Decaying Gravitino Dark Matter

Home , Gravitino

Michael Grefe Werkstattseminar – 28.04.2009

Outline

1 Gravitino Cosmology 2

2 Bilinear R-parity Breaking 2

3 Gravitino Decay Channels 4

4 Fluxes from Gravitino Dark Matter Decay 6

5 Neutrino Observation 7

6 Signals from Gamma Rays and Antimatter 10

References

[1] L. Covi, M. Grefe, A. Ibarra and D. Tran, JCAP 0901 (2009) 029 [arXiv:0809.5030 [hep-ph]].

[2] M. Grefe, DESY-THESIS-2008-043

[3] M. Bolz, A. Brandenburg and W. Buchmuller,¨ Nucl. Phys. B 606 (2001) 518 [Erratum-ibid. B 790 (2008) 336] [arXiv:hep-ph/0012052].

[4] R. Barbier et al., Phys. Rept. 420 (2005) 1 [arXiv:hep-ph/0406039].

[5] T. Montaruli, arXiv:0901.2661 [astro-ph].

[6] K. Ishiwata, S. Matsumoto and T. Moroi, arXiv:0903.0242 [hep-ph].

1 1 Gravitino Cosmology

If gravitinos are in thermal equilibrium in the early universe depending ◦ on the gravitino mass their relic density might overclose the universe. An inﬂationary phase that dilutes any primordial gravitino density ⇒ is needed! Thermal gravitino production during the reheating phase of the uni- ◦ verse can lead to the correct relic density for dark matter [3]:

2 2 TR 100 GeV mg˜ Ω3/2h 0.27 10 . ' 10 GeV m3/2 1 TeV Thermal leptogenesis requires a reheating temperature T & 109 GeV. ◦ R A gravitino mass m & (10) GeV is reasonable. ⇒ 3/2 O If the gravitino is not the lightest supersymmetric particle (LSP) it is ◦ very long-lived due to its MPl suppressed couplings and can spoil the successful predictions of big bang nucleosynthesis (BBN). If the gravitino is the LSP it is a natural candidate for cold ⇒ dark matter. Then the next-to-lightest supersymmetric particle (NLSP) is long-lived and can spoil the BBN predictions. One possible solution is the introduction of a tiny R-parity violation. ◦ It must be large enough to make the NLSP decay into standard model particles before BBN and small enough to guarantee that the baryon asymmetry is not washed out by sphaleron processes before the elec- troweak phase transition. These conditions lead to a gravitino lifetime exceeding the age of ⇒ the universe by many orders of magnitude.

2 Bilinear R-parity Breaking

The most general MSSM superpotential contains renormalizable lepton ◦ and baryon number violating terms that are usually removed by the introduction of R-parity to avoid rapid proton decay [4]:

/ 1 1 W Rp = µ H L + λ L L Ec + λ0 L Q Dc + λ00 U cDcDc . MSSM i u i 2 ijk i j k ijk i j k 2 ijk i j k

set to zero in the case of bilinear R/ p | {z } 2 R-parity breaking introduces a mixing between the Hd and Li ﬁelds. ◦ Thus there is an ambiguity in the choice of the basis for these ﬁelds:

0 Hd Hd Hd Lα = 0 = U . Li → Li Li

We choose the basis where the bilinear R-parity breaking term vanishes: ◦ µ µ H = H0 i L0 and L = L0 + i H0 . d d − µ i i i µ d

In this case trilinear lepton number violating couplings are generated ◦ from the MSSM superpotential:

e c d c W = µHuHd + µiHuLi + λjkHdLjEk + λjkHdQjDk + . . . µ µ W 0 = µH H0 i λe L0 L0 Ec i λd L0 Q Dc + . . . . → u d − µ jk i j k − µ jk i j k

No baryon number violating term is generated in this way. Therefore ◦ the proton stability is maintained. There are also R-parity violating terms in the soft scalar potential: ◦ R/ p ˜ 2 † ˜ Vsoft = BiHuLi + m˜ diHdLi + h.c. + . . . .

