B-L Neutralino Dark Matter Roger Hernandez-Pinto in collaboration - - PowerPoint PPT Presentation

B-L Neutralino Dark Matter

Roger Hernandez-Pinto

in collaboration with

• A. Perez-Lorenzana

Outline

Beyond SM

✦

Neutrinos and Cosmology

✦

Neutrino mass in SM extensions

B-L Model

✦

The supersymmetric B-L model

✦

RGE

✦

Neutrinos and Higgses

✦

B-L neutralinos

Conclusions

Neutrinos and Cosmology

Observational inconsistencies have motivated to look for physics beyond the SM,

Neutrinos and Cosmology

Observational inconsistencies have motivated to look for physics beyond the SM,

It cannot explain neutrino masses, the mass hierarchy, etc.,

Neutrinos and Cosmology

Observational inconsistencies have motivated to look for physics beyond the SM,

It cannot explain neutrino masses, the mass hierarchy, etc., It doesn’t explain the origin of the cosmological ingredients,

Neutrinos and Cosmology

Observational inconsistencies have motivated to look for physics beyond the SM,

It cannot explain neutrino masses, the mass hierarchy, etc., Galactic rotation curves, It doesn’t explain the origin of the cosmological ingredients,

Neutrinos and Cosmology

Observational inconsistencies have motivated to look for physics beyond the SM,

It cannot explain neutrino masses, the mass hierarchy, etc., Gravitational Lensing, Galactic rotation curves, It doesn’t explain the origin of the cosmological ingredients,

Neutrinos and Cosmology

Observational inconsistencies have motivated to look for physics beyond the SM,

It cannot explain neutrino masses, the mass hierarchy, etc., Gravitational Lensing, Galactic rotation curves, It doesn’t explain the origin of the cosmological ingredients, “Bullet Cluster”, ...

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. The inclusion of RHN preserve B-L anomaly free The Majorana term breaks B-L, so it must be broken somehow.

δL = hσ¯ νc

RνR + h ¯

L ˜ HνR

If the Higgs mechanism is responsible for the particle mass generation, breaking of a symmetry could explain neutrino masses too. The previous lagrangian suggest the breaking of B-L. Including SUSY one can have an estimation of the value of parameters at low energies using the RGE formalism. In general, neutrino masses can be originated via the lagrangian,

The superpotential that contain neutrino masses is,

∆W = ¯ NYD

NLHu + NYM N Nσ1 + µσ1σ2,

where, under , they transform as,

¯ N = (1,1, 0, −1) σ1 = (1,1, 0, 2) σ2 = (1,1, 0, −2) .

Kinetic terms are also included,

∆K = ˆ N †e2V ˆ N + ˆ σ†

1e2V ˆ

σ1 + ˆ σ†

2e2V ˆ

σ2,

the gauge part, W α

(B−L)Wα(B−L)|θθ = −2i ˜

ZB−Lσµ∂µ ¯ ˜ ZB−L + D2 − 1 2AµνAµν − i 4 ˜ AµνAµν and the soft breaking terms,

∆LSB =1 2MBL ˜ ZBL ˜ ZBL + ˜ ¯ NhD

N ˜

LHu + ˜ N chM

N ˜

Nσ1 + Bσ1σ2 + m2

σ1σ† 1σ1 + m2 σ2σ† 2σ2 + ˜

N †m2

N ˜

N

R-parity is no longer imposed. B-L symmetry forbids R-parity violating terms.

The supersymmetric B-L model

() × () × () × ()−

RGE

RGE are more complicated in this model. Mixing between the unitary groups are coming even at one loop due to, which, due to non zero beta-function for the mixing term, one needs to define an effective coupling and gaugino masses. In this sense, one have the running of the gauge couplings in terms of, and for gaugino masses the beta-functions need a similar treatment. Nevertheless, once the gauge structure is fixed, 1-loop RGE can be computed and solved.

β()

=

• π

L ⊂ ¯ ψγµ

ψµ ⇒

=

MB−L/gB−L > 6 TeV

Diagonalizing the unitary couplings, the effective running is determined to be, Therefore, at the mass of the Z, Besides, Z’ searches has a limit on, It means,

(Q/GeV)

10

Log 2 4 6 8 10 12 14 16 20 40 60 80 100 120 140 160

• 1

1

• 1

2

• 1

3

• 1

B-L

• Unification is not achieved at
• ne loop. But it might be fixed

considering threshold effects.

gB−L(mZ) ≈ 0.2894

MB−L > 1.7 TeV

M 2

B−L = g2 B−L(4v2 σ1 + 4v2 σ2 + v2 ˜ N)

B-L broken due to Sneutrino contributes to the mass of the B-L gauge boson. In the most general case, B-L breaking happens at high energies Following the same spirit, one finds the running of the masses to be,

˜ N

(Q/GeV)

10

Log 2 4 6 8 10 12 14 16 50 100 150 200 250 300 350 400 450 500

squarks sleptons sneutrino

H

m

H

m

• m

• m

= 30

• tan

= -1000 A > 0 µ

The breaking of B-L can be analyzed by looking at the scalar potential, VEV of the sneutrino remains at the GeV scale.

