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TAE 2018, Centro de Física de Benasque “Pedro Pascual”, Benasque, Spain, 2-15 September, 2018
A. Pich IFIC, U. València - CSIC
1
3ud ub cd cb td tbV V V V V V Al
B0 ─ B0 MIXING ¯
01(0.5064 0.0019) ps
dBM −∆ = ± tdV
20 0 2 24 ˆH ( , )3t t B B BtdB B V S r r M f B
01(17.757 0.021) ps
sBM −∆ = ±22
ts tdV V
0 02 2/ 1tbB BM m m
2 21 /c tq p m m
0 0 0.770 0.004d dB BM∆ Γ = ±
( )0Re 0.0005 0.0004dBε = − ±
very small
0 0 0.130 0.009s sB B∆Γ Γ = − ±
0 0 26.72 0.09s sB BM∆ Γ = ±
( )0Re 0.0002 0.0007sBε = − ±
2 Flavour Physics A. Pich – TAE 2018
12
* *12 12
12 12
2 22 2 *12 1
2 2 1212 12 2 2 12 12
1
2 2
2
2 2
1
0 0
2
0
1/
1 21
2
1( ) ( ) 4 , 4 R
1|
e
|,
1/ 1 1 sin , arg2
( )4
| |
,
e
f f
e
B B
B
B
tb
B B B B
B p B q B
iMqip
qM M m m Mp M
p q M
M M M M
M M M
12 12
* *12 12
2
M M iM M
M
1 20 01
0 02
2 1
/2cos( ) ( )
2 2( ) ( ),
( ) ( )( ) ( ) sin2 2
e eiM t t
i tq Mg t g tB t B g tp
B t B g tp i tg t g t i Mq
3 Flavour Physics A. Pich – TAE 2018
Widths & Mass Differences
M. Gersabeck
4 Flavour Physics A. Pich – TAE 2018
,2
Mx y∆ ∆Γ≡ ≡
Γ Γ
K0 : x ∼ y ∼ 1
D0 : x ∼ y ∼ 0.01 Slow oscillation (decays faster)
Bd : x ∼ 1 , y ∼ 0.01
Bs : x ∼ 25 , y ∼ 0.05 Fast oscillation (averages out to 0)
5
BELLE
± ± ±
± ± ±
−+
0 0 ( ) ( )d de e B B X Yν ν+ − → →
Time Scales: ( )sin / 2x iy t− Γ Oscillation ∼
Flavour Physics A. Pich – TAE 2018
, 2x M y≡ ∆ Γ ≡ ∆Γ Γ
K0 : x ∼ y ∼ 1
D0 : x ∼ y ∼ 0.01 Slow oscillation (decays faster)
Bd : x ∼ 1 , y ∼ 0.01
Bs : x ∼ 25 , y ∼ 0.05 Fast oscillation (averages out to 0)
6
Time Scales: ( )sin / 2x iy t− Γ Oscillation ∼
Flavour Physics A. Pich – TAE 2018
B0 ─ B0 MIXING AND DIRECT ¯ 0B
0B
f 0 0f f f f f
0 0f f f f f
T T[ f ] ; T T[ f ] ; T / T
T T[ f ] ; T T[ f ] ; T / T
B B
B B
ρ
ρ
≡ → ≡ − → ≡
≡ → ≡ − → ≡
( )( )
0
0
*12
12
*
* 22 ; M
d
s
Mtqtb i
tqtb s
B
Bq Mp M
e φ βφ
β λ η− ≈
−
≈ −
≈ ≈ =V VV V
M
0 0 ; f fB B= − =
2f2 ff f
2 2 2 2f f f f
2 Im 2 Im1 | |1 | | ; ; ;
1 | | 1 | | 1 | | 1 | |
q pp q
f f f fC S C Sρ ρ
ρρρ ρ ρ ρ
− −− ≡ ≡ ≡ − ≡
+ + + +
0 2 2f f
0 2 2f f
1[ ( ) f ] | T | | T | 1 cos( ) sin( )2
1[ ( ) f ] | T | | T | 1 cos( ) sin( )2
t
t
B t e M t M t
B t e M t M t
f f
f f
C S
C S
7 Flavour Physics A. Pich – TAE 2018
0B
0B
f
0 0 ; f fB B= − =
2f2 ff f
2 2 2 2f f f f
2 Im 2 Im1 | |1 | | ; ; ;
