Experimental tests of the SM (2):CP violation and the CKM matrix

FK8022, Lecture 6

Core text: Status of the CKM Matrix and CP Violation, A. Stocchi

Lecture outline

• Standard Model flavour parameters• C, P, CP reminders• CP violation in the SM • CP violation and the CKM matrix • Unitarity triangle

Free parameters of the Standard ModelMassesParameter Value Method

mu1.9 MeV Lattice

md4.4 MeV Lattice

ms87 MeV Lattice

mc1.3 MeV Collider

mb4.24 MeV Collider

mt173 GeV Collider

me511 keV Non-collider

mm106 MeV Non-collider

mt1.78 GeV Collider

mz91.2 GeV Collider

mH125 GeV Collider

CouplingsParameter Value Method

a 0.0073 non-collider + collider

GF1.17x10-5 Non-collider

as0.12 Lattice + collider

Parameter Value Method

q12 (CKM) 13.1o Colliderq23 (CKM) 2.4o Colliderq13 (CKM) 0.2o Colliderd (CKM-CPV) 0.995 Colliderq (strong CP) ~0 Non-collider

Flavour and CP violation

This lecture:Flavour physics, CP-violation and CKM matrix measurements from colliders.

Parameter Value Method

q12 (CKM) 13.1o Colliderq23 (CKM) 2.4o Colliderq13 (CKM) 0.2o Colliderd (CKM-CPV) 0.995 Collider

Flavour and CP violation

Parameters of the SM

Flavour physics: weak charged current interactions involving hadron decays.

Very very brief reminder (1): parity , , , ,r x y z r x y z

Transformation:

Physical quantities are or under a parity transformation.

Converts a left-handed to a right-handed particle (and vice-versa..)Symmetry respected by strong

even odd

P

and em but not weak force:LH: RH: : RH never seen in laboratory!

LH RH

v

ParityQuantity Even Odd

Time Mass

Energy Angular

momentum Position Velocity

Force Helicity

•

: ,

h S p

P S S p ph h

Helicity:

Apply

Very very brief Reminder (2): charge conjugation (C) and CP

3

.

.

CC

I

a aCharge conjugation

converts each particle to its antiparticle, to changes the sign of all "internal" quantum numbers:

charge, lepton number, baryon number, strangeness, charm,bottomness, Mas

,

C

C P

CP

s, energy, momentum, spin unchanged.Symmetry respected by strong and em but not weak force.

LH: LH: : LH never seen in laboratory!

maximally violated.

CPLH: RH: : Ok !

But decay rate for 0

0 0) ~ 0.1%.e

e e

K e

CP K e K e

CP

and

( = differ by

Small (and messy) violation in the weak force.

Mechanism for CP violation in SM

1 1

1 1

1

1 1

1 1

: .

i i

i i

X f X f

X f A e e

CP CP

CP X f A e e X f A e

d

d

d

M

M M

Consider particle decaying to state

Amplitude:

Two complex phases: ( conserving-"strong" phase), ( violating-"weak" phase)

Apply : 1 1

2 21

.i ie

A

d

MIf CP violation occurs the "weak" phase changes sign.

But this is unobservable since any observable

X f 1

CP violation in the SM

1 1 2 2 1 1 2 2

1 1 2 2 1 1 2 2

1 2 1 2

2 2 21 2 1 22

2

i i i i i i i i

i i

X f CP

X f A e e A e e X f A e e A e e

e eX f A A A A

d d d d

d d d d

M M

M

Two mechanisms Interference makes -violating complex phase visible.

+ ;

1 1 2 2 1 1 2 2

2 21 2 1 2 1 1 2 2

2 2 21 2 1 2

2 21 2 1 2 1 1 2 2

22

1 2

2 cos

22

2 cos

i i

A A A A

e eX f A A A A

A A A A

X f X f

d d d d

d d

d d

M

M M

At least two "strong" phases ( , ) and 1 2

1 2

,

A A CPV

d d "weak" phases ( )needed.

Individual amplitudes , and phase differences large to see .

Different ways to violate CP

22

2 20 0 0 0

( ) ( )

(2)

(3)

CPV

X f X f

CPV CPV

X X X X

CPV

M M

M M

(1) Direct in decay

in mixing (indirect )

in interference between mixing and decay.

Direct CP violation

1 2

2 20 0

1 2

( ) ( )

2 cos cos

B K B K

A A

d d

M M

Two different ways (1 and 2) to achieve final decay mode.Comparible sized amplitudes and large enough phase difference to be visible.

0Eg B K

Direct CP-violation in B-sector

0 0

0 0

0

0

0.088 0.011 0.008

0.027 0.008 0.02s s

s s

B K B KCP

B K B K

B K B KCP s

B K B K

A B K

A B K

Discovery at Babar (2004)Most precise measurement at LHC-B.

