Dark Matter and Neutrinos

Home , Majorana fermion

Viviana Niro

Max Planck Institut fuer Kernphysik, Heidelberg

Heidelberg, 19 July, 2010

based on VN, A. Bottino, N. Fornengo, S. Scopel, 0909.2348 [hep-ph]; M. Lindner, A. Merle, VN, 1005.3116 [hep-ph]

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 1/26 Outline

1 Dark Matter and neutrino production

2 Neutralino Dark Matter The eﬀective MSSM Hadronic uncertainties Fluxes from the Earth Fluxes from the Sun

3 Direct neutrino production Scalar Dark Matter s-channel: The triplet scalar mediator t-channel: The singlet fermionic mediator

4 Summary and conclusions

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 2/26 Dark Matter and neutrino production

Dark Matter: form of non-luminous matter almost 23% of the total mass-energy of the Universe ⇒

Detection of Dark Matter: direct detection experiments scattering of DM particles oﬀ atomic nuclei inside a detector ⇒ indirect detection experiments DM annihilation products (γ-rays, antimatter and neutrinos) ⇒ in the GC, in the GH, in dSph, in the Earth and in the Sun DM production at collider experiments detection of a new particle that could act as DM ⇒

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 3/26 Particles of Dark Matter gravitationally trapped inside celestial bodies accumulate in ⇒ the central part of the body annihilate producing neutrinos ⇒ The diﬀerential neutrino ﬂux is: dN Γ dN ν ann BR f = 2 f , dEν 4πd dEν Xf d = distance from the source; Γann = annihilation rate inside the celestial body

C 2 −1/2 Γann = tanh (t0/τA) , τA ( σann v ) 2 ∝ h i Production: Diﬀerent annihilation channels

χχ qq¯, ττ,¯ νν,¯ ZZ, W +W −, gg, Higgs channels → Propagation: inside the Sun oscillation, neutral and charged current interactions → inside the Earth mainly vacuum oscillation (we considered θ13 = 0) → Cirelli et al., hep-ph/0506298; Blennow et al., 0709.3898 [hep-ph] Detection: Super-Kamiokande detector stopping and through-going muons →

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 4/26 Neutralino Dark Matter: the effective MSSM Effective MSSM at the EW scale is defined by five independent parameters

M1 = U(1) gaugino mass M2 = SU(2) gaugino mass µ = Higgs mixing mass parameter tan β = ratio of the two Higgs vevs mA = mass of the CP-odd neutral Higgs boson mq˜ = squark soft mass commont to all squarks m˜l = sleptons soft mass commont to all sleptons A = trilinear parameter for the third family (A˜ = A˜ A mq˜ , Aτ˜ A m˜) b t ≡ ≡ l No gaugino-mass uniﬁcation at the GUT scale is assumed ⇒ Bottino et al., hep-ph/0212379, hep-ph/0401186

2 lower limit on neutralino mass from upper bound on (ΩCDM h ): ⇒ 2 (ΩCDM h )max = 0.122 mχ 7 GeV → ≥ Bottino et al., hep-ph/0304080

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 5/26 Hadronic uncertainties Coupling between the Higgs boson and the nucleon

h,H h,H h,H Ih,H = k mq N qq¯ N = k gu + k gd , q h | | i u−type d−type q X introducing 1 1 σπN = (mu + md ) N uu¯ + dd¯ N , σ0 (mu + md ) N uu¯ + dd¯ 2¯ss N , 2 h | | i ≡ 2 h | − | i

r = 2ms /(mu + md )

4 19 1 2 23 25 gu (mN + σπN r(σπN σ0)) , gd (mN + σπN + r(σπN σ0)) ⇒ ≃ 27 8 − 2 − ≃ 27 4 4 −

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 6/26 Hadronic uncertainties Coupling between the Higgs boson and the nucleon

r = 2ms /(mu + md )

4 19 1 2 23 25 gu (mN + σπN r(σπN σ0)) , gd (mN + σπN + r(σπN σ0)) ⇒ ≃ 27 8 − 2 − ≃ 27 4 4 − Experimental values:

