Neutrino Mass Seesaw Version 3 : Recent Developments Ernest Ma Physics and Astronomy Department University of California Riverside, CA 92521, USA Neutrino Mass Seesaw Version 3: Recent Developments (SanCarlos08) back to start 1
Contents • Neutrino Mass • Gauge Coupling Unification • LHC Phenomenology • New U(1) Gauge Symmetry • Scotogenic Radiative Neutrino Mass • Fermion Triplet Dark Matter • Conclusion Neutrino Mass Seesaw Version 3: Recent Developments (SanCarlos08) back to start 2
Neutrino Mass: Six Generic Mechanisms Weinberg(1979): Unique dimension-five operator for Majorana neutrino mass in the standard model (SM): 2Λ( ν α φ 0 − l α φ + )( ν β φ 0 − l β φ + ) ⇒ M ν = f αβ v 2 f αβ . Λ Ma(1998): Three tree-level realizations: (I) fermion singlet N , (II) scalar triplet ( ξ ++ , ξ + , ξ 0 ) , (III) fermion triplet (Σ + , Σ 0 , Σ − ) [Foot/Lew/He/Joshi(1989)]; and three generic one-loop realizations (IV), (V), (VI). Neutrino Mass Seesaw Version 3: Recent Developments (SanCarlos08) back to start 3
φ 0 φ 0 φ 0 φ 0 ξ 0 ν β ν β ν α ν α N Σ 0 Neutrino Mass Seesaw Version 3: Recent Developments (SanCarlos08) back to start 4
✆ ✟ ✠ ✡☞☛ �☎✄ �✂✁ ✆✞✝ ✡☞☛ Neutrino Mass Seesaw Version 3: Recent Developments (SanCarlos08) back to start 5
✆ ✟ ✠ ✡☞☛ ✡☞☛ �☎✄ �✂✁ ✆✞✝ Neutrino Mass Seesaw Version 3: Recent Developments (SanCarlos08) back to start 6
✆ ✝ ✆ ✞ ✠ �✂✁ �☎✄ ✝✟✞ ✡☞☛ ✡☞☛ Neutrino Mass Seesaw Version 3: Recent Developments (SanCarlos08) back to start 7
Gauge Coupling Unification It is well-known that gauge-coupling unification occurs for the minimal supersymmetric standard model (MSSM) but not the SM. The difference can be traced to the addition of gauginos and higgsinos, transforming under SU (3) C × SU (2) L × U (1) Y as (8,1,0), (1,3,0), (1,2, ± 1/2), and a second Higgs scalar doublet. Note that the fermion triplet (1,3,0) is what makes the SU (2) L and U (1) Y couplings meet at high enough an energy scale to be acceptable for suppressing proton decay. Neutrino Mass Seesaw Version 3: Recent Developments (SanCarlos08) back to start 8
The one-loop renormalization-group equations for the evolution of gauge couplings between M 1 and M 2 are α i ( M 1 ) − 1 − α i ( M 2 ) − 1 = ( b i / 2 π ) ln( M 2 /M 1 ) , where α i = g 2 i / 4 π , and the numbers b i are determined by the particle content of the model. In the SM, these are SU (3) C : b C = − 11 + (4 / 3) N f = − 7 , SU (2) L : b L = − 22 / 3 + (4 / 3) N f + 1 / 6 = − 19 / 6 , U (1) Y : b Y = (4 / 3) N f + 1 / 10 = 41 / 10 , where N f = 3 is the number of families and unification means α C ( M U ) = α L ( M U ) = (5 / 3) α Y ( M U ) = α U . Neutrino Mass Seesaw Version 3: Recent Developments (SanCarlos08) back to start 9