The bilinear R-parity breaking term in the superpotential and those in ◦ the soft scalar potential cannot be rotated away simultaneously. One can easily see that there arises a VEV for the sneutrino ﬁelds from ◦ the soft R-parity breaking bilinear terms:

2 ˜ 2 ˜ 2 † ˜ V = mL˜ Li + BiHuLi + m˜ diHdLi + h.c. + . . . i | | = m2 ν˜ 2 + B H0ν˜ + m˜ 2 (H0)∗ν˜ + h.c. + . . . ν˜i | i| − i u i di d i ∂Vmin 2 2 0 = ∗ = mν˜i ν˜i Bivu + m˜ divd ∂ν˜i h i − 2 Bi sin β m˜ di cos β ν˜i = v −2 . ⇒ h i mν˜i

In fact one has to perform the minimization of the complete scalar ◦ potential for the Higgs and the sneutrino ﬁelds. Then one ﬁnds for the sneutrino VEV: 2 Bi sin β m˜ di cos β ν˜i = v 2 1− 2 . h i mν˜i + 2 mZ cos 2β

3 With bilinear R-parity breaking we have Higgs–slepton mixing terms ◦ that appear in the soft scalar potential and gaugino–lepton mixing terms that arise from MSSM gauge vertices in the presence of a sneutrino VEV.

3 Gravitino Decay Channels

The gravitino decay channels are determined by the gravitino interac- ◦ tion Lagrangian and the MSSM gauge Lagrangian:

i ∗ ∗i µ ν i i i ν µ int = D φ ψ¯ν γ γ PLχ Dµφ χ¯ PRγ γ ψν L − √2 M µ − Pl i ¯ ν ρ µ (α) a (α) a −2 ψµ [γ , γ ] γ λ Fνρ + (MPl ) , − 8MPl O = √2g λ¯(α) aφ∗iT (α) P χj √2g χ¯iP T (α) φjλ(α) a + . . . . Lgauge − α a, ij L − α R a, ij In the presence of bilinear R-parity breaking we ﬁnd the following tree ◦ level diagrams for gravitino two-body decays: γ, Z0; W Z0; W

ψ3/2 ν˜ + ψ3/2 ν˜, h li h li χ˜0; χ˜∓

∓ ∓ νl; l νl; l

h h

∗ ν˜l ψ3/2 + ψ3/2 ν˜ , h li χ˜0

νl νl

The three-body decays from trilinear R-parity breaking terms are ne- ◦ glected in the calculation.

4 0 10 Wl

ν Z l 10-1 ν h l

10-2 Branching Ratio γν l

10-3 100 1000 m3/2 (GeV)

Figure 1: Gravitino branching ratios for the two-body decays.

0 Then, for instance, the gravitino decay width into Z and νl is given ◦ by:

2 m3 0 ξl 3/2 2 2 8 mZ 1 Γ ψ Z ν β U f U ˜ ˜ j + h , 3/2 → l ' 64π M 2 Z Z˜Z˜ Z − 3 m ZZ Z 6 Z Pl 3/2

2 4 ∗ ν˜l mZ SZ˜αSαZ˜ ξl = h i , βZ = 1 , UZ˜Z˜ = mZ , v − m2 m 0 3/2 Xα=1 χ˜α 2 4 2 2 4 2 mZ 1 mZ 1 mZ mZ mZ fZ = 1 + 2 + 4 , jZ = 1 + 2 , hZ = 1 + 10 2 + 4 . 3 m3/2 3 m3/2 2 m3/2 m3/2 m3/2 The branching ratios are independent of the sneutrino VEV in contrast ◦ to the total decay width.

In the phenomenological studies the lifetime (τ = 1/Γ ) and the ◦ 3/2 3/2 mass are unknown parameters.

Most of the two-body decay products are unstable. The lepton l sub- ◦ sequently decays (if l = µ, τ) and the Z0, W and h bosons fragment into stable particles:

− + γ , νi , e , e , p , p¯.