41 MeV σπN 57 MeV R. Koch (1982) , 55 MeV σπN 73 MeV Pavan et al. (2001) ≤ ≤ ≤ ≤

30 MeV σ0 40 MeV Gasser and Leutwyler (1982) ≤ ≤ Nuclear sets considered:

(σπN , σ0, r) MIN = (41, 40, 25); REF = (45, 30, 29); MAX = (73, 30, 25) ⇒

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 6/26 Through-going muons from the Earth

Hadronic uncertainties

Cored-isothermal sphere with isotropic velocity dispersion

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 7/26 Stopping muons from the Earth

Hadronic uncertainties

Cored-isothermal sphere with isotropic velocity dispersion

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 8/26 Stopping muons from the Sun

Hadronic uncertainties

Cored-isothermal sphere with isotropic velocity dispersion

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 9/26 Conﬁgurations compatible with DAMA region

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 10/26 “GOLDEN” channel for indirect detection experiments with neutrinos:

DM DM νν¯ or νν (¯νν¯) → Neutrino energy spectra:

a line at Eν mχ ≃ clear and distinct hint for a DM annihilation origin ⇒ eventually a soft part due to incoherent neutrino interaction with matter during propagation (DM annihilations inside the Sun and the Earth)

ΝΜ from ΝΜ Ν Μ channel at 1 AU Ν Μ from ΝΜ Ν Μ channel at 1 AU 10 10

mΧ@GeVD mΧ@GeVD 10 10 100 100 1 500 1 500 1000 1000 dx dx

Ν 0.1 Ν 0.1 dN dN

0.01 0.01

0.001 0.001 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

x = EΝmΧ x = EΝmΧ

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 11/26 In which cases a DM particle can have a sizable branching ratio into neutrinos? In the literature, it is often stated that DM pair-annihilation directly into neutrinos is always suppressed 0 2 this is true for the SUSY neutralinoχ ˜ , since σannv(χχ f f¯) m : ⇒ 1 → ∝ f Higgs exchange: s-channel h, H, A couplings to fermions are proportional to mf

2 σannv(χχ f f¯) m → → ∝ f

Z-boson exchange: s-channel

µ µ f f 5 j = f¯L,R γ (g g γ )fL,R Z,f V − A fL describes particle with negative helicity and anti-particle with positive helicity fR describes particle with positive helicity and anti-particle with negative helicity s-wave: one fermion in the “wrong helicity” state (analogy with π decay)

2 2 σannv(χχ f f¯) m + (v ) → → ∝ f O

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 12/26 Sfermion exchange: t and u-channel

v¯¯PR,Luχv¯χPL,R uf M ∼ f zero-velocity χχ spinors (see arXiv:hep-ph/0510257):

5 u¯χ(p1)vχ(p2) u¯χ(p2)vχ(p1) = (mχ + P//2)γ , P = pf + p¯ − f 5 v¯¯PR,L(mχ + P//2)γ PL,R uf M ∼ f 2 2 Thus: σannv(χχ f f¯) m + (v ) (see also Heather Logan’s talk, Universite de → ∝ f O Montreal, 2006-03-29)

Considering f˜L-f˜R mixing

v¯¯PL,R uχv¯χPL,R uf M ∼ f But f˜L-f˜R mixing is proportional to mf , thus

2 2 σannv(χχ f f¯) m + (v ) → → ∝ f O

2 Is the suppression mf present in general? key point of our work: investigate possible unsuppressed cases ⇒

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 13/26 Neutrino production

Model-independent analysis:

we restrict our work to the SM gauge group, SU(3)c SU(2)L U(1)Y × × (gauge boson exchange only Z-boson) →

να Lα L = (1, 2, 1) , να R (1, 1, 0) , α = e,µ,τ α ∼ − ∼ „ «L we consider explicitly scalar and fermionic DM and the corresponding s, t, and u channels (a spin one DM can have sizable BRν ) → we consider the DM particle χ and the mediator particle φ to be a singlet, doublet, or triplet representation of SU(2)L:

