phenomenon 103.42 $CP$ violation in charm decays
open in the book ·
parts/11-qft-standard-model/05-flavour-neutrinos.tex:1999
· p. 2052
- phenomenon-tested: no experiment declares a \tests edge to it and it is not listed in untested.txt
Rests on
-
depends_on
definition 103.25
Standard parametrization
¶
- proves proof ch:05-flavour-neutrinos@proof-13 ¶
-
depends_on
theorem 103.11
GIM suppression at one loop
¶
-
depends_on
theorem 101.62
The mixing matrix is unitary
¶
-
depends_on
proposition 5.155
Averaging trick
¶
-
depends_on
definition 5.18
Inner product
¶
- depends_on definition 4.33 Vector space ¶
-
depends_on
definition 5.145
Equivalent representations
¶
- depends_on definition 5.141 Representation of a group ¶
-
depends_on
definition 5.144
Unitary representation
¶
- depends_on definition 5.18 Inner product ¶ ↺
- depends_on definition 5.141 Representation of a group ¶ ↺
- depends_on equation 5.171 eq:rep-unitary-group ¶
- depends_on equation 5.183 eq:rep-unitary-invariance ¶
-
depends_on
proposition 5.28
Gram–Schmidt
¶
- depends_on definition 5.14 Linear independence ¶
- depends_on definition 5.18 Inner product ¶ ↺
- depends_on definition 5.27 Orthonormal basis ¶
- depends_on equation 5.44 eq:lin-norm-assoc ¶
- proves proof ch:03-linear-algebra-representations@proof-5 ¶
- proves proof ch:03-linear-algebra-representations@proof-66 ¶
-
depends_on
definition 5.18
Inner product
¶
-
depends_on
proposition 5.153
prop:rep-unitary-completely-reducible
¶
-
depends_on
corollary 5.29
Orthogonal decomposition
¶
- depends_on definition 5.18 Inner product ¶ ↺
- depends_on definition 5.7 Vector subspace ¶
- depends_on proposition 5.28 Gram–Schmidt ¶ ↺
- proves proof ch:03-linear-algebra-representations@proof-6 ¶
-
depends_on
definition 5.148
Irreducible representation
¶
- depends_on definition 5.147 Invariant subspace ¶
-
depends_on
definition 5.149
Totally reducible representation
¶
- depends_on definition 5.147 Invariant subspace ¶ ↺
- depends_on equation 5.52 eq:lin-orthogonal-complement ¶
-
depends_on
lemma 5.150
Invariance of the orthogonal complement
¶
- depends_on definition 5.147 Invariant subspace ¶ ↺
- depends_on definition 5.144 Unitary representation ¶ ↺
- depends_on equation 4.25 eq:alg-hom-inverse ¶
- depends_on equation 5.52 eq:lin-orthogonal-complement ¶ ↺
- depends_on equation 5.183 eq:rep-unitary-invariance ¶ ↺
- proves proof ch:03-linear-algebra-representations@proof-63 ¶
- proves proof ch:03-linear-algebra-representations@proof-65 ¶
-
depends_on
corollary 5.29
Orthogonal decomposition
¶
- proves proof ch:03-weak-interactions@proof-43 ¶
-
depends_on
proposition 5.155
Averaging trick
¶
- proves proof ch:05-flavour-neutrinos@proof-6 ¶
-
depends_on
theorem 101.62
The mixing matrix is unitary
¶
- proves proof ch:05-flavour-neutrinos@proof-22 ¶
Supports
Nothing declares a dependency on this node yet.
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
cites |
→ | Observation of CP Violation in Charm Decays | derived | parts/11-qft-standard-model/05-flavour-neutrinos.tex:2008 |
depends_on |
→ | Standard parametrization | declared | parts/11-qft-standard-model/05-flavour-neutrinos.tex:2011 |
depends_on |
→ | GIM suppression at one loop | declared | parts/11-qft-standard-model/05-flavour-neutrinos.tex:2011 |
proves |
← | ch:05-flavour-neutrinos@proof-22 | declared | parts/11-qft-standard-model/05-flavour-neutrinos.tex:2014 |