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Baryogenesis through singlet quarks:
Q-genesis
---Self-tuning solutions---
29. 08. 2005
COSMO-2005
Bonn
J. E. Kim
Long history
GUTS: Yoshimura, …
Kolb+Turner
Sphaleron: Kuzmin+Rubakov+Shaposhnikov, …
EW baryogenesis: cosmo-05
D. Grigoriev, T. Constandin
L. Fromme, M. Seniuch
Use global symmetry(B):
Scalars: Affleck-Dine, Davidson-Hempfling
Leptogenesis: let’s call N-genesis, Fukugita+Yanagida
ν-genesis: Dick-Lindner-Ratz, here B. Katlai.
Q-genesis: I will talk on this now.
It looks like all three fermion geneses are constrained, but
any of them are not ruled out so far.
1. Introduction
2. Heavy quark
3. Q-genesis by heavy quarks
4. Lifetime
5. FCNC
1. Introduction
Observed facts in astroparticle cosmology deal with
•CMBR
• Abundant light elements(nucleosynthesis)
• Galaxies and intergalacic molecules(baryogenesis)
• Dark matter and dark energy(?)
In this talk, we present a new type the barygenesis.
H. D. Kim, K. Morozumi, JEK, PLB 616, 108 (2005).
Sakharov’s three conditions for generating B ≠ 0
from a baryon symmetric universe:
• Existence of B ≠ 0 interaction
• C and CP violation
• These realized in a nonequilibrium state
GUTs seemed to provide the basic theoretical framework for
baryogenesis, because in most GUTs B ≠ 0 interaction is
present. Introduction of C and CP viol. is always possible
if not forbidden by some symmetry. The third condition
on non-equilibrium can be possible in the evolving
universe but it has to be checked with specific interactions.
Thus, a cosmological evolution with B ≠ 0 and C and CP
violating particle physics model can produce a nonvanishing
B . The problem is “How big is the generated B?”. Here,
we need
B  0.610-9 nγ
For example, the SU(5) GUT with X and Y gauge boson
interactions are not generating the needed magnitude when
applied in the evolving universe. In the SU(5) GUT, two
quintet Higgs are needed for the required magnitude.
So, GUTs seemed to be the theory for baryogenesis for some
time.
But high temperature QFT aspects changed this view
completely.
The spontaneously broken electroweak sector of the SM does
not allow instanton solutions. When the SU(2)W is not broken,
there are electroweak SU(2) instanton solutions. Tunneling via
these electroweak instantons is extremely suppressed, exp(2/αw). This tunneling amplitude is the zero temperature
estimate. At high temperature where the electroweak phase
transition occurs, the transition rate can be huge, and in
cosmology this effect must be considered. (Kuzmin, Rubakov,
Shaposhnikov)
This sphaleron effect transforms SU(2) doublets. The ‘t Hooft
vertex must be an SM singlet.
l1
l2
q1
l3
q1
B-L conserved
q1
q3
q2
q3
q2
q2
q3
The baryon number violating interaction washes out the
baryon asymmetry produced during the GUT era. Since the
sphaleon interaction violates B+L but conserves B-L, if
there were a net B-L, there results a baryon asymmetry
below the weak scale. The partition of (B-L) into B and L
below the electroweak scale is the following if the
complete washout of B+L is achieved,
1
B  ( B  L)orig ,
2
1
L  ( B  L)
2
orig
The leptogenesis uses this transformation of the (BL) number(obtained from heavy N decays) to baryon
number. The ν-genesis also uses this transformation.
Thus, in some L to B transformation model, we
need to generate a net (B-L) number at the
GUT scale (Q-genesis does not need this).
The SU(5) GUT conserves B-L and hence
cannot generate a net B-L.
So, for the baryon number generation one has
to go beyond the SU(5) GUT.
Three examples from fermions proposed so far:
1. Leptogenesis, 2. Neutrino genesis, 3. Q-genesis
2. Introduction of heavy quarks
• SU(2) singlets avoid the sphaleron process.
• So singlet quarks survive the electroweak era.
※ They must mix with light quarks so that after
the electroweak phase transition they can
generate the quark(B/3) number.
※ They must be sufficiently long lived.
※ Of course, a correct order of B ≠ 0 should
be generated.
The SU(2) singlet quarks were considered before
in connection with
 FCNC (Kang-K, Glashow-Weinberg)
 For the recent BELLE data (Handoko-Morozumi)
For the absence of FCNC at tree level, the ew isospin T3
eigenvalues must be the same. Thus, introducing L-hand
quark singlets will potentially introduce the FCNC
problem.
But in most discussions, the smallness of mixing angles
with singlet quarks has been overlooked. Since the quark
singlets can be superheavy compared to 100 GeV, the small
mixing angles are natural, rather than being unnatural.
For definiteness, let us consider Q= -1/3 heavy quark D.
1. D generation mechanism
2. 10 –10 s < τD < 1 s
3. Sphaleron should not wash out all D
4. Satisfy FCNC bound
Theoretically, is it natural to introduce such a heavy
quark(s)?
In E6 GUT, there exist D’s in 27F. Trinification also!
27 → 16 + 10 + 1 → 10 + 5* + 1 + 5 + 5* + 1
→ (q+uc+e+) + N5 + (l+dc) + (D+L2) + (Dc+L1) +N10
When we consider this kind of vector-like quarks, there are
three immediate related physical problems to deal with.
Heavy quark axionNelson-Barr typeFCNC
Consider one family first.
It gives all the needed
features. The mass matrix is
m J 

