Thermalisation of Sterile Neutrinos. Thomas Tram LPPC/ITP EPFL

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1 Thermalisation of Sterile Neutrinos Thomas Tram LPPC/ITP EPFL

2 Outline Introduction to ev sterile neutrinos. Bounds from Cosmology. Standard sterile neutrino thermalisation. Thermalisation suppression by a large lepton asymmetry. Thermalisation suppression by a secret sterile neutrino interaction. Conclusions. Thomas Tram (thomas.tram@epfl.ch) 2

3 What is a sterile neutrino? Not charged under the SM gauge group Non-zero mixing angle with active neutrinos Thomas Tram (thomas.tram@epfl.ch) 3

4146 Galium detectors (SAGE and GALLEX) Short baseline oscillation experiments (LSND and MiniBooNE) A small deficit in the ν e - flux from 51 Cr and 37 Ar decay. νμ νe and ν μ ν e oscillations.

4 Motivation: Neutrino anomalies Experiment What do they measure? Estimate of significance Nuclear reactors (ILL, Bugey, Gösgen...) A small deficit in the νe flux from 235 U, 238 U, 239 Pu and 241 Pu fission σ Galium detectors (SAGE and GALLEX) Short baseline oscillation experiments (LSND and MiniBooNE) A small deficit in the ν e - flux from 51 Cr and 37 Ar decay. νμ νe and ν μ ν e oscillations σ 3. 8σ + 0σ σ ( ) Big Bang Nucleosynthesis (BBN) Cosmic Microwave Background (WMAP + ACT/SPT + BAO + H 0 ) Amount of radiation at T=1 MeV Amount of radiation at recombination + other effects Consistent with 0 or 1 fully thermalised neutrino. 1. 5σ 2. 5σ ( ) Thomas Tram (thomas.tram@epfl.ch) 4 Planck

5 Planck bounds eff m ν,sterile ΔN eff 3 4 thermal m sterile DW ΔN eff m sterile Δm ν,sterile eff =1.5eV Likelihood represented by density of points. Non-trivial that DW and thermal are equivalent. Large Neff models corresponds to more CDM. Ω ν h 2 = m eff ν,sterile 94.1eV Thomas Tram (thomas.tram@epfl.ch) 5

6 Planck (neutrino?) anomalies Planck+WP for ΛCDM model Parameter H 0 in 68% limits Ω m ± σ 8 Ω m 0.27 σ 8 Ω m 0.27 σ ± km s Mpc ± ± ± Other datasets Local H 0 measurement: H 0 = ± 2. 4 km s Mpc Cluster counts: σ 8 Ω m Weak lensing: σ 8 Ω m = ± = ± Hamann&Hasenkamp arxiv: Thomas Tram (thomas.tram@epfl.ch) 6

7 Sterile neutrino resurrection? CMB only CMB+BAO+H0+ Clusters+Weak Lensing Hamann&Hasenkamp arxiv: Thomas Tram 7

8 Producing sterile neutrinos Freeze-Out at high temperature: Initial population is completely diluted. Propagation and measurement! Rate: Γ t sin 2 2θ m Γ ν Mixing angle depends on medium Quantum Zeno effect Thomas Tram (thomas.tram@epfl.ch) 8

9 1+1 approximation 2 level system 2x2 density matrix active ν entanglement ρ = entanglement sterile ν Hermitian and unitary Expansion in Pauli matrices: ρ = 1 2 f 0 P 0 I + P σ ρ = 1 2 f 0 P 0 I + P σ I σ x 1 i σ y i σ z 1 1 Thomas Tram (thomas.tram@epfl.ch) 9

10 Change of variables ρ = ν a ent. ent. ν s We do the change of variables: P a ± = P 0 + P z ± P 0 + P z P s ± = P 0 P z ± P 0 P z P x ± = P x ± P x P y ± = P y ± P y Note that: P a ± = 2 f 0 P s ± = 2 f 0 ρ aa ± ρ aa ρ ss ± ρ ss I σ x 1 i σ y i σ z 1 1 Thomas Tram (thomas.tram@epfl.ch) 10