The spectra of γ, ν and e∓ (if l = e) contain a peak from the two-body ◦ i decay and all spectra have a continuum contribution from fragmenta- tion.

5 4 Fluxes from Gravitino Dark Matter Decay

If the gravitino accounts for the dark matter, its decays produce an ◦ astrophysical ﬂux of decay products. dJ dN dE ≡ dE dA dt dΩ

The diﬀerential ﬂux from a volume element in the galactic halo is given ◦ by (~l = (s, b, l) are galactic coordinates):

~ ~ dJ(l) n3/2(l) dN 2 = 2 s cos b ds db dl . dE 4π s τ3/2 dE

In contrast to charged particles (see Christoph’s talk) gamma rays and ◦ neutrinos propagate freely over cosmic distances (neutrino oscillations distribute the signal equally into all flavors). Thus the differential flux is simply given by the line-of-sight integral

dJhalo(b, l) 1 dN ~ = %halo(l) ds . dE 4π τ3/2 m3/2 dE Z line of sight

There is a second, subdominant contribution from the cosmic dark ◦ matter density:

∞ dJ Ω % dN (1 + z)−3/2dz eg = 3/2 c . 1/2 −3 dE 4π τ3/2 m3/2H0Ωm Z d(E (1 + z)) 1 + ΩΛ/Ωm (1 + z) 0 p In the case of WIMP annihilation the halo ﬂux reads ◦ dJhalo(b, l) σv dN 2 ~ = h 2i %halo(l) ds . dE 8π mDM dE Z line of sight

2 Due to the nDM dependence the signal from annihilating dark matter ◦ is much more sensitive to the dark matter distribution in the halo and in particular to the inner slope of the halo proﬁle.

In that case one expects a dominant signal from the galactic center and ◦ also neutrino signals from the annihilation of WIMPs that accumulate inside the Sun and the Earth.

6 ) -2 ) -2

-1 10 -1 10 atmospheric neutrinos upper hemisphere sr -3 sr -3 -1 10 -1 10 s νµ s νµ -2 -4 ν -2 -4 ν 10 e 10 e ν τ ν 10-5 10-5 τ

10-6 10-6

10-7 10-7

x dJ/dE (GeV cm -8 m3/2 = 300, 600, 1200 GeV x dJ/dE (GeV cm -8 m3/2 = 300, 600, 1200 GeV 2 10 2 10 E E 0.1 1 10 100 1000 10000 0.1 1 10 100 1000 10000 E (GeV) E (GeV)

Figure 2: Neutrino ﬂux from gravitino decay compared to the atmospheric background for the complete sky (left) and for the upper hemisphere (right).

For decaying gravitinos on the other hand the best strategy is to look ◦ for a diﬀuse signal in gamma rays and neutrinos.

Therefore in the following we use the averaged halo ﬂux: ◦ 2π π/2 dJ 1 dJ (b, l) halo = dl halo cos b db . dE 4π Z Z dE 0 −π/2

5 Neutrino Observation

There are three important questions: ◦ – How large is the neutrino flux from gravitino decay compared to background fluxes? – How large are the expected neutrino event rates? – What is the detection efficiency of neutrino experiments?

We choose the gravitino mass and lifetime to account for the rise of the ◦ positron ﬂux in the PAMELA data:

m = 300 , 600 , 1200 GeV and τ = (1026) s . 3/2 3/2 O The main background in the GeV to TeV range are atmospheric neutri- ◦ nos. Interactions of cosmic rays with the atmosphere produce mainly pions and kaons which subsequently decay into muon and electron neutrinos besides other particles.

7 The dominant tau neutrino background comes from the conversion of ◦ atmospheric muon neutrinos due to neutrino oscillations.

This tau neutrino background can be reduced signiﬁcantly if only the ◦ upper hemisphere is considered.

