Download Lecture 2

Particle Physics II – CP violation
(also known as “Physics of Anti-matter”)
Lecture 2
N. Tuning
Niels Tuning (1)
Plan


1) Wed 9 Feb:
Anti-matter + SM
2) Mon 13 Feb:
CKM matrix + Unitarity Triangle
3) Wed 15 Mar:
Mixing + Master eqs. + B0J/ψKs
4) Mon 13 Mar:
CP violation in B(s) decays (I)
5) Wed 15 Mar:
CP violation in B(s) and K decays (II)
6) Wed 22 Mar:
Exam
Final Mark:

if (mark > 5.5) mark = max(exam, 0.8*exam + 0.2*homework)

else mark = exam
In parallel: Lectures on Flavour Physics by prof.dr. R. Fleischer

Tuesday + Thrusday
Niels Tuning (2)
Recap: Motivation
• CP-violation (or flavour physics) is about charged
current interactions
• Interesting because:
1) Standard Model:
in the heart of quark
interactions
2) Cosmology:
related to matter – anti-matter
asymetry
3) Beyond Standard Model:
measurements are sensitive to
new particles
Matter
Dominates !
b
s
s
b
Niels Tuning (3)
Recap: Anti matter
• Dirac equation (1928)
– Find linear equation to avoid negative energies
– and that is relativistically correct
 Predict existence of anti-matter
• Positron discovered (1932)
• Anti matter research at CERN very active
– 1980: 270 GeV anti protons for SppS
– 1995: 9 anti hydrogen atoms detected
– 2014: anti hydrogen beam
•
´` detection of 80 antihydrogen atoms 2.7 metres downstream of their production``
 Test CPT invariance: measure hyperfine structure and gravity
Niels Tuning (4)
Recap: C and P
• C and P maximally violated in weak decays
– Wu experiment with
60Co
– Ledermann experiment with pion decay
 Neutrino´s are lefthanded!
• C and P conserved in strong and EM interactions
– C and P conserved quantitites
 C and P eigenvalues of particles
• Combined CP conserved?
Niels Tuning (5)
Q == Q
Y
T3-+TY
3
Fields: Notation
Explicitly:
• The left handed quark doublet :
I
I
I
I
I
I
I
I
I






u
,
u
,
u
c
,
c
,
c
t
,
t
,
t
r
g
b
r
g
b
r
g b
I
QLi (3, 2,1 6)   I I I  ,  I I I  ,  I I I 
 d , d , d   s , s , s  b ,b ,b 
 r g b L  r g b L  r g b L
T3   1
2
T3   1
2
(Y  1 6)
• Similarly for the quark singlets:
uRiI (3,1, 2 3) 
d RI i (3,1, 1 3) 
• The left handed leptons:
u , u , u  ,  c , c , c  , t , t , t 
 d , d , d  ,  s , s , s  , b , b , b 
I
r
I
r
I
r
I
r
I
r
I
r
R
R
I
r
I
r
I
r
I
r
I
r
I
r
R
I
r
R
I
r
I
r
I
r
I
r
 eI   I   I 
L (1, 2, 1 2)   I  ,   ,  I 
 e    I   
 L  L  L
I
Li
• And similarly the (charged) singlets:
lRiI (1,1, 1)  eRI , RI , RI
 Y  2 3
R
I
r
Y
R
T3   1 2
T3   1 2
  1 3
Y   1 2 
Y  1
Niels Tuning (6)
Weak interaction: parity violating
(and not only for neutrinos!)
L kinetic : i (    )  i ( D    )
with   QLiI , u RiI , d RiI , LILi , lRiI
For example, the term with QLiI becomes:
L kinetic (QLiI )  iQLiI   D  QLiI
 iQLiI   (  
i
i
i
g s Ga a  gWb b  g B  ) QLI i
2
2
6
0 1

1 0
 0 i 
2  

i 0 
1 0 
3  

 0 1 
1  
Only acts on the left-handed doublet!
Niels Tuning (7)
Recap: SM Lagrangian
• C and P violation in weak interaction
• How is weak (charged) interaction described in SM?
LSM  LKinetic  LHiggs  LYukawa
L kinetic : i (    )  i ( D    )
with   QLiI , u RiI , d RiI , LILi , lRiI
L Kinetic 
 LYuk
g I   I
g I   I
uLi W d Li 
d Li W uLi  ...
2
2


 I

d
I
I
 Yij (uL , d L )i  0  d Rj  ...
 
Niels Tuning (8)
L SM
 LYuk
L Kinetic
Recap
 L Kinetic  L Higgs  LYukawa


 I

d
I
I
 Yij (uL , d L )i  0  d Rj  ...
 