ψs;1 (1, 1, 0) , ψf ;1 (1, 1, 0) ∼ ∼ ψ+ ψ0 ψs;2 = (1, 2, 1) , ψf ;2 = (1, 2, 1) ψ0 ∼ ψ− ∼ − „ « „ « ψ+/√2 ψ++ ψ−/√2 ψ0 ψs;3 = (1, 3, 2) , ψf ;3 = (1, 3, 2) ψ0 ψ+/√2 ∼ ψ−− ψ−/√2 ∼ − „ − « „ − «

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 14/26 Dirac mass term

αβ αβ mass = Y LαL H˜ νβR + h.c. vH Y ναLνβR + h.c. L − D → − D ∗ vH = 174 GeV, H˜ = iσ2H

Majorana mass terms

1 αβ C 1 αβ C mass = Y (LαL) (iσ2 T ) LβL + h.c. m (ναL) νβL + h.c. L − 2 L → − 2 L

1 αβ C mass = M (ναR ) νβR + h.c. L − 2 R αβ αβ mL = vT YL , vT : VEV of the neutral component of the scalar triplet

See-saw mechanisms

−1 T T type I Mν mD M m = UDν U → ≡ − R D

−1 T T type II Mν mL mD M m = UDν U → ≡ − R D mD = vH YD

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 15/26 four diﬀerent neutrino scenarios: Dirac neutrinos (νL and νR independent), C Majorana neutrinos (νR (νL) ), → Majorana neutrinos with see-saw type I or see-saw type II

see-saw type I: ′ yD might be sizable, νL ν , but NR θ mD /MR ≃ L → ≃ see-saw type II: 2 mν = yT vT m /MR yT larger than mν if ﬁne tuning − D → triplet w/o vev: yT might be sizable, no restriction on the size of yT from the neutrino sector (check the coupling of the triplet with the SM Higgs)

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 16/26 Scalar Dark Matter

Scalar mediator: s-channel

αβ C Y = Y (ναR ) φs;1 νβR + h.c. only sterile ν produced L ν;1 − ν;1 → αβ Y = Y LαL φ˜s;2 νβR + h.c. problem with DM vertex L ν;2 − ν;2 → αβ C Y = Y (LαL) (iσ2 φs;3) LβL + h.c. OK if φs;3 = 0 L ν;3 − ν;3 → h i (2,3) (2,3) † γ (χ φs;3χ˜s;2) + h.c. → Lχφ ⊃ χφ s;2 h αβ 2 (2,3) 2 i Yν;3 γχφ σannv | | | | ⇒ ∝ (4m2 m2 )2 χ − φ

Z-boson mediator: s-channel

kin µ g µ L = LLiγ DµLL νLγ νLZµ L ⊃ − 2 cos θW kin † µ kin † µ = (Dµχs;2) (D χs;2) , = Tr (Dµχs;3) (D χs;3) → Lχ;2 Lχ;3 2 2 h i σannv m v (angular momentum conservation) ⇒ ∝ χ

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 17/26 Fermionic mediator: t and u-channels

Either the scalar DM or the fermionic mediator has to be ﬂavoured

(1,1) (1,1) α k = ν χ [φf ;1] + h.c. only sterile ν produced Lχφν Tαk R s;1 L → (2,1) (2,1) α k = L χ˜ [φf ;1] + h.c. OK Lχφν Tαk L s;2 R → α index in ﬂavour space, k index that denotes the lightest scalar particle: k β χs;1 = Wkβ χs;1, with W being a rotation matrix

Considering φf ;1 as Majorana fermion:

(2,1) 4 αk 2 annv m σ |T2 |2 2 φ ⇒ ∝ (mχ + mφ)

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 18/26 Scalar Dark Matter: summary table

