Kev Scale Sterile Neutrino Dark Matter

Fedor Bezrukov

The University of Manchester

Invisibles18 Workshop 3-7 September 2018 Karlsruhe Institute of Technology (KIT) Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions Outline

1 SM, Cosmology and sterile neutrinos

2 X-ray observations

3 Pure νMSM – just three sterile neutrinos

4 Other DM generation mechanisms

5 Laboratory searches Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions Standard Model – describes nearly everything

Three Generations

of Matter (Fermions) spin ½ CDHSW I II III Experimental CHORUS NOMAD NOMAD mass→ 2.4 MeV 1.27 GeV 171.2 GeV 0 NOMAD

0 KARMEN2 CHORUS charge→ ⅔ ⅔ ⅔ 0 10 MiniBo oNE u c t g Bugey LSND 90 /99 % name→ up charm top gluon Left Right Left Right Left Right Einstein problems: SuperK 90 /99 % CHOOZ 104 MeV 4.2 GeV 0 MINOS 4.8 MeV –3 10 K2K -⅓ -⅓ -⅓ 0 + all solar 95% γ Cl 95% d s b ] KamLAND down strange bottom photon 2 95% Left Right Left Right Left Right

Quarks gravity

[eV SNO 0 eV 0 eV 0 eV 91.2 GeV >114 GeV Laboratory 2 0 –6 95% m 10 0 0 0 0 0 Super-K e νμ ντ ∆ 95% ν Z 0 H electron muon tau weak Higgs Ga 95% neutrino force boson neutrinoLeft Left neutrinoLeft

105.7 MeV 1.777 GeV 80.4 GeV ? Neutrino 0.511 MeV spin 0 –9 ± 10 νe↔ν X -1 -1 -1 ± 1 νµ↔ν τ ν ↔ν μ e τ e τ W ν ↔ν e µ muon tau weak electron force All limits are at 90%CL Left Right Left Right Left Right Leptons Bosons (Forces) spin 1 oscillations unless otherwise noted 10 –12 10 –4 10 –2 10 0 10 2 tan2θ Describes Cosmology http://hitoshi.berkeley.edu/neutrino all laboratory experiments ? Baryon asymmetry of the Universe – electromagnetism, nuclear processes, etc. ? Dark Matter all processes in the evolution of the Universe after the Big Bang ? Inﬂation Nucleosynthesis (T < 1 MeV, t > 1sec) ? Dark Energy Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions Sterile neutrino as DM

Nearly always present in SM extensions Feebly interacting Quite stable if light (keV scale) Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions Outline

1 SM, Cosmology and sterile neutrinos

2 X-ray observations

3 Pure νMSM – just three sterile neutrinos

4 Other DM generation mechanisms

5 Laboratory searches Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions DM properties – Radiative decay Leads to constraints from the X-ray observations Main decay channel

N1 ν τ > τUniverse - easy: θ Z 5 1 ν¯ 2 4 10keV θ < 3.3 10− M ν × 1 not visible, really. . .

Second decay channel: N νγ 1 → γ 2 5 27 θ1 M1 1 + Γ 5.5 10− 10 5 1keV s− θ1 W ' × − N ν 1 e, µ,τ Monochromatic: Eγ = M1/2 We should see an X-ray ( keV) W + line following the DM distribution∼ in N1 ν θ1 γ the sky Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions

Bounds for the N1 – DM sterile neutrino

8 10− Excluded by X-ray observations ) 1 α

θ 10 10 2 − ( 2 sin α

∑ 12 10−

14 10− 1 2 5 10 20 50 M1, keV

Universal constraint for all DM models [Boyarsky, Ruchayskiy, Shaposhnikov’09] Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions Bounds from observed structure in the Universe Look at the compact object with DM (dwarf spheroidals) Check that sterile neutrinos can “ﬁt” there – Pauli blocking MDEG > 0.5keV Stricter bound – phase space density arguments

