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T - CERN
Lecture 3
Concepts for Baryogenesis
Andreas Höcker, CERN
Lectures at the the 5th Particle Physics Workshop, Islamabad, Pakistan, Nov 20-25, 2006
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
M.C. Escher
1
Lecture Themes
I.
Phenomenology beyond the Standard Model
Empirical & theoretical limitations of the Standard Model
Supersymmetry
Extra Dimensions
Little Higgs
II.
Experimental Searches
LHC, ATLAS and CMS: Experimental Challenges
Searches at the LHC: SUSY, Extra Dimensions, Little Higgs
III.
Concepts for Baryogenesis
(out-of-series lecture)
Lectures based on introductory course by Werner Bernreuther, hep-ph/0205279
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
2
Prerequisites
Antimatter
Matter-antimatter asymmetry
Dynamics of the universe
Equilibrium thermodynamics
Higgs mechanism
CP violation in the quark sector: CKM matrix
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
3
Paul Dirac
Combining quantum mechanics with special relativity,
and the wish to linearize /t, leads Dirac to the equation
i     x,t   m  x,t   0
for which solutions with negative energy appear
Dirac, imagining holes
and seas in 1928
Energy
E 
me
s  1/ 2
Dirac identified holes in this sea as “antiparticles” with
opposite charge to particles … (however, he conjectured
that these holes were protons, despite their large difference in mass,
because he thought “positrons” would have been discovered already)
0
me
Vacuum represents a “sea” of such negative-energy
particles (fully filled according to Pauli’s principle)
E
s  1/ 2
This picture fails for bosons !
An electron with energy E can fill this hole, emitting an
energy 2E and leaving the vacuum (hence, the hole
has effectively the charge +e and positive energy).
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
4
1956
Antineutron
Antiproton discovery 1955
incoming
Antiparticles
incoming
antiproton
antiproton
Positron discovery in cosmic rays by Carl Anderson in 1932 (Caltech)
Reproduction
Antiproton
chargeof an
Has the same mass as the electron but positive charge
antiproton reaction
exchange
annihilation
intostar
as seen in nuclear emulsion
neutron-antineutron
pair in
(source:
O. Chamberlain,
Nobel Lecture)
propane
bubble chamber
Anderson saw a track in a cloud
(source: E.G. Segrè, Nobel Lecture)
chamber left by “something
positively charged, and with the
same mass as an electron”

p + anti-p  n + anti-n
History of antiparticle discoveries:
protons and
1955: antiproton
 particles
“annihilation star”
(Chamberlain-Segrè, Berkeley)
(large energy release
from antiproton destruction)
“annihilation star”
1956: antineutron (Cork et al., LBNL)
protons and(large energy release
1965: antideuteron (Zichichi, CERN and
Lederman, from
BNL)antineutron destruction)
 particles
1995: antihydrogen atom (CERN, by now millions produced !)
Every particle has an antiparticle
Some particles (e.g., the photon) are their own antiparticles !

5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
5
Particles and Antiparticles Annihilate
What happens if we bring particles and antiparticles together ?
A more modern
A particle
can annihilate with its
example:
antiparticle to form gamma rays
An example whereby matter is
converted into pure energy by
Einstein’s formula E = mc2
Conversely, gamma rays with
sufficiently high energy can turn
ALEPH
into a particle-antiparticle pair
Higgs candidate
ee  ZH (Z )  qqbb
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
Particle-antiparticle tracks in a
bubble chamber
A. Höcker  Baryogenesis
6
Matter-Antimatter Asymmetry
q
q
1
Early universe
Current
universe
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
7
Sakharov Conditions
(*)Bigi-Sanda,
•
The Universe is not empty* !
•
The Universe is almost empty* !
nbaryon
n

nbaryon  nbaryon
n
CP Violation, 2000
~ O 1010 
Initial condition ? Would this be possible ?
Dynamically generated ?
Sakharov conditions (1967) for Baryogenesis
1.
2.
Baryon number violation
C and CP violation
3.
Departure from thermodynamic equilibrium (non-stationary system)
So, if we believe to have understood CPV in the quark sector, and that it cannot
account for the observed baryon asymmetry … what does it signify ?
A sheer accident of nature ?
What would be the consequence of a different value for the CKM phase ?
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
8
Expansion of the Universe
Robertson-Walker space-time metric describes curvature and expansion of the Universe:
Cosmic scale factor
with [R] = length
 dr 2
2
2
2
2 
ds  dt  R (t ) 

r
d


sin

d


2
 1  kr

2

2

k = (–1, 0, +1) for
negative, vanishing,
positive spatial curvature
The Friedmann equation (defining the Hubble parameter) describes the time evolution of R(t)
Total energy
density of Universe
2
 R (t ) 
8 GN
k