Channel Mediator DM rep. Dir. ν Maj. ν See-saw I See-saw II s Scalar 1 1, 2, 3 L/ - R, θ2 R, θ2 s Scalar 3 2 L/ 2 2 2 s Scalar 1 w/ vev 1, 2, 3 L/ - R, θ2 R, θ2 s Scalar 2 w/ vev 1, 2, 3 mν - θ θ s Scalar 3 w/ vev 1, 2, 3 L/ mν - f.t. s Z-boson 2, 3 4(p) 4(p) 4(p) 4(p) t, u Fermion 1 1 R - R, θ2 R, θ2 t, u Fermion 1 2 2 2 2 2 t, u Fermion 2 1, 3 2 2 2 2 t, u Fermion 2 2 R - R, θ2 R, θ2 t, u Fermion 3 2 2 2 2 2 t, u Fermion 3 3 R - R, θ2 R, θ2

2: potentially unsuppressed; 4(p): suppressed for non-relativistic DM; f.t.: ﬁne tuning required between two couplings to get a sizable rate; L/: LNV terms are present; R: yields only right-handed neutrinos; θn: suppressed by the n-th power of the mixing angle between heavy and light neutrinos; mν : the Yukawa coupling involved is proportional to the light neutrino mass Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 19/26 s-channel: The triplet scalar mediator

Experimental constraints: − φs;3 might transmit LNV muon decay experimental uncertainty on GF of about − − → 10 10 GeV 2: −10 2 2 ee 2 µµ 2 10 mφ Yν;3 Yν;3 . 0.1 2 | | | | GeV !

− φ might transmit a LNV tau decay experimental limit on Γτ of about 0.1%: s;3 → −5 2 2 ττ 2 ee 2 µµ 2 10 mφ Yν;3 Yν;3 + Yν;3 . 0.1 2 | | | | | | GeV ! “ ” Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 20/26 ee µµ weaker constraints on Yν;3 and Yν;3 from electron and muon anomalous magnetic moment m m Y ee . (10−4) φ , Y µµ . (10−6) φ | ν;3| O MeV | ν;3 | O MeV oﬀ-diagonal elements constrained“ by”µ 3e and τ lll “ ” → →

If Y ee Y µµ, the only sizable diagonal Yukawa entry is given by: ν;3 ≃ ν;3 10−1m2 ττ 2 min φ GeV ττ 2 Yν;3 . 1, 2 , since mφ & 100 Yν;3 . 1 | | GeV ! → | |

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 21/26 10-22 Halo Average -23 200 10 Halo Angular

10-24 100 D

1 BF=10 - s 3 10-25 500 cm @ Natural Scale v

ann -26 800 Σ 10 BRΝΤ =0.1

10-27

ΓH2,3L=100 GeV, ÈYΤΤ È2=1 10-28 ΧΦ Ν;3 100 200 500 1000 2000 5000 1 ´ 104

mΧ@GeVD

Gray band: limits (at 3σ level) set using contained muon events in a 1km3 neutrino th ◦ telescope with Eµ = 100 GeV (cone half-angle of 30 around GC and 1yr exposure)

−7 −5 Sun: 5σ discovery if σpBRν 6 10 pb for mχ 200 GeV or if σpBRν 10 pb ≃ × ≃ ≃ for mχ 1 TeV (after one year of data with IceCube) ≃

SI −10 Earth: 5σ discovery if σp BRν 9 10 pb for mχ 200 GeV and if SI −9 ≃ × ≃ σ BRν 3 10 pb for mχ 1 TeV p ≃ × ≃ Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 22/26 t-channel: The singlet fermionic mediator

Experimental constraints:

− For a scalar DM particle, the charged scalar χs;2 and the fermionic singlet φf ;1 can mediate the µ eγ process and the τ µγ process → →

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 23/26 limit on the BR(µ eγ) provided by the MEGA experiment → m2 /GeV2 9 µ 4 H2 t . −11 3.2 10 4 4 ξ1 ( ) 1.2 10 , × ms /GeV ×

∗ with ξ2 = (2,1) (2,1) , t = m2/m2 and H(t) given by 1 Tek Tkµ f s h i 2 2 H(t) = 2t +5t−1 t ln t for scalar DM 12 (t−1)3 − 2 (t−1)4 limit on the BR(τ µγ) provided by the BELLE experiment → m2 /GeV2 6 τ 4 H2 t . −8 2.1 10 4 4 ξ2 ( ) 4.5 10 , × ms /GeV ×

