Leptogenesis with dark matter

Transcription

1 Leptogenesis with dark matter This talk is based on my work: Pei-Hong Gu, NPB 872, 38 (2013)

2 Outline 1. Introduction 2. Common origin of Dirac neutrino masses, baryon asymmetry and dark matter 3. Summary

3 Introduction Although the SU(3) c SU(2) L U(1) Y standard model is a very successful theory, new physics beyond the standard model is necessary. L = µ 2 (φ φ) + λ(φ φ) 2 +(D µ φ) D µ φ + i q L γ µ D µ q L + i d R γ µ D µ d R + iū R γ µ D µ u R +i γ µ D µ + iē R γ µ D µ e R y u q L φu R y d q L φd R y e φe R + H.c.. φ(1, 2, 1) = [ φ 0 φ φ(1, 2, +1) = iτ 2 φ ; ], q L (3, 2, ) = [ ul d L ], d R (3, 1, 2 3 ), u R (3, 1, ); (1, 2, 1) = e R (1, 1, 2). [ νl e L ], D µ = µ + ig 3 8 a=1 λ a 2 Ga µ + ig 2 3 a=1 τ a 2 W µ a + ig Y 1 2 B µ

4 Neutrino masses In the standard model, the charged fermions obtain their masses through the Yukawa couplings to the Higgs scalar, while the neutral neutrinos have no such Yukawa couplings and hence keep massless, m d = y d φ 0, m u = y u φ 0, m e = y e φ 0 with φ GeV. However, variable neutrino oscillation experiments (Super-K, K2K; SNO, KamLAND; Daya Bay;...) have established the phenomenon of massive and mixing neutrinos. We need extend the standard model to explain the neutrino masses! The simplest way to induce the neutrino masses seems to introduce some right-handed neutrinos ν R (1, 1, 0), L y ν φν R + H.c. = m ν = y ν φ 0 = y ν < O(10 12 ) for m ν < O(0.1 ev)

5 The most popular scheme for generating the small neutrino masses is to consider the type- I (Minkowski, 77 ; Yanagida, 79 ; Gell-Mann, Ramond, Slansky, 79 ; Glashow, 80 ; Mohapatra, Senjanović, 80.), type-ii (Magg, Wetterich, 80 ; Schechter, Valle, 80 ; Cheng, Li, 80 ; Lazarides, Shafi, Wetterich, 81 ; Mohapatra, Senjanović, 81.) type-iii (Foot, Lew, He, 89.) seesaw mechanisms or their combinations. Type-I seesaw : L y N φn R 1 2 M N N c R N R + H.c. m ν = y N Type-II seesaw : L M 2 Tr( ) µφ T iτ 2 φ 1 2 f l c L iτ 2 + H.c. m ν = f µ φ 0 2 Type-III seesaw : L y T l c L iτ 2 T L φ 1 2 M T Tr(iτ 2 T c L iτ 2 T L ) + H.c. m ν = y T N R (1, 1, 0), (1, 3, +1) = [ 1 2 δ + δ ++ ] δ 0 1 δ + 2, T L (1, 3, 0) = [ 2 1 TL 0 T + L T L 1 T 0 2 L ]. φ 0 2 M N y T N. M 2. φ 0 2 M T y T. φ 0 φ 0 φ 0 φ 0 φ 0 φ 0 δ 0 ν L ν L ν L ν L ν L ν L N R N R T 0 L T 0 L

6 Baryon asymmetry In our universe, there is no primordial antimatter. This is the so-called matter-antimatter asymmetry, which is the same as a baryon asymmetry. The cosmological observations have precisely measured (e.g. Planck collaboration, ), Ω B h 2 = ρ B ρ c h 2 = ± , ρ B = n B m p, η B = n B n γ (Ω B h 2 ) = (5.91 ± 0.08) We need a dynamical baryogenesis mechanism to understand this matter-antimatter asymmetry because (i) any causal, Lorentz invariant, quantum theory requires that all particles should come in particle-antiparticle pairs. (ii) any initial matter-antimatter asymmetry cannot survive after an inflation epoch