M > 1 2keV − Tremaine, Gunn 79; Gorbunov, Khmelnitsky, Rubakov 08; Boyarsky, Ruchayskiy, Iakubovskyi 08 Light sterile neutrino being relativistic after generation (warm) provides cut off in the structure formation at smaller (sub-Mpc) scales. Presence of this cut off can be searched by the analysis of the Lyman-α absorption line of the intergallactic hydrogen. The bound depends on velocities of the neutrinos, not on masses – bound depends on distribution function – production mechanism Boyarsky, Lesgourgues, Ruchayskiy, Viel’08; Viel, Becker, Bolton, Haehnelt’13; Baur et.al.17 Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions

Bounds for the N1 – DM sterile neutrino

8 10− Excluded by X-ray observations ) 1 α

θ 10 10 2 − ( 2 sin α

∑ 12 10− Excluded by phase space analysis

14 10− 1 2 5 10 20 50 M1, keV

Universal constraints for all models 3

Dataset Exposure χ2/d.o.f. Line position Flux ∆χ2 6 2 [ksec] [keV] 10− cts/sec/cm +1.6 M31 ON-CENTER 978.9 97.8/74 3.53 0.025 4.9 1.3 13.0 ± − M31 OFF-CENTER 1472.8 107.8/75 3.53 0.03 < 1.8 (2σ) ... ±+0.044 +2.6 PERSEUS CLUSTER (MOS) 528.5 72.7/68 3.50 0.036 7.0 2.6 9.1 − +3− .1 PERSEUS CLUSTER (PN) 215.5 62.6/62 3.46 0.04 9.2 3.1 8.0 ±+0.019 +2.2 − PERSEUS (MOS) 1507.4 191.5/142 3.518 0.022 8.6 2.3 (Perseus) 25.9 Outline Introduction X-ray observations νMSM − Beyond−+1νMSM.4 Laboratory searches Conclusions +M31ON-CENTER 4.6 1.4 (M31) (3 dof) − BLANK-SKY 15700.2 33.1/33 3.53 0.03 < 0.7 (2σ) ... ± TABLE I: Basic properties of combinedSearch observations used for in this paper. the Second line column denotesin X-rays the sum of exposures of individual observations. The last column shows change in ∆χ2 when 2 extra d.o.f. (position and ﬂux of the line) are added. The energies for Perseus are quoted in the restUnidentiﬁed frame of the object. line at 3.5 keV in X-rays

10.00 0.36 M31 ON-center 0.34 M31 ON-center No line at 3.5 keV 0.32 1.00 0.30 0.28

[cts/sec/keV] 0.10 [cts/sec/keV] 0.26 0.24

Normalized count rate Normalized count rate 0.22 0.01-2 -2 1⋅10 No line at 3.5 keV 1⋅10 No line at 3.5 keV -3 8⋅10-3 8⋅10 Line at 3.5 keV -3 6⋅10 6⋅10-3 -3 4 10 -3 ⋅ 4⋅10 2⋅10-3 2⋅10-3 0⋅100

[cts/sec/keV] [cts/sec/keV] 0 -3 0⋅10 Data - model -2⋅10 Data - model -3 -4⋅10-3 -2⋅10 -6⋅10-3 -4⋅10-3 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 3.0 3.2 3.4 3.6 3.8 4.0 Energy [keV] Energy [keV] seen by two different satellites (XMM-Newton and FIG. 1: Left: Folded count rate (top) and residuals (bottom) for the MOS spectrum of the central region of M31. Statistical Y-errorbarsonthe top plot are smallerChandra) than the point size. The line around 3.5 keV is not added,hencethegroupofpositiveresiduals.Right:zoomontotheline region. the line has proper redshift for different sources