∗ with ξ2 = (2,1) (2,1) 2 Tµk Tkτ h i weaker constraints on (2,1) and (2,1) from electron and muon anomalous Tek Tµk magnetic moment

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 24/26 If (2,1) (2,1), the only sizable coupling is given by: Tek ≃ Tµk 2 GeV2 (2,1) 2 min −4 ms / 1 τk . 1, 8.7 10 |T | × mτ /GeV H(t) „ «

In the case of a chiral mediator φf ;1: mτ mf stronger constraints → ⇒

10-22 Halo Average -23 10 Halo Angular

10-24 D 1 BF=10 - s 3 -25 cm

@ 10

v Natural Scale ann Σ 10-26 BRΝΤ =0.1

-27 10 100 500 T H2,1L 2 È Τk È = 1 200 800 10-28 100 200 500 1000 2000 5000 1 ´ 104

mΧ@GeVD

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 25/26 Summary and conclusions Neutralino Dark Matter ◮ Neutrino signal from neutralino annihilations inside the Earth and the Sun ⇒ dependence on hadronic parameters and WIMP distribution function ◮ Signal in through-going and stopping muons ⇒ stopping muons are a powerful source ◮ Under favourable conditions ⇒ neutrino detectors might provide important informations on light neutralinos

Neutrino production ◮ We have performed a detailed model-independent analysis of the process of DM annihilation directly into neutrinos ◮ We have considered diﬀerent neutrino mass models and diﬀerent SU(2)L representations for the DM and the mediator particles ◮ We have shown how to systematically search for possible unsuppressed scenarios ◮ We have explicitely considered numerically two examples: a promising s-channel and t-channel diagram

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 26/26 BACKUP SLIDES Fermionic Dark Matter

Scalar mediator: s-channel

αβ C Y = Y (ναR ) φs;1 νβR + h.c. only sterile ν produced L ν;1 − ν;1 → αβ Y = Y LαL φ˜s;2 νβR + h.c. only for chiral fermion DM L ν;2 − ν;2 → αβ C Y = Y (LαL) (iσ2 φs;3) LβL + h.c. OK if φs;3 = 0 L ν;3 − ν;3 → h i (2,2) (2,2) C = Y [χf ;2] (iσ2φs;3) [χf ;2] + h.c , → LYχ;3 − χ;3 L L αβ 2 2 ∗ Yν;3 Yχ 2 (2,2) (2,2) annv | | | | m Y Y Y σ 2 2 2 χ , χ = χ;3 + χ;3 ⇒ ∝ (4mχ mφ) − h i 0 for φs;3 exchange, due to parity conservation I Z-boson mediator: s-channel“ ”

2 DM is a Dirac fermion σannv m ⇒ ∝ χ constraints from DM direct detection experiments → 2 2 DM is a Majorana fermion σannv m v ⇒ ∝ χ

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 28/26 Scalar mediator: t and u-channels

Either the fermionic DM or the scalar mediator has to be ﬂavoured

(1,1) (1,1) α k = ν [χf ;1] φ + h.c. only sterile ν produced Lχφν Tαk R L s;1 → (2,1) (2,1) α k = L [χf ;2] φ + h.c. OK Lχφν Tαk L R s;1 → α index in ﬂavour space, k index that denotes the mass eigenstate of the scalar mediator

(2,1) 4 αk 2 annv m σ |T2 |2 2 χ ⇒ ∝ (mχ + mφ)

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 29/26 Fermionic Dark Matter: summary table

Channel Mediator DM rep. Dir. ν Maj. ν See-saw I See-saw II s Scalar 1 1, 2, 3 L/ - R, θ2 R, θ2 s Scalar 3 2 L/ 2 2 2 s Scalar 1 w/ vev 1, 2, 3 L/ - R, θ2 R, θ2 s Scalar 3 w/ vev 2 L/ mν - f.t. s Z-boson 2, 3 2/4(p) 2/4(p) 2/4(p) 2/4(p) t, u Scalar 1 1 R - R, θ2 R, θ2 t, u Scalar 1 2 2 2 2 2 t, u Scalar 2 1, 3 2 2 2 2 t, u Scalar 2 2 R - R, θ2 R, θ2 t, u Scalar 3 2 2 2 2 2 t, u Scalar 3 3 R - R, θ2 R, θ2