7 If CPT (C charge conjugation, P parity, T time reversal.) is invariant, any baryogenesis mechanisms should satisfy the Sakharov conditions (Sakharov 67 ): (i) baryon number nonconservation, (ii) C and CP violation, (iii) departure from equilibrium. B C B for q L(R) B CP B for q L C q c L(R) CP q c R = n b n b = 1 3 (n q L n ql + n qr n qr ) C,CP 0. B = Tr(e H T B) = Tr[e H T (CP T ) 1 B(CP T )] = Tr[e H T ( B)] = B B =

8 At the classical level, the standard model conserves the baryon (B) and lepton (L) numbers. However, t Hooft pointed out that both B and L should be violated by quantum effects ( t Hooft, 76.). The transition of the baryon and lepton numbers from one vacuum to the next vacuum is µ J µ B = µ J µ L = N f g π 2ɛ µνρσ Tr (W µν W ρσ ) B = L = N f, (B L) = 0. At zero temperature, the baryon and lepton number violating processes via a tunneling between the topologically distinct vacua are highly suppressed. However, such sphaleron processes could become efficient during the temperatures near and above the electroweak phase transition (Kuzmin, Rubakov, Shaposhnikov, 85.), 100 GeV < T < GeV

9 In the standard model, the sphaleron processes, the CKM phase and the electroweak phase transition can fulfill the three Sakharov conditions to realize an electroweak baryogenesis scenario (e.g. Morrissey, Ramsey-Musolf, 12.). Unfortunately, this electroweak baryogenesis cannot explain the observed value of the baryon asymmetry because (i) the Higgs mass is too heavy and hence the electroweak phase transition is not strongly first-order, (ii) the CP violation from the CKM matrix is not sufficient. We need extend the standard model to explain the baryon asymmetry! Due to the sphaleron processes, any baryogenesis mechanisms above the electroweak scale should produce a (B L)-asymmetry, which is a pure B-asymmetry, a pure L- asymmetry, or a combination of B-asymmetry and L-asymmetry. Alternatively, the baryogenesis mechanisms must generate a B-asymmetry if they work at a lower scale where the sphaleron processes are not active

10 Currently, the leptogenesis (Fukugita, Yanagida, 86.) mechanism within the seesaw context is one of the most attractive baryogenesis scenarios, because it can simultaneously explain the matter-antimatter asymmetry and the small neutrino masses. Specifically, an L-asymmetry, which is equivalent to a (B L = L)-asymmetry in the absence of a B- asymmetry, can be firstly produced by some lepton number violating interactions which are also responsible for giving the small neutrino masses, and then can be partially converted to a B-asymmetry. φ N i φ N i φ N j φ N i N j φ l c L l c L φ l c L N i φ N i φ N j φ N i N j φ

11 Dark matter Cosmology and astrophysics have provided several convincing evidences of the existence of dark matter. For example, the observation on the galactic rotation curves implies the existence of a dark halo. Currently, a number of cosmological data have precisely measured the amount of the dark matter in the present universe (e.g. Planck collaboration, ), Ω DM h 2 = ρ DM ρ c h 2 = ± , ρ DM = n DM m DM. A dark matter candidate must satisfy several conditions: (i) keeping stable on the cosmological time scale, (ii) interacting very weakly with electromagnetic radiation, (iii) having the right relic density. We need extend the standard model to explain the dark matter!

12 There have been many dark matter models. However, the true identity of dark matter still remains a mystery. In the most popular dark matter scenario, the dark matter particles can annihilate into some lighter species such as the standard model fields, and will leave a relic density after their annihilations go out of equilibrium at a frozen temperature. It is expected to find the dark matter particles in the future: (i) Colliders: the dark matter particles may be produced as a missing energy; (ii) Indirect search: the dark matter particles may annihilate and/or decay into the standard model species; (iii) Direct search: the dark matter particles may scatter off nucleons