M 1/ 3  
0 M
t
 
 b L
bR
The entry 0 is a natural
choice, by redfinition of
R-handed singlets.
It can be diagonalized by considering MM†
 | mb |2  1
2
2
2
2
2
2
2





|
M
|

|
m
|

|
J
|

[(|
M
|

|
m
|)

|
J
|
][(|
M
|

|
m
|)

|
J
|
]
 | m |2  2
 D 
| M |2 | m |2 , | mJ |

| mb || m | | mD || M |
With vanishing phases,
| b

 1 

 ,
 J / M 
| D

J /M 


 1 
Since J is the doublet VEV and M is a parameter or a singlet
VEV, the mixing angle can be sufficiently small. This is the
well-known decoupling of vectorlike quarks.
It can be generalized to three ordinary quarks and n heavy quarks.
(3+n)x(3+n) matrix
M

 Md

 J'
J 

MD 
can take the form by redefining R-handed b and D fields,
M

 Md

 0
J 

MD 
For the estimate, we express J as
|J|= f mb
3. Q-genesis by heavy quarks
Hyung Do Kim, Takuya Morozumi, JEK(PLB616, 108, 2005)
• Generation of D number is done as usual in GUTs
cosmology through the Sakharov mechanism.
• In the end, D number is identified as 3B number.
The relevant interaction we introduce is
g Di X i u D  g ei X u e  h.c.
c
c
* c c
i
uc
X1
uc
X1
ec
uc
Dc
X1, X2
Dc
Plus self-energy diagrams.
The interference is needed to generate a nonvanishing
D number. The cross term contributes as
*
e1 e 2
*
D1 D 2
g g g g
If we allow arbitrary phases in the Yukawa couplings,
the relative phases of gD1 and gD2 can be cancelled only
by the relative phase redefinition of X2 and X1. The
same applies to ge1 and ge2 . Thus, the phase  appearing
*
e1 e 2
*
D1 D 2
g g g g
is physical. The D number generated by these is
nD
 0.5  10 2 
n

  10 2 [ F ( x )  F (1 / x )],
8
1
F ( x )  1  x ln[ 1  ]
x
x
mX 1
mX 2
4. Lifetime
Decay of D proceeds via
D → tW, bZ, bH0
from which we obtain
2GF
D 
| J |2 mD ,
8
fmb

mD
| J | fmb
The lifetime of D must be made longer than 2x10 –11 s.
And should be shorter than 1 s.
[2x10 –11 s , 1 s]
This gives
1
6
(10 mD,GeV )
3/ 2
1
|  |
2
3/ 2
(2.7 10 mD,GeV )
The mixing of D with b is of order ε. For one period of
oscillation, we expect that a fraction | ε |2 of D is
expected to transform to b. Since the period keeping the
electroweak phase in cosmology is of order,
1
3M P2


