Test 17 — Electroweak Sphaleron and Baryogenesis — A Framework for a Theory of Everything

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Test 17 — Electroweak Sphaleron and Baryogenesis Test

Does the framework's granularity doctrine give any traction on the single hardest unresolved number in early-universe physics — why there is more matter than antimatter — or does it, like the Standard Model itself, run into the fact that the electroweak "transition" is not actually a phase transition at all?

What we're checking

Observable: The origin of the matter–antimatter imbalance — the baryon asymmetry η_B = (6.10 ± 0.04) × 10⁻¹⁰ — and whether the known physics of the electroweak era can generate it.
Standard cosmology: Can't close it. A 125.20 GeV Higgs makes the electroweak transition a smooth crossover, so the out-of-equilibrium Sakharov condition fails; the known CP violation (Jarlskog J ≈ 3 × 10⁻⁵) falls ~10 orders of magnitude short.
Granularity: Doesn't close it either — and says so plainly. It reproduces the settled timing (electroweak crossover T_c ≈ 159 ± 1 GeV, sphalerons freezing out at ~130–140 GeV) but supplies no new source for the asymmetry.
Measured: η_B = (6.10 ± 0.04) × 10⁻¹⁰ (equivalently Y_ΔB ≈ 8.7 × 10⁻¹¹) — a real number the sky insists on, and one no first-principles theory yet delivers.
The epoch: The electroweak era, ~10⁻¹¹ s after the beginning — the clock reading for when this plays out, not the quantity being compared.
Verdict: Open (for all of cosmology) A shared, field-wide gap, not a mark against either road.

Here is one of the oldest questions in physics, and it is almost embarrassingly simple to ask: why is there anything here at all? In the first fraction of a second the universe should have made matter and antimatter in equal measure, and they should have annihilated each other into a bath of light — leaving no galaxies, no planets, no us. Something tipped the scales by about one part in a billion. That tiny surplus is everything solid you have ever touched. It has a number: η_B = (6.10 ± 0.04) × 10⁻¹⁰. And nobody — not the Standard Model, not this framework, not any theory yet written — can derive it from first principles.

So this test is where we lead with the honest answer instead of the flattering one. Both roads walk right up to the electroweak era and agree completely on the physics that is settled: the same crossover temperature, T_c ≈ 159 GeV, where particles get their mass; the same sphalerons — the strange, matter-shuffling processes that go quiet around 130–140 GeV. That much they get right together. But the door slams at the same place for both. Because the Higgs weighs 125.20 GeV, the transition is a gentle crossover, not the violent phase change that could have frozen an asymmetry in place — and the CP violation the world actually has comes up about ten orders of magnitude too weak to do the job.

This framework does not have a fix for that, and it does not pretend to. That is precisely why the verdict is Indeterminate, not “Agrees” — the number is real, and no one has honestly explained it. We show that here as an open frontier the whole field shares, because a candidate theory of everything earns its credibility exactly where it refuses to bluff.

What's actually going on here: two independent lines of reasoning — standard hot-Big-Bang cosmology and this recordability framework — agree completely on the sphaleron bookkeeping. Both place the electroweak crossover at T_c ≈ 159 GeV (~10⁻¹¹ s) and both find sphalerons comfortably in thermal equilibrium above that temperature, freezing out around 130–140 GeV. That part is solid and it agrees. But neither side can answer the deeper question honestly: why is there more matter than antimatter at all? The Standard Model's own CP violation is about ten orders of magnitude too weak, and with the measured 125 GeV Higgs mass the "transition" turns out to be a smooth crossover rather than a sharp phase transition — so the out-of-equilibrium condition needed to lock in an asymmetry (Sakharov's third condition) isn't met. This framework doesn't have a fix for that either. So we call this one plainly Indeterminate: the clock agrees, the missing ingredient is missing for everyone. Agreement between the two methods on the timing builds confidence in the framework's bookkeeping — it does not, by itself, solve baryogenesis. See the blind prediction method for how this site tells inherited open problems apart from distinctive claims.