with such a largethe exposure intensity requires special is consistent analysis (as de- theThe observed Dark brightness Matter of a decaying profiles DM line should be pro- scribed in [16]). This analysis did not reveal any line-like portional to the dark matter column density DM = ρDMdℓ – residuals in the range 3.45 3.58 keV with the 2σ upper bound integral along the line of sight of the DM densityS distribution: the line7− is2 absent in the blanc sky observations ! on the flux being 7 10− cts/cm /sec.Theclosestdetected line-like feature (∆×χ2 =4.5)isat3.67+0.10 keV, consistent 0.05 cts Ωfov 3 − 6 with the instrumental Ca Kα line. FDM 2.0 10− 2 (1) Bulbul, Markevitch, Foster, Smith et.al.’14, Boyarsky,≈ × Ruchayskiy,cm2 sec 500 arcmin × " # 29 · CombinedIakubovskyi, fit of M31 + Perseus. Franse’14Finally, we have performed DM 10 s keV S 2 . asimultaneousfitoftheon-centerM31andPerseusdatasets 500 M /pc τDM mDM " # " # (MOS), keeping common position of the line (in the rest- ! frame) and allowing the line normalizations to be different. The line improves the fit by ∆χ2 =25.9 (Table I), which M31 and Perseus brightness profiles. Using the line flux constitutes a 4.4σ significant detection for 3 d.o.f. of the center of M31 and the upper limit from the off-center observations we constrain the spatial profile of the line. The Results and discussion. We identified a spectral feature at DM distribution in M31 has been extensively studied (see an +0.019 E =3.518 0.022 keV in the combined dataset of M31 and overview in [13]). We take NFW profiles for M31 with con- − Perseus that has a statistical significance 4.4σ and does not centrations c =11.7 (solid line, [22]) and c =19(dash-dotted coincide with any known line. Next we compare its properties line). For each concentration we adjust the normalization so with the expected behavior of a DM decay line. that it passes through first data point (Fig. 2). The c =19 profile was chosen to intersect the upper limit, illustratingthat the obtained line fluxes of M31 are fully consistent with the density profile of M31 (see e.g. [22, 24, 25] for a c =19 22 3 Previously this line has only been observed in the PN camera [9]. model of M31). − Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions

Sterile neutrino N1 parameters would be

NR production ( 8 10− µ | α = Excluded| 0) by X-ray observations ) 1 α

θ 10 10 2 − ( 2 sin α

∑ 12 10− Excluded by phase space analysis

14 10− 1 2 5 10 20 50 M1, keV Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions Current status of 3.5 keV line and future Not seen in Seen in Coma, Virgo and Perseus, Coma, and Ophiuchus clusters Ophiuchus galaxy clusters Galaxy center Galaxy center Stacked galaxies Stacked clusters Dwarf spheroidals M31 (Adromeda galaxy) Bullet cluster

Future High resolution X-ray missions XARM LYNX Athena+ (2030?) Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions Outline

1 SM, Cosmology and sterile neutrinos

2 X-ray observations

3 Pure νMSM – just three sterile neutrinos

4 Other DM generation mechanisms

5 Laboratory searches Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions Summary of sterile neutrino Dark Matter constraints

Dark Matter stay like DM Decay constraints – small enough radiative decay width (X-ray observations) always there behave like DM Structure formation constraints Heavy enough to form existing structures out of fermions always there Cold enough to leave observed small scale structure intact depends on generation mechanism (spectrum) appear like DM Production of proper DM abundance depends on generation mechanism Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions Minimal Scenario – νMSM Just three sterile neutrinos

Three Generations of Matter (Fermions) spin ½ I II III

mass→ 2.4 MeV 1.27 GeV 171.2 GeV 0 charge→ ⅔ ⅔ ⅔ 0 t t t h h h t t t g f f f g g g i i i e u e c e t name→ L up R L charm R L top R gluon

4.8 MeV 104 MeV 4.2 GeV 0 s

k - - 0 r -⅓ ⅓ ⅓ t t t a h h h t t t f f f

u γ g g g i i i e d e s e b Q L down R L strange R L bottom R photon 1 <0.0001 eV ~10 keV ~0.01 eV ~GeV ~0.04 eV ~GeV 91.2 GeV >114 GeV n i 0 0 0 0 p 0 0 s

