Testing keV sterile neutrino dark matter in future direct detection experiments.
Miguel Campos
work done in collaboration with Werner Rodejohann. Based on [arXiv:1605.02918] Max-Planck-Institut für Kernphysik & Heidelberg Universität
IMPRS Seminar, 04 Nov. 2016 • What it actually is.
What we don't know
• It is essential for galaxy formation.
(KIPAC/Stanford Simulation)
Brief Introduction Method Results
Dark Matter.
What we do know
• Its approximate abundance.
(Chandra X-Ray Center/NASA)
2 of 23 • What it actually is.
What we don't know
(Chandra X-Ray Center/NASA)
Brief Introduction Method Results
Dark Matter.
What we do know
• Its approximate abundance. • It is essential for galaxy formation.
(KIPAC/Stanford Simulation)
2 of 23 • What it actually is.
(Chandra X-Ray Center/NASA)
(KIPAC/Stanford Simulation)
Brief Introduction Method Results
Dark Matter.
What we do know What we don't know • Its approximate abundance. • It is essential for galaxy formation.
2 of 23 (Chandra X-Ray Center/NASA)
(KIPAC/Stanford Simulation)
Brief Introduction Method Results
Dark Matter.
What we do know What we don't know • Its approximate abundance. • It is essential for galaxy • What it actually is. formation.
2 of 23 CDM is usually characterized by a heavy non-relativistic parti- cle that would lead to the forma- tion of small structures rst.
Extracted from [New Astron. Rev. 58, 1
(2014)]
Brief Introduction Method Results
Dark Matter classi cation.
Three options In general terms, we can classify (Particle) Dark Matter in three cate- gories: • Cold Dark Matter (CDM). • Warm Dark Matter (WDM). • Hot Dark Matter (HDM).
3 of 23 CDM is usually characterized by a heavy non-relativistic parti- cle that would lead to the forma- tion of small structures rst.
Extracted from [New Astron. Rev. 58, 1
(2014)]
Brief Introduction Method Results
Dark Matter classi cation.
Three options In general terms, we can classify (Particle) Dark Matter in three cate- gories: • Cold Dark Matter (CDM). • Warm Dark Matter (WDM). • Hot Dark Matter (HDM).
3 of 23 Brief Introduction Method Results
Dark Matter classi cation.
CDM is usually characterized by a heavy non-relativistic parti- Three options cle that would lead to the forma- tion of small structures rst. In general terms, we can classify (Particle) Dark Matter in three cate- gories: • Cold Dark Matter (CDM). • Warm Dark Matter (WDM). • Hot Dark Matter (HDM).
Extracted from [New Astron. Rev. 58, 1
(2014)]
3 of 23 Extracted from [arXiv:1609.06154 [astro-ph.CO]]
Brief Introduction Method Results
Cold Dark Matter.
Weakly Interacting Mas- sive Particles (WIMPs) fall in this category and due to the absence of con rmed detection, only limits on its properties (mass and cross section) have been derived.
4 of 23 Brief Introduction Method Results
Cold Dark Matter.
Weakly Interacting Mas- sive Particles (WIMPs) fall in this category and due to the absence of con rmed detection, only limits on its properties (mass and cross section) have been derived.
Extracted from [arXiv:1609.06154 [astro-ph.CO]]
4 of 23 Despite being able to suc- cessfully describe large scale structures, CDM seems to predict a higher value of satellite galaxies than the one observed...
...and a cuspy distribution for DM density near the cen- ter of galaxies, in contradic- tion to observation.
Extracted from [Proc. Nat. Acad. Sci. 112, 12249 (2014)]
Brief Introduction Method Results
CDM Di culties.
5 of 23 ...and a cuspy distribution for DM density near the cen- ter of galaxies, in contradic- tion to observation.
Extracted from [Proc. Nat. Acad. Sci. 112, 12249 (2014)]
Brief Introduction Method Results
CDM Di culties.
