ:

10−4 sec.

q e−

e+

ν

νγ

e+e− → γγ:

1 sec.

q e− νν

γ ⇐ CMB

us




Sacharow condition for baryogenesis:

l B

r small B/ is natural in LEESM scenario due to the close-by dimension 6operators

Weinberg 1979, Buchmuller, Wyler 1985,Grzadkowski et al 2010

r suppressed by (E/ΛPl)2 in the low energy expansion. At the scale of theEW

phase transition the Planck suppression factor is 1.3 × 10−6.

r six possible four-fermion operators all B − L conserving!

l C , CP , out of equilibrium

X is the Higgs! – “unknown” X particles now known very heavy Higgs insymmetric phase of SM: Primordial Planck medium Higgses




All relevant properties known: mass, width, branching fractions, CPviolation properties!

Stages: r kBT > mX Ü thermal equilibrium X production and X decayin balance

r H ≈ ΓX and kBT < mX Ü X-production suppressed,out of equilibrium

r H → tt, bb, · · · predominantly (largest Yukawa couplings)

r CP violating decays: H+ → td [rate ∝ ytyd Vtd ] H− → bu [rate ∝ ybyu Vub ]and after EW phase transition: t → de+ν and b→ ue−νe etc.




t c u

b s d

Higgses decay into heavy quarks afterwards decaying into light ones

Note: large CP violation in Vtd and Vub • • linksSeems we are all descendants of four heavy Higgses via top-bottom stuff!

Baryogenesis most likely a “SM + dim 6 operators” effect!




A hint for the fermion mass hierarchy?

Note: for our existence C and CP violations are mandatory and as we knowin a minimal way it only works with 3 families. What is the mass hierarchygood for, which as we know in the SM is a hierarchy of the Yukawacouplings? And why so dramatic? About 7 MeV for the u and d quarks and173 GeV for the top (∼ 3.5 × 10−5) ? The top must have its coupling in theballpark of the gauge couplings and the Higgs self-coupling to allow for thecompetition or conspiracy to stabilize the vacuum. The top is then alsoproduced overwhelmingly in the early universe. In order CP violation canoperate at all top matter must decay into lighter species in two steps, andthis works most efficiently with a pronounced hierarchy as we know it to berealized. As important for our existence at the end is the inverted ratiomu/md ∼ 0.75 < 1 vs. mt/mb ∼ 40 “” mc/ms ∼ 15 “”1. It is important thatneutral currents to leading order are absent in the SM, so the hopping has togo via CP violating channels.




Preheating is absent in LEESM Higgs inflation

After inflation stops a phase of reheating must have set in in order not toend up with a universe which would be much emptier than the one we know..

o inflation ends when the slow-roll conditions are violated and, in our sce-nario this is the result of the fast diminution of the Higgs field

o while the radiation energy decays very fast ρrad ∝ T 4(t) ∝ 1/a4(t), the fourheavy Higges essentially supply the dominating part of the energy densityat this stage

o the energy density of the Higgs system decreases because of the ex-pansion (1st term) and, in fact primarily, because of the decay into otherSM particles (2nd term), predominantly “would be heaviest” Fermion pairs.With Γφ the inflaton width the density evolves as

ρφ +(3 H + Γφ

)ρφ = 0 .




Accordingly, the inflaton undergoes damped oscillations and decays intoradiation which equilibrates rapidly at a temperature known as the reheattemperature TRH.

o in standard inflation scenarios the inflation is expected also to decay intoboson pairs

In the case of bosons however, one cannot ignore the fact that the inflatonoscillations may give rise to parametric resonance. This is signified by anextremely rapid decay, yielding a distribution of products that is far fromequilibrium, and only much later settles down to an equilibrium distributionat energy TRH. Such a rapid decay due to parametric resonance is known aspreheating (Kofman, Linde, Starobinsky 1994).

o preheating as a consequence of the decays of the inflaton field into bo-son pairs, cannot not happen in SM inflation, since triple couplings likeHWW or HZZ are absent at tree level in the symmetric phase (in the brokenphase triple boson couplings exist and are proportional to the Higgs VEV




v). Hence, before the Higgs mechanism takes place, Higgs decays into yetmassless gauge bosons are heavily suppressed (absence of bosonic triplecouplings or suppresses by lacking phase space). Higgs self-interactions(all quartic in the symmetric phase) between the equal mass heavy Hig-gses are ineffective as well (phase space suppressed, not matter produc-ing at all).