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 30/26 Fermionic Dark Matter: summary table

Channel Mediator DM rep. Dir. ν Maj. ν See-saw I See-saw II s Scalar 2 (1,2) ,(2,3) 2 - θ θ s Scalar 3 (1,3) L/ 2 2 2

s Scalar 2 w/ vev (1,2) ,(2,3) mν - θ θ s Scalar 3 w/ vev (1,3) L/ mν - f.t. t , u Scalar 1 (1,2) 2 - θ θ t , u Scalar 2 (1,2) 2 - θ θ t , u Scalar 2 (1,3) 2 2 2 2 t , u Scalar 3 (2,3) 2 - θ θ for chiral fermion DM strong constraints from EW precision measurements: → 2 S = NC (t3L(i) t3R (i)) /3π − Xi Considering a SM Higgs mass MH = 117 GeV, the new physics contribution to the S parameter is constrained to be . 0.06 at 95% C.L.

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 31/26 10-22 Halo Average 200 -23 10 Halo Angular 100

10-24 D 1 500 BF=10 - s 3 -25 cm

@ 10

v 800 Natural Scale ann Σ 10-26

BRΝ =0.1 10-27 Τ 2 ΤΤ 2 ÈYΧÈ = 1, ÈYΝ;3È = 1 10-28 100 200 500 1000 2000 5000 1 ´ 104

mΧ@GeVD

Gray band: limits (at 3σ level) set using contained muon events in a 1km3 neutrino th ◦ telescope with Eµ = 100 GeV (cone half-angle of 30 around GC and 1yr exposure)

−7 −5 Sun: 5σ discovery if σpBRν 6 10 pb for mχ 200 GeV or if σpBRν 10 pb ≃ × ≃ ≃ for mχ 1 TeV (after one year of data with IceCube) ≃

SI −10 Earth: 5σ discovery if σp BRν 9 10 pb for mχ 200 GeV and if SI −9 ≃ × ≃ σ BRν 3 10 pb for mχ 1 TeV p ≃ × ≃ Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 32/26 t-channel: The singlet scalar mediator

Experimental constraints:

− For a fermionic DM, the charged fermion χf ;2 and the scalar singlet φs;1 can mediate the µ eγ process and the τ µγ process → → limit on the BR(µ eγ) provided by the MEGA experiment → m2 /GeV2 9 µ 4 H2 t . −11 3.2 10 4 4 ξ1 ( ) 1.2 10 , × ms /GeV × ∗ with ξ2 = (2,1) (2,1) , t = m2/m2 and H(t) given by 1 Tek Tkµ f s h i 2 H t t −5t−2 t ln t ( ) = 12 (t−1)3 + 2 (t−1)4 for fermionic DM limit on the BR(τ µγ) provided by the BELLE experiment → m2 /GeV2 6 τ 4 H2 t . −8 2.1 10 4 4 ξ2 ( ) 4.5 10 , × ms /GeV × ∗ with ξ2 = (2,1) (2,1) 2 Tµk Tkτ weaker constraintsh on i(2,1) and (2,1) from electron and muon anomalous Tek Tµk magnetic moment

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 33/26 If (2,1) (2,1), the only sizable coupling is given by: Tek ≃ Tµk 2 GeV2 (2,1) 2 min −4 ms / 1 τk . 1, 8.7 10 |T | × mτ /GeV H(t) „ «

In the case of a chiral DM χf ;2: mτ mf stronger constraints → ⇒

10-22 Halo Average -23 10 Halo Angular

10-24 100 D 1 BF=10 - 200 s 3 -25 cm

@ 10

v Natural Scale ann

Σ 500 10-26 800

BRΝΤ =0.1 10-27 T H2,1L 2 È Τk È = 1 10-28 100 200 500 1000 2000 5000 1 ´ 104

mΧ@GeVD

Viviana Niro (MPIK, Heidelberg) Dark Matter and Neutrinos MPIKseminar2010 34/26