Neutrinos and Dark Matter in the minimal B L SUSY Model Roger Hern - PowerPoint PPT Presentation

Beyond SM B − L model Conclusions Neutrinos and Dark Matter in the minimal B − L SUSY Model Roger Hern´ andez-Pinto in collaboration with Dr. A. P´ erez-Lorenzana based on arXiv:1105.0713 arXiv:1109.xxxx Supersymmetry 2011 Fermilab

Beyond SM B − L model Conclusions Outline Beyond SM 1 Neutrinos and Cosmology Neutrino mass in SM extensions B − L model 2 The supersymmetric B − L model Unification Sparticle spectrum B − L breaking Neutrino mass B − L Neutralino DM Relic Density Conclusions 3 Supersymmetry 2011 Fermilab

Beyond SM B − L model Conclusions Neutrinos and Cosmology Observational inconsistencies are motivating to look for physics beyond the SM, It can not explain neutrino masses, It does not explain the origin of the cosmological ingredients, Galactic Rotation Curves Gravitational Lensing “Bullet Cluster”. . . Supersymmetry 2011 Fermilab

Beyond SM B − L model Conclusions Neutrino mass in SM extensions In the SM, there is only one helicity state per generation for neutrinos. We also know that B − L current is conserved to all orders in perturbation theory. Without the right handed component, it is not possible to build a mass term for neutrinos. The inclusion of right handed neutrinos preserve B − L anomaly free. The Majorana term breaks B − L ⇒ it must be broken somehow. Supersymmetry 2011 Fermilab

Beyond SM B − L model Conclusions Neutrino mass in SM extensions In the SM, there is only one helicity state per generation for neutrinos. We also know that B − L current is conserved to all orders in perturbation theory. Without the right handed component, it is not possible to build a mass term for neutrinos. The inclusion of right handed neutrinos preserve B − L anomaly free. The Majorana term breaks B − L ⇒ it must be broken somehow. In general, neutrino masses can be analyzed via, ν c R ν R + h ′ ¯ L ˜ δ L = h σ ¯ H ν R and it has a direct connection with the DM problem and the barionic asymmetry of the universe. It suggest as a natural symmetry to SU (2) L × U (1) Y × U (1) B − L . It is needed to include 3 families of right handed neutrinos to preserve anomaly cancelation. Supersymmetry can help to know the value at low energies of the parameters of the model, also the breaking scale of U (1) B − L . Supersymmetry 2011 Fermilab

Beyond SM B − L model Conclusions The supersymmetric B − L model The superpotential that contains neutrino masses is, ∆ W =¯ N Y D N LH u + N Y M N N σ 1 + µ ′ σ 1 σ 2 , where under SU (3) c × SU (2) L × U (1) Y × U (1) B − L the extra superfields transform as ¯ N = ( 1,1 , 0 , − 1) σ 1 = ( 1,1 , 0 , 2) σ 2 = ( 1,1 , 0 , − 2) . Kinetic terms are also included, N † e 2 V ˆ 1 e 2 V ˆ 2 e 2 V ˆ ˆ σ † σ † ∆ K = N + ˆ σ 1 + ˆ σ 2 , And the gauge part, Z B − L + D 2 − 1 2 A µν A µν − i Z B − L σ µ ∂ µ ¯ W α ( B − L ) W α ( B − L ) | θθ = − 2 i ˜ ˜ A µν A µν ˜ 4 The soft breaking term, which involves the new scalars is, ∆ L SB = 1 Z B − L + ˜ 2 M B − L ˜ Z B − L ˜ N h D ¯ N ˜ LH u + ˜ N c h M N ˜ N σ 1 + B ′ σ 1 σ 2 + m 2 σ 1 σ † 1 σ 1 + m 2 σ 2 σ † 2 σ 2 + ˜ N † m 2 N ˜ N We do not need to impose R − parity, because R − parity violating terms are forbidden by gauging under U (1) B − L . Supersymmetry 2011 Fermilab

Beyond SM B − L model Conclusions Unification RGE were obtained by considering that U (1) gauge groups are orthogonal. In the most general case one needs to consider the mixing between these abelian groups. F. del Aguila, G.D. Coughlan, M. Quiros, Nucl. Phys. B 307, 633 (1988). Within this approach we have, � m � �� α − 1 α − 1 ( m Z ) + (2 π ) − 1 b i ln ( m ) = c i , i i m Z where c i embedding factors can be computed from the normalization of the gauge groups at the GUT scale. In this sense, it is not needed to know the unifying gauge group. And b i it is also known from � b = 3 C 1 ( G ) − C 2 ( R ) R where C 1 ( G ) is the quadratic Casimir invariant, and C 2 ( R ) the Dynkin index. Therefore ( c 1 , c 2 , c 3 , c B − L ) = (3 / 5 , 1 , 1 , 3 / 8) , ( b 1 , b 2 , b 3 , b B − L ) = ( − 11 , − 1 , 3 , − 24) . Supersymmetry 2011 Fermilab

Beyond SM B − L model Conclusions Unification RGE were obtained by considering that U (1) gauge groups are orthogonal. In the most general case one needs to consider the mixing between these abelian groups. F. del Aguila, G.D. Coughlan, M. Quiros, Nucl. Phys. B 307, 633 (1988). Within this approach we have, Low energy value for the B − L gauge coupling is 80 -1 α g B − L ( m Z ) ≈ 0.2565 70 This value put a constraint on the 60 associated B − L gauge boson -1 α B-L 50 given by LEP 40 M B − L / g B − L > 6 TeV α -1 1 30 M. Carena et al. α -1 2 Phys. Rev. D 70, 093009 (2004) 20 α -1 3 10 Therefore 0 2 4 6 8 10 12 14 16 M B − L > 1.5 TeV Log (Q/GeV) 10 Supersymmetry 2011 Fermilab

