Relic Neutrino, Gravitation and UHECR Yu. E. Pokrovsky (RRC “Kurchatov Institute”, Moscow)

1. Relic Neutrino, Gravitation and UHECRYu. E. Pokrovsky (RRC “Kurchatov Institute”, Moscow) • Towards relic neutrino (RN) observation: dNint/(dV dt) ~ n1(x) vrelσint(s) n2(x). • RN characteristics. • RN interactions and cross sections ~ Eν. • RN ground states in gravitational fields. • UHECR + Sun as the target + Earth as the detector.

2. Relic neutrino characteristics • Ntot ~ 1084 (Big Bang estimation) • n ~ 3 · 54 cm-3 • T ~ 1.9oK ≈ 1.6 10-4 eV • mν ~ 0.3 eV < 2 eV • λν= ћ/(mν c) = 0.2 nm (1eV/mνc2) • Δmν2Sun~ 10-5 eV2, Δmν2Atm~ 10-3 eV2 or less • μν < 10-12μB < 10-6μB (e+ e- → ννγ) • dν < 10-17 e cm (e+ e- → ννγ)

3. Interactions and cross sections • Gravitation => atom like ν-states: • αQED = e2/(ћc) → αG = G M mν/(ћc) = rg(M)/(2λν) • If M >> M1 = 2.7 1020 (1eV/mνc2) kg αG>> 1

4. rBohr = 2 λν2/rg(M) rBohr ~ RAsteroid ~ 1 km For planets and stars rBohr << RPlanet, Star νe, νμ , ντmν = 1eV. In Thomas-Fermi approach: nAsteroid ~ 10-12 cm-3 nAverage ~ 102 cm-3 nEarth ~ 1 cm-3 nSun ~ 105 cm-3 nNeutron Star ~ 1013 cm-3

5. Electroweak interactions: • s < (2 me)2(Crewther, Finjord, and Minkowski - 1982) σνν→γγ = 4.6 10-87 (mνc2/1eV)6 cm2 • s ~ mρ2 Eν~ 3 1017 eV σνν→ρ-burst≈ 3 10-39 cm2 ρ0 →π+π-→2μ, 2ν in angle 10-9 s ~ mZ2 Eν~ 4 1021 eV σνν→Z-burst≈ 4 10-32 cm2 Z → 2.7 h, 30 γ, and 28 ν in angle 10-11

6. UHECR + Sun as target + Earth as detector • nν~ 105 cm-3 1 AU ≈ 240RSun Act.gal.-ν-→☼==>◦ REarth≈ 0.01RSun • ρ0→π±: 2.6 10-8 s c 1017eV/139MeV ≈ 8 RSun • ρ0 →π+π-→2μ, 2ν Rspot ≈ 150 m • Z →π±: 2.6 10-8 s c 1021eV/139MeV ≈ 400 AU • Z → 2.7 h, 30 γ, and 28 ν Rspot ≈ 1.5 m