1 | | 1 | | 1 | | 1 | |
q pp q
f f f fC S C Sρ ρ
ρρρ ρ ρ ρ
− −− ≡ ≡ ≡ − ≡
+ + + +
0 2 2f f
0 2 2f f
1[ ( ) f ] | T | | T | 1 cos( ) sin( )2
1[ ( ) f ] | T | | T | 1 cos( ) sin( )2
t
t
B t e M t M t
B t e M t M t
f f
f f
C S
C S
CP self-conjugate: ff fη=f f f f ff f fT T ; T T ;
;
1/
f ff fC C S S
η η ρ ρ
=
=
=
= ≡
8
B0 ─ B0 MIXING AND DIRECT ¯ 0 0
f f f f f0 0
f f f f f
T T[ f ] ; T T[ f ] ; T / T
T T[ f ] ; T T[ f ] ; T / T
B B
B B
ρ
ρ
≡ → ≡ − → ≡
≡ → ≡ − → ≡
Flavour Physics A. Pich – TAE 2018
CP self-conjugate: ff fη=
( )( )
0
0
*2
2* ; M
d
s
Mtqtb i
stqtb
B
Bqp
eV VV V
φ βφ
β λ η− ≈
−≈
≈ −=
0B
0B
f
9
B0 ─ B0 MIXING AND DIRECT ¯
Assumption: Only 1 decay amplitude *
2*
AA
Dqqb qqq qb i
qqqbb qqq
eV VV V
φ′→ ′ −
′→ ′
= =2*
0
Dif ff
f
e
C
φρ ρ η= =
=
Direct information on the CKM matrix
( ) ( )( ) ( )
0 0
f0 0
f fsin(2 ) sin( ) ;
f f M D
B BM t
B Bη φ φ φ φ
Γ → − Γ →= − ∆ = +
Γ → + Γ →
Flavour Physics A. Pich – TAE 2018
0dB π π+ −→0 0/ SdB J K→ Ψ 0 0 0
SsB Kρ→
2cscbV V Al
2tstbV V Al
3ub udV V A il r h
3 1tb tdV V A il r h
3ub udV V A il r h
3 1tb tdV V A il r h
f b f b g p a φ γ≠
*** ** BAD 10
ρ0
Flavour Physics A. Pich – TAE 2018
0 0
0 0 f( / ) ( / )
sin(2 ) sin( )( / ) ( / )
S S
S S
B J K B J KM t
B J K B J Kψ ψ
η βψ ψ
Γ → − Γ →= − ∆
Γ → + Γ →
Signal
HFAG:
sin(2β) = 0. 691 ± 0.017
0,/ , (2 ) , ,c cS L S S SB J K S K K Kψ ψ χ η→
11
BELLE 2012
KS KL 0B0B
Flavour Physics A. Pich – TAE 2018
2tstbV V Al
b → qqs −
Sensitive to New Physics in Penguin diagram
Agreement with
No signal of
direct
0 / ( )S cB J K b c s
12
,q d s=
Flavour Physics A. Pich – TAE 2018
B0 → ππ
Penguins
2f
f 2f
1 | | 01 | |
C ρρ
−≡ ≠
+
Direct
( ) ( )( ) ( )
0 0
0 0
f fcos( ) sin( )
f f f f
B BM t M t
B BC S
Γ → − Γ →= − ∆ + ∆
Γ → + Γ →
3ub udV V A il r h
3 1tb tdV V A il r h
sin(2 )fS a ?
*
*arg td tb
ud uba
V VV V
13
0 0 0
0( ) 0.37 (5)( )BB
π ππ π+ −
Γ →=
Γ →
Flavour Physics A. Pich – TAE 2018
B0 → ππ , ρρ , ρπ
Penguins
2f
f 2f
1 | | 01 | |
C ρρ
−≡ ≠
+
Direct
14
*
*arg 8HFAG 20 8 517: td tb
ud ub
V VV V
a
0 0 0
0( ) 0.035 (6)( )BB
ρ ρρ ρ+ −
Γ →=
Γ →
Flavour Physics A. Pich – TAE 2018
MEASURING HADRONIC CONTAMINATIONS Time Evolution Transversity Analysis: B → V V Isospin Relations (Gronau-London)
Mixing (Gronau-London-Wyler, Atwood-Dunietz-Soni)
Dalitz Analysis SU(3) Relations: B → π K , π π , ...