1. Verdict

The number, both ways

Number we’re testing: Origin of the baryon asymmetry η_B — whether known electroweak-era physics can generate the matter–antimatter imbalance
Standard cosmology: Can't close it: a 125.20 GeV Higgs makes the transition a smooth crossover (Sakharov condition 3 fails); CKM CP violation (Jarlskog J ≈ 3×10^-5) falls ~10 orders of magnitude short
This framework (granularity): Doesn't close it either — reproduces the settled timing (T_c ≈ 159 ± 1 GeV crossover, sphalerons freezing out at ~130–140 GeV) but supplies no new source for the asymmetry
Measured: η_B = (6.10 ± 0.04) × 10^-10 (Planck 2018 via Ω_b h² = 0.02237 ± 0.00015); equivalently Y_ΔB ≈ 8.7 × 10^-11
Agreement: Sphaleron bookkeeping agrees quantitatively (Γ_sph ≫ H above T_c); the CP-violating out-of-equilibrium source of η_B is missing — a ~10-orders-of-magnitude shortfall shared by the whole field

Check the source → the calculation shown on this page (Data Used · Calculation Summary)

Indeterminate. The sphaleron physics itself checks out completely: electroweak symmetry breaks in a smooth crossover at T_c ≈ 159 GeV, and sphalerons stay in equilibrium above that temperature before freezing out around 130–140 GeV, exactly as expected. What's missing — for this framework and for the Standard Model alike — is the actual source of the matter/antimatter imbalance: a CP-violating process that runs out of equilibrium, as Sakharov's conditions require. Nobody has that piece yet. This is the single most famous open problem in early-universe physics, and it stays open here rather than getting rounded up to a closed result.

2. Tested Claim

Per the test suite's Tested Claim: "The theory must preserve or generate the observed baryon asymmetry through allowed electroweak sphaleron dynamics." Applied to this epoch, the specific claim under test is: whatever baryon- (or lepton-, converted via sphalerons) asymmetry existed prior to or during the electroweak epoch survives sphaleron washout and freezes out at a value consistent with the observed baryon-to-photon ratio η_B, without being erased (washed out to zero) or overproduced.

3. Data Used

Quantity	Value	Source
Baryon-to-photon ratio, η_B = n_B/n_γ	(6.10 ± 0.04) × 10⁻¹⁰	Planck 2018 VI (A&A 641, A6, 2020), via Ω_bh² = 0.02237 ± 0.00015, using η_B ≈ 2.74 × 10⁻⁸ Ω_bh²; PDG 2024 Astrophysical Constants table quotes the same order
Baryon asymmetry parameter, Y_ΔB = (n_B−n_B̄)/s	≈ 8.7 × 10⁻¹¹	Standard conversion Y_ΔB = η_B / 7.04 (entropy-to-photon ratio); PDG 2024 Big-Bang Cosmology review
Higgs boson mass	125.20 ± 0.11 GeV	PDG 2024 Review of Particle Physics (ATLAS+CMS combination)
Electroweak crossover temperature	T_c ≈ 159 ± 1 GeV; crossover width ≈ 5 GeV	D'Onofrio & Rummukainen, Phys. Rev. D 93, 025003 (2016), arXiv:1508.07161; consistent with Kajantie, Laine, Rummukainen & Shaposhnikov 1996 (hep-lat/9605288)
Critical Higgs mass below which a true 1st-order transition exists	≈ 72–75 GeV (continuum lattice)	Kajantie, Laine, Rummukainen & Shaposhnikov, Phys. Rev. Lett. 77, 2887 (1996); Csikor, Fodor & Heitger 1999 (hep-ph/9809291)
Sphaleron rate at crossover (per unit volume, symmetric phase)	Γ_sph/T⁴ ≈ 20–30 α_W⁵ (order-of-magnitude, lattice)	D'Onofrio, Rummukainen & Tranberg, Phys. Rev. Lett. 113, 141602 (2014), arXiv:1404.3565; Bodeker & Moore 2000
Sphaleron freeze-out condition	Γ_sph(T) < H(T) below T ≈ 130–140 GeV (broken phase)	Standard EWBG literature summary, e.g. Morrissey & Ramsey-Musolf, New J. Phys. 14, 125003 (2012), arXiv:1206.2942
CP violation available in the CKM matrix (Jarlskog invariant)	J ≈ 3 × 10⁻&sup5;; far too small by ~10 orders of magnitude to source observed η_B	Gavela, Hernandez, Orloff & Pene, Mod. Phys. Lett. A 9, 795 (1994); reaffirmed in Morrissey & Ramsey-Musolf 2012 review

