Experimental tests of the SM (2): CP v iolation and the CKM matrix
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Transcript of Experimental tests of the SM (2): CP v iolation and the CKM matrix
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.