Baryogenesis through singlet quarks: Q-genesis ---Self-tuning solutions 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  n γ 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  /α w ). 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. q1q1 q1q1 q1q1 q2q2 q2q2 q2q2 q3q3 q3q3 q3q3 l1l1 l2l2 l3l3 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.

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 T 3 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 –10 s < τ D < 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 E 6 GUT, there exist D’s in 27 F. Trinification also! 27 → → * * + 1 → (q+u c +e + ) + N 5 + (l+d c ) + (D+L 2 ) + (D c +L 1 ) +N 10

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 The entry 0 is a natural choice, by redfinition of R-handed singlets.

It can be diagonalized by considering MM † With vanishing phases, 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 can take the form by redefining R-handed b and D fields, For the estimate, we express J as |J|= f m b

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

X1X1 ucuc DcDc X1X1 ucuc DcDc X 1, X 2 ucuc ecec Plus self-energy diagrams. The interference is needed to generate a nonvanishing D number. The cross term contributes as

If we allow arbitrary phases in the Yukawa couplings, the relative phases of g D1 and g D2 can be cancelled only by the relative phase redefinition of X 2 and X 1. The same applies to g e1 and g e2. Thus, the phase  appearing is physical. The D number generated by these is

4. Lifetime Decay of D proceeds via D → tW, bZ, bH 0 from which we obtain 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 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,

Thus, the following fraction is expected to be washed out via D oscillation into b, For m D of order > 10 6 GeV, we need f< In this range, some heavy quarks are left and the sphaleon does not erase this remaining D number. For m D of order > 10 6 GeV, we need f< 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: Therefore, we obtain

To implement a small f naturally, we can impose a discrete symmetry. Let us introduce a parity Z 2. The discrete symmetry forbid a mixing between doublets. We introduce a soft term, violating the discrete symmetry, which can mix them. Z 2 symmetry

The potential is given by The soft term violates the Z 2 symmetry. If the Z 2 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 Z 2 and a tiny VEV of  is generated.

|J|=fm b, ε=J/M D Typical values for m D is given by constraints. The mass of , M  2, can be superheavy.

FCNC

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, W NR ~ (1/M T ) u c d c d c 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 Z 2 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, ν R : fermion singlets Q L +Q R : vectorlike fermion N L +N R : 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 Cambridge J. E. Kim