V ( ˜ N) =

• |yM|2 + 1

8g2

B−L

• | ˜

N|4 + m2

N| ˜

N|2

(Q/GeV)

10

Log

2 4 6 8 10 12 14 16

VEV (GeV)

50 100 150 200 250 300

> N ~ <

It is sizable experimentally.

• []

(νL, N, ˜ χ0)

• ˜

ψ0T = ( ˜ B0 ˜ W 0 ˜ H0

d

˜ H0

u

˜ Z0

B−L

˜ σ1 ˜ σ2)

M˜

χ0 =

• M˜

χ0

MSSM

M˜

χ0

B−L

• Neutrinos and Higgses

Neutrino masses can be extracted from a double see-saw mechanism. Neutrinos and neutralinos are mixed are in the same mass matrix, therefore the first implementation will be with the complete mass matrix, In the basis where neutralino mass matrix in the basis, is,

Mν ˜

χ0 =

  

yDvsβ √ 2

Λ

yDvsβ √ 2

Ω ΛT ΩT M˜

χ0

  

[GeV]

M 100 200 300 400 500 600 700 800 [GeV]

m 1 10

10

Then, after the second see-saw, neutralino mass matrix elements are, A random scannig over the parameter space let the mass of RHN to be

• i

mνi < 2 eV

by requiring the cosmological constraint,

mN > O(1) GeV.

[Mν]11 = v2

Ry2 D

4µ

• tβ −

M1M2µc−2

β

m2

Z(M1+M2+(M1−M2)c2θW )

, [Mν]12 = vyDsβ √ 2 , [Mν]22 = −2g2

B−Lv2 R

MB−L .

L = Φ

ΦΦ,

• Φ =
• −
• (

)

• (Φ) = (

ν, ν†

,

ν,

, )

Higgs

The MSSM Higgses have to be reanalyzed. With extra Higgses in the model, and with the vev of the sneutrino, the effective lagrangian reads as, where, the mass matrix is more complex, in the basis, Minimization conditions reduces the number of parameters in the model.

50 100 150 200 250 50 100 150 200 250 300

Heavy Higgs

50 100 150 200 250

m/m Δ 0.5 1 1.5 2 2.5 3 (GeV)

m 50 100 150 200 250 0.5 1 1.5 2 2.5 3 50 100 150 200 250 Mass (GeV) 50 100 150 200 250 300

MSSM = 10 GeV

D

a = 50 GeV

D

a = 100 GeV

D

a

Light Higgs

The MSSM Higgses are only sensitive to the soft parameter, .

aD

B-L Neutralino

Which is the LSP in the model ?? Lightest neutralino is still B-like, but the B-L is relatively close Depending on the parameter space, one can get the B-L eigenstate be the lightest one.

M˜

χ0

B−L =

  MBL −µ −µ  

(Q/GeV)

10

Log

2 4 6 8 10 12 14 16

Mass [GeV]

100 200 300 400 500 600 700 800 900

B-L

Z ~ g ~ W ~ B ~

f ¯ f ˜ f ˜ ZB−L ˜ ZB−L ˜ σ1(2) ¯ σ1(2) σ1(2)

Relic Density

If the DM component is dominated completely by the B-L gauge boson, the proceses that contribute to the Relic Density in which an sfermion or a sigma is exchanged in the t and u channel.

Points which satisfied all constraints have been used to compute the relic density For a B-L gauge boson mass in the range between 150 and 900 GeV, we are in agreement with WMAP

˜ σ1 ˜ σ1 ZB−L f ¯ f ˜ N N ¯ N ˜ ZB−L σ1 ¯ σ1

If the DM component is dominated by, we get

˜ σ1

˜ σ1 ˜ σ1 ZB−L f ¯ f ˜ N N ¯ N ˜ ZB−L σ1 ¯ σ1

ZB−L f ¯ f ˜ σ2 ˜ σ2 ˜ ZB−L σ2 ¯ σ2

If the DM component is dominated by, we get And, if the DM composition is dominated, thus,

˜ σ1

˜ σ2

Conclusions

We have studied the supersymmetric extension of a gauge group, where we have added a RHN superfield, and two extra B-L Higgs. We solved the renormalization group equations for all the parameters of the model. Breaking of B-L is mediated by the sneutrino fields. Its vev at low energies is under control due to contributions of all sparticles. By applying a double see-saw procedure, neutrinos can acquire a mass which can solve some problems in neutrino phenomenology. We have studied the contribution to the relic density by considering that the B-L sector contains the LSP .

Thank you...