11 Quantum Kinetic Equations ρ = ν a ent. ent. ν s The equations of motion become: Pa ± = V x P ± ± y + Γ a 2 f a,eq ± f 0 P a Ps ± = V x P ± ± y + Γ s 2 f s,eq ± f 0 P s P x ± = V z P ± y + V L P y ± DP x P y ± = + V z P ± x + V L P x ± DP y 1 2 V x P ± ± a P s Thomas Tram (thomas.tram@epfl.ch) 11

12 Pa ± = V x P ± ± y + Γ a 2 f a,eq ± f 0 P a Ps ± = V x P ± ± y + Γ s 2 f s,eq ± f 0 P s P x ± = V z P ± y + V L P y ± DP x P y ± = + V z P ± x + V L P x ± DP y 1 2 V x P ± ± a P s ρ = ν a ent. ent. ν s Effective scattering terms Γ a and Γ s Coherrence damping D 1 2 Γ a + Γ s Vacuum and matter potentials: V x = δm s 2 2p ν sin 2θ s, V L G F T 3 L, V z = V a + V s V x V a G F M2 p ν T 4 n + νa, V s G X + Z M2 p ν u νs X Thomas Tram (thomas.tram@epfl.ch) 12

13 the code: LASAGNA Solves the QKEs numerically. Adaptive grid follows N resonances. Written in C, data analysis in MATLAB. Stiff ODE solvers: RADAU5 and ndf15. Linear Algebra solvers: dense, sparse, SuperLU. Thomas Tram (thomas.tram@epfl.ch) 13

14 ρ = ν a ent. ent. Scenario 1: Lepton asymmetry ν s The equations of motion become: Pa ± = V x P ± ± y + Γ a 2 f a,eq ± f 0 P a Ps ± = V x P ± ± y + Γ s 2 f s,eq ± f 0 P s P x ± = V z P ± y + V L P y ± DP x P y ± = + V z P ± x + V L P x ± DP y 1 2 V x P ± ± a P s V z = V a + V s V x Thomas Tram (thomas.tram@epfl.ch) 14

15 δn eff for δm s 2 > 0, L = 0 Hannestad, Tamborra, TT arxiv: Thomas Tram (thomas.tram@epfl.ch) 15

16 δn eff for δm s 2 < 0, L = 0 Hannestad, Tamborra, TT arxiv: Thomas Tram (thomas.tram@epfl.ch) 16

17 δn eff for δm s 2 > 0, L = 10 2 Hannestad, Tamborra, TT arxiv: Thomas Tram (thomas.tram@epfl.ch) 17

18 δn eff for δm s 2 < 0, L = 10 2 Hannestad, Tamborra, TT arxiv: Thomas Tram (thomas.tram@epfl.ch) 18

19 Thermalisation cartoon Thomas Tram 19

20 Thermalisation cartoon Thomas Tram 20

21 Thermalisation cartoon Thomas Tram 21

22 Thermalisation cartoon Thomas Tram 22

23 Thermalisation cartoon Thomas Tram 23

24 Thermalisation cartoon Thomas Tram 24

25 Scenario 1 discussion It is possible to suppress thermalisation for interesting values of the mixing parameters. A lepton asymmetry of this size is not ruled out by any data. Generating a sufficiently large lepton asymmetry is non-trivial. Partial thermalisation is not natural. Thomas Tram (thomas.tram@epfl.ch) 25

26 Scenario 2: Secret ν s interactions Basic idea is the quantum Zeno effect: Rapid scatterings keep the density matrix diagonal. We assume a new massive gauge boson in the sterile sector and integrate it out. Thomas Tram (thomas.tram@epfl.ch) 26

27 Scenario 2: Secret ν s interactions The equations of motion become: Pa ± = V x P ± ± y + Γ a 2 f a,eq ± f 0 P a Ps ± = V x P ± ± y + Γ s 2 f s,eq ± f 0 P s P x ± = V z P ± y + V L P y ± DP x P y ± = + V z P ± x + V L P x ± DP y 1 2 V x P ± ± a P s V z = V a + V s V x L = 0 P + and P decouple. ρ = ν a ent. ent. ν s Thomas Tram (thomas.tram@epfl.ch) 27