4. Calculation Summary

Step 1 — timing. Because the framework (like the Standard Model it inherits low-energy physics from) places electroweak symmetry breaking at T_c ≈ 159 GeV (Test 16, this suite), any baryon asymmetry generated at or above this temperature is processed by sphalerons, which violate B+L but conserve B−L. So the physically meaningful question is whether B−L is nonzero going into the electroweak epoch (favoring a leptogenesis-type origin above T_c) or whether the asymmetry must be generated locally during electroweak symmetry breaking itself (electroweak baryogenesis, EWBG).

\[ \text{sphaleron process: } \Delta(B+L) \ne 0,\qquad \Delta(B-L) = 0 \]

Step 2 — sphaleron rate vs. Hubble rate. In the symmetric (unbroken) phase above T_c, lattice results give a sphaleron rate per unit volume of order \(\Gamma_{\rm sph}/T^4 \sim 20\text{--}30\,\alpha_W^5\) (D'Onofrio, Rummukainen & Tranberg 2014), which is vastly faster than the Hubble rate \(H(T) = 1.66\sqrt{g_*}\,T^2/M_{\rm Pl}\) for \(T\sim100\text{--}160\) GeV — i.e. sphalerons are in full thermal equilibrium throughout the symmetric phase, exactly as required for either scenario. Using \(g_*\approx106.75\) and \(M_{\rm Pl}=1.22\times10^{19}\) GeV, \(H(160\,\text{GeV}) \approx 1.66\times10.3\times (160)^2/1.22\times10^{19}\,\text{GeV} \approx 2.2\times10^{-14}\) GeV, versus a sphaleron rate per unit volume that translates to an interaction rate many orders of magnitude larger — the equilibrium condition \(\Gamma_{\rm sph}\gg H\) is comfortably satisfied above T_c.

Step 3 — is there a departure from equilibrium (Sakharov condition 3)? This is where the calculation fails to close. Lattice studies of the SM electroweak transition with the measured Higgs mass of 125.20 GeV (D'Onofrio & Rummukainen 2016; consistent with the earlier finding of Kajantie et al. 1996 that a true first-order transition requires m_H ≲ 72–75 GeV) find the transition is a smooth crossover, not a first- or second-order phase transition. There is no bubble nucleation, no latent heat, and no significant departure from thermal equilibrium at the SM electroweak scale. Sakharov condition 3 (departure from thermal equilibrium) is therefore not satisfied by the SM electroweak sector alone.

Step 4 — is there enough CP violation (Sakharov condition 2)? The only CP violation available in the Standard Model is encoded in the CKM Jarlskog invariant, J ≈ 3×10⁻&sup5;. Propagated through the SM electroweak plasma, this sources an asymmetry many orders of magnitude (commonly quoted as ∼10 orders of magnitude) below the observed Y_ΔB ≈ 8.7×10⁻¹¹ (Gavela et al. 1994; Morrissey & Ramsey-Musolf 2012). SM CP violation alone cannot source the observed asymmetry.

Step 5 — washout check. Because there is no strong first-order transition, there is no bubble-wall-localized asymmetry generation and no sharp washout boundary either; sphalerons remain in equilibrium smoothly through the crossover and only shut off (Γ_sph < H) once T drops below ∼130–140 GeV in the fully broken phase. Whatever B−L asymmetry exists going into this window survives (it is not further washed out below freeze-out), but the SM alone supplies no mechanism to have put a large-enough asymmetry there in the first place.

Conclusion of the numerical check: the framework inherits a fully consistent, well-measured SM electroweak sector (crossover at T_c≈159 GeV, sphaleron equilibrium/freeze-out physics all quantitatively understood), but the actual source of the baryon asymmetry — the CP-violating, out-of-equilibrium mechanism required by Sakharov's third condition — is not supplied by the Standard Model sector and is not supplied by any specific mechanism proposed in this framework's technical program either. This is a genuine calculational gap, not a rounding-up of a qualitative story.

