Electron e
Light deficit0.300%
Heavy supply
Fully accounted for
The neutrino carrier arc
One carrier.
Linked signals.
What the light sector is missing,
the heavy sector must carry.
Here, a carrier is the complete physical source behind the linked responses. In the arc’s two completed branches, its light and heavy parts obey one precise, testable relation.
Follow the clueStructural prediction · awaiting qualified experimental testing
A complete carrierHighlight what each part contributes
Select a part to see what it contributes.
The two responses belong together.
The light response and matching heavy strength are parts of one complete physical carrier. The connection between them is what the proposed test checks.
Highlighting a part changes the emphasis, not the source. This is a structural diagram of the exact symmetric example; the curves are connections, not particle paths.
19 papersTwo completed source branchesMany possible realizations · one carrier within each
01 / What oscillation leaves open
The same rhythm.
Different underlying sources.
Oscillation tells us that the neutrino response changes between preparation and detection. But the same low-energy response can come from different physical source structures.
A and B are two possible underlying sources. In this example, the control changes B’s heavy scale and its coupling together. Follow the three steps to see why oscillation alone cannot distinguish them.
Start with the same source settings. Then choose step 2 to change B.
The underlying sourcesRelative to source A
Higher line = higher heavy scale. Thicker bridge = stronger coupling.
Fine-tune source B yourself
B’s heavy scale1.50×+50%
B’s coupling1.22×+22.5%
Oscillation patternSameFor both sources
What oscillation reveals
Source ASource B
The same oscillation.
UnchangedBoth sources leave exactly the same oscillation pattern. The dashed green trace lies on the solid lavender trace.
The scales separate.
50% higherKeep the heavy-scale information and these sources become distinguishable. Oscillation alone had hidden this difference.
Why does the oscillation stay the same?
1.50coupling²÷1.50heavy scale=1.00×same coefficient
Source B’s heavy scale is 50% higher and its coupling is 22.5% stronger. Oscillation still cannot tell A and B apart.
An illustration of PCR5B’s compensated source family. Relative source parameters and schematic records, not an oscillation fit or a predicted heavy mass.
The same oscillation can hide a different heavy scale. That is why the arc asks for more kinds of measurements.
The invariant behind the slider
For the displayed family, Mλ = λM₀ and Yλ = √λY₀. The matched coefficient YλMλ−1YλT is unchanged, while the retained heavy threshold and matching structure distinguish the sources. The chart is schematic; its curve is not fitted to experimental data.
PCR5B establishes at least continuum many standing-carrier realization classes. The later targets add absolute mass response, lepton-number violation, heavy-state and active-closure response, cosmology, and symmetry. They must agree on one common physical source.
PCR5B · Exact standing-carrier stratificationPCR5E · Joint standing-carrier closure02 / Why vectorlike?
Build the heavy connection.
Start with two matching field components. Add an allowed mass pairing, then connect them to the light weak sector.
The completed connection
A direct mass and a connection to light matter.
The heavy components have matching gauge charges, allowing a direct Dirac mass pairing. A separate Higgs/Yukawa coupling connects the right-chiral heavy component to the left-chiral light lepton doublet.
This matching of the left and right gauge identities is what vectorlike means here.
The source terms, chirality, and the two symmetry branches
PCR5E §8.2 constructs equal-rank singlet multiplets NL and NR, together with three νR fields. The heavy left- and right-chiral singlets transform in the same Standard Model representation (1, 1, 0) and both have conventional B−L = −1. The two displayed operators are:
−N̄L MN NR + h.c.
−L̄ H̃ YLN NR + h.c.
The first is a gauge-invariant direct Dirac mass term. The second connects the Standard Model lepton doublet to the heavy singlet through the Higgs field. The complete source also contains the νR Yukawa term and NL–νR mixing. Its common mass-map factorization, active incidences and retained physical relations supply the later light/heavy structure.
“Vectorlike” specifies how chiral components transform. The Dirac/Majorana distinction concerns mass and particle–antiparticle structure; it is a separate question. In the exact-global B−L child, the symmetry forbids the retained lepton-number-violating response. The bounded-accidental child preserves B−L through operator dimension four and admits additional higher-dimensional lepton-number-violating responses. A null search alone does not select between them.
This exhibit isolates selected field types and source operators. It neither counts heavy states nor derives carrier identity from a pairing diagram. PCR6 establishes the rank-three heavy sector and one complete terminal carrier within each accepted realization using the full source and its response structure. No numerical heavy mass or lifetime is assigned here.
PCR5E · §8.2, the vectorlike sourcePCR6 · Physical nature and minimal identity03 / The connected prediction
Something is missing.