Despite being able to suc- cessfully describe large scale structures, CDM seems to predict a higher value of satellite galaxies than the one observed...
5 of 23 ...and a cuspy distribution for DM density near the cen- ter of galaxies, in contradic- tion to observation.
Extracted from [Proc. Nat. Acad. Sci. 112, 12249 (2014)]
Brief Introduction Method Results
CDM Di culties.
Despite being able to suc- cessfully describe large scale structures, CDM seems to predict a higher value of satellite galaxies than the one observed...
5 of 23 Extracted from [Proc. Nat. Acad. Sci. 112, 12249 (2014)]
Brief Introduction Method Results
CDM Di culties.
Despite being able to suc- cessfully describe large scale structures, CDM seems to predict a higher value of satellite galaxies than the one observed...
...and a cuspy distribution for DM density near the cen- ter of galaxies, in contradic- tion to observation.
5 of 23 Brief Introduction Method Results
CDM Di culties.
Despite being able to suc- cessfully describe large scale structures, CDM seems to predict a higher value of satellite galaxies than the one observed...
...and a cuspy distribution for DM density near the cen- ter of galaxies, in contradic- tion to observation.
Extracted from [Proc. Nat. Acad. Sci. 112, 12249 (2014)] 5 of 23 WDM behaves like CDM at large scales, but diers at small scales (less than 50 kpc) solving the missing satellites problem.
CDM WDM
Extracted from [Mon. Not. Roy. Astron. Soc. 420, 2318 (2012)]
Brief Introduction Method Results
Warm Dark Matter. WDM particles are lighter than in the CDM case, usually in the order of ∼keVs.
6 of 23 Brief Introduction Method Results
Warm Dark Matter. WDM particles are lighter than in the CDM case, usually in the order of ∼keVs. WDM behaves like CDM at large scales, but diers at small scales (less than 50 kpc) solving the missing satellites problem.
CDM WDM
Extracted from [Mon. Not. Roy. Astron. Soc. 420, 2318 (2012)]
6 of 23 ...as Dark Matter. Constitute a DM candidate if M ∼ keV, when one speci es the production mechanism: • Dodelson and Widrow mechanism. • Shi-Fuller mechanism. • Decay of heavier scalar singlets.
Brief Introduction Method Results
Sterile neutrinos as WDM
Sterile neutrinos...
• Don't perceive gauge SM interactions. • Mix with the light active ones. • Can generate neutrino masses through the (type I) seesaw mechanism (if M ∼ 1015 GeV).
7 of 23 Brief Introduction Method Results
Sterile neutrinos as WDM
Sterile neutrinos...... as Dark Matter. Constitute a DM candidate if • Don't perceive gauge SM interactions. M ∼ keV, when one speci es the production mechanism: • Mix with the light active ones. • Dodelson and Widrow mechanism. • Can generate neutrino masses through the (type I) • Shi-Fuller mechanism. seesaw mechanism (if • Decay of heavier scalar M ∼ 1015 GeV). singlets.
7 of 23 During 2014 a 3.5 keV line was de- tected using the measurements from the XMM-Newton satellite, but the DM explanation is still controver- Extracted from [Phys. Rev. Lett. 113, 251301 sial. (2014)]
Brief Introduction Method Results
Signals of WDM.
W One of the process proposed to mea- γ sure sterile neutrinos as DM is us- ing their 1-loop decay into an active- Ns νℓ ℓ νℓ like neutrino and an X-ray photon, in which 1 E = M (1) γ 2 ν
8 of 23 Brief Introduction Method Results
Signals of WDM.
W One of the process proposed to mea- γ sure sterile neutrinos as DM is us- ing their 1-loop decay into an active- Ns νℓ ℓ νℓ like neutrino and an X-ray photon, in which 1 E = M (1) γ 2 ν During 2014 a 3.5 keV line was de- tected using the measurements from the XMM-Newton satellite, but the DM explanation is still controver- Extracted from [Phys. Rev. Lett. 113, 251301 sial. (2014)]
8 of 23 Brief Introduction Method Results
The mysterious 3.5 keV line
Using an electron beam ion trap the research group from the Max- Planck-Intitut für Kernphysik demonstrated that bare Sulphur ions (S16+) can emit gamma lines at around 3.47 keV from Hydrogen atoms, an eect not considered before and published in
[arXiv:1608.04751 [astro-ph.HE]] .