…
0 0D -D0 0 0
0 0 0 0 0 0
2 T( ) T( ) T( )
2 T( ) T( ) T( )S S Sd d d
B D K B D K B D K
B D K B D K B D K
+ + + + + ++
+
→ = → + →
→ = → + →
01
2( )T B π π+ −→
0 0 0( )T B π π→
0 0( ) ( )TT B Bπ ππ π+ −+ −= →→
01
2( )T B π π+ −→
0 0 0( )T B π π→
15 Flavour Physics A. Pich – TAE 2018
0 0 0
0 0 0 0 0 0
2 T( ) T( ) T( )
2 T( ) T( ) T( )S S Sd d d
B D K B D K B D K
B D K B D K B D K
+ + + + + ++
+
→ = → + →
→ = → + →
Mixing
Gronau-London-Wyler Atwood-Dunietz-Soni
Giri-Grossman-Soffer-Zupan
0 0D -D
*
5.86.4*arg 74.0g
ud ub
cd cb
V VV V
16 Flavour Physics A. Pich – TAE 2018
UNITARITY TRIANGLES
( )2 3
2 2
3 2
41 /2 ( )
1 /2(1 ) 1
A iA
A i AV
λ λ λ ρλ λ λ
λ ρ λ
η
ηλ
− − − − − − −
≈ +
17
( )0 i j* * *ui uj ci cj ti tjV V V V V V ≠+ + =
Flavour Physics A. Pich – TAE 2018
* * * 0ud ub cd cb td tbV V V V V V+ + =
* *ud ub cd cbV V V V * *
td tb cd cbV V V V2
2
11 0.343 0.011211 0.153 0.0132
η η λ
ρ ρ λ
≡ − = ± ≡ − = ±
91.0 2.5 ; 23.2 1.2 ; 65.3 2.0α β γ= ± ° = ± ° = ± °
UTfit
18 Flavour Physics A. Pich – TAE 2018
Tree-level determinations Loop processes
CP Conserving CP Violating
19 Flavour Physics A. Pich – TAE 2018
9th CERN Latin-American School of High-Energy Physics San Juan del Rio México, 8 –21 March, 2017
arXiv:1112.4094
Backup
20 TAE 2018, Centro de Física de Benasque “Pedro Pascual”, Benasque, Spain, 2-15 September, 2018
21
P0 ─ P0 MIXING ¯ 0 0( ) ( ) ( )t a t P b t Py ( ) ( )di t t
dty y M
12 12
* *12 12
2
M M iM M
M : : * *
12 12 12 12,M M
0 0 0 02 112 12
12 P X P PX
dsP H P PP dQ P H X X H PM
MM s
212
0 01 1( )X P PX
ds dQ s M P H X X H PMp d
Dispersive: Absorptive:
Phase convention: 0 0P P
2 2
0 00 ,
| | | |
p P q PP
p q
* *12 12
12 12
1/ 2
1 21
2
iMqip M
εε
− Γ −≡ = + − Γ
Eigenvalues:
2 2
2 2 2
| | | | 2 Re( )|| | | | 1 | |p qP Pp q
ee
/ 1q p 0 01,2
1 ,2
P P P 1,2 1,2P P
Flavour Physics A. Pich – TAE 2018
22
Bs Asymmetries
( )*
*SM
2
2 2 arg
ccs M Ds ss
ccs ts tbss
cs cb
V VV V
φ φ φ
φ β
≡ +
≈ − ≡ − −
( ) ( )-10.085 0.007 ps , 0.030 0.033 rads
ccss φ∆Γ ± − ±= =
12 12
2
2argqq q c
b
mMm
f
0
0
0
4 4
4 40
S
0 0
0 0L
12
12
( ) ( )( ) ( )
( )
4 Re( ) sin tanq
q
q
q
Bq qB
B
q q
q q
p qp q
A BB X X
B X
M
X
M
BB
e f f
0 0SL SL( ) 0.0021 0.0017 , ( ) 0.0006 0.0028d sA B A B
Flavour Physics A. Pich – TAE 2018
23
* * * 0us ub cs cb ts tbV V V V V V+ + =
* *sb sb us ub cs cbi V V V Vρ η+ = −
λ4 λ2 λ2
Flavour Physics A. Pich – TAE 2018
24
D0 ─ D0 MIXING ¯
,2
Mx y∆ ∆Γ≡ − ≡ −
Γ Γ
Flavour Physics A. Pich – TAE 2018
25
D0 ─ D0 MIXING: ¯ No evidence of ( ) ( )CP CP CPa a K K a π π+ − + −∆ = −
Flavour Physics A. Pich – TAE 2018