unitarity triangle
E815597
The unitarity triangle is a geometric representation in the complex plane of quark mixing and CP violation in the Standard Model, derived from the unitarity of the CKM matrix.
All labels observed (2)
| Label | Occurrences |
|---|---|
| unitarity triangle canonical | 2 |
| CKM unitarity relations | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9689372 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: unitarity triangle Context triple: [Kobayashi–Maskawa theory, relatedConcept, unitarity triangle]
-
A.
Cabibbo–Kobayashi–Maskawa matrix
The Cabibbo–Kobayashi–Maskawa matrix is a fundamental component of the Standard Model of particle physics that describes how quarks change flavor via the weak interaction and accounts for CP violation in the quark sector.
-
B.
Kobayashi–Maskawa theory
The Kobayashi–Maskawa theory is a fundamental framework in particle physics that explains CP violation in the Standard Model through a three-generation quark mixing matrix (the CKM matrix).
-
C.
Weinberg angle
The Weinberg angle, also known as the weak mixing angle, is a fundamental parameter in the electroweak theory that quantifies the mixing of electromagnetic and weak forces and determines the relative strengths of their interactions.
-
D.
Goldberger–Treiman relation
The Goldberger–Treiman relation is a fundamental result in particle physics that links the strong pion–nucleon coupling constant to the axial-vector coupling of the nucleon and the pion decay constant, illuminating the role of chiral symmetry in low-energy hadron interactions.
-
E.
Υ(4S) resonance
The Υ(4S) resonance is an excited bottomonium state that lies just above the threshold for B-meson pair production and is widely used at B-factories to study B-meson decays and CP violation.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: unitarity triangle Target entity description: The unitarity triangle is a geometric representation in the complex plane of quark mixing and CP violation in the Standard Model, derived from the unitarity of the CKM matrix.
-
A.
Cabibbo–Kobayashi–Maskawa matrix
The Cabibbo–Kobayashi–Maskawa matrix is a fundamental component of the Standard Model of particle physics that describes how quarks change flavor via the weak interaction and accounts for CP violation in the quark sector.
-
B.
Kobayashi–Maskawa theory
The Kobayashi–Maskawa theory is a fundamental framework in particle physics that explains CP violation in the Standard Model through a three-generation quark mixing matrix (the CKM matrix).
-
C.
Weinberg angle
The Weinberg angle, also known as the weak mixing angle, is a fundamental parameter in the electroweak theory that quantifies the mixing of electromagnetic and weak forces and determines the relative strengths of their interactions.
-
D.
Goldberger–Treiman relation
The Goldberger–Treiman relation is a fundamental result in particle physics that links the strong pion–nucleon coupling constant to the axial-vector coupling of the nucleon and the pion decay constant, illuminating the role of chiral symmetry in low-energy hadron interactions.
-
E.
Υ(4S) resonance
The Υ(4S) resonance is an excited bottomonium state that lies just above the threshold for B-meson pair production and is widely used at B-factories to study B-meson decays and CP violation.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
concept in particle physics
ⓘ
geometric representation ⓘ tool in flavor physics ⓘ |
| angleAlphaAlsoCalled | phi_2 ⓘ |
| angleBetaAlsoCalled | phi_1 ⓘ |
| angleGammaAlsoCalled | phi_3 ⓘ |
| assumes | three generations of quarks ⓘ |
| constrainedBy |
B meson decays
ⓘ
CP asymmetries in B decays ⓘ K meson decays ⓘ neutral meson mixing ⓘ rare flavor-changing processes ⓘ |
| definedIn | complex plane ⓘ |
| derivedFrom |
CKM unitarity relation V_ud V_ub* + V_cd V_cb* + V_td V_tb* = 0
ⓘ
unitarity of the CKM matrix ⓘ |
| encodes |
information on CP violation in the quark sector
ⓘ
magnitudes of CKM matrix elements ⓘ phases of CKM matrix elements ⓘ |
| hasAngle |
angle α
ⓘ
angle β ⓘ angle γ ⓘ |
| hasArea |
measure of CP violation in the quark sector
ⓘ
proportional to Jarlskog invariant ⓘ |
| hasComponent |
side proportional to V_cd V_cb*
ⓘ
side proportional to V_td V_tb* ⓘ side proportional to V_ud V_ub* ⓘ |
| hasParameterization | apex coordinates (ρ̄, η̄) ⓘ |
| hasProperty | closed triangle in the complex plane ⓘ |
| hasVariant |
bd unitarity triangle
ⓘ
bs unitarity triangle ⓘ |
| introducedFor | studying CP violation in B meson system ⓘ |
| relatedTo |
CKM matrix unitarity
ⓘ
CP violation ⓘ Cabibbo–Kobayashi–Maskawa matrix ⓘ Standard Model of particle physics ⓘ
linked to:
Standard Model
Wolfenstein parameterization ⓘ quark mixing ⓘ |
| sensitiveTo | new physics in flavor sector ⓘ |
| testedAt |
B factories
ⓘ
BaBar experiment ⓘ
linked to:
BaBar detector
Belle experiment ⓘ
linked to:
Belle II detector
LHCb experiment ⓘ
linked to:
LHCb
|
| usedFor |
constraining CKM matrix parameters
ⓘ
global fits of flavor observables ⓘ testing consistency of the Standard Model ⓘ visualizing CP-violating phase ⓘ |
| visualizes | one of the six unitarity relations of the CKM matrix ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: unitarity triangle Description of subject: The unitarity triangle is a geometric representation in the complex plane of quark mixing and CP violation in the Standard Model, derived from the unitarity of the CKM matrix.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.