Beyond SM B − L model Conclusions Sparticle spectrum 900 tan β = 30 A =900 0 800 U (1) B − L is broken by � σ 1 � and � ˜ N � . 700 Moreover, right-handed sneutrino vev will contribute to the mass of the 600 associated B − L gauge boson, Mass(GeV) 500 squarks M 2 B − L = g 2 B − L (4 v 2 σ 1 + 4 v 2 σ 2 + v 2 N ) 400 ˜ m 300 1/2 m Hd The lightest neutralino corresponds 200 m to ˜ σ 2 Z B − L . sleptons m 100 0 m Breaking of U (1) B − L occurs too m Hu sneutrino σ 1 fast !!! 0 2 4 6 8 10 12 14 16 Log (Q/GeV) 10 Supersymmetry 2011 Fermilab

Beyond SM B − L model Conclusions B − L breaking ˜ N becomes negative so fast, so it is worth asking the vev scale at low energies; the potential includes a mixing with the σ 1 , therefore, � | y M | 2 + 1 � N | 2 + 1 N | 4 + m 2 B − L | σ 1 | 4 + µ ′ + m 2 V (˜ 8 g 2 | ˜ N | ˜ 8 g 2 | σ 1 | 2 � � N , σ 1 ) = σ 1 B − L N | 2 | σ 1 | 2 + a M σ 1 | ˜ + 4 | y M | 2 | ˜ N | 2 and the numerical solution is VEV (GeV) Even if both fields acquire a vev almost at the GUT scale, their 300 ~ vevs are at the GeV scale. < N > 250 The phase appearing for � σ 1 � has 200 been considered for Inflation and Baryogenesis models. 150 D. Delepine et al. |< σ >| 1 100 Phys. Rev. Lett. 98, 161302 (2007) 50 0 2 4 6 8 10 12 14 16 Log (Q/GeV) 10 Supersymmetry 2011 Fermilab

Beyond SM B − L model Conclusions Neutrino mass Due to RGE, we have found that the elements of the neutrino mass matrix will have B − L components, other than the expected Majorana term. In order to find the corresponding mass matrix we need to implement a double see saw mechanism. This feature rise by the fact that the neutrinos and neutralinos are mixed in the same mass matrix. P. Fileviez-Perez and S. Spinner, Phys. Lett. B 673, 251 (2009). The mass mixing between neutrinos and neutralinos has the following form, y D vs β   0 Λ √ 2 y M v ′ s θ y D vs β   M ν ˜ χ 0 = Ω √ √   2 2   Λ T Ω T M ˜ χ 0 χ 0 ). The neutralino mass matrix has been also where we have taken the basis ( ν L , N , ˜ ψ 0 � T � ˜ ˜ = (˜ B 0 H 0 ˜ H 0 ˜ Z 0 ˜ W 0 modified and now read, in the basis σ 1 ˜ σ 2 ), ˜ u d B − L as, � M ˜ 0 � χ 0 M ˜ χ 0 = MSSM 0 M ˜ χ 0 B − L Supersymmetry 2011 Fermilab

Beyond SM B − L model Conclusions where all matrices are,   0 − c β s W m Z M 1 s β s W m Z 0 M 2 c β c W m Z − s β c W m Z   M ˜ MSSM =  , χ 0   − c β s W m Z 0 − µ c β c W m Z  s β s W m Z − s β c W m Z − µ 0 and √ √  2 g B − L v ′ s θ 2 g B − L v ′ c θ  M B − L 2 − 2 √ 2 g B − L v ′ s θ − µ ′ M ˜ B − L = 2 0 χ 0  √  2 g B − L v ′ c θ − µ ′ − 2 0 � v R y D � 0 0 0 0 0 0 Λ = √ , 2 √ � y M v R � = 0 1 × 4 − 2 g B − L v R 0 , Ω √ 2 and we have taken N � ≡ v R � ˜ , � σ 1 � ≡ v ′ s θ , and � σ 2 � ≡ v ′ c θ √ 2 Supersymmetry 2011 Fermilab

Beyond SM B − L model Conclusions Therefore, the neutrino mass matrix is given by, v 2 R y 2 D [ M ν ] 11 = � , M 1 M 2 µ c − 2 � β 4 µ t β − m 2 Z ( M 1 + M 2 +( M 1 − M 2 ) c 2 θ W ) [ M ν ] 12 = vy D s β √ , 2 R ( µ ′ − v ′ y M c θ ) 2 2 g 2 B − L v 2 [ M ν ] 22 = v ′ s θ y M √ − � . � B − L s 2 θ v ′ 2 2 M B − L − 4 g 2 µ ′ 2 µ ′ A random scan over the parameter space let the mass of the right handed neutrino to be, m N > O (1) GeV , by requiring the cosmological constraint � i m ν i < 2 eV to be satisfied. J. Lesgourgues and S. Pastor, Phys. Rept. 429, 307 (2006). Supersymmetry 2011 Fermilab

Beyond SM B − L model Conclusions B − L Neutralino In this model, which particle is the LSP ?!?! The lightest gaugino belongs to the U (1) B − L sector. Nevertheless, we can still tune the µ ′ parameter and, therefore the lightest particle would be ˜ σ 1 , 2 . 900 Mass(GeV) 800 700   M B − L ∆ s θ − ∆ c θ − µ ′ M ˜ B − L = ∆ s θ 0 χ 0   600 ~ − µ ′ g − ∆ c θ 0 500 √ 2 g B − L v ′ where ∆ = 2 400 m 300 ~ 1/2 W 200 ~ B ~ Z B-L 100 0 2 4 6 8 10 12 14 16 Log (Q/GeV) 10 Supersymmetry 2011 Fermilab