13 Common origin of Dirac neutrino masses, baryon asymmetry and dark matter It is intriguing that the baryonic and dark matter contribute comparable energy densities to the present universe (e.g. Planck collaboration, ), Ω DM h 2 : Ω B h 2 = ( ± ) : ( ± ) 5. This coincidence can be elegantly explained if (i) the dark matter relic density is an asymmetry between dark matter and antimatter, (ii) the dark matter asymmetry has a common origin with the baryon asymmetry. There have been a lot of papers (Nussinov, 85 ; Barr, Chivulula, Farhi, 90 ; Barr, 91 ; Kaplan, 92 ; Dodelson, Greene, Widrow, 92 ; Kuzmin, 97 ; Kitano, Low, 05 ; Agashe, Servant, 05 ; Cosme, Lopez Honorez, Tytgat, 05 ; PHG, Sarkar, Zhang, 09 ; PHG, Sarkar, 09; An, Chen, Mohapatra, Zhang, 09 ; An, Chen,Mohapatra, Nussinov, Zhang, 10 ; Davoudiasl, Morrissey, Sigurdson, Tulin, 10 ; PHG, Lindner, Sarkar, Zhang, 10 ; Blennow, Dasgupta, Fernandez-Martinez, Rius, 10 ; McDonald, 10 ; Hall, March-Russell, West, 10 ; Dutta, Kumar, 11 ; Falkowski, Ruderman, Volansky, 11 ; Haba, Matsumoto, Sato, 11 ; Graesser, Shoemaker, Vecchi, 11 ; Frandsen, Sarkar, Schmidt-Hoberg, 11 ; McDermott, Yu, Zurek, 11 ; Iminniyaz, Drees, Chen, 11 ; Bell, Petraki, Shoemaker, Volkas, 11 ; March- Russell, McCullough, 11 ; Davoudiasl, Morrissey, Sigurdson, Tulin, 11 ; Cui, Randall, Shuve, 11 ; Arina, Sahu, 11 ; Cirelli, Panci, Servant, Zaharijas, 11 ; Petraki, Trodden, Volkas, 11 ; Blennow, Fernandez-Martinez, Rendondo, Serra, 12 ; PHG, 12 ; PHG, 13 ;...) studying the asymmetric dark matter scenarios

14 The Dirac neutrino masses, the baryon asymmetry and the dark matter can have a common origin (PHG, Nucl. Phys. B 872, 38 (2013).). SU(3) c SU(2) L U(1) Y SU(3) c SU(2) L U(1) Y ordinary sector Y ukawa scalar messenger sector Y ukawa scalar dark sector common origin baryon asymmetry neutrino masses dark matter

15 The ordinary and dark sectors q L (3, 2, ) = [ ul d L ] q L (3, 2, 1 3 ) = [ d L u L ], d R (3, 1, 2 3 ) d R (3, 1, +2 3 ), (1, 2, 1) = u R (3, 1, ) u R (3, 1, 4 3 ) ; [ νl e L ] l L (3, 2, +1) = [ e L ν L ], e R (1, 1, 2) e R (1, 1, +2) ; [ φ 0 ] [ φ + ] φ(1, 2, 1) = φ 0 φ (3, 2, +1) = φ 0, δ(1, 1, 4) δ (1, 1, +4) ; Like the hypercharges, the baryon and lepton numbers of the dark fields are assumed opposite to those of the ordinary fields

16 The scalars will develop their vacuum expectation values as below, φ [ 0 φ 0 ] φ [ φ 0 0 ] 174 GeV, δ δ 0, to drive the expected symmetry breaking pattern: SU(3) c SU(2) L U(1) Y φ SU(3) c U(1) em, SU(3) c SU(2) L U(1) Y φ SU(3) c U(1) em δ SU(3) c. The dark photon will become massive while the ordinary photon will keep massless

17 Analogous to the ordinary Yukawa couplings, L (y d ) ij q Li φd Rj (y u ) ij q Li φu Rj (y e ) ij i φe Rj (y δ ) ij δē Ri e c Rj + H.c., the dark Yukawa couplings can be given by L (y d ) ij q Li φ d Rj (y u ) ij q Li φ u Rj (y e ) ij l Li φ e Rj (y δ ) ij δ ē Ri e c Rj + H.c.. We can read the Dirac masses of the ordinary and dark fermions, respectively, m d = y d φ m d = y d φ, m u = y u φ m u = y u φ, m e = y e φ m e = y e φ. The dark charged leptons should be the so-called quasi-dirac particles since they also have a small Majorana mass term, δm e = y δ δ m e