(MPIK)
9 of 23 Brief Introduction Method Results
Direct Detection Experiments
(LUX Collaboration)
10 of 23 Extracted from [Phys. Rev. Lett. 107, 131302
(2011)] In an attempt to use the discarded ER, one needs a signal that can be discriminated from this background.
Brief Introduction Method Results
Electron Recoil vs Nuclear Recoil
11 of 23 In an attempt to use the discarded ER, one needs a signal that can be discriminated from this background.
Brief Introduction Method Results
Electron Recoil vs Nuclear Recoil
Extracted from [Phys. Rev. Lett. 107, 131302
(2011)]
11 of 23 Brief Introduction Method Results
Electron Recoil vs Nuclear Recoil
Extracted from [Phys. Rev. Lett. 107, 131302
(2011)] In an attempt to use the discarded ER, one needs a signal that can be discriminated from this background.
11 of 23 This process is suppressed due to the mixing angle between the sterile and the active neutrinos:
2 |USe| 1. (2) On the other hand if we as- sume here that the sterile neu- trinos constitute all Dark Mat- ter the estimated local density of 0.3 GeV/cm3 implies a high ux. Also, as they are non-relativistic
Eν ≈ mS. (3)
Brief Introduction Method Results
The Process
12 of 23 On the other hand if we as- sume here that the sterile neu- trinos constitute all Dark Mat- ter the estimated local density of 0.3 GeV/cm3 implies a high ux. Also, as they are non-relativistic
Eν ≈ mS. (3)
Brief Introduction Method Results
The Process
This process is suppressed due to the mixing angle between the sterile and the active neutrinos:
2 |USe| 1. (2)
12 of 23 Brief Introduction Method Results
The Process
This process is suppressed due to the mixing angle between the sterile and the active neutrinos:
2 |USe| 1. (2) On the other hand if we as- sume here that the sterile neu- trinos constitute all Dark Mat- ter the estimated local density of 0.3 GeV/cm3 implies a high ux. Also, as they are non-relativistic
Eν ≈ mS. (3)
12 of 23 1.×10- 43 Cross sections for mS=40 keV and |U|²=5x10⁻⁴ 1s wave function 4d wave function 1.×10- 45 2s wave function 5s wave function 2p wave function 5p wave function 3s wave function Free electrons 1.×10- 47 3p wave function 3d wave function 4s wave function - 49 1.×10 4p wave function [cm ² /keV] k 1.×10- 51 d σ /dE 1.×10- 53
1.×10- 55 0 5 10 15 20 25 30 35
Ek [keV]
Brief Introduction Method Results
The Analysis
To calculate the cross sections we used the Roothan-Hartree-Fock method considering an eective mass for the bound electron as
2 2 where . m˜ := EB − |~pB| EB = me − ε [Based on method developed in Phys. Lett. B 525, 63 (2002)]
13 of 23 Brief Introduction Method Results
The Analysis
To calculate the cross sections we used the Roothan-Hartree-Fock method considering an eective mass for the bound electron as
2 2 where . m˜ := EB − |~pB| EB = me − ε [Based on method developed in Phys. Lett. B 525, 63 (2002)]
1.×10- 43 Cross sections for mS=40 keV and |U|²=5x10⁻⁴ 1s wave function 4d wave function 1.×10- 45 2s wave function 5s wave function 2p wave function 5p wave function 3s wave function Free electrons 1.×10- 47 3p wave function 3d wave function 4s wave function - 49 1.×10 4p wave function [cm ² /keV] k 1.×10- 51 d σ /dE 1.×10- 53
1.×10- 55 0 5 10 15 20 25 30 35 13 of 23 Ek [keV] If T is the exposure time and M the mass of the detector we can de ne the dierential number of events as:
dNt 2 dRt 2 (mS, |USe| ) = M · T · (mS, |USe| ) . (5) dEk dEk
Brief Introduction Method Results
Relevant quantities
We calculate the dierential event rate as: Z dRt 2 ρ0 dσt 2 (mS, |USe| ) = ne (mS, |USe| )f(v)vdv. (4) dEk mS dEk measured in DRU's = [kg×day×keV]−1.