CP-violation in mixing0 0

0 0

0 0

0 0e

K K

pp

K K

pp K K pp K K

K e K e

Eg Different virtual quarksDifferent processes. CP-Lear experiment (low energy at CERN 1990s)

Tag or at production :

; Tag again from decay.

;

0 0 0 03

0 0 0 06.6 1.6 10 .

e

CP

P K K P K KA

P K K P K K

CP violation between mixing+decay0 /Consider the decay mechanisms of , eg, SB J K

CPV CP

CPV

can occur when two decay mechanisms to a eigenstate are possible:One is a "direct" decay and the other occurs after mixing.The interference between the mixing + decay causes .More in inlämningsuppgiften.

Observations of CP violationProcess Type of CP violation

1 Mixing

2 Direct

3 Interference of mixing and decay

4 Interference of mixing and decay

5 Interference of mixing and decay

6 Interference of mixing and decay

7 Interference of mixing and decay

8 Interference of mixing and decay

9 Interference of mixing and decay

10 Direct

11 Direct

12 Direct

, K K

K

0 related modes.B K

0'B K

SB K K K

B

0B

* *B D D

0 *0B K

0 0B K

B D D

0B K

CKM matrix

'' .

'''

ud us ub

ud us ub ud us ub

cd cs cb cd c

td ts tb

d V d V s V bu d u d

V V V V V Vd ds V V V s N N V V Vb bV V V

Mass and weak eigenstates differ. Eg ...Charged current and not

matrix

2 22

s cb

td ts tb

VV V V

N N

CKM

CKM matrix.

=9 complex numbers =18 real numbers but not all are independent.

Find the minimum number of parameters for the in the SM. Start with the 18 numbers, argue away some of them and see what

remains.

Unitarity constraint 2 2 2

†

* * *

* * *

* * *

2 2 2

' 1ud us ub ud us ub

ud cd tdud us ub

cd cs cb us cs ts

td ts tb ub cb tb

ud us ub ud

d V d V s V b V V V

VV I

V V VV V VV V V V V VV V V V V V

V V V V V

Unitarity (probabilities add to 1 !)

* * * * * *

2 2 2* * * * * *

2 2 2* * * * * *

cd us cs ub cb ud td ts ts tb tb

cd ud cs us cb ub cd cs cb cd td cs ts cb tb

td ud ts us tb ub td td ts ts tb tb td ts tb

V V V V V V V V V V

V V V V V V V V V V V V V V V

V V V V V V V V V V V V V V V

1 0 00 1 00 0 1

18 - 9 -.....CKM

9 constraints Number of parameters

' '

' '

. .L CKM L

L L

L L L L

L L

CKM CKM

Au V d W h c A

u du c d s

t b

V V

m

LCharged current: constant

Quark fields: , up-like, down-like weak states.

Lagrangian unaffected for transformation:

11

2 2

3 3

'

(2 -1 5)

du

du

u d

CKM

iiLLL L

iiL L L L

i iL LL L

V

e de uu dc e c s e st be t e b

N

where complex phases have been removed from

Quark fields absorb complex phases: ,

1 2 1 3 1 1 1 2 1 3, ,u u u u u d u d u d

independent phase differences:Eg , ,

We don't need to consider 5 phases.

We are now left with 18-9-5=4 parameters.

Freedoms in the quark fields

Check with Cabibbo theory

2 2

Cabibbo theory: '

'

Number of parameters =2 (2 1) 8 4 3 1cos sin'

' sin cos

One parameter needed.

Obs! Cabibbo theory doe

ud us

cd cs

c c

c c

V Vs sd V V d

N N N

s sd d

q qq q

s not allow -violation. KM predicted a 3rd quark generation to get an extra

-violating parameter (and won a Nobel prize for this).

CP

CP

CKM matrix - 112 23 13

12 13 12 13 13

12 23 12 23 13 12 23 12 23 13 23 13

12

Mixing angles , , and complex phase

'' '

i

i i

c c s c s eds s c c s s e c c s s s e s cb s

d

d d

q q q d

23 12 23 13 12 23 12 23 13 23 13

12 13 23 13

-

cos cos

Current measurements:  1  3.04 0.05 ,     0.201 0.011 ,     2.38 0.06 ,    1  .20 0.08 r

i i

ij ij ij ij

dsbs c c s e c s s c s e c c

c s

d d

q q

q q q d

ad.

Extension of Cabibbo formalism. Note - compex phase . We've been given only one parameter.We need to describe all observed -violation with it (if the SM works..)We also have to describe all non

CPd

- violating weak decays with just 3 parameters.