18 The messenger sector The messenger sector can be composed of some gauge-singlet fermions, { NR with a lepton number L = +1, N R with a lepton number L = 1. In addition to their kinetic terms, the gauge-singlet fermions are only allowed to have the lepton number conserving interactions, L (y N ) ij i φn Rj (y N ) ij l Li φ N Rj (M N ) ij N c Ri N Rj + H.c.. The gauge-singlet fermions can form the Dirac fermions, with a diagonal and real mass matrix, i.e. N i = N Ri + N c Ri, M N = diag{m N1, M N2,...}

19 The messenger sector can be also composed of [SU(2) L SU(2) L ]-bidoublet Higgs scalars, Σ a (1, 2, 1)(1, 2, +1) = [ σ + σ 0 σ 0 σ ] a. Here the first and second parentheses stand for the quantum numbers under the ordinary and dark gauge groups, respectively. The [SU(2) L SU(2) L ]-bidoublet Higgs scalars Σ a don t carry any lepton numbers. Their lepton number conserving terms include L f a Σ a l c L ρ a φ Σ a φ + H.c. M 2 Σ a Tr(Σ a Σ a )

20 Neutrino mass generation If the messenger sector only contains the gauge-singlet fermions, the mass matrix involving the ordinary and dark neutrinos should be L [ ν L N c R ] [ 0 y N φ y T N φ M N ] [ ν c L N R ] + H.c.. We can block diagonalize the above mass matrix to be L [ ν L N c R ] [ m ν 0 0 M N ] [ ν c L N R as long as the seesaw condition is satisfied, i.e. ] y N φ, y N φ M N. + H.c. with m ν = y N φ φ M N y T N mi ν, The ordinary and dark neutrinos thus will form three light Dirac neutrinos

21 We can also understand the Dirac neutrino masses by the figure as below, φ 0 φ 0 ν L N R N R ν L This mechanism for generating the Dirac neutrino masses may be named as the type-i Dirac seesaw, since it is similar with the usual type-i seesaw for generating the Majorana neutrino masses. The Dirac neutrino mass matrix should be rank-1 and have one nonzero eigenvalue if there is only one gauge-singlet Dirac fermion. To explain the neutrino oscillation data, the neutrino mass matrix at least should be rank-2 and have two nonzero eigenvalues. We hence need two or more gauge-singlet Dirac fermions

22 If the messenger sector only contains the [SU(2) L SU(2) ]-bidoublet Higgs scalars L Σ a, we can also obtain the light Dirac neutrinos in a natural way. Specifically, the Higgs bidoublets can pick up their seesaw-suppressed vacuum expectation values: Σ a = [ 0 σ 0 a 0 0 ] ρ a φ φ M 2 Σ a φ, φ, and then the ordinary and dark neutrinos can acquire their Dirac masses, L m ν ν L ν c L + H.c. with m ν = a f a Σ a a m IIa ν m II ν. φ 0 φ 0 As shown in the right figure, the above mechanism for the Dirac neutrino masses is very similar to the usual type-ii seesaw for the Majorana neutrino masses. So, it may be named as the type-ii Dirac seesaw. ν L σ 0 a ν L

23 If the messenger sector contains not only the gauge-singlet fermions but also the Higgs bidoublets, the masses involving the ordinary and dark neutrinos should be L [ ν L N c R ] [ a f a Σ a y N φ y T N φ M N ] [ ν c L N R ] + H.c.. Under the seesaw condition, f a Σ a y N φ, y N φ M N, a the masses between the ordinary and dark neutrinos should be a sum of the type-i Dirac seesaw and the type-ii Dirac seesaw, i.e. L m ν ν L ν L c + H.c. with m ν = mi ν + mii ν = y φ φ N yn T M N a f a ρ a φ φ M 2 Σ a