14 of 23 Brief Introduction Method Results
Relevant quantities
We calculate the dierential event rate as: Z dRt 2 ρ0 dσt 2 (mS, |USe| ) = ne (mS, |USe| )f(v)vdv. (4) dEk mS dEk measured in DRU's = [kg×day×keV]−1. If T is the exposure time and M the mass of the detector we can de ne the dierential number of events as:
dNt 2 dRt 2 (mS, |USe| ) = M · T · (mS, |USe| ) . (5) dEk dEk
14 of 23 Brief Introduction Method Results
Detector input
To take into account the background, it is necessary to consider the intrinsic β decays of 222Rn and 85Kr present in xenon. From calibration data it is possi- ble to obtain a background model.
Extracted from [Phys. Rev. D 90, no. 6, 062009 (2014)]
15 of 23 The dierential number of events is then
dNT X dNt (m , |U |2) = Acc(Conv(E ))n (m , |U |2) , dE S Se k t dE S Se k t k
where nt is the number of electrons in the t state.
Brief Introduction Method Results
Detector input
We must also consider the conversion function Conv(Ek) that relates the measured PE with the recoil energy of the scattered elec- trons Ek and the acceptance of the detector for ER Acc(PE).
16 of 23 Brief Introduction Method Results
Detector input
We must also consider the conversion function Conv(Ek) that relates the measured PE with the recoil energy of the scattered elec- trons Ek and the acceptance of the detector for ER Acc(PE).
The dierential number of events is then
dNT X dNt (m , |U |2) = Acc(Conv(E ))n (m , |U |2) , dE S Se k t dE S Se k t k
where nt is the number of electrons in the t state.
16 of 23 300
250
200
150
[keV ⁻ ¹ ] b
k F 100 dN / dE 50
0 5 10 15 dN /dEk20
Th 0 E E Ek [keV] XENON1T dierential number of events for
2 −4 mS = 40 keV and |USe| = 5 × 10
Brief Introduction Method Results
Statistical Method
In the region in which the signal is above than the background we can integrate and de ne:
Z E0 dN Ns := dEk, ET h dEk Z E0 Nb := FbdEk. ET h (6)
17 of 23 Brief Introduction Method Results
Statistical Method
In the region in which 300 the signal is above 250 than the background we can integrate and 200 de ne: 150
[keV ⁻ ¹ ] b
k F 100 Z E0 dN N := dE , dN / dE s k 50 ET h dEk Z E0 0 5 10 15 dN /dEk20 Nb := FbdEk. E Th 0 T h E E Ek [keV] (6) XENON1T dierential number of events for
2 −4 mS = 40 keV and |USe| = 5 × 10
17 of 23 Brief Introduction Method Results
Statistical Method
From this simple block space analysis, we de ne the signi cance in 2 terms of a χ distribution, as a function of Ns and Nb:
2 2 2 2 2 (Ns(mS, |USe| ) − Nb(mS, |USe| )) (7) χ (mS, |USe| ) := 2 . Nb(mS, |USe| )
Imposing that χ2 ≥ 4.60 (13.82) for 90% (99.9%) C.L. we obtain 2 the region in terms of mS and |USe| that can be excluded in the dierent experiments.
18 of 23 Brief Introduction Method Results
Detector characteristics: XENON100
Characteristics
• Bckgr ∼ 3 × 10−3 [kg×day×keV−1] • T = 224.6 live days. • M = 34 kg ducial mass.