H 2 (t )  
 (t ) 

 
3
R (t ) 3
 R (t ) 
Cosmological constant
For a flat universe (k = 0), the sign of  determines the universes fate
Hubble “constant”: H0 = H(t = today) ≈ 71 km s–1 Mpc–1
Baryogenesis happens at a time t where the universe is radiation dominated, and where the
 term can be neglected. In this era one finds:
 (t )  R 1(t ),
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
and
H(t )  t 1
A. Höcker  Baryogenesis
9
Equilibrium Thermodynamics
The early Universe can be seen as a dense plasma of particles in thermal equilibrium (TE)
with phase space function for a particle A with mass mA:
Boson/Fermion
nA
EA  A  kTA
Chemical potential
f

e
1 actual
A
nC

 abundance
Temperature
Considering the (fast) reaction: A + B  C, one finds in equilibrium: µA + µB = µC
equilibrium
abundance
The particle number NA is obtained from phase-space integration of fA. We can distinguish
andT 1 TA  R 1
Ultrarelativistic particles (T0A  mA):
N A  const,
Nonrelativistic particles (TA  mA) :
NA   mA kBTA 
32
e
 mA   A  kTA
Departure from TE: consider reaction rate [s –1]: A    A  target  C   ntarget  | v A-target |
A > H : reaction occurs rapidly enough to maintain thermal equilibrium
A < H : particles A will fall out of equilibrium
when T < mA decreasing, nA decreases following the exponential law; if A stayed in TE it would
almost fully disappear; however, once A < H the interactions of A “freeze out”
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
10
The Higgs Mechanism
The fermion and gauge-boson masses of the SM are dynamically generated via the
Higgs mechanism when spontaneously breaking electroweak symmetry
Recall the Higgs “Mexican hat” potential at T ≈ 0:
V ( ) 
2
2

2  4
4
with vacuum expectation value: 0  0
T 0

T 0
2
At T < TEW, the massless fermion fields interact with
the non-vanishing Higgs field that is always present:
g v
f
=
propagator: 1 q
+
1 q
T
×
2
T 0  

1 q
+
1 q
2


×
1
 246 GeV
2GF
+
1 q 1 q
…
×
Geometric series yields massive propagator creating effective mass for fermion:
n
1 1  g f vT  1 1  g f vT  1  g f vT  1
1    g f vT  1 
1
 


...





q q  2  q q  2  q  2  q
q n 0   2  q 
q  gf vT

5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
2

similar
for gauge
bosons
11
CP Violation in the Quark Sector: the CKM Matrix
The charged weak current generates
transitions between left-handed quark
families:
UL,i Vij DL, j
U L ,i
CP conservation is: A Ui  D j   A Ui  D j 
Ui  D j
Ui
The CKM matrix:
The KM mechanism
describes all CP-violating
effects observed so far
Vij
DL, j
(up to unphysical phase)
Kobayashi
-Maskawa,
1973
Ui
Vij
VCKM 
d
u
c
t
W
only, if:
Dj
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
There are 33 of these
 CKM matrix
Ui  D j
W
=
Vij
W
Vij  Vij
Dj
s
b
Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb
A. Höcker  Baryogenesis
arg(Vub )  0
arg(Vtd )  0
CP Violation
(Im[...]  0)
12
Baryogenesis
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
13
CP Violation and the
Genesis of a Matter Universe
astronomical units:
1 pc
1 GeV
1 GeV
1
1.
Has Antimatter Really Disappeared ?
2.
Baryogenesis in the Early Universe
3.
Baryogenesis through Electroweak Phase Transitions
4.
Baryogenesis through Leptogenesis
3.2 light years
1013 K
6  10
25
s
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
14
Through the
Looking
Glass
What’s the
Matter with
Antimatter ?
David Kirkby, APS, 2003
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
15
Antimatter in the Universe ?
Balloon-borne Superconducting
Solenoidal (BESS) spectrometer
Does stable antimatter exist in the universe ?
No antinuclei (e.g., Antihelium) seen in cosmic rays (relative limit from BESS: < 10–6)
No significant (diffuse) cosmic  rays from nucleon-antinucleon annihilation in the
boundary between matter & antimatter regions
No evidence of antimatter in our domain of the universe (~20 Mpc = 0.6108 light years)
Could our universe be (like) inverse Suisse cheese,
with distant matter or antimatter regions(*) ?
void
antimatter
Difficult within the current limits
matter
Likely: no antimatter in our universe
(apart from the antimatter created dynamically in particle collisions)
void
The voids would create anisotropy
in CMB spectrum, which is not seen
(*) “If
we accept the view of complete symmetry between positive and negative electric charge so far as concerns the fundamental laws of nature,we must regard it rather as an accident
that the Earth (and presumably the whole solar system), contains a preponderance of negative electrons and positive protons. In fact there may be half the stars of each kind. The two
kinds of stars would both show exactly the same spectra, and there would be no way of distinguishing them from present astronomical methods." P. A. M. Dirac, Nobel Lecture (1933)
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
16
Baryogenesis and CP Violation
Matter counting:
Asymmetry parameter:  
nB  nB
n
nB
, observed to be ~ 1 10–10 <  < 6 10–10
n
Obtain naïve guess by comparing the estimated atom density in the universe (~1.6/m3)
with the photon gas density at 2.73 K cosmic background radiation temperature (~4.2108/m3)
Problem: (anti)nucleon densities in
thermal equilibrium:
High temperature plasma
(thermal equilibrium)
p  p     I n  np , np
m 

