Evidence for a dark matter particle Yukio Tomozawa University of Michigan March 2016

Contents Physical metric in General Relativity High energy cosmic rays from AGN AGN = (Active Galactic Nuclei = Massive Black Holes) The knee energy mass scale GLMR-RS supersymmetry DMP (Dark Matter Particle) mass TeV gamma ray data by HESS Gamma ray peak in energy spectrum Other DMP signatures

Physical metric ds^2 = e^ν(r)dt(r)^2 -e^λ(r)dr^2-r^2e^µ(r)dΩ Schwarzschild metric, µ(r)=0, does not fit the experimental data of time delay experiment. Physical metric, ω=e^ν(r)=e^µ(r), fits the data. Δt=2r_s ln(2r/b) with 10^-5 accuracy r_s/r = ω^1/2(1-ω), e^λ(r)=(2ω/(3ω-1))^2 for r > (3√3)/2 r_s =2.60 r_s For r < 2.60 r_s, Dr_s/r=ω^1/2(Aω-1),A=2D+3, (A>3, D>0), e^λ(r)=A(2ω/(3Aω-1))^2.

ω=g_00 (for a point source)

Extended horizon R=(3√3)/2 r_s =2.60 r_s, where r_s = 2GM/c^2 is the Schwarzschild radius. R is the size of compact objects, black holes and neutron stars. For neutron star with M=1.4 M_ʘ, R=10.9 km. This is close to the radius assigned to this neutron star.

Internal solution with constant density For r<R, ω = e^ν(r)=1/(B+(8πGρr^2)/3) and e^λ(r) = B ω^2 B=2.615 p = - ρ

Inside R, the gravity is repulsive force Supernova explosion can be explained by this gravity after gravitational collapse. Cosmic rays can be emitted from black holes, by the repulsive forces. The nature of black hole must be changed accordingly. Temperature of compact objects is very high (negative inside)

High energy cosmic rays from AGN Data from the Pierre Auger Project

Pierre Auger Observatory 30 % still coinside with AGN position.

Cosmic ray energy spectrum

Structure of cosmic ray energy spectrum (log-log scale) Knee energy = 3PeV ankle E^-2.5 E^-3MeV=10^6eV GeV=10^9 eV TeV=10^12eV PeV=10^15eV EeV=10^18eV ZeV=10^21eV …………….. GZK cutoff by cmb

Traditional model for cosmic rays Below knee energy: Galacic components by supernova acceleration Above knee energy: Extragalactic components Two problems (difficulties) in the model 1.Acceleration mechanism for extragalactic CR 2.Exact matching of intensities of two different components of CR

Matching problem Galactic component: suppressed by galactic magnetic field above knee energy Add extragalactic component (How two different components can match perfectly?)

Repulsive forces at short distances Exact solution for special case e ν(r) =e -λ(r) =1+r 2 /ξ-(r 4 /ξ 2 +2Kr/ξ) 1/2

High energy particle emission

The knee energy Cosmic ray energy spectrum E > a few PeV (10 15 eV) ~ E -3 E < E -2.5 The knee energy = 3 PeV GeV (10 9 ), TeV (10 12 ), PeV (10 15 ), EeV (10 18 ), ZeV (10 21 ),….in the units of eV.

The knee energy of cosmic rays If all particles involved are nucleons, then they behave like radiation, or equivalently p=ρ/3 at kT≈ 3 PeV. In order to create a knee energy at a few PeV, there has to exist a new particle of a few PeV mass range. They have to be created in AGN (black holes) abundantly.

New Particles with a PeV mass scale If the new mass scale is weakly interacting, then the stable lowest mass state becomes a candidate for a dark matter particle (DMP). Since the acceleration is caused by gravity, there is no problem in accelerating a neutral and weakly interacting particle. Is it possible to find DMP in cosmic rays?

Dark matter

Supersymmetry with big mass ratio GLMR-RS theory Giudice-Luty-Murayama-Rattazzi, JHEP 12, 027 (1998) Randall-Sundrum, Nuclear Phys. B557, 79 (1999) Impossible to find in LHC, since one needs 16 TeV for a pair production.

PeV Supersymmetry (II) GLMR-RS supersymmetry theory M 2 = (alpha/4Pi (sinTheta W )^2) m 3/2 = 2.7 x m 3/2 For m 3/2 = 3 Pev, M 2 = 8.1 TeV (with 10% accuracy) DMP mass is 8.1±0.8 TeV Impossible to find in LHC, since one needs 16 TeV for a pair production.

How to find DMP? DMP+Anti-DMP  gamma+gamma Gamma ray is peaked at the mass of DMP This is similar to positron+electron  2 gamma gamma ray is peaked at 511 keV 511 keV = mass of electron and positron

Gamma ray peak for positron-electron annihilation into 2 gammas electron+positron  γ + γ from the galactic center

Gamma Ray Peak of DMP DMP + Anti-DMP  γ + γ Peak at the DMP energy

HESS (High Energy Stereoscopic System)

HESS II (2005)

HESS data HESS very-high energy gamma-ray sources without identified counterparts F.Ahronian et. al., Astron. & Astrophys. 477, 353 (2008)

Summary of spectral parameters from 8 unidentified sources

Sum of 8 data sets Peak at 7.6 ± 0.1 TeV, to be compared to the theoretical prediction, 8.1 ± 0.8 TeV

Other masses in the theory M_1 = 26.7 TeV M_3 = -78 TeV 3 PeV

IceCube Neutrino Data High energy neutrino above TeV Good chance of discovery