Conclusion

q The LHC made tremendous step forward in SM physics and cosmology:the discovery of the Higgs boson, which fills the vacuum of the universefirst with dark energy and latter with the Higgs condensate, therebygiving mass to quarks leptons and the weak gauge bosons,but also drives inflation, reheating and all that

q Higgs not just the Higgs: its mass MH = 125.9± 0.4 GeV has a very peculiarvalue!! tailored such that strange exotic phenomena like inflationand likely also the continued accelerated expansion of the universeare a direct consequence of LEESM physics.

à ATLAS and CMS results may “revolution” particle physics in anunexpected way, namely showing that the SM has higher self-consistency(conspiracy) than expected and previous arguments for the existence ofnew physics may turn out not to be compelling




à SM as a low energy effective theory of some cutoff system at MPlanckconsolidated; crucial point MPlanck >>>> ... from what we can see!

à change in paradigm:

Natural scenario understands the SM as the “true world” seen from far awayÜ Methodological approach known from investigating condensed matter

systems. (QFT as long distance phenomenon, critical phenomena)Wilson NP 1982

à cut-offs in particle physics are important to understand early cosmology,i.e. inflation, reheating Baryogenesis and all that

à the LEESM scenario, for the given now known parameters, the SMpredicts dark energy and inflation, i.e. they are unavoidable




Paths to Physics at the Planck Scale

M–theory(Brain world)candidate TOE

exhibits intrinsic cut-off↓

STRINGS↓

SUGRA↓

SUSY–GUT↓

SUSY

Energy scale

Planck scale‖

1019 GeV

Û

1016 GeVÛ1 TeVÛ

E–theory(Real world)“chaotic” system

with intrinsic cut–off

↑

QFT↑

↑

“??SM??”

SMsymmetry high → → → symmetry low

?? symmetry ≡ blindness for details ??

top-down

approach

bott

om-u

pap

proa

ch




Keep in mind: the Higgs mass miraculously turns out to have a value as itwas expected form vacuum stability. It looks like a tricky conspiracy withother couplings to reach this “purpose”. If it misses to stabilize the vacuum,why does it just miss it almost not?

l The Higgs not only provides masses to all SM particles[after the EW phase transition].

l For some time at and after the Big Bang the Higgs provides a

huge dark energy which inflates the young universe dramatically.

l The Higgs likely is the one producing negative pressure and henceblowing continuously energy into the expanding universe up to-dateand forever.

Of course: a lot yet to be understood!v the big issue is the very delicate conspiracy between SM couplings:

precision determination of parameters more important than ever Üthe challenge for LHC and ILC: precision values for λ, yt and αs,and for low energy hadron facilities: more precise hadronic crosssections to reduce hadronic uncertainties in α(MZ) and α2(MZ)




Imagine...

· · · a world upside down?

Hello Ether World: we can see you from far far away!




Last but not least: today’s dark energy = relict Higgs vacuum energy?

WHAT IS DARK ENERGY?Well, the simple answer is that we don’tknow.It seems to contradict many of our un-derstandings about the way the uni-verse works.· · ·

Something from Nothing?It sounds rather strange that we haveno firm idea about what makes up 74%of the universe.

3

SM

?




the Higgs at work




Thanks

Thanks for your attention!Thanks for the kind hospitality at IFJ Krakow!

Dziekuje bardzo!

Down to earth again.




Backup Material




Plenty of questions remain

l Two ways to get rid of massless Yang-Mills fields:Ê Higgs mechansism, SSB of the S U(2)L via spontaneous beraking of Z2, pro-vide mass to S U(2)L gauge fields and the FermionsË spontaneous breaking of the chiral GF = S U(Nq)⊗S U(Nq), [GF, S U(3)c] = 0 ,which is exact before the Higgs mechanism takes place, what is triggering SSBof chiral symmetry? and at what time in the evolution of the Universe? Whatis the role of the gluon condensate? What that of the quark condensates?Ì How does confinement emerge? Before the Higgs mechanism massive boundstates could have been formed (frozzen binding energy)? Aparently not asmp ≈ mn ≈ 1 GeV, i.e. hadrons can have formed only very late.




