https://superphysics.org/material/principles/part-4/chapter-08/section-04/ Recent content in Intro-Aetherspace Relationalities on Superphysics Hugo en Sun, 17 Nov 2024 00:00:00 +0000 https://superphysics.org/material/principles/part-4/chapter-08/section-04/unit-01/ Sun, 17 Nov 2024 00:00:00 +0000 https://superphysics.org/material/principles/part-4/chapter-08/section-04/unit-01/ <p>This the most prevalent neutrino-nucleus weak scattering</p> <ul> <li>ν + N → ν + N (neutral current, whole nucleus recoils)</li> <li>Enhanced cross section ∝ N² (coherence)</li> <li>Dominant for neutrinos below ~50 MeV on nuclei</li> <li>Huge rates in supernovae, stellar cores, detectors</li> </ul> https://superphysics.org/material/principles/part-4/chapter-08/section-04/unit-02/ Sun, 17 Nov 2024 00:00:00 +0000 https://superphysics.org/material/principles/part-4/chapter-08/section-04/unit-02/ <p>This gives: ν + n → ℓ⁻ + p; ν̄ + p → ℓ⁺ + n</p> <ul> <li>Charged current, threshold ~E_ν &gt; m_ℓ</li> <li>Dominant CC channel for MeV–GeV neutrinos</li> <li>Major in supernovae, solar (νₑ), reactors, accelerator beams</li> </ul> <p>Neutrino-nucleon deep inelastic scattering (ν + N → ℓ + X)</p> https://superphysics.org/material/principles/part-4/chapter-08/section-04/unit-03/ Sun, 17 Nov 2024 00:00:00 +0000 https://superphysics.org/material/principles/part-4/chapter-08/section-04/unit-03/ <h2 id="tier-1-dominant-by-sheer-number-cosmicthermal-backgrounds">Tier 1: Dominant by sheer number (cosmic/thermal backgrounds)</h2> <p><strong>1. (ν + e⁻ → ν + e⁻)</strong></p> <ul> <li>Both CC (νₑ only) and NC (all flavors)</li> <li>Happens constantly throughout the universe: solar neutrinos, cosmic neutrino background (CνB), supernova neutrinos, reactor neutrinos</li> <li>Cross section ~10⁻⁴⁴ cm² (MeV scale), but neutrino fluxes are enormous</li> <li><strong>Most prevalent weak scattering process in the universe</strong></li> </ul> <hr> <h2 id="tier-2-very-common-in-specific-environments">Tier 2: Very common in specific environments</h2> <p><strong>5. Neutrino-nucleus resonance scattering (Δ resonance, etc.)</strong></p> https://superphysics.org/material/principles/part-4/chapter-08/section-04/unit-04/ Sun, 17 Nov 2024 00:00:00 +0000 https://superphysics.org/material/principles/part-4/chapter-08/section-04/unit-04/ <h2 id="beta---decay">Beta - Decay</h2> <p>A neutron downgrades to a proton, emitting:</p> <ul> <li>an electron</li> <li>an electron antineutrino</li> </ul> <p>(n → p + e⁻ + ν̄ₑ)</p> <h2 id="beta--decay">Beta + Decay</h2> <p>A proton upgrades to a neutron, emitting an antielectron and an electron neutrino</p> https://superphysics.org/material/principles/part-4/chapter-08/section-04/unit-05/ Sun, 17 Nov 2024 00:00:00 +0000 https://superphysics.org/material/principles/part-4/chapter-08/section-04/unit-05/ https://superphysics.org/material/principles/part-4/chapter-08/section-04/unit-06/ Sun, 17 Nov 2024 00:00:00 +0000 https://superphysics.org/material/principles/part-4/chapter-08/section-04/unit-06/ <!