Flavour Physics & CP Violationbenasque.org/2018tae/talks_contr/065_TAE_2018_Flavour_3.pdf3 V V V V...

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


Widths & Mass Differences

M. Gersabeck


,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 ∼


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


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

≡ → ≡ − → ≡

≡ → ≡ − → ≡


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 →


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


f b f b g p a φ γ≠

*** ** BAD 10

ρ0


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


2tstbV V Al

qq

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=


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


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 →


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 →


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→


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


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 ≠+ + =


* * * 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


Tree-level determinations Loop processes

CP Conserving CP Violating


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


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


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


24

D0 ─ D0 MIXING ¯

,2

Mx y∆ ∆Γ≡ − ≡ −

Γ Γ


25

D0 ─ D0 MIXING: ¯ No evidence of ( ) ( )CP CP CPa a K K a π π+ − + −∆ = −


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