 N 
n n  kBT 
np
np
Decay
3/2
e  mN / kBT
Departure from
thermal equilibrium
p  p  
k B / 2m p
Freezing out
np , np
 pp -annih. (T )  H (T )
n
T 1
for nB/n=10–10, one has: T ~ 40 MeV, but Tfreeze-out ~ 20 MeV  nB/n=10–18 
significant  > 0 already at T > 40 MeV
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
17
The Sakharov Conditions
Assuming that at the Big Bang  (t=0) = 0 (baryon asymmetry is not an initial condition),
let’s recall the three Sakharov conditions for a dynamical generation of the asymmetry:
Sakharov conditions (1967) for Baryogenesis
However:
an number
initial violation
 (t=0) > 0 would be futile,
1. Baryon
2.since
C andinflation
CP violationwould
3.
have wiped out the trace of it
Departure from thermal equilibrium [DTE] (non-zero derivative for entropy)
Proofs (digression):
1.
2.
see later
examples for DTEs:
be 0 initial density of the universe with nB 0 net
tr baryon
0nB asymmetry
0
cosmic photon & neutrino backgrounds

time evolution given by: i
nucleosynthesis
 ,H  0
t
… many more




if [C,H ] = 0, or [CP,H ] = 0  [C, ] = 0, or [CP, ] = 0
since the baryon number operator is C and CP-odd:

1.




ˆ 1  (CP )Bˆ (CP )1  Bˆ
CBC
nB  tr   nB   tr C 1C  nB  tr CnBC 1   nB  0
use: tr  A  B   tr  B  A 
similar as 2. using the fact that the baryon number operator is CPT odd
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
18
(I) Baryogenesis in the Early Universe (much simplified!)
Grand unification (GUT) of the forces at ~1016 GeV
simplest GUT model, SU(5), has 52–1=24 gauge fields, of which 12 belong to SM
12 new heavy leptoquark fields, X, Y, carrying charge and color, and allowing transitions
between baryons and leptons; also: X < H(T) for T  TEW
(out of equilibrium decays)
Toy
example for of
X decays
(note that quark (antiquark) has baryon +
B=+1/3 (–1/3), and lepton has B=0)
Discovery
proton
decay, e.g., p e number
0, would
r
the
Xsupport
  u  u B
2/3
r
X   u  u B2 / 3
1r
hypothesis
baryogenesis
if direct CP violation
X   d  e of
 GUT-type