CP

CKM matrix-2

0.9739 0.9751 0.221 0.227 0.0048 0.0140.221 0.227 0.9730 0.9744 0.037 0.043

0.0029 0.0045 0.039 0.044 0.9990 0.9992ijV

2 312 23 13

2

0.2, sin , sin , , , 1

, ...

A A i e A

CP

d q q q

O

Off-diagonal terms (cross-generation interactions) suppressed. Wolfenstein parameterisation

=sin

Off-diagonal elements small , violatio 3st rdn 1 generation at low order.2 31

22 2 41

23 2

1 ( ) 1 ( )

(1 ) 1CKM

A iV A O

A i A

Revisiting CP violation

2 312

212

1 ( )1

ud us ub

CKM cd cs cb

td ts tb

V V V A iV V V V

V V V

So we have the CKM matrix and want to study CPV with hadron decays.What do we want to measure ?

2 4

3 2

( )(1 ) 1

,

1 -3 , )ub td

st rd

A OA i A

CP V V

b u t dCP

Basic reasoning: (1) violation occurs for amplitudes with

Decays involving generations: ( .(2) violation is usually a small effect se

en on few decay channels . Long-lived particles with limited decay channels and good change for CPV loops.

Hadron type Naive CPV prospects

Top Top hadrons don’t exist!!

Bottom

Charm No promising tree-level decays. D-mesons decay quickly (t~1011 s) with many decay possibilities

Strange No promising tree-level decays. Long lifetime (t~108 s) , promising with CPV loops/oscillations. Size ~0.1% .

b u Direct: promising. Also in loops. Size up to 10%

CP violation timeline>

2010 LHC-B:

CPV in Bs decays

Kaon Experiments

B-hadron experiments

Series of dedicated small and not so-small experiments on K’s and B’s to study CPV.

Determination of non-CPV CKM parameters

2

:ud

ud

V

V

Magnitudes typically determined from ratios of particle decay rates.

Decay rates of neutron and muon

Ratio

222 5

22

( ) 1 22 3 2192 1 1

l F bb

d b u l G m xx xd x

Vx x

aa

,u ca 2

2b

mm

a

2 l

b

Exm

Determination of non-CPV CKM parameters

0 *

:cbV

B D Decay rates and muon

* * *

2 2

0

1 11 12 2

ud ub cd cb td tbV V V V V VR i

Unitarity demands : Represented as a "unitarity" triangle in complex plane.

,

Five other unitarity triangles possible.

Unitarity triangle

CP

viol

ation

Re

Im

* *

* *

*

*

arg arg

arg

td tb cd cb

ud ub td tb

ud ub

cd cb

V V V VV V V V

V VV V

a

In an ideal world Many experiments measure and from many different

decay channels to check the CKM matrix precisely respects unitarity (if no new physics is lurking).

CP

viol

ation

Re

Im

* *

* *

*

*

arg arg

arg

td tb cd cb

ud ub td tb

ud ub

cd cb

V V V VV V V V

V VV V

a

In the real world – experiments measure contours

Vintage 2005.

0

Hyperbola:CP-violation in -sector

mixing

K

K

sin 2

/

Straight lines:measurement of

d SB J K

,

Quadrangle:measurements of

d

d

B

B K

0,

Circle:CP-violation in B-sector.Length of triangle side.

mixingd sB

, .Ellipse:best fit value for

,

Circle:oscillation parameters

mixings dm m B

Why the large errors ?

We want to test the EW sector of the SM and extract CKM parameters. But we observe the electroweak+strong stuff.

The strong stuff is poorly understood.• Use models to separate the contributions.• Large uncertainties.• Large widths for some contours.

CKMfitter collaborationhttp://ckmfitter.in2p3.fr/Determines CKM matrixparameters.Test consistency of the SM.

Observable Fit result

A 0.823[+0.012 -0.033]

l 0.22457 [+0.00186 -0.00014]

0.1289 [+0.0176 -0.0094]

0.347 [+0.012 -0.012]

Overconstrain the unitarity triangle with multiple measurements

sensitivity to new physics but none seen!

State of the art unitarity triangle

Why flavour is important for searches9Ultra-rare decay B 10

Suppressed flavour-changing processes in SM (tops).

Predicted in many SUSY scenarios.Measurement kills parameter space (but SUSY lives on...)

Measurement of a BR

s BRm m

910 is a huge experimental achievement!

MeVMm m

ExcludedAllowed SM

Summary

• CP violation in the Standard Model is an interference effect

• CKM matrix governs all quark mixing + CP violation with four parameters

• Many, many measurements of hadron decay.• The CKM matrix consistently describes them

all.