24 Ordinary and dark lepton asymmetries l L N i φ N i φ N j φ l c L l c L N i φ N i φ N j φ In the type-i Dirac seesaw context, the lepton number conserving decays of the gaugesinglet Dirac fermions N i can simultaneously generate a lepton asymmetry η ll in the [SU(2) L ]-doublet leptons and an opposite lepton asymmetry η l in the [SU(2) ]-doublet L L leptons l L, i.e. η ll = η l L ε Ni

25 The CP asymmetry ε Ni can be calculated at one-loop order, ε Ni = Γ N i φ Γ N c i lc L φ Γ Ni = Γ N c i l L φ Γ Ni l c L φ Γ Ni = 1 4π ] Im [(y N y N ) ij (y N y N ) ij M Ni M Nj (y N y N ) ii + (y N y N ) ii MN 2 M 2, j N i j i with Γ Ni being the decay width, Γ Ni = Γ Ni φ + Γ N i l c L φ = Γ N c i lc L φ + Γ N c i l L φ = 1 16π [(y N y N ) ii + (y N y N ) ii ]M Ni. At least two gauge-singlet Dirac fermions should be introduced to give a nonzero CP asymmetry ε Ni

26 φ Σ a Σ a Σ b l L φ l L φ φ Σ a Σ a φ l L Σ b φ In the type-ii Dirac seesaw context, the lepton number conserving decays of the [SU(2) L SU(2) ]-bidoublet Higgs scalars L Σ a can simultaneously generate a lepton asymmetry η ll in the [SU(2)L ]-doublet leptons and an opposite lepton asymmetry η l in the [SU(2) ]- L L doublet leptons l L, i.e. η ll = η l L ε Σa

27 The CP asymmetry ε Σa can be calculated at one-loop order, ε Σa = Γ Σ a l L Γ Σ a l c L l c L Γ Σa = Γ Σ a φ φ Γ Σa φφ Γ Σa = 1 4π [ ( )] Im Tr f b f a ) Tr (f af a b a + ρ2 a M 2 Σ a ρ b ρ a M 2 Σ b M 2 Σ a, with Γ Σa being the decay width, Γ Σa = Γ Σa l + Γ L Σa φφ = Γ Σ a lc L l c L + Γ Σ a φ φ = 1 16π [ Tr ( f a f a ) + ρ 2 a M 2 Σ a ] M Σa. Note at least two [SU(2) L SU(2) L ]-bidoublet Higgs scalars should be introduced to give a nonzero CP asymmetry ε Σa

28 N i φ N i l L φ N j φ N i l L φ Σ a φ l c L l c L l c L N i φ N i φ N j φ N i φ Σ a φ In the type-i+ii Dirac seesaw context, the CP asymmetry ε Ni in the decays of the gaugesinglet Dirac fermions N i should be ε Ni = 1 4π +2 Im 1 [ ] (y N y N ) ii + Im (y (y N N y N ) ii y N ) M Ni M Nj ij (y N y N ) ij M 2 j i N M 2 j N i [ ( )]} [ ] (y N f a y N ) ρa ii ln. M Ni 1 M 2 Σ a M 2 N i 1 + M 2 N i M 2 Σ a

29 φ φ Σ a l L Σ a φ Σ b l L Σ a φ N i l L φ φ φ Σ a φ Σ a l L Σ b φ Σ a l L N i φ In the type-i+ii Dirac seesaw context, the CP asymmetry ε Σa bidoublets Σ a should be in the decays of the Higgs ε Σa = 1 4π + i 1 Tr(f af a ) + ρ2 a M 2 Σ a Im Im b a [ (y N f a y N ) ii] ρa M Ni M 2 Σ a [ ( )] Tr f b f a ρ b ρ a MΣ 2 M 2 b Σ a ( ln 1 + M 2 Σ a M 2 N i )}

