Neutrino masses, muon g-2, dark matter, lithium probelm, and leptogenesis at TeV-scale SI2009 AT FUJI-YOSHIDA

Transcription

1 Neutrino masses, muon g-2, dark matter, lithium probelm, and leptogenesis at TeV-scale SI2009 AT FUJI-YOSHIDA Chian-Shu Chen National Cheng Kung U./Academia Sinica with C-H Chou 08/20/2009 arxiv:

2 Outline Introduction The model of neutrino masses Side effects on anomalous muon g-2 Inert doublet dark matter candidate of the model Catalyzed BBN as the solution to lithium problem Possibility of low energy leptogenesis Test the model Conclusion

3 Introduction SM describes the experimental data so well, but we already have some discoveries that are not comparable with it. Several deviations between theoretical predictions and experimental data appear both in Standard Model of Particle Physics and Cosmology due to precision measurement. Nentrino masses, anomalous μ magnetic moment, Lithium problem, matter-antimatter asymmetry, dark matter dark energy, PAMALA/ATIC/FERMI.. Many scenarios beyond SM are proposed, including top-down and bottom-up approaches.

4 Neutrino data $'( "& $% "#! )! "" $+!$$#* ). 0 ;5*.! $)12$ :! 63 "" $)12<$=.2<$==2$3-4- / & #!!! $)12$3-4- $)12$3-4- $)12$3-4-! $$)12$ * * *-. # #-. & &-. / /-.!, $+!$#* ) $'( "& $% "#! sin 2 θ δm 2 ( m 2 sol, m 2 12) = 7.92(1 ± 0.09) 10 5 ev 2 sin 2 θ 12 = 0.314( ) m 2 ( m 2 atm, m 2 23) = 2.4( ) 10 3 ev 2 sin 2 θ 23 = 0.44( )

5 Among the ways to measure the neutrino masses, three ways are sensitive to the absolute scale : 0νββ decay, tritium β- decay, and cosmology m β = [c 2 13c 2 12m c 2 13s 2 12m s 2 13m 2 3] 1/2 m ββ = c 2 13c 2 12m 1 + c 2 13s 2 12m 2 e iφ 2 + s 2 13m 3 e iφ 3

6 Anomalous muon g-2 : the deviation between SM calculations and the experimental result is 3.2σ The existence of dark matter in our universe DarkMatterPie

7 Lithium problem states the discrepancy between SBBN and the abundance of Li 6,7 we observed. Too much 7 Li and too less 6 Li are predicted theoretically 3 times 7 Li larger / 1000 times 6 Li smaller than the observation The universe appears to be populated exclusively with matter rather than antimatter, the amount of asymmetry is around Many scenarios are proposed : 1. GUT thermal baryogenesis, 2. Leptogenesis, 3. Affleck-Dine mechanism, 4. CPT violation 5.

8 The model The evidence of dark matter Z 2 symmetry All the new particles besides SM sectors are Z 2 odd The masses of all new particles are around TeV scale New Yukawa couplings L Y = f αi l T LαC 1 L Li S + + y αi LLi φ2 l Rα + g αi llα φ2 E Ri + h.c. = f αi ( ν α E i + l α N c i )S + + y αi (N i φ + 2 l Rα E+ i φ0 2 l Rα ) +g αi ( νφ + 2 E Ri l α φ 0 2 E Ri )+h.c.