Quark-Gluon Plasma: its Role in Cosmology

AbstractOn the role of QCD in Cosmology: some time ago the proliferation of hadrons of increasingmasses turned the early universe into an unpredictable opaque state. QCD the moderntheory of strong interactions of hadrons was bringing new light into the game.




How QCD made early cosmology predictable

Looking back in time in

the early history of our universe :

The universe is expanding according to Hubble’s law velocity = H × distance(cosmological solutions of Einstein-Friedmann equations). The further we lookback in the past, the universe appears to be compressed more and more. Wetherefore expect the young universe was very dense and hot:




At Start a Light-Flash: à Big-Bang (fireball)Light quanta very energetic, all matter totally ionized, all nuclei disintegrated.Elementary particles only!: γ, e+, e−, u, u, d, d, · · ·

Processes: 2γ ↔ e+ + e−

2γ ↔ u + u, d + d...

'

&

$

%

Particle–AntiparticleSymmetry!

'

&

$

%

quantum fieldsin full

blossom

* Digression into high energy physics: example LEP




e+e− Annihilation at LEP

Mini Big Bang !

•What happens in Electron Positron Collisions?




Matter and Antimatter annihilate to pure light or heavy light(Z’s), which re-materializes in new forms of matter

(mostly showers of unstable particle).

Science Fiction as Reality!

Theory: Matter↔ Antimatter Symmetry [Dirac 1928, Andersen 1932, . . .]To every particle there exists an antiparticle

of opposite chargeNature: in our universe today: antimatter is missing [got lost somehow]!




Energy versus temperature correspondence:

1K ≡ 8.6 × 10−5eV(Boltzmann constant) ⇒

temperature of an eventT ∼ 1.8 × 1011 × T

In nature such temperatures only existed in the very early universe:

t = 2.4√g∗(T )

(1MeV

kT

)2sec.

↓

t ∼ 0.3 × 10−10 sec. after B.B.early universe

0K ≡ −273.15 C absolute zero temperatureT ' 5700 K surface temperature of the Sun

LHC looks further back in time: tLHC ∼ 1.185 × 10−15 seconds A.B.B.




History of the Universe (continuation)

10−43 sec. quantum-chaos... ???

2 × 10−6 sec. quark-gluon plasma, nucleon–antinucleon annihilation

Relict: nB/nγ ' 10−9mattervisibletoday

2 sec. electron–positron annihilation200 sec. Helium synthesis

→yields more neutrinos ! have tiny masses may contributesubstantially to matter density of the universe

400’000 years Hydrogen recombinationuniverse transparent, almost no free charges anymore,photons decouple and cool down further,

500’000 years from now on matter (neutral atoms) dominates1 Billion years stars, galaxies, clusters of galaxies, · · · form

13.7 Billion years today




“Annihilation Drama of Matter”

10−35 sec.

X

X

???

· · ·

· · ·

q

q

e−

e+

ν

νγ

X, X–Decay: ⇒ q : q = 1,000 000 001:1e− : e+ = 1,000 000 001:1

10−30 sec.

W

W

q

q

e−

e+

ν

νγ

1.2× 10−15 sec. LHC events

0.3× 10−10 sec. LEP events

qq → γγ:

10−4 sec.

q e−

e+

ν

νγ

e+e− → γγ:

1 sec.

q e− νν

γ




“Nucleo-Synthesis”

After 400 000 years: light atoms (electrically neutral)

H : He ∼ 3 : 1F. Jegerlehner, IFJ-PAN, Krakow Lectures 2014, —≪x Lect. 8 x≫ 556



together 98% of baryonic matter !Where are the γ’s ?

⇒ Cosmic Microwave Background (today: T ' 2.725 K)




Early Simplicity

Surprisingly, the early universe was much simpler than itis today, for several reasons:

1) Everything was spread out uniformly.2) Atoms & light were in thermodynamic equilibrium,

which is a particularly simple physical state.3) Changes due to expansion are also simple.