28 Scenario 2: Secret ν s interactions Assuming L = 0 leads to Pa + = V x P y + Γ a 2 f a,eq f 0 P a Ps + = V x P y + Γ s 2 f s,eq f 0 P s Px + = V z P + + y DP x Py + = +V z P x + DP y V x P a + P s + V z = V a + V s V x ρ = ν a ent. ent. ν s Thomas Tram (thomas.tram@epfl.ch) 28

29 ΔN eff evolution G x = g x 2 M x 2 Hannestad, Hansen, TT arxiv: Thomas Tram (thomas.tram@epfl.ch) 29

05 Thermalisation depends almost entirely on M x : Γ G x 2 sin 2 2θ m 1 2 V M

30 Thermalisation G x = g x 2 M x 2 M x = 100MeV M x = 200MeV M x = 300MeV Oscillation parameters δm s 2 = 1eV 2 sin 2 2θ s = 0.05 Thermalisation depends almost entirely on M x : Γ G x 2 sin 2 2θ m 1 2 V M x 4 2 s G x Γ t Γ sin 2 2θ m M4 x Hannestad, Hansen, TT arxiv: Thomas Tram (thomas.tram@epfl.ch) 30

31 ΔN eff as a function of M x Hannestad, Hansen, TT arxiv: Thomas Tram (thomas.tram@epfl.ch) 31

32 ΔN eff > 1? Hannestad, Hansen, TT arxiv: Thomas Tram 32

33 ΔN eff > 1? Hannestad, Hansen, TT arxiv: Thomas Tram 33

34 Extension: Self-Interacting DM Missing satellites problem Cusp vs. core problem Too big to fail Dasgupta&Kopp arxiv: Thomas Tram 34

35 Conclusions ev-scale sterile neutrinos in conflict with LSS and Planck if fully thermalised. But viable/preferred if partly thermalised Thermalisation can be supressed by Potential from large lepton asymmetry Potential from sterile neutrino self-interactions Second scenario can be naturally extended to self interacting Dark Matter. Thomas Tram 35

36 Small bonus: Open questions Assuming that terrestrial evidence grows significantly! How is BBN (through ν e -distribution) affected? What happens after decoupling? How much equilibration between active and sterile? Extending LASAGNA: More than 2 species Actual SM scattering kernels Thomas Tram (thomas.tram@epfl.ch) 36

Large bonus: Chaoticity In the inverted hierarchy δm s 2

exponentially The final sign of the lepton asymmetry

δm s 2 ev 2 sin 2 2θ s Enqvist, Kainulainen&Sorri

37 Large bonus: Chaoticity In the inverted hierarchy δm s 2 < 0, a small initial lepton asymmetry can grow exponentially The final sign of the lepton asymmetry depends chaotically on the initial sign in QRE. δm s 2 ev 2 sin 2 2θ s Enqvist, Kainulainen&Sorri hep-ph/ Abazajian&Agrawal arxiv: Thomas Tram (thomas.tram@epfl.ch) 37

38 Chaos in QRE confirmed Hannestad, Hansen, TT arxiv: Thomas Tram 38

39 Hannestad, Hansen, TT arxiv: Thomas Tram 39

40 Chaos disappears in QKE! Hannestad, Hansen, TT arxiv: Thomas Tram 40

Steen Hannestad Department of Physics and Astronomy, Aarhus University, Ny Munkegade, DK-8000 Aarhus C, Denmark

Steen Hannestad Department of Physics and Astronomy, Aarhus University, Ny Munkegade, DK-8000 Aarhus C, Denmark Department of Physics and Astronomy, Aarhus University, Ny Munkegade, DK-8000 Aarhus C, Denmark E-mail: sth@phys.au.dk In recent years precision cosmology has become an increasingly powerful probe of particle