Using the input α C ( M Z ) = 0 . 122 , α L ( M Z ) = 0 . 0340 , α Y ( M Z ) = 0 . 0102 , it is easy to check that gauge couplings do not unify in the SM. Model b Y − b L b L − b C new fermions new scalars SM 7.27 3.83 none none MSSM 5.60 4.00 (1,3,0),(8,1,0) (1,2,1/2) (1,2, ± 1/2) m05 5.27 3.83 (1,3,0) (1,3,0) × 2 (8,1,0) × 4 bs07 5.60 3.00 (1,3,0), (8,1,0) (1,3,0) (8,1,0) Neutrino Mass Seesaw Version 3: Recent Developments (SanCarlos08) back to start 10
If all particles transforming under SU (2) L × U (1) Y are at the electroweak scale, then ln( M U /M Z ) ≃ √ 2 π 2 [(3 / 5 tan 2 θ W ) − 1] /G F M 2 W ( b Y − b L ) . Hence M U > 10 16 GeV ⇒ b Y − b L < 5 . 7 . Ma(2005): all new particles ∼ TeV. Bajc/Senjanovic(2007): color octets ∼ 10 8 GeV. Instead of just one (Σ + , Σ 0 , Σ − ) fermion triplet, let there be three copies at an intermediate scale M I , then gauge-coupling unification ∼ 10 16 GeV ⇒ M I ∼ 10 10 GeV, which is also the right scale for leptogenesis through the decay of the lightest Σ [Fischler/Flauger(2008)]. Neutrino Mass Seesaw Version 3: Recent Developments (SanCarlos08) back to start 11
LHC Phenomenology If Σ exists at the TeV scale, it may be probed at the LHC. Its production is by pairs from quark fusion via the electroweak gauge bosons with a cross section of the order 1 fb for m Σ of about 1 TeV, and rising to more than 10 2 fb if m Σ is 300 GeV. The mass splitting between Σ 0 and Σ ± is radiative and comes from electroweak gauge interactions. For large m Σ , it is about 168 MeV, thus allowing Σ ± → Σ 0 π ± and Σ 0 l ± ν . The dominant decays are however Σ ± → νW ± , l ± Z ( h ) and Σ 0 → l ± W ∓ , νZ ( h ) unless a symmetry forbids them. Neutrino Mass Seesaw Version 3: Recent Developments (SanCarlos08) back to start 12
del Aguila/Aguilar-Saavedra(2008): final state m N (100 GeV) m ξ (300 GeV) m Σ (300 GeV) 6 leptons – – × 28 fb − 1 5 leptons – – l ± l ± l ± l ∓ 15 fb − 1 – – l + l + l − l − 19 fb − 1 7 fb − 1 – l ± l ± l ± 30 fb − 1 – – l ± l ± l ∓ < 180 fb − 1 3.6 fb − 1 2.5 fb − 1 l ± l ± < 180 fb − 1 17.4 fb − 1 1.7 fb − 1 l + l − 15 fb − 1 80 fb − 1 × l ± × × × Neutrino Mass Seesaw Version 3: Recent Developments (SanCarlos08) back to start 13
New U(1) Gauge Symmetry Ma(2002) : Consider SU (3) C × SU (2) L × U (1) Y × U (1) X with ( u, d ) L ∼ (3 , 2 , 1 / 6; n 1 ) , u R ∼ (3 , 1 , 2 / 3; n 2 ) , d R ∼ (3 , 1 , − 1 / 3; n 3 ) , ( ν, e ) L ∼ (1 , 2 , − 1 / 2; n 4 ) , e R ∼ (1 , 1 , − 1; n 5 ) , Σ ∼ (1 , 3 , 0; n 6 ) . Absence of the axial-vector anomaly requires [ SU (3)] 2 U (1) X : 2 n 1 − n 2 − n 3 = 0 . [ U (1) Y ] 2 U (1) X : n 1 − 8 n 2 − 2 n 3 + 3 n 4 − 6 n 5 = 0 . U (1) Y [ U (1) X ] 2 : n 2 1 − 2 n 2 2 + n 2 3 − n 2 4 + n 2 5 = (3 n 1 + n 4 )(7 n 1 − 4 n 2 − 3 n 4 ) / 4 = 0 . Neutrino Mass Seesaw Version 3: Recent Developments (SanCarlos08) back to start 14