9 Potential V (φ 1, φ 2,S ) = µ 2 1 φ λ 1 φ m 2 2 φ λ 2 φ λ 3 φ 1 2 φ λ 4 φ 1 φ λ [ ] [ 5 (φ 1 2 φ 2) 2 ] + h.c. + m 2 s S 2 + λ s S 4 + µ [ (φ 0 1 φ 2 φ 1 φ0 2 )S+ + h.c. ]. ( ( φ + 2 S + ) ( µ λ 3v 2 µv 2 2 µv 2 m 2 s ) ( φ 2 S )

10 Neutrino mass generation No tree level seesaw due to Z 2 symmetry, neutrino masses are generated in one-loop level (m ν ) αβ = ig αi f βi M Ei µ φ 0 1 d 4 q 1 (2π) 4 (q 2 Ms 2 ) 1 (q 2 Mφ 2 2 ) 1 (q 2 M 2 E i ) = Assuming g αi f βi µvm Ei 16 2π 2 (M 2 E i M 2 φ 2 ) [ F (M 2 Ei ) F (M 2 φ 2 ) ], (m ν ) αβ g αif βi 16 2π 2 µv M Ei 10 3 g αi f βi µ 10 2 ev, Eq. (1)

11 Muon g-2 μ anomalous magnetic moment is one of the most precisely measured quantities in particle physics. A recent experiment at Brookhaven it has been measured with a remarkable 14-fold improvement of the previous CERN result. 3.2σ

12 Neutrino masses and μ g-2 a µ = (290 ± 90) A similar mechanism a NP sin δ cos δ µ(n k ) = 16π 2 (f µk y µk ) m µ [F (x P1 ) F (x P2 )] M k sin δ cos δ(f µk y µk ) ( ) ( )( ) Eq. (2) ( P 1 P 2 ) = F (x) = ( cos δ sin δ sin δ cos δ )( φ 2 S ) sin δ cos δ = µv 2(m 2 P1 m 2 P 2 ) 1 trino masses we know that sin (1 x) 3 [1 x2 +2xln x]. x Pi = m 2 P i /Mk 2 harged scalars. T c

13 And G(x) = a NP µ(e k,(a)) = g µky µk 12π 2 m µ M k G(x φ 0 2 ) g µk y µk 10 5, 3 [ 3 4x + x 2 2(1 x) ln x ] Eq. (3) [ ] x φ 0 2 = M 2 k /m2 φ 0 2. muon g 2, a NP µ(e k,(b)) y2 µk 48π 2 m 2 µ M 2 φ 0 2 y 2 µk

14 Dark matter A dark matter can be realized in the inert scalar doublet φ 0 2 The lightest Z 2 odd component is determined by the sign of quartic coupling λ 5 m 2 φ 2(R,I) = m (λ 3 + λ 4 ± λ 5 )v 2. The relic abundance of DM in our universe Ω CDM h 2 =0.106 ± 0.008, Numerically a WIMP will freeze out at temperature T f m φ 0 2 /25 and the (co)anni The relation of final abundance and the (c0)annihilations rate can be well approximated as Ω φ 0 2 h cm 3 s 1 σ ija v ij. with v ij = (p i p j ) 2 m 2 i m2 j E i E j During the freeze out temperature v ij ~ 0.3

15 The dominant annihilation channel of DM is into gauge bosons ant annihilatio, φ 0 2 φ0 2 AA, σ A v 3g4 2 + g 4 Y +6g2 2g 2 Y 256πM 2 φ 0 2 DM can (c0)annihilate into or through SM Higgs by trilinear and quartic couplings of the scalars σ ij λ = λij 32πm 2 φ 0 2, i, j = {0, 1, 2, 3, 4} = where {i, j = {φ 0 2R, φ0 2I, φ+ 2, φ 2,S± } the combinations of qu λ 00 = λ 11 = 5 2 λ2 3 +2λ λ 3 λ 4 +2λ 2 5 λ 22 = λ 33 =2λ 01 = 8λ 2 5 λ 02 = λ 03 = λ 12 = λ 13 = 2(λ 3 /2+λ 4 ) 2 +2λ 2 5 λ 23 = 4(λ 3 + λ 4 ) 2 + λ 2 3 λ 24 = λ 34 = 4(λ 3 + λ 4 ) 2 +(µ/v) 2. ( V 3,4 = λ 1 vh 3 + λ 1 4 h4 + λ 2 φ λ 3 vh φ λ 3 2 h2 φ 2 2 +λ 4 vh φ λ 4 2 h2 φ λ 5 vh(φ 02 2R φ 02 2I) + λ [ 5 µ 2 h2 (φ 02 2R φ 02 2I)+λ s S hφ 2 S+ + h.c.]