Does the heavy side account for it?
The prediction links two sides of the same accounting: the light sector carries a little less charged-current strength, and the heavy sector must supply exactly that missing amount in each flavor channel.
Try it: choose a possible heavy response. Check whether it reaches the required mark in every flavor.
3 of 3 match · every missing amount is supplied
100%Full reference strength
−99.7%Carried by the light sector
=0.3%Missing in each flavor
The outlined slot is the missing amount. The green fill is the heavy weight. A match fills the slot exactly; a gap or an overrun leaves a visible difference.
Muon μ
Light deficit0.300%
Heavy supply
Fully accounted for
Tau τ
Light deficit0.300%
Heavy supply
Fully accounted for
Required by the light deficitSupplied heavy weightEnlarged scale · pp = percentage points
The weights match in all three flavors.3 of 3 flavors match
All three missing amounts are supplied by the corresponding heavy response. This pattern passes the displayed matching check. A complete test also needs correlations, rank and heavy support.
Illustrative response patterns for the arc’s two completed source branches. The 0.3% deficit is chosen for this explanation; it is not a measured value or a numerical value selected by the paper. Coupling weights are not detector event rates.
Light deficit=Heavy weight=δE I₃
The complete matrix relation and its scope
In the exact source, N = cEU and VH = −sEU, where U is unitary and cE² + sE² = 1. Thus Δact = I₃ − NN† = VHVH† = ΩH = δEI₃, with δE = sE² > 0 and rank ΩH = 3. The off-diagonal Gram entries vanish in this limit. Matching three bars alone does not determine the complete matrix.
The claim applies to the completed vectorlike-joint branches with bounded accidental B − L or exact global B − L, using the D3-1.3 and public-summary cosmology targets. These branches retain many distinct realizations and do not close the unresolved parent neutrino theory. The marked source has 0 < δE ≤ 1/256; no universal positive lower bound or measured deficit follows.
These diagrams show inclusive coupling weights, not a universal detector event rate. A real comparison needs common weak normalization, source and detector response, all three flavors, and the appropriate heavy-support and correlation records.
PCR7 · Observable projection and prediction lockPCR8 · Robustness and experimental testing04 / Change one thing at a time
Two different kinds of equal.
What happens when you change one?
The heavy modes can share one source scale, and the three flavors can carry equal weights. These are independent features. Try changing one while holding the other fixed.
Start with an example. Then use either slider to make your own comparison.
Both features equal · choose one to change
One scale—or three?
ExactAt the starting point, the three mode markers line up. Splitting moves them to different source values.
The three source values coincide.
Relative structural source values. No physical mass, lifetime or detector peak is assigned here.
Choose another example ↑Equal weight in every flavor?
ExactCompare the rows. Changing the flavor balance changes their sizes; each heavy amount still matches its own light deficit.
Light deficitHeavy weight
ElectronLight = heavy 0.300%
MuonLight = heavy 0.300%
TauLight = heavy 0.300%
Every flavor has the same weight.
A constructed example with positive weights. Both sides are normalized together, so the light–heavy relation remains exact.
Choose another example ↑Start with both features equal. Try “Split the scales” or “Unbalance the flavors” and watch which side changes.
Heavy response directionsThreeAll three remain nonzero in this constructed family.
Light–heavy accountingPreservedEach flavor’s missing weight is still supplied.
One complete carrierOne in the exact sourcePersistence after a change needs the paper’s separately certified source-support domain.
The source modes and interaction flavors are different classifications. Neither slider certifies a physical source domain. Internal splitting alone does not establish a second complete carrier.
What is robust, and under which conditions?
Exact heavy degeneracy has zero unrestricted symmetry-breaking radius: a nonzero traceless Hermitian perturbation can separate the support. Exact flavor universality likewise requires equal singular values of the charged-current heavy block. Neither property follows from the other.
Rank three persists for a sufficiently small perturbation of a full-rank heavy coupling, with a separate condition retaining the heavy spectral cluster. The closure identity Δ′act = Ω′H holds on the complete block-isometry class. One terminal carrier persists on a certified source-support and continuation domain. A claim that all three survive together uses the intersection of those domains.
Here Ω′H = δ diag(1 + a, 1, 1 − a), with 0 ≤ a ≤ 0.6, and the light weights are chosen as its normalized complement. Rank and closure follow by construction. The sliders do not certify a physical source-support domain. Internal splitting alone supplies no independently complete second carrier.
PCR6 · Physical nature and minimal identityPCR7.5 · Structural stability and degeneracy lifting05 / From a collision to a test
Follow the signal.
Keep what the test needs.