30 Ordinary and dark baryon asymmetries The ordinary lepton asymmetry η ll and the dark lepton asymmetry η l L other after they are produced by the decays of the messenger fields. will decouple each The dark SU(2) L sphaleron processes will partially transfer the dark lepton asymmetry η l L to a dark baryon asymmetry η B, η B = C η l. L while the ordinary SU(2) L sphaleron processes will partially transfer the ordinary lepton asymmetry η ll to an ordinary baryon asymmetry η B, η B = Cη ll. Note there will be a lepton number violating Majorana mass term of the dark charged leptons after the U(1) em symmetry is broken. The U(1) em symmetry breaking and then the lepton number violation should appear at a lower temperature, where the SU(2) L sphaleron processes have become very weak, to avoid the washout of the dark baryon asymmetry

31 The exact relation between the baryon and lepton numbers can be calculated by means of the analysis of the chemical potentials. The excess of a particle i over its antiparticle can be described by the net number density (e.g. Kolb, Turner, The Early Universe.), n i = n + i n i = { 1 6 g i T 3 ( µ i T ) for fermion, 1 3 g i T 3 ( µ i T ) for boson, n B = (n qi + n ui + n di ), i=1 n L = 3 (n li + n ei ). i=

32 A B L asymmetry can be partially converted into a baryon asymmetry (Kuzmin, Rubakov, Shaposhnikov, 85.). Yukawa : µ q + µ u + µ φ = 0, µ q + µ d µ φ = 0, µ l + µ e µ φ = 0, Hypercharge : 3(µ q + 2µ u µ d µ l µ e ) 2µ φ = 0, Sphalerons : 3(3µ q + µ l ) = 0, n B = 1 6 T 2 3 i=1 (2µ q + µ u + µ d ) = 2 3 µ l T 2 n L = 1 6 T 2 3 i=1 (2µ l + µ e ) = µ l T 2 n B = C(n B n 28 L ) with C = 79. Yukawa : µ q + µ u + µ φ = 0, µ q + µ d µ φ = 0, µ l + µ e µ φ = 0, µ δ 2µ e = 0 ; Hypercharge : 3( µ q 2µ u + µ d + µ l + µ e ) + 2µ φ + 4µ δ = 0 ; Sphalerons : 3(3µ q + µ l ) = 0 ; n B = 1 6 T 2 3 i=1 (2µ q + µ u + µ d ) = 2 3 µ l T 2, [ n L = 1 6 T 3 ] 2 i=1 (2µ l + µ e ) + 4µ δ = 3 2 µ l T 2 n B = C (n B n L ) with C =

33 Predictive dark matter mass The U(1) Y and U(1) Y gauge fields can have a kinetic mixing (Foot, He, 91.), L 1 4 B µνb µν 1 4 B µν B µν ɛ 2 B µνb µν = 1 4 B µν B µν 1 4 B µν B µν with B µ = B µ + ɛb µ, B µ = 1 ɛ 2 B µ. We then can define the orthogonal fields, A µ = W 3 µ s W + B µ c W, Z µ = W 3 µ c W B µ s W, A µ = W 3 µ s W + B µ c W, Z µ = W 3 µ c W B µ s W, among which the field A is exactly massless and is the ordinary photon, while the dark photon A is massive and mixes with the Z and Z bosons

34 For ɛ 1 and Σ, δ φ φ, the mass eigenstates of the A, Z and Z bosons can approximate to  A ɛs W c W Z, Ẑ Z + ɛs W c W A, Ẑ Z. The dark photon can couple to the ordinary fermions besides the dark fermions, L g 2 s W  µ [( 1 3 d γ µ d 2 ) 3ū γ µ u + ē γ µ e + ɛc 2 W ( 1 3 dγ µ d + 2 3ūγµ u ēγ µ e )]. As long as the dark photon is heavy enough, ( ) δ m 2 m 2  A = 8g2 2 s2 W δ 2 (400 MeV) 2 2, 470 MeV it can efficiently decay into the ordinary fermions, Γ A = Γ A e e + Γ + A µ µ + Γ + A uū + Γ A d d + Γ A s s 5 3 ɛ2 m A αc 4 W ( ) 2 1 ɛ ( m ) A sec MeV