Generally the signal-to-background ratio increases for increasing grav- ◦ itino mass. However, only in the tau ﬂavor the signal from gravitino decay exceeds the background.

It might be possible to extract the muon and electron neutrino signals ◦ if large statistics is available.

Since the ﬂuxes are very small km3 detectors are necessary in order to ◦ obtain considerable event rates.

The νN cross section is proportional to the neutrino energy. This eﬀect ◦ compensates the 1/m3/2 behavior of the neutrino ﬂux from gravitino decay.

Cherenkov detectors like IceCube have virtually no eﬃciency to detect ◦ shower events (i.e. νe and ντ ) at sub-TeV energies. By contrast charged current interactions of ν produce a muon that ◦ µ leaves a clear signal in the detector.

The eﬀective detector volume for muon neutrinos increases by the fact ◦ that the muon can penetrate several kilometers of surrounding material before it reaches the detector. This muon range increases with the muon energy.

The neutrino event rate is given by the convolution of the flux with the ◦ neutrino effective area: dN dJ ∆Ω Aeff(E) dE . dt ∼ Z dE

The neutrino effective area encodes all effects of neutrino attenuation ◦ from the passage through Earth, the νN cross section, the muon range and the detection and selection efficiencies.

Using the eﬀective area of the completed IceCube experiment, we ex- ◦ pect (10 1000) events from gravitino decay per year. O − 8 Figure 3: Neutrino eﬀective areas of present neutrino telescopes. Figure taken from [5].

This number has to be compared to an expected atmospheric muon ◦ neutrino background of (105) events per year. O Still it seems possible to achieve a statistic signiﬁcance of S/√B (1) ◦ in one year depending on the gravitino mass and lifetime. ∼ O

9 6 Signals from Gamma Rays and Antimatter

1 1000 Gravitino LSP (a) Gravitino LSP (a) Lepton: electron Lepton: electron Data: PAMELA sec str) ) - 2 e /m Φ 2 + +

e 0.1 100 Φ ) (GeV - / ( e + e Φ Φ + + e Data: ATIC,PPB-BETS Φ ( 3 E 0.01 10 10 100 1000 10 100 1000 E (GeV) E (GeV)

10 -51 1000101 BESS 95+97 Gravitino LSP Gravitino LSP(b) GravitinoGravitino LSP LSP (b) Lepton: electron Lepton: electron BESS 1999 Data: EGRET 0 m3/2=300 GeV BESS 2000 Data: PAMELA 10 26

sec str) τ BESS Polar

) =2.0x10 sec -

2 3/2

e CAPRICE 98 -6 sec str) /m Φ 10 2 2

str sec) -1 2 + 10 +

e 0.1 100 Φ ) (GeV - / (

e -2 + 10 e Φ

(GeV/cm -7 γ

Φ 10 + Φ +

2 e -3 Data: ATIC,PPB-BETS E Φ 10 ( AntiP flux (/GeV m 3 E

0.01-8 10 -4 10 10 100 1000 10 10 100 1000 0.1 1 10 100 1000 0.1 1 10 100 E (GeV) ET (GeV) (GeV) 101 101 BESS 95+97 BESS 95+97 Gravitino LSP BESS 1999 Gravitino LSP BESS 1999 m =600 GeV BESS 2000 m =1.2 TeV BESS 2000 100 3/2 100 3/2 τ =1.1x1026sec BESS Polar τ =8.6x1025sec BESS Polar 3/2 CAPRICE 98 3/2 CAPRICE 98 sec str) sec str) 2 2 10-1 10-1

10-2 10-2

10-3 10-3 AntiP flux (/GeV m AntiP flux (/GeV m

10-4 10-4 0.1 1 10 100 0.1 1 10 100 T (GeV) T (GeV)

Figure 4: Signals in other particle species from gravitino dark matter decay. From top left to bottom right: Positron fraction (MED propagation parameters), electron + positron flux (MED propagation parameters), gamma ray flux, antiproton flux (300, 600, 1200 GeV). Figures taken from [6].