The theory proposes a linked light–heavy response. Follow a possible decay through the detector, decide which records survive, and connect them to the measurement the theory asks for.
Before there is a dataset
Most events never
reach the archive.
The detector responds to a flood of collision products. Triggers make rapid decisions about which events to keep. More than 99% of crossing events are filtered out before full recording in the conventional stream.
40 millioncrossing events / second
↓100,000pass the first trigger
↓3,000retained / second
ATLAS’s published Run-3 design (2022): approximately 99.99% filtered out. This is the overall event reduction, not a signal-loss estimate.
The recording numbers and newer ways to keep information
The rates above are the ATLAS Run-3 design example, not a live counter or a measurement of this proposed signal’s trigger efficiency. Physics triggers can retain a high fraction of a chosen signal while rejecting most ordinary events. CMS Level-1 scouting provides a separate route that records reduced trigger information from all 40 million crossings per second; it does not retain every full detector event.
Follow an eventIllustrative events · geometry not to scale
Charged tracks, energy deposits and muon hits form a record of the decay products. The neutral heavy state is reconstructed from those products.
Example channel: W⁺ → μ⁺N, followed by N → μ⁻ + jets. The dashed N segment is a guide to the hypothesis, not a measured track. Vertex separation is enlarged for readability.
Four steps to a testable record
The response begins inside the detector.
A heavy-state hypothesis connects an associated lepton with a set of decay products. Each detector layer records a different part of that visible response.
Hypothetical responseOther eventsFiltered out
The sample is constructed to explain selection. Its mixture and retention counts are not predicted event rates or measured efficiencies.
Follow the same sample through all four stages.
Change what gets recorded
Lower the threshold to retain less energetic tags. Watch the recording load increase along with the hypothetical response.
Change what gets reconstructed
Additional methods can recover some crowded or displaced records. Missing usable track information still limits reconstruction.
Change what enters the analysis
Keep the charge, flavor and decay categories needed by the proposed test.
Events recorded42 / 60of the constructed sample
Hypothetical response selected6 / 30after all stages
Other events selected6background study still required
An online rejection prevents full recording through that stream. A stored event excluded by a later analysis may be available for a different analysis.
The theory sets the destination
A heavy signal is one part
of a linked measurement.
Reconstruct the heavy response across electron, muon and tau channels. Measure the light-sector normalization under common controls. Then test whether the two sides obey the predicted relation, including their flavor structure and heavy-support rank.
Light-sector deficit=Inclusive heavy response
PCR7.5 · Proposed search architecturePCR8 · Experimental frameworkHow the detector example relates to the proposed programme
The schematic illustrates a lepton-number-conserving semileptonic channel. The proposed programme includes both conserving and violating categories, inclusive leptonic and semileptonic reconstruction, and electron, muon and tau records. The diagram is one example, not the complete decay inventory; a same-sign pair alone does not diagnose lepton-number violation in a multi-lepton event.
The event sample uses invented tags and properties to separate online recording, reconstruction and analysis choices. Its selections are not a current ATLAS or CMS menu. Current HNL searches already use dedicated triggers and reconstruction, and some recorded samples can be reinterpreted. PCR7.5 identifies specific published-selection and interpretation mismatches with the complete carrier test.
Adjustments to a real search require efficiencies, resolution, backgrounds, calibration and common light–heavy normalization. A retained event is not itself a discovery; the linked statistical comparison follows.
CMS · Existing multi-lepton HNL searchOnce the right records are retained
Make the comparison precise.
Increase exposure and change the systematic floor to explore when two illustrative responses can be distinguished.
Illustrative measurement designExplore precision
Statistical part0.200%
Systematic floor0.025%
Illustrative radius0.225%
Illustrative scalar response bands using a 0.3% example. Exposure is relative; the full test compares the light and heavy matrices.
More precision needed
The design bands overlap. Increase exposure or lower the systematic floor to see whether this example becomes distinguishable.
From theory to experiment
A prediction.
An experimental programme.
The theory specifies the linked response and how to test it. Experimental teams can develop the trigger, reconstruction, calibration and background strategy around that target.
This is a proposed experimental programme; detector-specific implementation and sensitivity studies are the next step.
The experimental benchmark and the remaining inputs
The earlier D3 study supplies a 28–30 GeV search benchmark with a 0.2 mm response-chart lifetime coordinate. Only 30 GeV is a direct ATLAS mass anchor in that band. These are not a derived numerical mass or proper lifetime for the final vectorlike carrier. The final structural heavy domain remains symbolic, and a bridge identifying it with that benchmark has not been supplied.