μ τ ) t νe t ν t ν

f f f 0 N N N s Z e e e H 1 muon 2 tau sterile3 e electronL L L weak Higgs sterile sterile neutrino c neutrino neutrino neutrino neutrino neutrino r force boson o F

105.7 MeV 1.777 GeV ( 80.4 GeV 0.511 MeV spin 0 s

s ± n -1 -1 -1 n ± 1 o t t t o t h h h s t t t p f f f g g g o i i i e e e e μ e τ W L R L R L R L

B weak electron muon tau force Model action

L = L + iN∂/N L FNΦ˜ NF †L Φ˜ † νMSM SM − L − L 1 (NcM N + NM† Nc). −2 M M

[Asaka, Shaposhnikov’05, Asaka, Blanchet, Shaposhnikov’05] Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions νMSM description – neutrino masses

M 1–50 keV – Dark Matter 1 ∼ M several GeV – Leptogenesys 2,3 ∼ M MD = F Φ – “see-saw” formula is working: I h i 1 Light neutrino masses Mν = (MD)T MD − MI

D † (M )αI Active-sterile mixings θαI = 1 MI Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions νMSM experimental consequences (DM)

ActiveJuly 5, neutrino 2012 0:12 WSPC/INSTRUCTION masses FILE bb0-hep X-rays require very small N1 mixing angle θ1, so 5 m1 < 10− eV

Neutrinoless12 double beta decay Before Daya Bay After Daya Bay Additional1 contributions 1 Current Bound Current Bound are negligible 10−1 10−1 N1 – X-ray constraints IS Cosmological Limit IS Cosmological Limit N2,3 – mass > 100 MeV −2 −2

| [eV] 10 | [eV] 10 ββ ββ

Mass spectrum|m strongly |m NS NS hierarchical10−3 – X-ray 10−3

constraints 1σ 1σ 2σ 2σ 3σ 3σ 10−4 10−4 10−4 10−3 3 10−2 10−1 1 10−4 10−3 10−2 10−1 1 m0νββ < 50 10−mmin eV [eV] mmin [eV] [FB’05] Fig. 2. Value× of the effective Majorana mass m as a function of the lightest neutrino mass | ββ| in the normal (NS, with mmin = m1)andinverted(IS,withmmin = m3)neutrinomassspectra 14 before and after the Daya Bay measurement of ϑ13 in Eq. (13). The current upper bound on m (see Eqs. (70), (72) and (74)) and the cosmological bound (seeRef.55)on m 3m | ββ| i i ! min in the quasi-degenerate region are indicated. ! Figure 2 shows the value of the effective Majorana mass m as a function of | ββ| the lightest neutrino mass56,57 in the normal and inverted neutrino mass spectra 14 before and after the Daya Bay measurement of ϑ13 in Eq. (13). We used the values of the neutrino oscillation parameters obtained in the global analysis presented in Ref.58: 2 +(0.20,0.40,0.60) 5 2 2 +(0.017,0.038,0.058) ∆m12 =7.59 (0.18,0.35,0.50) 10− eV , sin ϑ12 =0.312 (0.015,0.032,0.042), (51) − × − and in the NS 2 +(0.09,0.18,0.26) 3 2 2 +(0.007,0.015,0.022) ∆m13 =2.50 (0.16,0.25,0.36) 10− eV , sin ϑ13 =0.013 (0.005,0.009,0.012), (52) − × − whereas in the IS 2 +(0.08,0.18,0.27) 3 2 2 +(0.008,0.015,0.023) ∆m13 =2.40 (0.09,0.17,0.27) 10− eV , sin ϑ13 =0.016 (0.006,0.011,0.015). (53) − − × − The three levels of uncertainties correspond to (1σ, 2σ, 3σ). In the “After Daya Bay” plot in Fig 2 we replaced the value of ϑ13 in Eqs. (52) and (53) with that measured by the Daya Bay Collaboration in Eq. (13). The uncertainties for m have been | ββ| calculated using the standard method of propagation of uncorrelated errors, taking into account the asymmetric uncertainties in Eqs. (51)–(53). In the following we discuss the predictions for the effective Majorana mass in three cases with characteristic neutrino mass spectra: (1) Hierarchy of neutrino massesd: m m m . (54) 1 # 2 # 3

dQuarks and charged leptons have this type of mass spectrum. Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions DM generation in the early Universe

