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, butany 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 forbaryogenesis, 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 evolvinguniverse but it has to be checked with specific interactions.

Thus, a cosmological evolution with B ≠ 0 and C and CPviolating particle physics model can produce a nonvanishingB . The problem is “How big is the generated B?”. Here, we need

B 0.610-9 nγ

For example, the SU(5) GUT with X and Y gauge bosoninteractions are not generating the needed magnitude whenapplied in the evolving universe. In the SU(5) GUT, twoquintet Higgs are needed for the required magnitude.So, GUTs seemed to be the theory for baryogenesis for sometime. But high temperature QFT aspects changed this viewcompletely.

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 Hooftvertex must be an SM singlet.

q1

q1

q1

q2

q2 q2q3

q3

q3

l1 l2

l3

B-L conserved

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,

The leptogenesis uses this transformation of the (B-L) number(obtained from heavy N decays) to baryon number. The ν-genesis also uses this transformation.

The leptogenesis uses this transformation of the (B-L) number(obtained from heavy N decays) to baryon number. The ν-genesis also uses this transformation.

origorig LBLLBB )(

2

1,)(

2

1

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

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-handquark singlets will potentially introduce the FCNCproblem.

But in most discussions, the smallness of mixing angleswith 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 boundTheoretically, 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 axionNelson-Barr typeFCNC

R

L

bb

t

Consider one family first.It gives all the needed features. The mass matrix is

M

JmM

03/1The entry 0 is a naturalchoice, by redfinition ofR-handed singlets.

It can be diagonalized by considering MM†

With vanishing phases,

||||||||||,||||

]|||)||][(||||)||[(|||||||2

1

||

||

22

2222222

2

2

MmmmmJmM

JmMJmMJmMm

m

Db

D

b

1

/|,

/

1|

MJD

MJb

Since J is the doublet VEV and M is a parameter or a singletVEV, the mixing angle can be sufficiently small. This is thewell-known decoupling of vectorlike quarks.

It can be generalized to three ordinary quarks and n heavy quarks.(3+n)x(3+n) matrix

can take the form by redefining R-handed b and D fields,

D

d

MJ

JMM

'

D

d

M

JMM

0

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

..* cheuXgDuXg cciei

cciDi

X1

uc

Dc

X1

uc

Dc

X1, X2uc

ec

Plus self-energy diagrams.

The interference is needed to generate a nonvanishingD number. The cross term contributes as

2*

12*1 DDee gggg

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. Thesame applies to ge1 and ge2 . Thus, the phase appearing

2*

12*1 DDee gggg

is physical. The D number generated by these is

]1

1ln[1)(

)],/1()([108

105.0

2

12

2

xxxF

m

mxxFxF

n

n

X

X

D

4. Lifetime

Decay of D proceeds via D → tW, bZ, bH0 from which we obtain

D

b

bDF

D

m

fm

fmJmJG

||,||

8

2 2

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

2/3,

22/3,

6 )107.2(

1||

)10(

1

GeVDGeVD mm

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,

2*

2 331

W

PP

M

M

g

M

H

Thus, the following fraction is expected tobe washed out via D oscillation into b,

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.

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.

GeVDDW

bP

m

ff

mM

mM

,

2162

2

2

10

5. FCNC

For the FCNC, we many consider the following:

Therefore, we obtain Therefore, we obtain

9

2

2

0

6

32

2

102

2

||3

)(

)(

103.7||;

104.1||:,

009.0||:005.0996.0,

sdFCNC

sd

D

sbsb

bb

z

eKBr

KBrfrom

zK

m

JJztreefromlXslB

zbbZ

GeVDGeVD mf

m ,4

,9 101.2

1||

108.4

1

To implement a small f naturally, we can impose a discrete symmetry. Let us introduce a parity Z2.

The discrete symmetry forbid a mixing between doublets.

We introduce a soft term, violating the discrete symmetry, which can mix them.

Z2 symmetry

,

,

:

,,,,

2

RLRLRLRL DDbb

Z

• The potential is given by

The soft term violates the Z2 symmetry. If the Z2 is exact,there is no mixing of D with b and hence D is absolutelystable: <> = v 0, <> = 0.

But the existence of the soft term violates the Z2 and a tinyVEV of is generated.

2

22

1

222

)()(

.).(),(

MchmV

smallnaturallybecanM

m

f

ff

MvmfJDqfM

vm

b

off

offRLoff

:2

/,

2

2

222

2

|J|=fmb, ε=J/MD

Typical values for mD is given by constraints.The mass of , M

2, can be superheavy.

FCNC

TeVDM ,

BproducesdecayQPossiblePossiblegenesisQ

BtoconvertePossiblePossiblegenesis

BtoconverteYesgenesisN

SphaleronLBLB

),(

),(

00

Here, the B-L number is that of light fermions. So, in theneutrino-genesis, one counts the R-handed light neutrino(R)number also in the B-L number. In the Q-genesis, whatever sphalerons doon the light lepton number, still there exists baryonnumber 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 muchheavier 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