Particle number in Thermal Equilibrium:

n FermionsBosons

=g

2π2~3

∫ ∞

mc2

√E2/c2 − m2c2

exp(

E−µkT

)± 1

E dEc2




Statistical occupation probability (quantum statistics).Fermions can occupy a state 0- or 1-times (Pauli-Principle),

à weight factor(exp

(E−µkT

)+ 1

)−1

Bosons can occupy any state arbitrarily often,à weight factor

(exp

(E−µkT

)− 1

)−1

g is the spin multiplicity




Limiting cases

In the relativistic limit (kT mc2) one hasnBosons = 4

3nFermions = ζ(3) gπ2

(kT~c

)3

εBosons = 87εFermions = π2g

30

(kT~c

)3kT

sBosons = 87 sFermions = 2π2g

45

(kT~c

)3k

p FermionsBosons

= 13ε Fermion

Bosons

In the non-relativistic limit (kT mc2) the difference between Fermions andBosons disappears:

n = g

(kT~c

)3√(

mc2

2πkT

)3

exp(−

mc2

kT

)F. Jegerlehner, IFJ-PAN, Krakow Lectures 2014, —≪x Lect. 8 x≫ 560



s =mc2n

T, ε = nmc2 , p = nkT

Energy density of the relativistic components: Stefan-Boltzmann law

ρc2 =π

30g∗

(~ckT

)3

kT

with g∗ the effective number of relativistic degrees of freedom = sum of allcontributions of the relativistic particle species.




Scanning the Standard Model from the heavy to the lightparticles




Leptons τ−, τ+ 1776.84 ± 0.171 MeV spin= 12 g = 2 · 2 = 4

µ−, µ+ 105.658 MeVe−, e+ 0.510999 MeV

12Neutrinos ντ, ντ < 18.2 MeV spin= 1

2 g = 2νµ, νµ < 190 keVνe, νe < 2 eV

6

Weak bosons W± 80.403 ± 0.029 GeV spin= 1 g = 3Z 91.1876 ± 0.0021 GeV

Photon γ 0 (< 6 × 10−17 eV) g = 211

Higgs H > 114.4 GeV spin= 0 g = 11




FFFthe QCD part FFF

Quarks t, t 171.3 ± 1.6 GeV spin= 12 g = 2 · 2 · 3 = 12

b, b 4.20+0.17−0.07 GeV 3 colors

c, c 1.27+0.07−0.11 GeV

s, s 105+25−35 MeV

d, d 3.5 − 6.0 MeVu, u 1.5 − 3.3 MeV

72Gluons 8 massless bosons spin= 1 g = 2 · 8 = 16

16

Remember: QCD = asymptotic freedom

strong interactions = weak at short distances strong at long distances




In nature today: hadrons only = color singlets, [color unobservable!] àConfinement [QCD Gell-Mann, Fritzsch, Leutwyler ]

Hadrons are made of Quarks and Gluons

QUARKS are permanently confined inside HADRONS

In early universe: hundreds of hadrons à quark-antiquark-gluon soup [36+36+16]




All SM : g f = 72 + 12 + 6 = 90 ; gB = 16 + 11 + 1 = 28

Thus the total energy density

ρ(T ) =∑

ρi(T ) =π2

30g∗(T ) T 4

which in general defines an effective number of degrees of freedom g∗(T ).

If all particles are ultra relativistic

g∗(T ) = gB(t) +78g f (T )

with gB =∑

i gi is the sum over relativistic bosons and g f =∑

i gi the sum over therelativistic fermions.

If all SM are relativistically excited we have




g∗(T ) = 106.75

Mass effects can be taken into account as done above for electrons and positronsin the discussion of the e+e−-annihilation. Mass effects manifest themselvesslightly different in energy density ρ, pressure p and entropy density s. Therefore

ρ(T ) =π2

30g∗(T ) T 4 ; p(T ) =

π2

90g∗p(T ) T 4 ; s(T ) =

2 π2

45g∗s(T ) T 3

define slightly different effective numbers of degrees of freedom when massesplay a role. Numerical results are shown in the following figure.




The functions g∗(T )) (solid), g∗p(T ) (dashed), and g∗s(T ) (dotted) calculated for theSM particle content.

In the following we will often adopt the convention to express temperatures inenergy units, as E = kB T (hence 1 K ∼ 8.6 × 10−5 eV) is a universal relation andas particle physicist we are more familiar with energy units.