Because of small mixing angle (X-ray constraints!) never enters thermal equilibrium Good – does not overclose the Universe Bad (or good?) – abundance depends on initial conditions or new physics

Nowadays called FreezeIn darkMatterParticle FeeblyInteractingMassiveParticle Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions DM generation in the early Universe Produced in l¯l νN , qq¯ νN , etc. → 1 → 1 Production is proportionol to the effective active-sterile mixing angle

θ 2 θ 2 (T ) 1 . M ' 2 1 + 2p b(p T ) c(T ) + θ 2 M2 , 1 1 ± 2 2 4 16GF 2 7π T b(p,T ) = p(2 + cos θW ) παW 360 2 c(T ) = 3√2G 1 + sin θ (nν nν¯ ) F W e − e (θ1 – vacuum mixing angle of N1 and active ν) Production can be Non-resonant( b dominates) or Resonant( c b) ∼ Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions DM generation – NR production

N1 never enter thermal equilibrium Momentum distribution is not thermal χ fN (p) = 1 ep/Tν + 1 2 with χ ∝ θ1 This is much hotter, than the “Thermal Relic” with 1 fTR(p) = ep/TTR + 1 of low temperature TTR < Tν The Lyman-α constraint is quite strong 4/3 mNRP,min ∝ (mTR,min) Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions

Bounds for the N1 – DM sterile neutrino

NR production ( 8 10− µ | α = Excluded| 0) by X-ray observations ) 1 α

θ 10 10 2 − ( 2 sin α

∑ 12 10− Excluded by phase space analysis

14 10− 1 2 5 10 20 50 M1, keV

Nearly universal constraints Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions DM generation – NR production

Bounds for the N1 – DM sterile neutrino

NR production ( 8 10− µ | α = Excluded| 0) by X-ray observations ) 1 α

θ 10 10 2 −

( NRP Ly-α, 2008 2 sin α

∑ 12 10− NRP Ly-α, 2013 Excluded by phase space analysis

14 10− 1 2 5 10 20 50 M1, keV

Nonresonant production is completely excluded Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions Resonant production – can provide much colder DM And much more of it 10-2 L6 = 10 L6 = 25 L6 = 16 M1 = 3 keV

10-3 Early Universe is Resonant component f(q)

Lepton 2 asymmetric q n L = νe = 0 10-4 nγ 6 Non-resonant component

10-5 0 1 2 3 4 5 6 7 q = p/Tν Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions

Bounds for the N1 – DM sterile neutrino

NR production ( 8 10− µ | α = Excluded| 0) by X-ray observations ) 1 α

θ 10 10 2 − ( 2 sin µα

α = | | 1.24

∑ 12 10 4 10− × − Excluded by phase space analysis

14 10− 1 2 5 10 20 50 M1, keV

Only for “pure νMSM” – production with lepton asymmetries [Canetti, Drewes, Shaposhnikov’13] Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions

Bounds for the N1 – DM sterile neutrino

NR production ( 8 10− µ | α = Excluded| 0) by X-ray observations ) 1 α

θ 10 10 2 − ( µα = 2 | | 0.08 10 4 µα = × − sin | 0 µα | .25 α | = 10 4 | 1.24 × −

∑ 12 10 4 10− × − Excluded by phase space analysis

14 10− 1 2 5 10 20 50 M1, keV

Only for “pure νMSM” – production with lepton asymmetries [Canetti, Drewes, Shaposhnikov’13] Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions Low T and low M leptogenesys

CP violation present in Yukawa matrices F

non-equilibrium process are for sterile neutrino NI production freeze-out decay

Note – for MI/T 1 the asymmetries can be generated in active and sterile sectors with opposite signs

[Asaka, Blanchet, Shaposhnikov’05, Canetti, Drewes, Shaposhnikov’13] Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions Thermal history of the Universe