35 Since the dark charged leptons are the quasi-dirac fermions, their lepton asymmetries cannot survive (Buckley, Profumo, 11.). The lightest dark charged lepton (the dark electron) thus should have a thermally produced relic density, which depends on its pair annihilation into the dark photon, σ e + e A A v rel πα 2 m 2 e pb ( ) α 2 ( ) MeV. α m e If the dark electron is at the GeV scale, it will have a frozen temperature far below its mass and give a negligible contribution to the dark matter relic density

36 We now have known η B = C C η B for η = η l. L If the dark matter relic density is dominated by the lightest dark nucleon N, the cosmological observations will imply Ω B h 2 : Ω DM h 2 = m p η B : m N ( η B ) m N = C C Ω DM h 2 Ω B h 2 m p, from which the dark matter mass can be determined by 5.67 GeV for Ω DM h 2 Ω B h 2 = , m N 5.88 GeV for Ω DM h 2 Ω B h 2 = , 6.09 GeV for Ω DM h 2 Ω B h 2 =

37 The sphaleron processes in the ordinary and dark sectors could work at different temperatures. It is possible that the sphalerons in the ordinary sector can keep in equilibrium till a lower temperature T sph = O( φ ) after those in the dark sector go out of equilibrium at a higher temperature T sph = O( φ ). If the leptogenesis processes cross the critical temperature T sph, the lepton asymmetries generated after this temperature can contribute to the ordinary baryon asymmetry but can not affect the dark baryon asymmetry. This is like the mechanism in the νmsm model for giving a large lepton asymmetry but a small baryon asymmetry (Asaka, Blanchet, Shaposhnikov, 05.). For a proper choice of the masses and couplings of the decaying gauge-singlet Dirac fermion(s) and/or [SU(2) L SU(2) L ]-bidoublet Higgs scalar(s), the dark baryon asymmetry can be smaller than the ordinary baryon asymmetry. In this case, the lightest dark nucleon as the dark matter particle can have a mass much bigger than the predictive value about 6 GeV

38 Effective neutrino number The BBN stringently restricts the existence of the new relativistic degrees of freedom. The constraint on the new degrees of freedom is conventionally quoted as N ν = N ν 3.046, the effective number of additional light neutrinos (e.g. Planck collaboration, ), N ν = 3.30 ± 0.27 N ν = 0.25 ± So, the gauge interactions of the dark neutrinos should decouple before the BBN. We can estimate ( g Γ 2 / cos θ W ) 4 ( ) 4 φ G 2 g 2 / cos θ W φ F T 5 = H(T ) = ( g ) ( ) 1 6 φ 4 ( 3 g2 / cos θ W T D 12 GeV φ g 2 / cos θ W [ 8π 3 g (T ) 90 ) 4 3. ] 1 2 T 2 M Pl T =TD The temperature of the dark neutrinos at the BBN epoch T BBN 1 MeV then should be about ( [ Tν g (T BBN ) T BBN ) 4 = g (T D ) ] 4 3 ( ) Nν = 4 7 ( Tν T BBN ) 4 <

39 Discrete mirror symmetry We can impose a discrete mirror symmetry (Lee, Yang, 56 ; Kobzarev, Okun, Pomeranchuk, 66 ; Pavsic, 74 ; Blinnikov, Khlopov, 82; Glashow, 86 ; Foot, Lew, Volkas, 91 ;...) under which the fields transform as G a µ Ga µ, W a µ W a µ, B µ B µ, q L q L, d R d R, u R u R, l L, e R e R, φ φ, δ δ, N R N R, Σ a ΣT a, to simplify the dimensionless parameters, g 3 = g 3, g 2 = g 2, g 1 = g 1, y d = y d, y u = y u, y e = y e, y δ = y δ, y N = y N, f a = f T a. Benefited from the discrete mirror symmetry, the neutrino mass matrix induced by the type-i, type-ii or type-i+ii Dirac seesaw will have a symmetric structure: Type-I Dirac seesaw: m ν = y N φ φ M N y T N with M N = diag{m N1, M N2,...}, Type-II Dirac seesaw: m ν = a f ρ a φ φ a with f M 2 Σ a = fa T, a φ φ Type-I+II Dirac seesaw: m ν = y N y T M N N a f ρ a φ φ a with M M 2 Σ N = diag{m N1,...}, f a = fa T. a As we will show later the dark vacuum expectation value φ is determined by the dark matter mass. Accordingly, our Dirac seesaw will not contain new parameters compared with the traditional type-i, type-ii or type-i+ii Majorana seesaw