The thermal history of the universe as a scan of the SM:

T event g∗(T ) comment∼ 200 GeV all states relativistic 106.75∼ 100 GeV EW phase transition 106.75< 170 GeV top annihilation 96.25< 80 GeV W±,Z,H annihilation 86.25< 4 GeV bottom annihilation 75.75< 1 GeV charm, τ annihilation 61.75∼ 175 MeV QCD phase transition 17.25 (u, d, g→ π±,0, 37→ 3)< 100 MeV π±, π0, µ annihilate 10.75 e±, ν, ν, γ left< 500 keV e± annihilation 7.25

Time after B.B.: t = 2.4√g∗(T )

(1 MeV

kBT

)2sec.




Quark-Gluon Plasma: The Stuff of the Early Universe




QCD under extreme conditions:

r High temperature matter: early universe

r High density matter: in neuron stars and other supernova remnants




r Laboratory test to come: heavy ion collisions RICH/Brookhaven, LHC/Geneva

Nuclei in collision:




QCD phase transition:

insulator↔ metall, hadrons get “ionized”




Physics of the early universe:

à Entropy per co-moving volume is conserved

à All entropy is in relativistic species Expansion covers many decades in T, sotypically either T m (relativistic) or T m (frozen out)

à All chemical potentials are negligible

Entropy S in co-moving volume (Dc)3 preserved

g∗S effective number of relativistic species

Entropy density SV = S

D3c

1a3 =

2p2

45 g∗S T 3

à T = (g∗S )−1/3 1a ; a spacial radius of universe




Broniowski, et.al. 2004

How many hadrons?Density of hadron mass states dN/dM increases exponentially:

dNdM ∼ Ma exp M/TH (TH ∼ 2 × K = 170 MeV)




from P. Stankus, APS 09F. Jegerlehner, IFJ-PAN, Krakow Lectures 2014, —≪x Lect. 8 x≫ 579



Before [QCD] we could not go back further than 200,000 years after the Big Bang.Today since QCD simplifies at high energy, we can extrapolate to very early timeswhen nucleons melted to form a quark-gluon plasma. David Gross, Nobel Lecture(RMP 05)




Cosmological phase transition....

...when the universe cools down below 175 MeV

10−5 seconds after the big bang...

Quarks and gluons form baryons and mesons

before: simply not enough volume per particle available

related baryogenesis? hadrons condense (get masses), others phase transitionsearlier?

Electroweak phase transition T= 150 GeV (∼ 1/√√

2GF GF Fermi constant)

∼ 6 × 10−12 seconds after big bang

fermions, W and Z bosons get mass

Standard model: cross over transition baryogenesis if 1st order bubble formation“out of vacuum”




QCD at High temperature, at high T less order more symmetry (magnets crystals):

l Quark-gluon plasma

l Chiral symmetry restored (no pions, no quark condensates)

l “Deconfinement” (no linear heavy quark potential at large distances)

l Lattice QCD simulations: both effects happen at the same temperature

QCD - phase transition

Quark-gluon plasma Hadron gasv Gluons: 8 × 2 = 16 v Light mesons: 8v Quarks: 9 × 7/22 = 12.5 v (Pions: 3)v DOF: 28.5 v DOF: 8Chiral symmetry Chiral symmetry brokenLarge difference in number of degrees of freedom !Strong increase of density and energy density at Tc !




quark-gluon plasma“deconfinement”

quark matter: superfluidB spontaneously broken

vacuum

nuclear matter: B,I spontaneously brokenS conserved

〈qq〉 6= 0

〈qq〉 6= 0

〈qq〉 6= 0

1st order

2nd order ?

T

µ

QCD phases: ms > mu, md

?

pion’s

protons, neutrons etc




v Is B broken spontaneously? Could it be responsible for matter-antimatterasymmetry? Likely not: need B − L conserved!

v What about dark matter? Is it frozen energy? Is there a phase transition like inbaryonic sector? and, and, and ?




Summary

l QCD new type of QFT: particle↔ fields intrinsically non-perturbative,confinement & asymptotic freedom

l Baryonic matter (98%) binding energy (induced by interaction,frozen energy, condensed energy bags)

l Debris of hadrons produced at higher and higher energies ends in simplequark-gluon plasma (early universe)

l Extend our understanding of early cosmology from QCD phase transition (175MeV; about 2 × 10−5 seconds back to the electroweak scale [200 GeV; about6 × 10−12 seconds A.B.B.])

l To go deeper back in time wait for news from the LHC!