T zero abundance of N1,2,3 thermal production of N2,3 lepton asymmetry generated ⇒ 10 Lα 10 ∼ − 200 GeV TEW Electroweak Symmetry Breaking lepton asymmetry converted to ⇒ baryon asymmetry ∆ 0.86 10 10 B ∼ × − T+ N2,3 reach equilibrium lepton asymmetry washed out ⇒ few GeV T N2,3 freeze out − lepton asymmetry generated ⇒ Td N2,3 decay lepton asymmetry generated ⇒ 6 Lα 8 10 & × − 100 MeV TDM resonant N1 Dark Matter production t Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions

Bounds for the N2,3 sterile neutrinos

10-5

10-7 D

eV -9 @ 10 M In order to generate enough ∆ 10-11 lepton asymmetry for resonant

10-13 DM production 0.1 0.2 0.5 1.0 2.0 5.0 10.0 20.0 eIm HΩL M very degenerate 1,2 NuTeV

∆M δmactive 10-6 CHARM PS191 ∼ BAU [Canetti, Drewes, Shaposhnikov’13] 2 10-8 BBN U BAU

DM 10-10 Seesaw

10-12 0.2 0.5 1.0 2.0 5.0 10.0 M @GeVD Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions Outline

1 SM, Cosmology and sterile neutrinos

2 X-ray observations

3 Pure νMSM – just three sterile neutrinos

4 Other DM generation mechanisms

5 Laboratory searches Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions More new physics

Warning 1 – Can easily add/change DM production! Can be nice Warning 2 – Can easily spoil/change everything! Can be also nice, but be careful (c.f. talk by Andrea Caputo on Monday) Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions Add more stuff – νMSM + scalar

separate mechanism generates proper DM abundance of N1 Add a scalar

¯ c L = LνMSM + Lscalar(X) + fIXN N

νMSM – N2,3 – leptogenesys Scalar is an inﬂaton, decays in equilibrium X NN after reheating [Shaposhnikov, Tkachev’06, FB, Gorbunov’10]→ Some scalar decaying in or out of equilibrium [Kusenko, Petraki’07] Decaying scalar which may be FIMP itself [Merle, Totzauer’15] New: Coherently oscillating ultralight scalar [FB, Chudaykin, Gorbunov, soon] Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions DM production happens in heavy particle decays

Scalar heavier than DM neutrino

MX > 2M1

Distribution is non-thermal with 1 3.9 1/3 p /Tγ = 2.45 h i S g (Tprod) ∗ (for in equilibrium decay at Tprod) 1/3 Colder, than non-resonant with p /Tγ = 3.15(4/11) h i Production abundance is controlles by scalar properties (width, mass, branching) – does not depend on θ

DM neutrino mass bound from Lyman-α

M1 & 8keV Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions

Bounds for the N1 – DM sterile neutrino

NR production ( 8 10− µ | α = Excluded| 0) by X-ray observations ) 1 α

θ 10 10 2 −

( Ly-α, 2008 2 sin α

∑ 12 10− Ly-α, 2013 Excluded by phase space analysis

14 10− 1 2 5 10 20 50 M1, keV

Production in decays of GeV scale scalar Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions Induced active sterile resonance mD=1·M0 MA=20·M0 n=8 ρ22

0.8 Scalar ﬁeld is light m 1 eV X ∼ 0.6 X oscillates coherently 0.4

Oscillating Majorana mass for 0.2

m t M1(t) M1 + MA sin(mX t) 10 20 30 40 ϕ 2 ∼ y fi(y) 0.0020 Narrow resonances for ν N1 at 2 2 M → 0.0015 y fFD(y) p A 4nmX ' 0.0010 Effective at low temperatures only 0.0005 2 y fs(y)

y Small average memntum N1 0.5 1.0 1.5 2.0 2.5 3.0 T , max, MeV 6 ∗ 10− 102 2/5 7 p 10− 1keV 8 h i 1.3 10− T M 9 ∼ 1 10− 10