40 Another implication of the mirror symmetry is that the beta functions of the QCD in the ordinary and dark sectors, i.e. α 1 s (µ) = n f 2π ( µ ln Λ), α 1 s (µ) = n f 2π ( µ ) ln Λ, can yield a relation between the electroweak and hadronic scales in the dark sector. Here n f (n f ) counts the number of the ordinary(dark) quarks involved at a given scale µ. By matching α s (µ) at the scale µ = m t with n f = 6 and n f = 5, at the scale µ = m b with n f = 5 and n f = 4, at the scale µ = m c with n f = 4 and n f = 3, respectively, we can deduce Λ (5) = m 2 23 t Λ (6), Λ (4) = m 2 25 b Λ (5), Λ (3) = m 2 27 c Λ (4) Λ QCD = Λ (3) = (m c m b m t ) 27Λ (6). Similarly, we can have Λ (5) = m 2 23 t Λ (6), Λ (4) = m 2 25 b Λ (5), Λ (3) = m 2 27 c Λ (4), Λ (2) = m 2 29 s Λ Λ QCD = Λ (0) = (m u m d m s m c m b m t ) 2 33Λ (6) for Λ QCD < m u. (4), Λ (1) = m 2 31 d Λ (2), Λ (0) = m 2 33 u Λ (1),

41 Due to α s (µ m t ) = α s (µ m t ) Λ (6) = Λ (6), φ φ = m u m u = m d m d = m s m s = m c m c = m b m b = m t m t, the dark hadronic scale Λ QCD should arrive at Λ QCD = ( φ φ ) 4 11 (mu m d m s ) 2 33Λ 9 11 QCD for Λ QCD < m u. So, by inputting φ = 630 φ, we can determine Λ QCD = 1.2 GeV for Λ QCD = 200 MeV, m u = 2.3 MeV, m d = 4.8 MeV, m s = 95 MeV. Consequently, the dark proton and neutron masses can be given by m p 2m u + m d 6.0 GeV, m n m u + 2m d 7.5 GeV with m u = 1.5 GeV, m d = 3.0 GeV

42 Dark matter scattering and self-interaction The dark proton as the dark matter particle can scatter off the ordinary nucleons, σ p N p N (Z, A) ɛ2 πα 2 c 4 W where µ r is the reduced mass, µ 2 r m 4 A ( Z A ) 2 ( ) 2 ɛ ( cm 2 µ ) ( ) 2 4 ( ) 2 r 400 MeV Z GeV m A A µ r = m p m p m p + m p 0.81 GeV for m p 6 GeV. p p  N N

43 The dark matter self-interaction is induced by the strong and electromagnetic interactions in the dark sector, σ em p p p p m p 4πα2 m p m 4 A cm 3 ( mp 6 GeV ) ( ) MeV < cm 3, m A σ strong p p p p m p g4 π N N m p m 4 π g 4 πnn m2 p m4 π σ np cm 3 ( gπ N N g πnn ) 4 ( mp ) ( ) 2 4 ( 6 GeV σ np ) 6 GeV m π cm 2. p p  p p p p π 0 p p

44 Summary The dark matter relic density can be an asymmetry between the dark matter and antimatter.if the dark matter asymmetry has a common origin with the baryon asymmetry, we can naturally explain the comparable energy densities of the baryonic and dark matter in the present universe. We have shown the interactions for simultaneously generating the baryonic and dark matter asymmetries can also be responsible for the Dirac neutrino masses. In this leptogenesis scenario with a conserving lepton number, the dark matter mass should be a determined value about 6 GeV. In the presence of a discrete mirror symmetry, our Dirac seesaw models will not require more unknown parameters than the conventional Majorana seesaw models.!