A real new challenge for QCD: the LHC




Paul Hoyer HU QCD lectures 2008

7

CERN, GenevaLHC




r In fact: LHC is designed to look for states and new forms of matter whichexisted in the early universe but have not yet be seen!

r The big step forward in SM physics and cosmology: the discovery of theHiggs boson, which not only gives mass to quarks leptons andthe weak gauge bosons, but also makes the universe look flat today.

r LHC 27 km beam line: is operated at a temperature of only 1.9 K (-271C)the coldest spot in the universe and producing hottest spots since10−15 seconds A.B.B.

l the QCD quark-gluon plasma is subject to intense investigations at the LHC




ALICE as well as CMS and ATLAS detectors should shed more light on it

R≫ R≫ R≫

l The quark-gluon plasma is there and the QCD phase-transition temperatureseems to be in accord with the lattice results?


http://www.youtube.com/watch?v=umFupRwWdJo&NR=1

http://www.youtube.com/watch?v=ictBOjWcVAg

http://www.youtube.com/watch?v=uJqGRzgad3s&feature=related



Big-Bang ...

Problem of fine-tuning

Time evolution of the density function:

Ω(t) =1

1− x(t)

x(t) =3k/R2

8πGρ

In order that the density today has a value 10 times higher or 10 times lower

than the critical value one has to assume that at Planck times the density was

coinciding to about 60 digits with the critical value 1.

|Ω(10−43sec.)− 1| <∼ 10−60 !

Solution by Inflation

Cure: add an inflation term, which blows up the early universe, such that it

looks flat today:8π

3m2Pl

(V (φ) +

1

2φ2

)

to be added to the right hand side of Friedmann’s equation (must be the

dominating for small times)

F. Jegerlehner Humboldt University, Berlin

45

Big-Bang ...

“Baryogenesis”

np/np ≃ 0 ; np/nγ ≃ 10−9

Conditions for the possibility of the baryogenesis: (A. Sacharov 1967)

① Baryon number violating processes must exist (B–L

violation!)

② CP violation ! Cronin, Fitch 1964 (NP 1980)

(Violation of time-reversal symmetry)

first seen in neutral Kaon decays 0.3% effect, more

recently established in B-meson physics ∼ 100% effect

CP violation precisely as predicted by SM of elementary

⇒ B-factories: BaBar and Belle

③ Thermal far from equilibrium ( non-stationary time

evolution (as predicted by Friedmann’s equations

[GRT]))

is true as the universe is expanding

Standard Model of elementary particle physics cannot

explain these facts: NEW PHYSICS REQUIRED likely at

energies not yet accessible by experiment (except LHC may

reveal new physics and hopefully does)!

GUT’S, SUSY, STRING’S ???in GUT’s: X–bosons and leptoquarks!

⇒ ATLAS, CMS and LHCB experiments at theLHC


46

Big-Bang ...

“Nucleosynthesis”

After baryogenesis and e+e−-annihilation:

np/np ≃ 0 ; np/nγ ≃ 10−9

At few seconds after B.B. and temperature T ∼ 1010 K

dropping fast

ne = np and nB = nP + nn conserved

neutrons, protons in thermal equilibrium

n+ ν p+ e− , n+ e+ p+ ν , n p+ e− + ν

① Ratio nn/np is given by the Boltzmann equation:

nn

np

= e−(mp−mn) c2/kBT

which at T ∼ 1010 K gives nn/np = 0.223.

② Below T ∼ 1010 K , no new neutrons are formed and

the ratio is fixed. Yet it is too hot for deuterium to form,

so protons and neutrons remain free. The free neutrons

decay into protons via β–decay (n → p+ e− + νe, half

life 617 seconds). About 4 minutes after B.B.

temperature has dropped to T ∼ 109 K , and deuterium

can form. At this point, neutron decay has rebalanced

the neutron to proton ratio to nn/np = 0.164.

