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Lecture-06 Baryogenesis
Ping He
ITP.CAS.CN
2006.04.21
http://power.itp.ac.cn/~hep/cosmology.htm
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6.1 Overview
Grand unification (Grand unified theories – GUTs): to unify the strong,
weak, and electromagnetic interactions and the quarks and leptons within
the framework of a gauge field theory based upon a simple or semi-simple,
non-Abelian symmetry group, e.g., SU(5), SO(10), E6.
Standard model: SU (3)c  SU (2) L  U (1)Y
GUTs predictions:
(1) new interactions violate baryon number B and lepton L conservations,
-- instability of the proton  proton decay;
(2) large amount of superheavy magnetic monopoles.
The B-violation interactions are extremely weak today, due to
the longevity of proton.
GB
M 2  1030 GeV 2 ,
GF  1.1664 105 GeV 2
(Eq-6.1)
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M: the energy scale of unification
M  1014 GeV
Baryogenesis, based on these B-violation interactions:
(1) can explain how the B-symmetry Universe can evolve into
the B-asymmetry Universe;
(2) can explain the present baryon-to-photon ratio;
(3) can provide a mechanism to unify quarks and leptons.
Predictions from baryogenesis based on GUTs conflicts with standard
cosmology, that there are too much superheavy monopoles that are
not observed.
 inflation
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6.2 Evidence for a Baryon Asymmetry
Anti-matter is rare on Earth, only in accelerator or cosmic ray.
Also rare in the solar system, cosmic ray coming from the galaxy indicates
that the galaxy is not anti-matter.
On large scales: if matter and anti-matter co-exist, then there are strong
gray emission from nucleon-antinucleon annihilation. The absence of
such gray flux indicates the asymmetry of matter and anti-matter.
In a locally-baryon-symmetric Universe nucleons and antinucleons remain
in chemical equilibrium down to T ~ 22 MeV, when nb / s  nb / s 7 1020 ,
In order to avoid the “annihilation catastrophe” a physical mechanism
11
should operate at T > 38 MeV, so that nb / s  nb / s 8 10 .
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The most reasonable conclusion then is that the Universe at early times
T>38MeV possessed an asymmetry between baryons and antibaryons
which prevented the annihilation catastrophe.
At high temperatures T>1GeV, thermal quark-antiquark pairs were
present in great numbers, nq ~ nq ~ ng , so that the baryon asymmetry
observed today corresponds to a tiny quark-antiquark asymmetry at
early times ( t  10 6 s ).
nq  nq
nq
3 108
(Eq-6.2)
Baryogenesis scenario provides a very attractive means by which this
tiny asymmetry can arise from initially baryon symmetric Universe.
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6.3 The Basic Picture
Three ingredients to generate non-zero baryon number from an initially
baryon symmetric state, i.e., Sakharov Criteria:
(1) Violation of Baryon number (B) symmetry;
(2) Violation of C and CP symmetries;
(3) A departure from thermal equilibrium.
1). It’s obviously. If baryon number is conserved in all interactions,
the present baryon asymmetry can only reflect asymmetric initial
conditions.
2). Without C and CP violation, B-nonconserving interactions will produce
baryon and antibaryon excesses at the same rate  zero net baryon
number.
3). In chemical equilibrium, the chemical potentials associated with all
non-conserved quantum numbers vanish, that is, b  b  0,
by CPT invariance, mb  mb , so, f (b)  f (b )  [1  exp(( p 2  m2 ) / T )]1
hence
nb  nb , nB  nb  nb  0
(Eq-6.3)
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A toy model: to illustrate the mechanics of baryogenesis.
particle
final state
branching ratio
B
X

qq
r
2/3
X

ql
1- r
-1/3
X

qq
r
-2/3
X

ql
1- r
1/3
Since the two final states have different baryon number,  B-nonconservation.
If C and CP are violated, then r  r .
symmetric initial
conditions
X and X bosons.
The mean net baryons produced by X is: BX  r (2 / 3)  (1  r )(1/ 3)
If a box containing equal numbers of
produced by X :
BX  r (2 / 3)  (1  r )(1/ 3)
The mean net baryon number produced by a pair of X and X decay is
  BX  BX  r  r  0
(C and CP violated)
(Eq-6.4) 7
 can be treated as indication of the degree of C and CP violation.
When T
mX , X and X can decay, but can also produce in pair
in thermal collision, then:
nX  nX
If always in thermal equilibrium, the process that produces baryon excess
balance the one that perishes baryon  nb  nb
when out-of-equilibrium (  
H ), due to B, C and CP violation,
nb  nb

(Eq-6.5)
The asymmetry can be roughly estimated in the following way
nb  nb
nX
A

nb
nb

(Eq-6.6)
The correct way to do so should be handled by Boltzmann equation,
which may have deviations of several orders of magnitude.
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6.4 Concluding Remarks
(1) Sakharov Three Criteria, but notice the scenario of spontaneous
baryogenesis;
(2) The precise evolution of the baryon asymmetry is handled by
Boltzmann Equation;
(3) Lepton-genesis can be treated in a similar way;
(4) The current GUTs are not successful.
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References
• E.W. Kolb & M.S. Turner, The Early
Universe, Addison-Wesley Publishing
Company, 1993
• D. Bailin & A. Love, Cosmology in Gauge
Field Theory and String Theory, IoP
Publishing, 2004
• 俞允强，热大爆炸宇宙学，北京大学出版
社，2001
• 范祖辉，Course Notes on Physical
Cosmology, See this site.
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