• ET h = 2 keVer threshold energy.
Data from [Phys. Rev. Lett. 109, 181301 (2012)]
19 of 23 Brief Introduction Method Results
Detector characteristics: XENON1T
Characteristics
• Bckgr ∼ 1.8 × 10−4 [kg×day×keV−1] • T = 2 ∗ 365 live days. • M = 1000 kg ducial mass.
• ET h = 1 keVer threshold energy.
Data from [JCAP 1604, no. 04, 027 (2016)]
20 of 23 Brief Introduction Method Results
Detector characteristics: DARWIN
Characteristics
• Bckgr ∼ 2.05 × 10−5 [kg×day×keV−1] • M · T = 200 year×ton
• ET h = 1 keVer threshold energy.
Data from [arXiv:1606.07001 [astro-ph.IM]]
21 of 23 10- 1
10- 2
10- 3
10- 4
experimentsNull results with the from constraint 0ν2β 10- 5
10- 6
90% exclusion limit of a 3 years differential measurement with a modified setup of KATRIN 10- 7 10 15 20 25 30 35 40
Brief Introduction Method Results
Results 10- 1
10- 2
10- 3
10- 4
10- 5
10- 6
10- 7 10 15 20 25 30 35 40
22 of 23 10- 1
10- 2
10- 3
10- 4
10- 5
10- 6
10- 7 10 15 20 25 30 35 40
Brief Introduction Method Results
Results 10- 1
10- 2
10- 3
10- 4
experimentsNull results with the from constraint 0ν2β 10- 5
10- 6
90% exclusion limit of a 3 years differential measurement with a modified setup of KATRIN 10- 7 10 15 20 25 30 35 40
22 of 23 Brief Introduction Method Results
23 of 23 Backup Slides: Acceptance & Conversion Functions
Both extracted from [Phys. Rev. D 90, no. 6, 062009 (2014)]
24 of 23 Backup Slides: Incoherent Scattering
−8 −9 If mS ≈ O(10 − 50) keV, then λS ≈ O(10 − 10 ) cm. −8 As RXe ∼ 1.1 × 10 cm the electron-neutrino scattering is in- coherent and all the bound electrons in the xenon atom must be considered. When considering just free electrons one would need masses higher than ∼ 20 keV to go beyond the minimum threshold of the detector hence entering the incoherent regime.
25 of 23 Backup Slides: Cross sections
For free electrons the cross section with a sterile neutrino is given by 2 2 dσfree GF 2 me 2 mS =2 |USe| 2 g1ES ES + dEk π |~pS| 2me 2 (8) 2 mS + g2(ES − Ek) ES − Ek + 2me 1 2 − g1g2(meEk + 2 mS) . where 1 1 gν = gν¯ := 1 + (g + g ) , gν = gν¯ := (g − g ) , 1 2 2 V A 2 1 2 V A
26 of 23 Backup Slides: Cross sections For bound electrons in a state t (t = 1s, 2s, 2p,...) the cross section in the rest frame of the atom where (pB, θ, φ) are the variables of the bound electron is
2 2 dσt R pBdpBd(cos θ)dφ |Rt(~pB)| = 3 dEk (2π) 4π (9) |M|2 1 du . 1/2 2 2 4ESEB|β − pB/m˜ | 8πλ (s, mS, m˜ ) dEk
Here Rt(~pB) are radial wave functions normalized such that
Z ∞ 2 k dk 2 (10) 3 |Rt(k)| = 1 . 0 (2π)
The function λ(a, b, c) := a2 + b2 + c2 − 2ab − 2bc − 2ca is the Källén function and s and u are the usual Mandelstam variables. 27 of 23 Backup Slides: The Roothaan-HartreeFock method
The HartreeFock method estimates the wave function and the energy of a quantum many-body system in a stationary state. The Roothaan equations are a representation of the HartreeFock equation in a non orthonormal basis set which can be of Gaussian- type or Slater-type.
28 of 23