③ Now time is ready for nucleosynthesis. At T ∼ 109 K ,

deuterium will survive. So nuclear reactions will form

deuterium, tritium, and helium:


47

Big-Bang ...

p+ n → Deuterium+ n → Tritium + p → He4

p+ n → Deuterium+ p → He3 + n → He4

④ Now per proper volume: nHe helium, nH hydrogen

nuclei: close to all neutrons are in helium: nHe = nn/2,

nH = np − 2nHe = np − nn ⇒ fractional abundance

by weight of helium Y = 4nHe/(4nHe + nH) =

2nn/(2nn + np − nn) = 2nn/(np + nn) = 2x/(1 + x),

with xnn/np = 0.164 at T ∼ 109 K we have

Y = 0.282. Observation close to 25%.

⑤ D is a steep function of baryon number nB ⇒Baryometer ΩB = 0.02

⑥ Cosmic concordance: one value of nB predicts light

element abundances 4He, D, 3He, 7Li rather well and in

agreement with value form CMB!


48

Big-Bang ...


49

Big-Bang ...

Under conditions after the B.B. (low density of baryons after baryon

antibaryon annihilation) only adding up nucleon by nucleon could be

successful. Start of nucleosynthesis hindered by small binding energy of

Deuteron [bottleneck]. Formation of D requires low enough temperature (at

about T = 0.1 MeV) but in the meantime neutrons density decreases by

neutrons decaying. At the end most of the remaining neutrons survive

bounded in the most sable of the light elements 4He.

1H

2H

3He

4He

6Li

7Li

9Be

No stablenuclei

The lack of stable elements

of masses 5 and 8 makes it

very difficult for BBN to

progress beyond Lithium

and even Helium. Need

conditions found in stars for

formation of the heavy elements.

8B 10B 11B 12B

7Be 8Be 9Be

6Li 7Li 8Li

3He 4He 5He

1H 2H 3H

1n

The Bottlenecks in BBN

• Elements of order Ä and Ç missing

(totally unstable)

• Barrier for productionof heavier elements in the early universe

• heavy elements must have been produced in stars(extreme temperature and pressure)


50

Big-Bang ...

The Standard Cosmological Model

Standard ΛCDM cosmological model is an exceedingly successful

phenomenological model

Rests on three pillars

Inflation: sources all structure

Cold Dark Matter: causes growth from gravitational instability

Cosmological Constant: drives acceleration of expansion that are

poorly understood from fundamental physics

ΛCDM and its generalizations to dark energy and slow-roll inflationary

models is highly predictive and hence highly falsifiable.

Wayne Hu’s summary


51

Big-Bang ...

The hot Big Bang is supported very

well by many facts. The picture of the

universe is one of the outstanding

intellectual achievements of the 20th

century. It bridges physics at

smallest scales with physics at largest

scales - the cosmic bridge. It

involves mysteries about its beginning

and leads us into a uncertain future.

Last but not least: Standard Model of particle physics

cannot explain

• Dark matter,

• Baryogenesis [matter vs antimatter asymmetry]

(missing B violation, missing amount of CP violation),

• Does not explain why cosmological constant is so small

• Why universe is flat [Inflation is beyond the SM physics]

One of today’s motivations and a great challenge for high

energy particle physics

Find what’s beyond the SM

dark matter B-violating interactions and all that ....


52

Big-Bang ...

10−18 10−16 10−14 10−12 10−10 10−8 10−6 10−4 10−2 1

104

108

1012

1016

1020

1

log(T

empera

ture

K)

log (Scale Factor)

decouplingof W and Z

bosons

baryonantibaryonannihilation

QCDphase

transition

electronpositron

annihilation

epoch ofnucleosynthesis

radiationdominated

matterdominated

epoch ofrecombination

the presentepoch

2.7 K

neutrinobarrier

photon

barrier

galaxies/quasars

15× 109 y106 y100 s20 µs10−12 s

Thermal History

Dark Ages after last scattering (epoch of recombination):

between 150 million to 1 billion years reionization of atoms takes place.

The first stars and quasars form from gravitational collapse. The intense

radiation they emit reionizes the intergalactic gas (hydrogen) of the

surrounding universe. From this point on, most of the universe is composed

of plasma. Stars cannot be seen until reionization becomes negligible due to

ongoing expansion and decreasing matter density (dilution).


53

Big-Bang ...

As far as we can see. As close as we can look.


54

HIGGS INFLATION ENDS HERE

FFFFFFFFFF

Previous ≪x , this was the last lecture.





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