16 In pure gauge interaction limit, the lower bound of DM mass is 530 GeV T.Hambye el. (09)

17 Lithium problem Big-bang nucleosynthesis (BBN) offers the deepest reliable probe of the early universe, being based on Standard Model physics. Predictions of the abundances of the light elements, D, 3 He, 4 He, and 7 Li, synthesized at the end of the first 3 minutes. A good overall agreement with the primordial abundances with the observational data span 9 orders of magnitude from 4 He/H 0.08, down to 7 Li/H BBN was generally taken to be a three-parameter theory Baryon density Neutron mean-life Number of neutrino flavors η 10 (WMAP2008)=6.23±0.17 Τ n =878.5±0.8 s 3

18 Li/H = (2.19 ± 0.28) 10 7 Li/H = ( ) SBBN predict the ratio of Lithium and Helium is about ± and 6 Li to 7 Li component Li/H is = small ( ) 6 Li/ 7 Li

19 Metal-poor halo stars --- Galactic cosmic rays --- primordial value Measurement from clusters (NGC 6397) --- Li/H = (1.23 ± 0.06) 10 10, 10 e pattern of neutrino mass Li/H = (1 2) Li/H = (1 ± 2) 10, Li/H Li/H = (2.19 ± 0.28) Recent high-precision measurements are sensitive to the tiny isotopic shift in Li absorption and indicate ±, 6 Li/ 7 Li 0.15 Lithium problem : The SBBN predicts primordial 6 Li abundance about 1000 times smaller than the observed abundance level and 7 Li abundance a factor of 2~3 larger than when one adopts a value of η inferred from the WMAP data.

20 Catalyzed BBN (CBBN) may provide the solution CBBN : Li/ Li , X SBBN : 4 He + D 6 Li + γ S ( 4 HeS ) 6 Li and S ( 4 HeS ) ( 8 BeX ) 9 Be. S ( 4 HeS )+D 6 Li + S and ( 8 BeS )+n 9 Be + S. M.Pospelov(07,08), K.Kohri,el(07), J.Ellis,K.A.Olive(03), M.Kaplinghat,el(06), T.T.Yanagida(07).. The most significant difference is seen in the 6 Li production SBBN : 4 He + D 6 Li + γ; Q = 1.47MeV CBBN : ( 4 HeS )+D 6 Li + S ; Q 1.13MeV The existence of a long-lived singly charged particle ~ 1000s to catalyze the chain reactions K.Kohri and F.Takayama (07)

21 A long-lived S + is needed ~ 1000 sec (a),(b) : Γ s αβ(ni ) (f αiy iβ ) 2 30π 3 M 4 N i (δm) 5 (1 5m2 l δm 2 ) fαiy 2 iβ ( δm GeV )5 GeV, τ αβ 6.6 f 2 αi y 2 iβ δm = M s M φ2 ( δm GeV ) sec, We have the constraint fαi 2 y2 βi ( δm GeV ) 5. Eq. (4)

22 The second kind of diagram decay through SM Higgs Γ s(h) = 10 6 µ (2π) 3 m s ( m 4 h (δm) 2 µ GeV )2 ( δm GeV )2 GeV, We obtain ( µ GeV )2 ( δm GeV ) Eq. (5)

23 We put all constraints to find a consistent solutions fg( µ GeV ) 10 8, fy 10 4, gy 10 5, f 2 y 2 ( δm GeV ) , µ ( GeV )2 ( δm GeV ) } } Neutrino masses Anomalous muon g-2 Lithium problem µ 10 5 GeV, δm < 1GeV, f 10 1, y 10 3, and g 10 2