A physical unstable-state pole and lifetime require the full propagator/self-energy and response construction. A detector peak or unresolved line is not enough to determine exact degeneracy. A real test also needs all relevant production and decay categories, weak normalization, nuisance and correlation handling, and certified coverage.
PCR8 reports FrozenPredictionAwaitingQualifiedEvaluation; an actual facility’s SPIC (the protocol’s identifiability and conditioning certificate) remains NotReady. Data used to define or calibrate the source cannot independently validate those same response coordinates.
PCR5D3 · Heavy-state, active-closure and CLFV extensionPCR8 · The experimental frameworkRead the complete arc
From the oscillation clue
to the experimental test.
Follow the argument through its foundations, additional physical targets, joint carrier structure, and prediction. Each title opens one paper record with its publication link.
The oscillation problem
Target-Fixed Physical Role Necessity for the Realized Neutrino Oscillation Interface
Identifies the physical response and interaction–propagation nonalignment required by the fixed oscillation interface before selecting its microscopic carrier.
Complete Physical Interface of the Neutrino Propagation Role Complex
Assembles the complete propagation interface, retaining active responses, source and detector attachments, and the shared physical witnesses needed for joint compatibility.
Source-First Exhaustion of the Physical Carrier Universe
Constructs a source-first universe of active carrier architectures before physical viability is assessed, retaining composition, matching and boundary structure.
Simultaneous Physical Constraint Collapse of the Neutrino Carrier Universe
Applies physical consistency requirements to one common realization, keeping their shared parameters and cross-sector conditions together.
Compatible Role-Occupancy Closure for the Neutrino Propagation Role Complex
Establishes compatible occupancy of the required neutrino role while retaining physically distinct carrier alternatives allowed by the oscillation target.
Standing identity and new targets
Standing-Carrier Upper Closure for the Neutrino Propagation Role Complex
Characterizes standing identity through seven retained response channels and exhibits four distinct ways that complete source contributions can survive or fail deletion.
Exact Standing-Carrier Stratification of the Neutrino Oscillation Realization Space
Constructs the exact symbolic standing atlas for the fixed oscillation target, including a continuum of different heavy thresholds with the same low-energy response.
Functorial Target Extension of Standing-Carrier Quotients
Explains how additional physical targets can eliminate, preserve or split existing standing classes, while retaining distinctions already established at the original target.
Direct Kinematic-Mass Target Extension of the Neutrino Standing-Carrier Space
Adds beta-endpoint mass response to the standing-carrier space and separates the added absolute-support information from the original oscillation distinctions.
Lepton-Number-Violating Target Extension of the Neutrino Standing-Carrier Space
Adds lepton-number-violating transition amplitudes, distinguishing accepted zero and nonzero responses without treating a null search as a unique carrier selector.
Heavy-State Active Closure and CLFV Extension of the Neutrino Standing-Carrier Space
Adds heavy-state, active-closure and charged-lepton-flavor constraints, with an explicit benchmark family and a declared source comparison scope.
Successor Target for Quantitative Active Closure in the Neutrino Standing-Carrier Space
Defines a separate quantitative successor target with retained active-event response, preserving the distinction between new target information and the earlier heavy-state branch.
Cosmological Population and Transport Extension of the Neutrino Standing-Carrier Space
Adds cosmological population and transport information, separating the public-summary target from the complete correlated cosmological likelihood still required for the broader inference.
Symmetry and Charge Extensions of the Neutrino Standing-Carrier Space
Separates seven symmetry and charge targets, retaining their source, matching, anomaly and remnant conditions instead of treating symmetry labels as interchangeable.
The carrier and its experimental prediction
Joint Standing-Carrier Closure for the Neutrino Sector
Combines the extended targets at one physical source and completes joint closure for two qualified vectorlike branches, while preserving unresolved parent branches and multiple realizations.
Physical Nature and Minimal Identity of the Neutrino Carrier
Identifies one complete terminal carrier within each accepted realization of the two qualified branches, with three light sectors and one rank-three heavy sector in the exact symmetric limit.
Observable Projection and Experimental Prediction Lock for the Neutrino Carrier
Derives the matched light charged-current deficit and inclusive heavy weight in the qualified branches, with a shared flavor structure and a prospective experimental protocol.
Structural Stability and Degeneracy Lifting of the Neutrino Heavy Sector
Separates the robustness of carrier identity, rank, closure, degeneracy and flavor equality, and specifies the response and resolution requirements for experimental inference.
A Neutrino Carrier Prediction: Robustness and a Framework for Experimental Testing
Combines the source-qualified carrier prediction and its robustness results into a framework for experimental testing, with numerical physical pole, lifetime and detector qualification still open.