B 1/ 3
1r

X d e


B  L  r  r  0
B 1/ 3
e.g.: r  r 
n(u,d,e  )  n(u ,d ,e  )
CPT invariance holds: total decay rates are equal
At T < mX  Boltzmann-suppressed; at X < H(T) out-of-equilibrium excess develops
(the real process how an over-abundance develops is quite subtle  based on unitarity)
Only tiny CP asymmetry is needed to obtain  ~ 10–10 this way
Pitfall: larger SO(10) group required to generate necessary B – L violation  see later
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
19
(II) Baryogenesis through EW Phase Transition
Within a picosecond, at the electroweak (EW) scale (100 GeV ~ 1015 K), where
EW forces are still unified, electroweak phase transition (1st order) can occur
Non-abelian theories (like weak interaction SU(2)L or QCD) have a non-trivial
vacuum structure with an infinite number of ground states (“topological charges”).
Periodic vacuum structure of EW
theory: for Ng=3 generations, the
distance between two ground states
is ΔB = ΔL = 3
(e.g., conversion of baryons into antileptons)
E
T 0
Boltzmann-suppr.
potential
barrier
sphalerons
height of
potential barrier
Esphal. (T  0)
~ 8  13 TeV  vT 
 no proton decay
 always: Δ(B – L) = 0 !
B  N g
(BL is conserved in the SM)
0
exp. suppr. tunneling:
(ΔB+L0)~10–164 !
T 0
Wa , Higgs
(non-abelian gauge fields)
Small perturbative changes in fields around zero charge will not change B and L
Sphaleron transition rate: ~ exp(–Esphal .(T)/kBT) for T < TEW (barrier), and ~ T4 for T > TEW
(BL conserving sphaleron processes for 10 2~1012 GeV  any B+L violating asymmetry in this energy range will be washed out  requires BL violation)
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
20
(II) Baryogenesis through EW Phase Transition
In SM for T TEW, no departure from thermal equilibrium (reactions much faster than
expansion of universe, H(T))
SM CP violation (KM mechanism) needs non-zero quark masses to occur, but fermions
acquire masses only at TEW
Need 1st order phase transition at Tc ~ TEW :
discontinuous change of vT  0 Higgs 0 T , since vT = 0 for T > Tc
condensation of Higgs field at T ~ Tc
schematic view
of 1st order
phase transition:
old phase
old phase & new phase
T  Tc
T  Tc
expanding bubble (Higgs condensates)
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
new phase
T  Tc
T 1
21
(II) Baryogenesis through EW Phase Transition
Phase
transitions
Higgs potential
versus Higgs vacuum expectation value:
1st order phase
transition
V (vT )
T  Tc
potential barrier
Higgs bubble expansion
Tphase
 Tcdiagram of water
V (vT )
vT -crit
T  Tc
higher order phase
transition
T  Tc
no degenerate minima
no bubble expansion,
adiabatic switching off
of sphaleron processes
T  Tc
T  Tc
vT
Condensation of Higgs field
vT
“spontaneous” phase transition
“continuous” phase transition
( time scale ~ particle reaction, DTE )
( time scale  particle reaction, DTE )
The bubbles must get filled with more quarks than antiquarks (CPV)  Baryogenesis has
to take place outside the bubbles (since  must be conserved), while the sphaleroninduced (B+L)-violating reactions must be strongly suppressed inside the bubbles
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
22
(II) Baryogenesis through EW Phase Transition
High temperature plasma
sketch of nonlocal
EW baryogenesis:
expanding v bubble wall
q
q
symmetric phase
vT = 0
expanding v bubble wall
q
q
Higgs condensate
CP
q
q
High temperature plasma
broken phase
vT  0
sphaleron
 ( B L )
sphaleron
 ( B L )
CP
0
HHubble
symmetric phase
vT = 0
q
q
See, e.g., W. Bernreuther,
Phys. 591 (2002) 237-293
Problem: the above 1st order phase transition only for mHiggs < 73 GeV; beyond this, the
phase transition becomes of 2nd order, and the thermal instability needed for baryogenesis
(3rd Sakharov rule) is not provided
LEP-2 limit for Higgs mass: mHiggs > 114 GeV 
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
Requires SM extensions !
(SUSY could do it)
23
The Role of the CP-Violating CKM Phase
If the SM extensions do not violate CP (this would be rather unnatural), could the CKM
phase generate the observed baryogenesis ?
KM CP-violating asymmetries, dCP, must be proportional to the Jarlskog invariant J :
dCP  J  FU  FD

where: J  Im VudVcsVus Vcd

A2 6 , and:
  3.1  0.2  105

 m

  m

  m
FU  mt2  mc2  mt2  mu2  mc2  mu2
FD
2
b
 ms2
2
b
 md2
2
s
 md2


Since (some) non-zero quark masses are required, CP symmetry can only be broken where
the Higgs field has already condensed to vT  0 (i.e., electroweak symmetry is broken)
To make dCP dimensionless, we divide by dimensioned parameter D = Tc at the EW
scale (Tc = TEW ~ 100 GeV), with [D] = GeV12
d
19
dˆCP  CP

