Neutrino Dynamics in Big Bang Nucleosynthesis Evan Grohs - PowerPoint PPT Presentation

Neutrino Dynamics in Big Bang Nucleosynthesis Evan Grohs University of California Berkeley 13 Sep 2019 Extraordinary Seminar: University College London Contributors: George Fuller Daniel Blaschke Vincenzo Cirigliano Luke Johns Chad Kishimoto Mark Paris Alexey Vlasenko Shashank Shalgar

Network for Neutrinos, Nuclear Astrophysics and Symmetries ❖ Funded by National Science Foundation ❖ 11 Institutions headquartered in Berkeley, CA. 10 Universities ➢ 1 National Laboratory ➢ ❖ 8 postdoctoral research fellows ❖ Research thrusts including Nucleosynthesis and ➢ the origin of the elements Neutrinos and ➢ fundamental symmetries Dense matter ➢ Dark matter ➢ a e

Outline and preliminaries ❖ Observational Cosmology Useful constructs: The coming era of precision cosmology ➢ Neutrino observables ➢ Current status and future goals ➢ ❖ Big Bang Nucleosynthesis Overview ➢ Weak decoupling ➢ Neutron-to-proton rates ➢ Neutron life time ➢ ❖ Neutrino Quantum Kinetics Generalized Neutrino Density Matrices ➢ Fermi-Dirac Equilibrium Preliminary Calculations ➢ ❖ Summary and future work (non-degenerate): 1 f (FD) ( ✏ ) = e ✏ + 1

The coming era of precision cosmology Cosmic Microwave Background Experiments I. CMB Stage IV: Simons Observatory & South Pole Observatory A. Other Ground-Based CMB experiments: CLASS and QUIET B. Future satellites: PICO & LiteBIRD C. II. Thirty-meter class telescopes EELT and GMT - Atacama A. TMT – Site to be determined B. III. Surveys DES - Cerro Tololo, Chile A. DESI - Kitt Peak, AZ B. LSST – Cerro Pachón, Chile C.

Primordial Helium Mass Fraction Sum of the light neutrino masses CMB Polarization data Large Scale Structure/Lensing Simons Observatory/Future Satellites CMB Stage-IV & DESI 5 Observables in Neutrino Cosmology Neutrino Energy Density Deuterium Abundance High-ℓ Temperature Data QSO Absorption Lines SPT & SO Thirty-Meter Class Telescopes Baryon Density Temperature Power Spectrum CMB Stage IV

Cosmological Neutrino Observables: Current Status Baryon Density, Planck VI, 2018 ω b = 0 . 02242 ± 0 . 00014 (1 σ ) Number of relativistic degrees of freedom, Planck VI, 2018 N e ff = 2 . 99 +0 . 34 − 0 . 33 (2 σ ) Sum of the Neutrino Masses, Planck VI, 2018 Σ m ν < 120 meV (2 σ ) Primordial Mass Fraction of Helium, Aver et al, 2015 Y P = 0 . 2449 ± 0 . 0040 (1 σ ) Primordial Abundance of Deuterium, Cooke et al, 2018 10 5 (D / H) = 2 . 527 ± 0 . 030 (1 σ )

BBN Epochs of Interest Equilibrium initial conditions Nonequilibrium evolution time Temp.

Weak Decoupling: Overview 1. Initially: neutrinos at the same temperature as electrons and positrons 2. Electrons and positrons annihilate to produce photon pairs, slightly raising temperature of plasma 3. Two processes create heat flow between neutrinos and plasma } ν i + e ± ↔ ν i + e ± Charged Current (𝜉 # ) ν i + ν i ↔ e − + e + Neutral Current (𝜉 # , 𝜑 ' , 𝜑 ( ) 4. Three processes redistribute energy within neutrino seas ν i + ν j ↔ ν i + ν j ν i + ν j ↔ ν i + ν j ν i + ν i ↔ ν j + ν j 5. End result: neutrinos cooler than photons

Boltzmann Neutrino Transport 1-D array for each neutrino flavor; 100 Bins in epsilon 0 ≤ 𝜗 ≤ 25 Deviation from FD spectra N e ff = 3 . 044

Differential Visibility of Neutrino-Electron Scattering Out-of-Equilibrium Neutrino Transport 10 ν i + ν i ↔ e − + e + D 8 ν i + e ± ↔ ν i + e ± 3 He 6 Red contours of constant differential visibility for electron flavor 4 He ✏ Γ 0 4 H e � τ ν i ν i 7 Li 2 Low T cm High T cm 0 . 5 0 . 0 − 0 . 5 − 1 . 0 − 1 . 5 Γ 0 ν i << H τ ν i >> 1 log 10 ( T cm / MeV) c/o Matthew J. Wilson

Entropy flows Entropy flow out of the plasma into the neutrino seas Charged leptons are hotter than neutrinos Total entropy in the universe increases

Without Transport: With Transport included: Relative change:

Neutron to proton rates I 6 Neutron-to-proton rates set n/p 𝜑 # capture on neutron, normalized to neutron lifetime ∞ λ ν e n → pe − = G 2 F (1 + 3 g 2 A ) Z dE ν C ( E ν + δ m np ) Z ( E ν + δ m np , E ν ) 2 π 3 0 q × E 2 ( E ν + δ m np ) 2 − m 2 ν ( E ν + δ m np ) e × [ f ν e ( E ν )][1 − g e − ( E ν + δ m np )] δ m np − m e = G 2 F (1 + 3 g 2 1 A ) Z dE ν C ( δ m np − E ν ) Z ( δ m np − E ν , E ν ) 2 π 3 τ n 0 q × E 2 ( δ m np − E ν ) 2 − m 2 ν ( δ m np − E ν ) e

Neutron to proton rates II 10 4 λ ν e n λ e − p λ e + n λ ¯ ν e p 10 2 λ ¯ λ n decay ν e e − p 10 0 H rate (s − 1 ) 10 − 2 10 − 4 10 − 6 10 − 8 10 − 10 10 1 10 0 10 − 1 10 − 2 10 − 3 T cm (MeV)

Neutron to proton ratio – Primordial Helium Equilibrium: µ ν e + µ n = µ p + µ e −  � − δ m np n/p = exp + φ e − ξ ν e T Common Approximation at late times after Weak Freeze-Out (WFO): n/p ( t ) = e − δ m np /T WFO e − ( t − t WFO ) / τ n 𝑈WFO ≃ 0.7 MeV � 2 n/p How Accurate is the WFO approximation? � Y P ' � 1 + n/p � f . o .

Lepton capture 0 . 6 rates set to zero at 𝑈WFO 0 . 5 No Pauli blocking 0 . 4 in free neutron decay 0 . 3 δ Y P 0 . 2 Helium-4 0 . 1 Deviation from 0 . 0 Baseline 1 . 0 0 . 8 0 . 6 0 . 4 0 . 2 0 . 0 T WFO (MeV) arXiv: 1607.02797

Helium vs. Neutron lifetime 0 . 251 Bottle expt. Steyerl et al (2016) 0 . 250 τ n = 882 . 5 ± 2 . 1 s 0 . 249 Beam expt. 0 . 248 Y (base) (1309.2623) P 0 . 247 τ n = 887 . 7 ± 3 . 1 s 0 . 246 0 . 245 UCN 𝜐 0 . 244 875 880 885 890 895 (1707.01817) τ n (s) τ n = 877 . 7 ± 1 . 1 s

Beyond the Boltzmann Approach Mass eigenbasis is not coincident with Weak eigenbasis 1. Unitary Transformation in vacuum: PMNS matrix 2. Neutrinos oscillate between weak eigenstates 3. Generalized density matrix for neutrino ensemble   cos θ 12 sin θ 12 0 U = U 23 U 13 U 12 − sin θ 12 cos θ 12 U 12 = 0   0 0 1 Mixing angles: θ 23 , θ 13 , θ 12 Mass squared differences: � = 7 . 5 × 10 � 5 eV 2 δ m 2 atm = 2 . 6 × 10 � 3 eV 2 δ m 2 c/o George Fuller

Neutrino Density Matrices Generalized 2n 𝒈 ⨉ 2n 𝒈 Neutrinos: density matrices n 𝒈 : number of flavors Antineutrinos: 2 helicity states

QKEs in the Early Universe See Sigl & Raffelt (1993); Vlasenko, Fuller, & Cirigliano (2013); Blaschke & Cirigliano (2016) Change array dimensions (Majorana or Dirac): 2 Generalized 3 ⨉ 3 density matrices (no spin coherence) Equations of motion for neutrinos: H : Hamiltonian-like potential (coherent) d f Ĉ : Collision term from dt = − i [ H, f ] − + C [ f ] Blaschke & Cirigliano (2016) → Nonlinear coupled ODEs

Freeze-Out 5 Spectra i = e, Q 4 i = µ, Q i = ⌧ , Q 3 i = e, B 10 2 × � f ii Full collision term, i = ⌧ , B vacuum Potential 2 in QKE calc. 1 Full collision term 0 in Boltzmann transport calc. − 1 0 2 4 6 8 10 ✏ = E ⌫ /T cm Preliminary Calc.

Concurrent epochs of BBN Equilibrium initial conditions Nonequilibrium evolution Weak interactions between leptons Weak interactions between leptons and baryons EM interactions between leptons and photons Strong and EM interactions between baryons and photons

Summary and future work 1. Neutrino cosmology a) 𝑂eff and Σ𝑛 = : energy densities b) D/H and 𝑍 ? : convolution in rates 2. Weak Decoupling & Weak Freeze-Out a) Neutrino spectra influence 𝑜/𝑞 b) Neutron lifetime may be important 3. Quantum Kinetic Equations E a) Coherent terms up to 𝐻 D b) Collisions with 𝑓 ± , 𝜉 , ̅ E 𝜉 up to 𝐻 D Observations 4. Future calculations will drive a) QKEs for transport: 𝑂eff the Theory! b) Charged-Current QKES: Abundances