n 4 = − 3 n 1 ⇒ U (1) Y , so n 2 = (7 n 1 − 3 n 4 ) / 4 will be assumed from now on. In that case, n 3 = ( n 1 + 3 n 4 ) / 4 and n 5 = ( − 9 n 1 + 5 n 4 ) / 4 . [ SU (2)] 2 U (1) X : 3 n 1 + n 4 − 4 n 6 = 0 . Mixed gravitational-gauge anomaly U (1) X : 6 n 1 − 3 n 2 − 3 n 3 +2 n 4 − n 5 − 3 n 6 = 3(3 n 1 + n 4 − 4 n 6 ) / 4 = 0 . [ U (1) X ] 3 : 6 n 3 1 − 3 n 3 2 − 3 n 3 3 + 2 n 3 4 − n 3 5 − 3 n 3 6 = 3(3 n 1 + n 4 ) 3 / 64 − 3 n 3 6 = 0 . Hence n 6 = (3 n 1 + n 4 ) / 4 satisfies all 3 conditions. If a fermion multiplet (1 , 2 p + 1 , 0; n 6 ) is used, the only solutions are p = 0 [ U (1) B − L ] and p = 1 [ U (1) X ]. Neutrino Mass Seesaw Version 3: Recent Developments (SanCarlos08) back to start 15
The scalar sector of this U (1) X model consists of two Higgs doublets ( φ + 1 , φ 0 1 ) with charge (9 n 1 − n 4 ) / 4 which couples to charged leptons, and ( φ + 2 , φ 0 2 ) with charge (3 n 1 − 3 n 4 ) / 4 which couples to up and down quarks as well as to Σ . To break the U (1) X gauge symmetry spontaneously, a singlet χ with charge − 2 n 6 is added, which also allows the Σ ’s to acquire Majorana masses at the U (1) X breaking scale. Adhikari/Erler/Ma(2008): The new gauge boson X may be accessible at the LHC. Its decay branching ratios could determine the parameter r = n 4 /n 1 = tan φ . Neutrino Mass Seesaw Version 3: Recent Developments (SanCarlos08) back to start 16
7000 95% CL excluded 6000 5000 M X /g X [GeV] 4000 3000 2000 1000 0 π 0 π/4 3/4 π π/2 φ Neutrino Mass Seesaw Version 3: Recent Developments (SanCarlos08) back to start 17
3.5 r � 1 3 2.5 ������� �� � 2 � � � � X �Μ Μ � � X � t t ���������������� 1.5 1 r � 2 r � 9 0.5 1 2 3 4 �� � � � X � b b ���������������� ������� �� � � � X �Μ Μ Neutrino Mass Seesaw Version 3: Recent Developments (SanCarlos08) back to start 18
Scotogenic Radiative Neutrino Mass Deshpande/Ma(1978): Add to the SM a second scalar doublet ( η + , η 0 ) which is odd under a new exactly conserved Z 2 discrete symmetry, then η 0 R or η 0 I is absolutely stable. This simple idea lay dormant for almost thirty years until Ma, Phys. Rev. D 73, 077301 (2006). It was then studied seriously in Barbieri/Hall/Rychkov(2006), Lopez Honorez/Nezri/Oliver/Tytgat(2007), Gustafsson/Lundstrom/Bergstrom/Edsjo(2007), and Cao/Ma/Rajasekaran, Phys. Rev. D 76, 095011 (2007). Neutrino Mass Seesaw Version 3: Recent Developments (SanCarlos08) back to start 19
Radiative Neutrino Mass: Zee(1980): (IV) ω = ( ν, l ) , ω c = l c , χ = χ + , η = ( φ + 1 , 2 , φ 0 1 , 2 ) , � φ 0 1 , 2 � � = 0 . Ma(2006): (V) [scotogenic = caused by darkness] ω = ω c = N or Σ , χ = η = ( η + , η 0 ) , � η 0 � = 0 . N or Σ interacts with ν , but they are not Dirac mass partners, because of the exactly conserved Z 2 symmetry, under which N or Σ and ( η + , η 0 ) are odd, and all SM particles are even. Using f ( x ) = − ln x/ (1 − x ) , h αi h βi M i � [ f ( M 2 i /m 2 R ) − f ( M 2 i /m 2 ( M ν ) αβ = I )] . 16 π 2 i Neutrino Mass Seesaw Version 3: Recent Developments (SanCarlos08) back to start 20
φ 0 φ 0 η 0 η 0 ν β ν α N i , Σ 0 i Neutrino Mass Seesaw Version 3: Recent Developments (SanCarlos08) back to start 21
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