R-Partity Breaking via Type II Seesaw, Gravitino Dark Matter and - - PowerPoint PPT Presentation

R-Partity Breaking via Type II Seesaw, Gravitino Dark Matter and Positron Excess

Shao-Long Chen University of Maryland

Pheno 2009 Based on arXiv:0903.2562 in collaboration with R. N. Mohapatra, S. Nussinov and Yue Zhang

Pheno 2009 – p.1/18

♦ Outline

• 1. Motivation;
• 2. R-parity violating via Type-II seesaw;
• 3. Cosmic electrons excess from Gravitino decay;
• 4. Summary.

Pheno 2009 – p.2/18

PAMELA positrons excess

Energy (GeV)

1 10 100

))

• (e

φ )+

+

(e φ ) / (

+

(e φ Positron fraction

0.01 0.02 0.1 0.2 0.3

PAMELA

kinetic energy (GeV) 1 10

2

10 /p p 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

• 3

10 ×

=500MV) φ Donato 2001 (D, =500MV) φ Simon 1998 (LBM, =550MV) φ Ptuskin 2006 (PD, PAMELA

PAMELA: positron excess but no anti-proton in the energy range of 10 ∼ 100 GeV.

PAMELA collaboration ArXiv:0810.4994, 0810.4995

Pheno 2009 – p.3/18

Fermi, HESS, ATIC electrons/positrons excess

Energy (GeV)

2

10

3

10 )

• 1

sr

• 1

s

• 2

m

2

dN/dE (GeV

3

E

2

10 15% ± E ∆

ATIC PPB-BETS Kobayashi H.E.S.S. H.E.S.S. - low-energy analysis Systematic error Systematic error - low-energy analysis Broken power-law fit

ArXiv:0905.0025, 0905.0105

Pheno 2009 – p.4/18

Modified background

ArXiv:0905.0636[astro-ph.HE]

The black continuos line corresponds to the conventional model used in (Strong et al. 2004 ) and the red dashed and blue dot-dashed lines are obtained with modified injection indexes in order to fit Fermi-LAT CRE data.

Pheno 2009 – p.5/18

Interpretation of the observations

♣ Astrophysical sources: Nearby pulsars, ... ♣ Dark matter: stable dark matter pair annihilation and decaying dark matter how to explain the lack of any excess in the hadrons? how does one get an adequate enough electron/positron production rate to explain the excess? ♦ dark matter pair annihilation: an additional enhancement (∼ 102−3) is required for the annihilation cross section required by relic density. (Sommerfeld enhancement, Breit-Wigner resonance, non-thermal relic density, or nearby clump dark matter, ...) ♦ dark matter decay: ∼ 1026 sec lifetime. with Leptophilic channels, either by dynamics or kinematically.

Pheno 2009 – p.6/18

Gravitino as the decaying dark matter with RPV.

Due to the factor 1/MP lanck suppression, gravitino has very long lifetime to be dark matter. Considering MSSM with RPV terms LLec, QLdc, ucdcdc and LHu. ˜ G mainly decays to Zν, γν, W ±ℓ∓. ⇒ both leptons as well as hadrons in the final states of gravitino decay. If one kept only the LLec term, then the predominant decay mode of the gravitino will only be to leptons. While the strength of the coupling λ required for keeping baryon asymmetry is too small (λ < 10−7) [B. A. Campbell et al. (1991); H. Dreiner et al. (1993).] to explain neutrino masses via loop corrections.

Pheno 2009 – p.7/18

We propose a new class of R-parity violating interactions that can arise in extensions of MSSM: ♦ explains small neutrino masses and mixings via the type II seesaw mechanism; ♦ keeps the baryon asymmetry of the universe untouched; ♦ able to explain the leptophilic nature of the PAMELA observations.

Pheno 2009 – p.8/18

A well hidden in low energy processes RPV term

extend MSSM by adding SU(2)L triplets ∆, ¯ ∆ with Y = ±2. with the superpotential as:

W = λuQT iτ2Huuc + λdQT iτ2Hddc + λlLT iτ2Hdec + µHuHd +fLT iτ2∆L + ǫdHT

d iτ2∆Hd + ǫuHT u iτ2 ¯

∆Hu + µ∆Tr ` ∆ ¯ ∆ ´ +fA e LT iτ2∆e L + ǫdAHT

d iτ2∆Hd + ǫuAHT u iτ2 ¯

∆Hu + b∆Tr ` ∆ ¯ ∆ ´ + h.c. .