) 10− 0 θ 10 11 (2 − 1 2 10 12 Scalar ﬁeld only induces the sin 10− 13 10− 14 resonance 10− 15 10− 10 16 [FB, Chudaykin, Gorbunov – very soon] − 100 100 101 M0, keV Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions Situation 3 – a lot of new physics

Assumptions

There are three right-handed neutrinos N1, N2, N3 At low energies they have Dirac and Majorana mass terms They are charged under some (non-SM) gauge group, with the (right) gauge boson mass M

Thermal history

DM Sterile neutrinos N1 enter thermal equilibrium Their abundance later diluted S times by out of equilibrium decay of N2,3

Leptogenesys – usual (resonant) in N2,3 decays.

Note: c.f. A.Caputo’s talk on Monday – either very small gR [FB, Hettmansperger, Lindner’10, Nemevsek, Senjanovic, Zhang’12] Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions DM mass bounds (from observed DM structure)

Phase space distribution is now different, and corresponds to the thermal relic case 1 f (p) = exp p + 1 Tν /S So, N1 are now cooled Ly-α bound – structure formation [Boyarsky, Lesgourgues, Ruchayskiy„ Viel’09, Viel, Becker, Bolton„ Haehnelt’13] M > 1.5 3.3 keV 1 − Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions Astrophysical constraints Sterile neutrino in beyond SM gauge multiplets

NR production ( 8 10− µ | α = Excluded| 0) by X-ray observations ) 1 , 2008 , 2013 α α α θ 10 10 2 − ( 2 sin α

∑ 12 10− Excluded by phase space analysis Thermal relic Ly- Thermal relic Ly- 14 10− 1 2 5 10 20 50 M1, keV For entropy diluted sterile neutrinos Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions Outline

1 SM, Cosmology and sterile neutrinos

2 X-ray observations

3 Pure νMSM – just three sterile neutrinos

4 Other DM generation mechanisms

5 Laboratory searches Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions Possibilities of (light) sterile neutrino lab search

Creation and detection Suppressed by mixing angle θ 4

Detection: X-ray experiments Sterile N in the DM clouds decay by the channel N νγ → providing the X-ray line with Eγ = M/2. 2 Limit on θ can be deduced as far as ΩDM is known

Creation only Forbidden decays Decay kinematics Partial kinematics kink search in electron beta decay spectrum. Full kinematics event-by-event mass measurement! Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions Troitsk – nu-mass Recent best laboratory bounds. arXiv:1703.10779 beta decay spectrum for 10 keV N1 Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions KATRIN – TRISTAN upgrade Promised future beta decay spectrum width N1 Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions Beta decay – Full kinematic reconstruction

ν¯, q 3H ⇒ p = 0 3He, p e, k

Neutrino mass is reconstructed from observed momenta in each event m2 = (Q Ekin Ekin)2 (p + k)2 ν − p − e − For 3H: Q = 18.591keV Typical ion energy Ekin 1 eV or p 100keV p ∼ | | ∼ Typical electron energy Ekin 10keV e ∼ [FB, Shaposhnikov’07] Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions HUNTER experiment Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions HUNTER experiment Outline Introduction X-ray observations νMSM Beyond νMSM Laboratory searches Conclusions Conclusions

keV scale sterile neutrino is a great DM candidate! Experiment: X-rays – already seen?! waiting for further experimens Laboratory – hard. . . but there are attempts! Theory: What is the best way to make them cool? Line follows the Dark Matter halo proﬁles

M31 surface brightness profile Perseus cluster surface brigtness profile 10 20 on-center NFW DM line, rs = 360 kpc off-center upper limit NFW DM line, rs = 872 kpc NFW, c = 11.7 β-model, β = 0.71, rc = 287 kpc NFW, c = 19 8 15 /sec] /sec] 2 2 6

10 R200 [cts/cm [cts/cm 6 6 4

5 Flux x 10 Flux x 10 2

0 0 0 0.2 0.4 0.6 0.8 1 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Radius [deg] Radius [deg]

FIG. 2: The line’s brightness profile in M31 (left) and the Perseus cluster (right). An NFW DM distribution is assumed, the scale rs is fixed to its best-fit values from [22] (M31) or [23] (Perseus) and the overall normalization is adjusted to pass through the left-most point.

