Neutrino-electron elastic scattering

Unit 3 Macro Displacement

Neutrino-electron elastic scattering

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Tier 1: Dominant by sheer number (cosmic/thermal backgrounds)

1. (ν + e⁻ → ν + e⁻)

  • Both CC (νₑ only) and NC (all flavors)
  • Happens constantly throughout the universe: solar neutrinos, cosmic neutrino background (CνB), supernova neutrinos, reactor neutrinos
  • Cross section ~10⁻⁴⁴ cm² (MeV scale), but neutrino fluxes are enormous
  • Most prevalent weak scattering process in the universe

Tier 2: Very common in specific environments

5. Neutrino-nucleus resonance scattering (Δ resonance, etc.)

  • ν + N → ℓ + Δ → ℓ + N + π
  • Intermediate energies (~0.3–2 GeV)
  • Significant in atmospheric and accelerator neutrino beams

6. Neutrino-electron CC scattering (ν̄ₑ + e⁻ → ν̄ₑ + e⁻ via W; νₑ + e⁻ → νₑ + e⁻ via W+Z)

  • Glashow resonance (ν̄ₑ + e⁻ → W⁻ → anything) at E_ν ≈ 6.3 PeV
  • Rare except at extreme energies or in νₑ beams
  • Solar νₑ e-scattering is measurable but subdominant to νe elastic NC

7. Neutrino-nucleus elastic scattering (NC, incoherent)

  • Subdominant to CEνNS at low energies; relevant at higher recoil

8. Inverse beta decay (ν̄ₑ + p → n + e⁺)

  • Technically a scattering/capture; dominant detection channel in liquid scintillator detectors (KamLAND, Daya Bay, JUNO)
  • Very high rates in reactors and supernovae

9. Neutrino-deuteron scattering (CC and NC)

  • ν + d → e + p + n (CC), ν + d → ν + p + n (NC)
  • Key in SNO solar neutrino detection
  • Moderate rates in solar/astrophysical environments

Tier 3: Common in detectors/lab, rare naturally

10. Parity-violating electron-nucleon scattering (e + N → e + N via Z⁰)

  • Møller (e⁻e⁻), Qweak (e-p), SLAC E158
  • Extremely small cross section (~10⁻⁶ of EM), but high-luminosity beams make it measurable
  • Negligible natural prevalence

11. Neutrino-proton elastic scattering (ν + p → ν + p, NC)

  • Subdominant to CEνNS and ν-e scattering

12. Neutrino-nucleus CC coherent pion production

  • ν + A → ℓ + π + A
  • Low rates, relevant in accelerator experiments

13. Muon capture (μ⁻ + p → n + ν_μ)

  • Weak “scattering”/capture; occurs in muonic atoms
  • Moderate rates in matter with stopped muons

14. Neutrino-antineutrino scattering (ν + ν̄ → …)

  • Extremely rare in normal matter (needs neutrino backgrounds)
  • Relevant in early universe, supernova neutrino spheres, CνB

Tier 4: Rare / exotic / hypothetical

15. Neutrino-neutrino scattering (ν + ν → ν + ν)

  • Via Z⁰; significant only in dense neutrino environments (supernova core, early universe)
  • Cross section tiny

16. W/Z-mediated electron-quark scattering at high Q²

  • Deep inelastic e-N scattering via Z exchange (parity-violating)
  • Dominated by photon exchange; weak contribution ~10⁻⁵

17. Neutrino scattering off dark matter / WIMPs

  • Hypothetical; if WIMPs have weak couplings
  • Negligible unless DM density × cross section is large

18. Right-handed W_R scattering

  • Hypothetical (left-right symmetric models)

19. Leptoquark-mediated scattering

  • Hypothetical

20. Neutrino-axion / neutrino-hidden-sector scattering

  • Hypothetical

21. Neutron-antineutron oscillation-related scattering

  • Hypothetical

Summary Ranking (natural prevalence, universe-wide)

RankProcessEnvironment
1ν–e elastic (CC+NC)Everywhere (CνB, solar, SN, reactors)
2CEνNS (ν–N coherent)Supernovae, stars, detectors
3ν–N quasi-elastic CCSupernovae, solar, reactors, beams
4ν–N deep inelastic (CC+NC)High-energy astrophysics, accelerators
5ν–N resonance (Δ)Atmospheric, accelerator
6ν̄ₑ + p → n + e⁺ (IBD)Reactors, supernovae
7ν–d scatteringSolar (SNO), astrophysical
8ν–e CC (ν̄ₑ Glashow)Ultra-high-energy only
9μ⁻ captureMuonic matter
10Parity-violating e–NLab only
11ν–ν scatteringSN core, early universe
12Exotic/hypothetical—

Key caveat: In a detector context (e.g., liquid scintillator), inverse beta decay and ν–e elastic dominate. In a supernova core, ν–N (CEνNS, QE, IBD) and ν–ν dominate. In the early universe, ν–e and ν–ν scattering set neutrino decoupling. In accelerator beams, DIS and resonance dominate. So “prevalence” is environment-dependent—the ranking above is a best-effort universe-wide average.

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