♣ add R-parity violating term:

δWR = a∆HdL.

The associated soft breaking terms is: LR = ρ L∆Hd + h.c.

Pheno 2009 – p.9/18

Neutrino masse: through by type II seesaw after the triplet Higgs gets vev vT ∼ ǫu,dv2

wk/MS.

mν = 2fvT 0.1eV , then implies that if vT ≤ MeV (ǫu,d ≤ 10−5), f ≥ 10−7. ν − ∆ mixing gives contribution ∼ (avwk)2/MSUSY via a seesaw-like formula, but negligible compared to that from type II. LFV constraints on the couplings f, eg. µ → 3e gives f11f12 ≤ 10−6.

Pheno 2009 – p.10/18

♣ RPV induced mixing and Gravitino decay: The ∆ − ℓ mixing: Ue

e∆ ≃ (ρ + aµ)vwk

m2

e e − m2 ∆

. Then the gravitino will decay through G → ℓδ → ℓℓν. These mixings between γν, Wℓ, Zν etc. are severely suppressed.

~ ~ <H d

0 >

W − l − ~ ~ <H d

0 >

~ Z <H d

0 >

~

− −

l ~ ~ ~ l l

♣ monochromatic neutrino signatures: ˜ G → νδ0(3ν) when m ˜

G > mδ. Pheno 2009 – p.11/18

Radiative stability

the radiative correction to ǫ is safe due to the non-renormalization theorem

• f SUSY.

for ǫA, due to symmetry argument (lepton number and restored PQ symmetry by assigning charges to fields and spurion’s parameters see Arxiv:0903.2562 appendix). δ ǫA vwk

• ∝

1 16π2 a2 .f So the smallness of ǫA is stable under radiative corrections. the usual R-parity violating MSSM terms generated through radiative corrections Their strengths are, however, very weak and do not lead to any

• bservable effects.

E c L H u H d H u − L H d H u − D c Q H u H d L H d L L

Pheno 2009 – p.12/18

Diffusion

The transport equation ∇ · (K(E, x)∇fe+) + ∂ ∂E (b(E, x)fe+) + Q(E, x) = 0 ,

fe+ is the number density of positron per unit energy, K(E, x) is the diffusion coefficient, b(E, x) is the rate of energy loss b(E) ≈ 10−16(E/1GeV)2sec−1.

The source term Q(E, x) =

ρ( x) m e

Gτ e G

dNe+ dE .

The solution of the transport equation at the Solar system can be expressed by the convention [Ibarra et al. 2008] fe+(E) = 1 m e

Gτ e G

Z Emax dE′G(E, E′)dNe+ dE′ , The positron flux from gravitino decay can then be obtained from Φprim

e+

(E) = c 4π fe+(E) = c 4πm e

Gτ e G

Z Emax dE′G(E, E′)dNe+ dE′ .

Pheno 2009 – p.13/18

Astrophysical background:

We use the parametrizations obtained in [Baltz et al 1998, Moskalenko 1997] with the fluxes in units of (GeV−1 cm−2 sec−1 sr−1): Φprim

e−

(E) = 0.16E−1.1 1 + 11E0.9 + 3.2E2.15 , Φsec

e− (E)

= 0.7E0.7 1 + 110E1.5 + 600E2.9 + 580E4.2 , Φsec

e+ (E)

= 4.5E0.7 1 + 650E2.3 + 1500E4.2 , where E is expressed in units of GeV.

Pheno 2009 – p.14/18

To fit the PAMELA’s data, as an example, we take m e

G = 350 GeV, m∆ = 700

GeV, |fUe

ℓ∆| = 2.5 × 10−8, therefore the lifetime of gravitino is about 2.1 × 1026

sec (for simplicity, degenerate neutrino mass hierarchy used).

• ))

Pheno 2009 – p.15/18

The fit after Fermi LAT data

• ))

• 2

• 1

• 1

Here we use m ˜

G = 3 TeV, mδ=2.9 TeV, τ ˜ G = 0.42 × 1026 sec by taking the

neutrino mass normal hierarchy. (Triplet Higgs ∆ mainly decay to µ and τ’s.)

Pheno 2009 – p.16/18

Summary

A new R parity violating scenario is proposed which related to the neutrino mass via type II seesaw. This provides a natural explain of small neutrino mass and the positron/electrons excess, but no excess in hadron. This class of R-parity breaking models remains very well hidden from low energy experimental probes.

Pheno 2009 – p.17/18

backup slides

Pheno 2009 – p.18/18