H

3 MP
g* M W2
Thus, the following fraction is expected to
be washed out via D oscillation into b,
2
b
2
M Pm 2
f
16
 2
f  10
M W mD
mD ,GeV
For mD of order > 106 GeV, we need f<10-5 .
In this range, some heavy quarks are left and
the sphaleon does not erase this remaining D
number.
5. FCNC
For the FCNC, we many consider the following:
Z  bb ,
zbb  0.996  0.005 :
B  Xsl  l  ,
from
|  |2  0.009
| zsb |
tree :
JbJs
 1.4  10 3
2
mD
K     ; | zsd | 7.3  106
from
9
Br ( K     ) FCNC 3 | zsd |2  2  10

Br ( K    0 e  )
22
Therefore, we obtain
1
4.8  10
9
mD ,GeV
| f |
1
2.1  104 mD ,GeV
Z2 symmetry
To implement a small f naturally, we can
impose a discrete symmetry. Let us
introduce a parity Z2.
Z2 :
bL,R  bL,R
, DL,R   DL,R
  ,
  
The discrete symmetry forbid a mixing between doublets.
We introduce a soft term, violating the discrete symmetry,
which can mix them.
• The potential is given by
V ( , )  ( m2    h.c.)   2    M 2  
 1 (   )2  2 (   )2    
The soft term violates the Z2 symmetry. If the Z2 is exact,
there is no mixing of D with b and hence D is absolutely
stable: <> = v  0, <> = 0.
But the existence of the soft term violates the Z2 and a tiny
VEV of  is generated.
m2 v
  2,
M
f off qLDR
2 f off m2
f 
f b M 2
 J  f off m2 v / M 2
: can be naturally
small
|J|=fmb, ε=J/MD
Typical values for mD is given by constraints.
The mass of , M2, can be superheavy.
FCNC

M D ,TeV
BL0 BL0
N  genesis
Sphaleron
Yes
( , e)  convert  to  B
  genesis
Possible
Possible
( , e)  convert  to  B
Q  genesis
Possible
Possible
Q  decay  produces  B
Here, the B-L number is that of light fermions. So, in the
neutrino-genesis, one counts the R-handed light neutrino(R)
number also in the B-L number.
In the Q-genesis, whatever sphalerons do
on the light lepton number, still there exists baryon
number generation from the Q decay.
The closest similar work is
Davidson+Hempfling (PLB 391, 287 (’97)),
where SUSY is used with B carrying singlet scalars S,
WNR ~ (1/MT) uc dc dc S + h.c.
where T is our heavy quark D. But here D is much
heavier than S.
5. Conclusion
• We presented a new mechanism for baryogenesis:
the Q-genesis.
• There are constraints on the parameters. There is a
reasonable parameter space for this to be realized.
With a Z2 discrete symmetry, the smallness of the
parameters is implemented naturally.
• N-genesis and ν–genesis seem to be the plausible ones
since the observed neutrino masses need R-handed
neutrinos. Survival hypothesis sides with N-genesis.
Q-genesis depends on the unobserved Q, but this may
be needed in solutions of the strong CP problem. Also, it
appears in E6 and trinification GUTs.
One should consider all possibilities of SM singlets
and vector-like representations for BAU:
N, νR: fermion singlets
QL+QR: vectorlike fermion
NL+NR: vectorlike fermion with Dirac mass, not
studied yet but certainly possible
S: singlet scalar carrying B number
(cf. Colored scalars: Affleck-Dine)
A new type baryogenesis: Q-genesis
---Self-tuning solutions---
25.01.2005
Cambridge
J. E. Kim