10
D12
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
  O 1010 
A. Höcker  Baryogenesis
KM CP violation seems to be
irrelevant for baryogenesis !
24
(III) Baryogenesis through Leptogenesis
Assume existence of 3 heavy right-handed (MN ~ 10101012 GeV) Majorana neutrinos Ni=1,2,3
The SU(2)LU(1)Y Lagrangian then allows lepton-number-violating decays
Ni  
lepton-number creating decays
would create rate differences (only tiny ~10–6 CPviolating asymmetry required)  needs interference !
Sakharov rule 2 :
Sakharov rule 3 :
Ni   
and
n
n
nN
n
nNequil.
n
n n
n
Departure from
thermal
equilibrium for
L=2(T) < H(T)
(to avoid L washout reactions)
at T < MN
sketch for evolution of nN /n as
universe expands (cools down):
0
MN1
T 1
Sakharov rule 1: ΔL feeds baryongenesis via rapid (B–L)-conserving sphaleron reactions !
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
25
Conclusions
Baryogenesis (most probably) requires Standard Model extension
We have discussed three mechanisms (others exist):
1)
Baryogenesis via CP-violating out-of-equilibrium decays
2)
Baryogenesis via electroweak phase transition
3)
Baryogenesis via leptogenesis
Due to heavy Higgs, electroweak phase transition (2) fails in SM  SUSY ?
GUT-type baryogenesis (1) cannot be verified in laboratory; however, proton
decay would give empirical support
Mechanism (3) seems to be most promising: to get the correct baryon
asymmetry, the light neutrino masses must lie in ranges consistent with data !
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
26
Appendix: CP Violation in the QCD Lagrangian
It was found in 1976 that the traditional perturbative QCD Lagrangian missed a term L
LQCD 

LpQCD
perturbative QCD
L ,
where:
L  
P ,T -violating
s
8
a
G
G  ,a
, and G  ,a 
Gluon field tensors
1
  G ,a
2
dual field tensor
that breaks through an axial triangle anomaly diagram the U(1)A symmetry of LpQCD , which
is not observed in nature
when classical symmetries are broken on
the quantum level, it is denoted an anomaly
a
 ,a
a
The term G
is P-and T-odd, since:
G ,a contained in LpQCD is CP-even, while G G

GG   Ea  Ba
a

2
GG   Ea  Ba
a

2

 E
P,T


2
a
a

P,T

   Ea  Ba
a
 Ba
2


color electric and magnetic fields
Relativistic invariants,
similar to electric field
tensors: F F  , F F 
  F   j  ,   F   0
Maxwell equations
This CP-violating term contributes to the EDM of the neutron:
dn
  5  1016 ecm, so that  tiny or zero
"Strong CP (finetuning) Problem"
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
27
The Strong CP Problem
Remarks:
If at least one quark were massless, L could be made to vanish; if all quarks are
massive, one has uncorrelated contributions, which have no reason to disappear
Peccei-Quinn suggested a new global, chiral UPQ(1) symmetry that is broken, with the
“axion” as pseudoscalar Goldstone boson; the axion field, a ,compensates the contribution
from L :

   a  ,a
axion coupling to SM particles is
L     a  s G
G
suppressed by symmetry-breaking
fa  8

scale (= decay constant)
QCD nonperturbative effects (“instantons”) induce a potential for a with minimum at a =  fa
The axion mass depends on the UPQ(1) symmetry-breaking scale fa
 107 GeV 
ma  
  0.62 eV ,
f
(GeV)
 a

and axion coupling strength: ga  ma
If fa of the order of the EW scale (v), ma~250 keV  excluded by collider experiments
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
A. Höcker  Baryogenesis
28
The Search for Axions (the axion is a dark matter candidate)
The axion can be made “invisible” by leaving scale and coupling free, so that one has:
ma ~ 10–12 eV up to 1 MeV  18 orders of magnitude !
Axion scale and mass, together
with the exclusion ranges from
experimental non-observation

Axion decays to 2, just as for the
0,
or in a static magnetic field:
a
f

Schematic view of
CAST experiment
at CERN:
Axion source
5th Particle Physics Workshop, Nov 20-25, Islamabad, Pakistan
Axion detection (LHC magnet)
A. Höcker  Baryogenesis
29
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