-- | Rank | Decay | Why it's prevalent | |------|-------|-------------------| | 1 | **Free neutron beta decay** (n → p + e⁻ + ν̄ₑ) | Neutrons are everywhere (nuclei, stars, early universe); free neutrons decay with τ ~880 s; enormous cosmic rate | | 2 | **Nuclear β⁻ decay** (e.g., fission products, ¹⁴C, ⁴⁰K) | Ubiquitous in Earth's crust, reactors, stars; fission products decay weakly | | 3 | **Nuclear β⁺ decay / electron capture** (e.g., ⁴⁰K, ⁵⁵Fe, ¹⁸F) | Widespread in nature and medical isotopes | | 4 | **Muon decay** (μ⁻ → e⁻ν̄ₑν_μ) | Copious in cosmic-ray showers, accelerators; τ ~2.2 μs | | 5 | **Pion decay** (π⁺ → μ⁺ν_μ) | Produced in cosmic-ray air showers, accelerators; feeds muon flux | | 6 | **Kaon decays** (K → ππ, K → μν, K → πeν) | Produced in cosmic rays, accelerators; τ ~10⁻⁸–10⁻¹⁰ s | --> <!-- ## B. Ranked by Detected/Experimental Event Rate | Rank | Decay | Why it's experimentally prevalent | |------|-------|----------------------------------| | 1 | **Muon decay** | Billions detected; cosmic-ray muons, accelerator beams; τ ~2.2 μs | | 2 | **Pion decay** | Copious in beams; feeds muon/neutrino beams | | 3 | **Nuclear β decay** (reactor fission products, ¹⁴C, ⁴⁰K) | Reactors produce ~10²⁰ decays/s; radiocarbon dating | | 4 | **Free neutron beta decay** | Neutron beams, ultracold neutron experiments; τ ~880 s | | 5 | **Kaon decays** | Dedicated experiments (KLOE, NA62, LHCb); ~10⁹–10¹⁰ events | | 6 | **Tau decay** | B-factories (BaBar, Belle), LHC; ~10⁹ events | | 7 | **Charm/bottom hadron decays** | LHCb, Belle II; ~10⁹–10¹⁰ events | | 8 | **Hyperon decays** | Fixed-target experiments; ~10⁶–10⁸ events | | 9 | **W/Z boson decays** | LHC, Tevatron, LEP; ~10⁶–10⁸ events | | 10 | **Top quark decay** | LHC, Tevatron; ~10⁵–10⁶ events | | 11 | **Higgs decay** | LHC; ~10⁴–10⁵ events (rare modes fewer) | | 12 | **Electron capture** | Medical isotopes, nuclear experiments; moderate rates | | 13 | **Double beta decay** | Dedicated experiments (GERDA, KamLAND-Zen); ~10–100 events/yr | | 14 | **Proton decay** | Not observed; limits only | --- ## C. Combined "Major Weak Decays by Prevalence" Ranking Blending cosmic abundance and experimental detection rate, with emphasis on **how often the decay occurs in nature and in detectors**: | Rank | Decay | Prevalence Class | |------|-------|-----------------| | 1 | **Free neutron beta decay** (n → pe⁻ν̄ₑ) | Extremely high (cosmic + lab) | | 2 | **Nuclear β⁻ decay** (fission products, ¹⁴C, ⁴⁰K) | Extremely high | | 3 | **Muon decay** (μ → eνν̄) | Extremely high (cosmic rays + accelerators) | | 4 | **Pion decay** (π → μν, π → eν) | Very high (cosmic rays + beams) | | 5 | **Nuclear β⁺ decay / electron capture** | Very high | | 6 | **Kaon decays** (K → ππ, K → μν, K → πeν) | High (cosmic rays + experiments) | | 7 | **Tau decay** (τ → eνν̄, μνν̄, πν) | High (accelerators) | | 8 | **Hyperon decays** (Λ, Σ, Ξ → Nπ, Λπ) | Moderate–high (cosmic rays + experiments) | | 9 | **Charm/bottom hadron decays** (D, B, Λ_c, Λ_b) | Moderate (colliders) | | 10 | **W/Z boson decays** | Moderate (colliders, cosmic rays) | | 11 | **Top quark decay** (t → Wb) | Low (colliders only) | | 12 | **Higgs decay** (weak modes) | Low (colliders only) | | 13 | **Double beta decay** (2νββ) | Very low (rare, dedicated experiments) | | 14 | **Proton decay** (hypothetical) | Not observed | --- ## D. Notes on "Prevalence" - **Free neutron beta decay** and **nuclear β decay** dominate cosmic prevalence because neutrons and radioactive nuclei are ubiquitous (stars, reactors, Earth's crust, early universe). - **Muon and pion decays** dominate experimental event rates because cosmic-ray showers and accelerator beams produce them in enormous numbers. - **Kaon, tau, charm, bottom, W/Z, top, Higgs** decays are prevalent **in colliders** but rare in nature (except cosmic-ray contributions). - **Double beta decay** is extremely rare (τ ~10²¹ yr) but is a major topic in neutrino physics. - **Proton decay** is hypothetical and not observed; included only for completeness. --- **Bottom line:** By cosmic prevalence, **neutron beta decay and nuclear beta decay** lead. By experimental event rate, **muon and pion decays** lead. By combined major-weak-decay prevalence, the top tier is **neutron β decay, nuclear β decay, muon decay, and pion decay**. ## Tier 1: Ultra-High Mass Scale (≫ 100 GeV) — Hypothetical / BSM | Rank | Decay | Energy Scale | Notes | |------|-------|-------------|-------| | 1 | **Top quark decay** (t → W⁺ + b) | ~173 GeV (m_t) | Weak decay; extremely short lifetime (~5×10⁻²⁵ s); only quark that decays weakly before hadronizing | | 2 | **Heavy BSM particle decays** (e.g., W' → WZ, Z' → ff̄, heavy neutrino N → ℓW) | ~TeV – PeV (hypothetical) | Not observed; weak-mediated if couplings are weak | | 3 | **Proton decay** (p → e⁺π⁰, p → ν̄K⁺, etc.) | ~10¹⁵–10¹⁶ GeV (GUT scale, hypothetical) | Mediated by GUT bosons, not purely weak; not observed | | 4 | **Neutron–antineutron oscillation** (n → n̄) | ~10⁵–10⁶ GeV effective scale (hypothetical, ΔB=2) | Not a decay per se but a weak/GUT transition; not observed | --- ## Tier 2: Electroweak / Heavy Quark Scale (1 – 200 GeV) | Rank | Decay | Energy Scale (Q or m) | Notes | |------|-------|----------------------|-------| | 5 | **W boson decay** (W⁺ → e⁺νₑ, μ⁺ν_μ, τ⁺ν_τ, ud̄, cs̄) | ~80.4 GeV (m_W) | Weak decay; τ ~3×10⁻²⁵ s | | 6 | **Z boson decay** (Z → ℓ⁺ℓ⁻, νν̄, qq̄) | ~91.2 GeV (m_Z) | Weak decay; τ ~3×10⁻²⁵ s | | 7 | **Higgs decay** (H → WW*, ZZ*, τ⁺τ⁻, bb̄, μ⁺μ⁻) | ~125 GeV (m_H) | Weak-mediated for WW*/ZZ*/ττ/μμ; τ ~1.6×10⁻²² s | | 8 | **Bottom quark decay** (b → c + W⁻ → c + ℓ⁻ν̄, b → uW⁻, b → sγ) | ~4.2 GeV (m_b) | Weak decay; τ ~1.5×10⁻¹² s; CKM-suppressed | | 9 | **Charm quark decay** (c → s + W⁺ → s + ℓ⁺ν, c → dW⁺) | ~1.3 GeV (m_c) | Weak decay; τ ~1×10⁻¹² s; CKM-favored (c→s) | | 10 | **Tau lepton decay** (τ⁻ → e⁻ν̄ₑν_τ, μ⁻ν̄_μν_τ, π⁻ν_τ, etc.) | ~1.78 GeV (m_τ) | Weak decay; τ ~2.9×10⁻¹³ s | | 11 | **B meson decays** (B⁰ → D*ℓν, B → πℓν, B → K*γ, etc.) | ~5.3 GeV (m_B) | Weak decay; τ ~1.5×10⁻¹² s | | 12 | **D meson decays** (D⁰ → K⁻ℓ⁺ν, D⁺ → K̄⁰ℓ⁺ν, etc.) | ~1.9 GeV (m_D) | Weak decay; τ ~1×10⁻¹² s | | 13 | **Λ_b baryon decay** (Λ_b → Λ_cℓν, etc.) | ~5.6 GeV | Weak decay | | 14 | **W/Z radiative and rare decays** (W → eνγ, Z → ℓℓγ, Z → νν̄γ) | ~80–91 GeV | Weak + EM; rare | --- ## Tier 3: Strange / Light Hadron Scale (100 MeV – 1 GeV) | Rank | Decay | Energy Scale (Q or m) | Notes | |------|-------|----------------------|-------| | 15 | **Kaon decays** (K⁺ → μ⁺ν_μ, K⁺ → π⁺π⁰, K⁰ → π⁺π⁻, K⁰ → π⁰π⁰, K⁺ → π⁰e⁺ν, K → πℓℓ, K → πνν̄) | ~494–498 MeV (m_K) | Weak decay; τ ~10⁻⁸–10⁻¹⁰ s; K⁰–K̄⁰ mixing | | 16 | **Hyperon decays** (Λ → pπ⁻, Σ⁺ → pπ⁰, Σ⁻ → nπ⁻, Ξ → Λπ, Ω⁻ → ΛK⁻) | ~1.1–1.7 GeV (m_hyperon) | Weak decay; τ ~10⁻¹⁰ s; nonleptonic + semileptonic | | 17 | **Charmed baryon decays** (Λ_c → pKπ, Λ_c → Λℓν, etc.) | ~2.3 GeV | Weak decay | | 18 | **η and η′ decays** (η → π⁺π⁻π⁰, η → π⁰γγ, η′ → ηππ) | ~548–958 MeV | EM/weak; some weak contributions | | 19 | **φ meson decay** (φ → K⁺K⁻, φ → K_SK_L) | ~1.02 GeV | Strong-dominated; weak contributions negligible | | 20 | **D_s meson decay** (D_s → φπ, D_s → K*K, D_s → τν) | ~1.97 GeV | Weak decay | | 21 | **Ξ_cc, Ω_c, etc.** (doubly/heavy charmed baryons) | ~2.5–3.8 GeV | Weak decay | --- ## Tier 4: Pion / Muon Scale (1 – 200 MeV) | Rank | Decay | Energy Scale (Q or m) | Notes | |------|-------|----------------------|-------| | 22 | **Pion decays** (π⁺ → μ⁺ν_μ, π⁺ → e⁺νₑ, π⁰ → γγ) | ~139–135 MeV (m_π) | π→ℓν is weak; π⁰→γγ is EM; τ ~2.6×10⁻⁸ s (π⁺) | | 23 | **Muon decay** (μ⁻ → e⁻ν̄ₑν_μ) | ~105.7 MeV (m_μ) | Pure weak; τ ~2.2×10⁻⁶ s; classic Fermi interaction | | 24 | **Charged kaon leptonic decay** (K⁺ → e⁺νₑ) | ~493 MeV | Weak; helicity-suppressed | | 25 | **η → μ⁺μ⁻, η → e⁺e⁻** | ~548 MeV | Weak/EM; rare | | 26 | **K_S → π⁺π⁻, K_S → π⁰π⁰** | ~498 MeV | Weak; CP-conserving | | 27 | **K_L → π⁺π⁻π⁰, K_L → πeν, K_L → πμν** | ~498 MeV | Weak; CP-violating in some modes | --- ## Tier 5: Nuclear / Beta Decay Scale (keV – 10 MeV) | Rank | Decay | Energy Scale (Q) | Notes | |------|-------|-----------------|-------| | 28 | **Free neutron beta decay** (n → p + e⁻ + ν̄ₑ) | ~0.782 MeV (Q) | Weak decay; τ ~880 s; classic beta decay | | 29 | **Tritium beta decay** (³H → ³He + e⁻ + ν̄ₑ) | ~18.6 keV (Q) | Weak; used in KATRIN ν mass experiment | | 30 | **Nuclear β⁻ decay** (e.g., ¹⁴C → ¹⁴N + e⁻ + ν̄ₑ) | ~0.156 MeV (Q) | Weak; radiocarbon dating | | 31 | **Nuclear β⁺ decay** (e.g., ¹⁸F → ¹⁸O + e⁺ + νₑ) | ~0.633 MeV (Q) | Weak; PET scans | | 32 | **Electron capture** (e.g., ⁵⁵Fe + e⁻ → ⁵⁵Mn + νₑ) | ~keV–MeV | Weak; competing with β⁺ | | 33 | **Double beta decay** (²⁷⁶Ge → ⁷⁶Se + 2e⁻ + 2ν̄ₑ) | ~2.039 MeV (Q) | Weak (2νββ); 0νββ hypothetical | | 34 | **Pion beta decay** (π⁺ → π⁰ + e⁺ + νₑ) | ~4.6 MeV (Q) | Weak; rare | | 35 | **Muon capture** (μ⁻ + p → n + ν_μ) | ~100 MeV released | Weak; not a decay of μ alone but a capture reaction | | 36 | **Neutron radiative beta decay** (n → p + e⁻ + ν̄ₑ + γ) | ~0.782 MeV | Weak + EM; rare | | 37 | **Proton beta decay** (p → n + e⁺ + νₑ) | ~1.8 MeV (if free p) | Energetically forbidden for free proton; occurs in nuclei | --- ## Tier 6: Ultra-Low Energy / Rare & Hypothetical (≪ keV) | Rank | Decay | Energy Scale | Notes | |------|-------|-------------|-------| | 38 | **Neutron–antineutron oscillation** (n → n̄) | ~10⁻⁶ eV (mass splitting) | Hypothetical; ΔB=2; not a decay but a transition | | 39 | **Neutrino decay** (ν → ν' + γ, ν → ν'νν̄, if massive) | ≪ eV (hypothetical) | Not observed; weak/BSM | | 40 | **Axion-like particle decays** (a → γγ, a → ee, if weakly coupled) | ~eV–MeV (hypothetical) | BSM; weak-like couplings | | 41 | **Dark matter decay** (χ → νν̄, χ → SM particles, if weak-coupled) | ~keV–TeV (hypothetical) | BSM; not confirmed | | 42 | **Proton decay** (p → e⁺π⁰, etc.) | ~10¹⁵–10¹⁶ GeV (GUT) | Hypothetical; not weak alone | --- ## Summary Ranking (by characteristic mass/Q scale, high → low) 1. Top quark decay — **~173 GeV** 2. Heavy BSM decays (W', Z', heavy N) — **~TeV–PeV** (hypothetical) 3. Proton decay — **~10¹⁵–10¹⁶ GeV** (hypothetical) 4. W boson decay — **~80.4 GeV** 5. Z boson decay — **~91.2 GeV** 6. Higgs decay (weak modes) — **~125 GeV** 7. Bottom quark decay — **~4.2 GeV** 8. B meson decays — **~5.3 GeV** 9. Λ_b baryon decay — **~5.6 GeV** 10. Charm quark decay — **~1.3 GeV** 11. D meson decays — **~1.9 GeV** 12. D_s meson decay — **~1.97 GeV** 13. Tau lepton decay — **~1.78 GeV** 14. Charmed baryon decays — **~2.3 GeV** 15. Hyperon decays — **~1.1–1.7 GeV** 16. Kaon decays — **~494–498 MeV** 17. η, η′ decays (weak modes) — **~548–958 MeV** 18. Pion decays (π→ℓν) — **~139 MeV** 19. Muon decay — **~105.7 MeV** 20. K⁺ → e⁺νₑ — **~493 MeV** 21. K_S, K_L decays — **~498 MeV** 22. Free neutron beta decay — **~0.782 MeV** 23. Nuclear β⁻ decay (¹⁴C) — **~0.156 MeV** 24. Nuclear β⁺ decay (¹⁸F) — **~0.633 MeV** 25. Electron capture — **~keV–MeV** 26. Double beta decay (²⁷⁶Ge) — **~2.039 MeV** 27. Pion beta decay (π⁺ → π⁰e⁺ν) — **~4.6 MeV** 28. Tritium beta decay — **~18.6 keV** 29. Muon capture — **~100 MeV released** (reaction, not pure decay) 30. Neutron radiative beta decay — **~0.782 MeV** 31. Neutrino decay — **≪ eV** (hypothetical) 32. Axion-like decays — **~eV–MeV** (hypothetical) 33. Dark matter decay — **~keV–TeV** (hypothetical) 34. Neutron–antineutron oscillation — **~10⁻⁶ eV** (hypothetical) --- **Key caveats:** - "Energy scale" here means the **characteristic mass of the decaying particle or the Q-value** of the decay, not a strict threshold. - Some entries (proton decay, W'/Z', heavy N, neutrino decay, dark matter decay) are **hypothetical/BSM** and included for completeness. - **Electron capture** and **muon capture** are capture reactions rather than pure decays, but are weak-mediated and often grouped with decays. - **Mixing/oscillation** (K⁰–K̄⁰, B⁰–B̄⁰, neutrino oscillation) is not listed because it is not a decay but a weak-mediated propagation phenomenon. -->