Blank sky dataset 0.10

For the Perseus cluster the observations can be grouped in 3radialbinsbytheiroff-centerangle.Foreachbinweﬁx

the line position to its average value across Perseus (3.47 [cts/sec/keV] 0.07 keV). The obtained line fluxes together with 1σ errors± Normalized count rate are shown in Fig. 2. For comparison, we draw the expected 2⋅10-3 line distribution from dark matter decay using the NFW pro- 2⋅10-3 1⋅10-3 file of [23] (best fit value rs =360kpc, black solid line; 1σ 5⋅10-4 upper bound rs =872kpc, black dashed line). The isother- 0⋅100 mal β-profile from [26] is shown in magenta. The surface -5⋅10-4

[cts/sec/keV] -3 brightness profile follows the expected DM decay line’s dis- Data - model -1⋅10 -2⋅10-3 tribution in Perseus. -2⋅10-3 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Finally, we compare the predictions for the DM lifetime from Energy [keV] the two objects. The estimates of the average column den- FIG. 3: Blank sky spectrum and residuals. sity within the central part of M31 give (rs) 200 600 M /pc2 [13]. The column density ofS clusters∼ follows− from the⊙ c M relation [27–29]. Considering the uncer- tainty on the− profile and that our observations of Perseus go the νMSM. beyond rs,theaveragecolumndensityintheregionofinterest is within ¯ 100 600 M /pc2.Thereforethesignalfrom The position and flux of the discussed weak line are inevitably Perseus canS ∼ be both− stronger⊙ and weaker than that of M31, by subject to systematical uncertainties. There are two weak in- 0.2 3.0.Thisisconsistentwiththeratioofmeasuredflux strumental lines (K Kα at 3.31 keV and Ca Kα at 3.69 keV), from− Perseus to M31 0.7 2.7. although formally their centroids are separated by more than − 4σ.Additionally,theregionbelow3 keV is difficult to model If DM is made of right-handed (sterile) neutrinos [30], the precisely, especially at large exposures, due to the presence of lifetime is related to its interaction strength (mixing angle): the absorption edge and galactic emission. However, although the residuals below 3 keV are similar between the M31 dataset 4 8 5 1024π 29 10− 1keV (Fig. 1) and the blank sky dataset (Fig. 3), the line is not de- τDM = 2 2 5 7.2 10 sec 2 . 9αG sin (2θ)m × sin (2θ) mDM F DM ! "! " tected in the latter. Although the count rate at these energies is 4 times larger for M31, the exposure for the blank sky is 16 times larger. This disfavors the interpretation of the line as due

Using the data from M31 we obtain the mass mDM =7.06 to a wiggle in the effective area. The properties of this line are 0.05 keV and the mixing angle in the range sin2(2θ)=(2.2± consistent (within uncertainties) with the DM interpretation. 11 − 20) 10− .Thisvalueisconsistentwithpreviousbounds, To reach a conclusion about its nature, one will need to find Fig.× 4. This means that sterile neutrinos should be produced more objects that give a detection or where non-observation of resonantly [31–33], which requires the presence of significant the line will put tight constraints on its properties. The forth- lepton asymmetry in primordial plasma at temperatures few coming Astro-H mission [34] has sufficient spectral resolution hundreds MeV. This produces restrictions on parameters of to spectrally resolve the line against other nearby featuresand 4

10 R200 [cts/cm [cts/cm 6 6 4

5 Flux x 10 Flux x 10 2 No line seen from the blanc sky

0 0 0 0.2 0.4 0.6 0.8 1 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Radius [deg] Radius [deg]

Blank sky dataset 0.10

For the Perseus cluster the observations can be grouped in 3radialbinsbytheiroff-centerangle.Foreachbinweﬁx

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