24 Leptogenesis The difficulties to have a simple leptogenesis at the TeV-scale 1. The out-of-equilibrium condition Couplings are tiny since Planck scale and decay width is in general linear to the mass of decaying particle in contrast to the Hubble constant which depends quadratically on this mass. 2.The amount of CP asymmetry

25 Three possibilities enhancement mechanisms 1. Mass degeneracy : CP asymmetry induced by self-energy diagram display an interesting resonant behavior when the masses of the decaying particles are nearly degenerate. 2. Hierarchy of couplings : Assuming two particles (A,B) decaying into the same decay products. The lighter one A with the suppressed coupling g A to reach the out-of-equilibrium condition while the heavier one B with unsuppressed coupling g B will produce large CP asymmetry through oneloop. 3. Three body decays : phase space suppression.

26 Leptogensis Two contributions Fikugita,Yanagita(86) l Rj l Rj l Rj N i φ ± 2 N i N m N i N m l n φ ± l n 2 φ ± 2 llj l Lj l Lj N i S ± N i N m N i N m l n S ± l n S ± Γ N1 = α (y 1α) 2 16π M N1 and Γ N1 = (f f) 11 8π M N1 The right-handed sector is not constrained by neutrino masses

27 ɛ 1 = Γ(N 1 lφ + 2 ) Γ(N 1 lφ 2 ) Γ(N 1 lφ + 2 )+Γ(N 1 lφ 2 ) = 1 8π If y (2) = = 3 16π m 1 m 1 Im[(y 1α )(y2α α )]2 (y 1α)(y1α ) M N2, M N1 Im[(y y) 2 1m ] {f v ( M 2 α (y y) 1α M1 2 m )+f s ( M 2 m M 2 1 )} Im[(y y) 2 1m ] M 1, (26) α (y y) 1α M m One has n B s = n L s = ɛ 1 η = , Out of equilibrium condition Γ N1 <H(T )= 4π3 g 45 T 2 M pl T =MN1. We have y (1) = Hierarchy couplings : y 1i 2 < MN GeV. i y (1) < 0.28 y (2) M N1 M N2 M N GeV. From these conditions, we can find the TeV solution of leptogenesis, s M N1 =1T ev, M N2 =5T ev, y (2) , and y (1) Consistent with the previous constraints

28 Washout effects from gauge interactions (Type II,III seesaw mechanism) N 1 f, h N 1 A N 1 A f, h N 1 N 1 A N 1 A N 1 A N 1 A A N 1 N 1 A

29 Boltzmann eqs. Boltzmann suppression factor in gauge fields at low scale Left-handed leptogenesis Contribute constrained by Neutrino masses -- subleading T. Hambye(07)

30 Test of the model LHC search see M. Hirsch,K.S. Babu Direct detection Experimental limit on Z exchange -- M H 0 - M A 0 ~ (10 2 )kev σdm N h f N 2 λ2 φ 0 2 4π ( m 2 N m DM m 2 ) 2. h σ 1 loop = 9f 2 N πα4 2 m4 N 64M 2 W ( 1 M 2 W + 1 m 2 ) 2. Independent of DM mass h

31 tion experiment aro, ρ 0 =0.3GeV/cm 3 m h = 120 GeV T.Hambye, el(09) Next generation experiment

32 Conclusions The neutrino masses generated through the radiative seesaw mechanism with GIM suppression from singly charged Higgs mixing is presented. Anomalous muon magnetic moment is given through the mechanism similar to neutrino masses generation. Dark matter candidate is realized in inert doublet scalar, and a direct measurement is possible in next-generation experiments. Lithium problem can be solved by a long-lived singly charged scalar S - to by Catalyzed BBN method. DM is produced during the period of BBN. TeV-scale leptogenesis utilizing right-handed lepton sector as well as lefthanded is presented. The model can be tested in near future at collider.