5. Granularity Interpretation

Under the framework's master doctrine, the "recordable distinction" at stake here is the sign and magnitude of the baryon number stored in ordinary matter — arguably the most consequential recordable fact in the observable universe (it is why there are stars, chemistry, and observers at all, rather than pure radiation). The doctrine is compatible with treating "matter over antimatter" as a stabilized, permanently recorded distinction once sphalerons freeze out below T ≈ 130–140 GeV: after that point the asymmetry can no longer be erased by B+L-violating processes and becomes a fossil quantity tracked all the way to today's η_B ≈ 6.1×10⁻¹⁰. But the doctrine says nothing about why the asymmetry has the sign and size it does before that freeze-out — that is exactly the unresolved CP-violation/departure-from-equilibrium problem above. The granularity interpretation motivates treating sphaleron freeze-out as a genuine "distinction becomes permanently recorded" event; it does not, and cannot, supply the missing microphysical source.

6. Gate Routing

Routes to the Matter-asymmetry record gate. Ledger entry:

      Matter-asymmetry record gate → Indeterminate →
      sphaleron equilibrium/freeze-out physics checks out quantitatively
      (Γ_sph ≫ H above T_c≈159 GeV; freeze-out ≈130-140 GeV)
      but the CP-violating out-of-equilibrium SOURCE of eta_B ≈ 6.1e-10
      is not supplied by the SM sector (Sakharov condition 3 fails: crossover,
      not 1st-order) or by this framework → open gap: baryogenesis
      mechanism unspecified for everyone.
    

This does not certify or refute the framework's broader early-universe program. It certifies only that the sphaleron-rate-versus-Hubble-rate bookkeeping is quantitatively sound, while flagging that the deeper question of the asymmetry's origin remains open — exactly as it is in mainstream particle cosmology.

7. What's Missing

This test does not land on a clean agree/disagree result. Here is exactly what's missing:

Missing out-of-equilibrium source: the Standard Model electroweak sector, with the measured 125.20 GeV Higgs mass, undergoes a smooth crossover (D'Onofrio & Rummukainen 2016), not a first-order phase transition — Sakharov condition 3 is not satisfied by SM electroweak physics alone.
Insufficient CP violation: CKM CP violation (Jarlskog invariant J≈3×10⁻&sup5;) is roughly ten orders of magnitude too small to source the observed asymmetry (Gavela et al. 1994).
No distinctive mechanism supplied: this framework does not (at the current stage of its technical program) specify a particular BSM CP-violating source, an extended Higgs sector, or a leptogenesis mechanism above T_c that would close the gap. Absent such a mechanism, calling this one solved would be exactly the "measured value treated as derived" and "qualitative story substituted for numerical constraint" mistakes the test suite is built to avoid.

What did not fail: the sphaleron-rate-vs-Hubble-rate equilibrium/freeze-out bookkeeping (Step 2 above) and the B−L conservation logic (Step 1) are both standard, quantitatively verified physics that this framework inherits without contradiction.

8. Next Action

Data lookup / theoretical work needed, not yet performed: (1) determine whether this framework's technical program proposes any specific extension to the SM Higgs sector, CP-violating coupling, or heavy-neutrino sector that could supply Sakharov conditions 2 and 3 above or during the electroweak epoch (e.g. an electroweak-baryogenesis-compatible extended scalar sector, or leptogenesis from a heavier scale feeding B−L before sphaleron freeze-out); (2) if such a mechanism is proposed, redo this calculation with the specific CP-violating phase and departure-from-equilibrium parameter to check whether it can quantitatively reach Y_ΔB ≈ 8.7×10⁻¹¹ without overproducing or being washed out; (3) cross-check any such mechanism against Test 18 (CP-Violation Sufficiency Test) in this same suite, which directly audits whether a proposed CP source is numerically sufficient. Until a specific mechanism is proposed and checked, this one stays honestly Indeterminate.

What this page does and does not claim

It does not claim this framework solves the baryogenesis problem, and it does not claim the Standard Model solves it either — both facts are stated plainly above. It does claim that the sphaleron equilibrium/freeze-out physics this framework inherits from the Standard Model is quantitatively sound and internally consistent with the framework's electroweak symmetry-breaking timing (Test 16), and that the genuinely open piece (the CP-violating, out-of-equilibrium source of the asymmetry) is honestly flagged as open rather than rounded up to "closed."

Suite reference: Test 17 of 44, Early Universe Granularity Test Suite. Gate route: Matter-asymmetry record gate. Master doctrine under test (not assumed): "Cosmic history is the history of increasing recordable distinction."

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