W
g I   I
g I   I

uLi W d Li 
d Li W uLi  ...
2
2
dI
Diagonalize Yukawa matrix Yij
– Mass terms
– Quarks rotate
– Off diagonal terms in charged current couplings
W
uI
u
 LMass 
LCKM
d,s,b
 d , s, b 
L
 md




ms
 d 
 
 s 
mb   b  R
dI 
 I
 s   VCKM
 bI 
 
u, c, t 
L
 mu




mc
d 
 
s
b
 
 u 
 
  c   ...
mt   t  R
g
g


5

ui W Vij 1    d j 
d j WVij* 1   5  ui  ...
2
2
L SM
 LCKM  L Higgs  L Mass
Niels Tuning (9)
CKM matrix
 LMass 
LCKM 
 d , s, b 
L
 md




ms



mb 
d 
 
s 
b
 R
u, c, t 
L
 mu




mc



mt 
u 
 
 c   ...
t
 R
g
g
ui WVij 1   5  d j 
d j  WVij* 1   5  ui  ...
2
2
dI 
 I
 s   VCKM
 bI 
 
d 
 
s
b
 
• CKM matrix: `rotates` quarks between different bases
• Describes charged current coupling of quarks (mass
eigenstates)
• NB: weak interaction responsible for P violation
 What are the properties of the CKM matrix?
 What are the implications for CP violation?
Niels Tuning (10)
Ok…. We’ve got the CKM matrix, now what?
• It’s unitary
– “probabilities add up to 1”:
– d’=0.97 d + 0.22 s + 0.003 b
(0.972+0.222+0.0032=1)
• How many free parameters?
– How many real/complex?
• How do we normally visualize these parameters?
Niels Tuning (11)
How do you measure those numbers?
• Magnitudes are typically determined from ratio of decay
rates
• Example 1 – Measurement of Vud
– Compare decay rates of neutron
decay and muon decay
– Ratio proportional to Vud2
– |Vud| = 0.97425 ± 0.00022
– Vud of order 1
Niels Tuning (12)
How do you measure those numbers?
• Example 2 – Measurement of Vus
– Compare decay rates of
semileptonic K- decay and
muon decay
– Ratio proportional to Vus2
– |Vus| = 0.2252 ± 0.0009
– Vus  sin(qc)
d ( K   e  e ) G m

Vus
dx
192
0
 
2
F
5
K
2
2

m 
f (q 2 ) 2  x2  4 2 
mK 

2
3/ 2
, x 
2 E
mK
How do you measure those numbers?
• Example 3 – Measurement of Vcb
– Compare decay rates of
B0  D*-l+ and muon decay
– Ratio proportional to Vcb2
– |Vcb| = 0.0406 ± 0.0013
– Vcb is of order sin(qc)2 [= 0.0484]
  u, c
d (b  u l  l ) GF2 mb5

V b
2
dx
192
2
 2  1  x   2 
2  
 2 x 
  3  2x   
 
1 x  
 1 x  

m2
  2
mb
2E
x l
mb
How do you measure those numbers?
• Example 4 – Measurement of Vub
– Compare decay rates of
B0  D*-l+ and B0  -l+
– Ratio proportional to (Vub/Vcb)2
– |Vub/Vcb| = 0.090 ± 0.025
– Vub is of order sin(qc)3 [= 0.01]
2
(b  ul  l ) Vub  f (mu2 / mb2 ) 

2 
2
2 

(b  cl  l ) Vcb  f (mc / mb ) 

How do you measure those numbers?
• Example 5 – Measurement of Vcd
– Measure charm in DIS with neutrinos
– Rate proportional to Vcd2
– |Vcd| = 0.230 ± 0.011
– Vcb is of order sin(qc) [= 0.23]
How do you measure those numbers?
• Example 6 – Measurement of Vtb
– Very recent measurement: March ’09!
– Single top production at Tevatron
– CDF+D0: |Vtb| = 0.88 ± 0.07
How do you measure those numbers?
• Example 7 – Measurement of Vtd, Vts
– Cannot be measured from top-decay…
– Indirect from loop diagram
– Vts: recent measurement: March ’06
– |Vtd| = 0.0084 ± 0.0006
– |Vts| = 0.0387 ± 0.0021
Vts
Ratio of frequencies for B0 and Bs
Vts
Vts
ms mBs f BBs Vts

md mBd f BBd Vtd
2
Bs
2
Bd
Vts ~ 2
Vtd ~3
Vts
2
2
mBs 2 Vts


mBd
Vtd
 Δms ~ (1/λ2)Δmd ~ 25 Δmd
 = 1.210 +0.047
-0.035 from lattice QCD
2
2
What do we know about the CKM matrix?
• Magnitudes of elements have been measured over time
– Result of a large number of measurements and calculations
 d '   Vud
  
 s '    Vcd
 b'  V
   td
 Vud

 Vcd
V
 td
Vus
Vcs
Vts
Vus Vub  d 
 
Vcs Vcb  s 

Vts Vtb 
b
 
Vub 

Vcb  
Vtb 
Magnitude of elements shown only, no information of phase
Niels Tuning (19)
What do we know about the CKM matrix?
• Magnitudes of elements have been measured over time
– Result of a large number of measurements and calculations
 d '   Vud
  
 s '    Vcd
 b'  V
   td
 Vud

 Vcd
V
 td
Vus
Vcs
Vts
Vub 

Vcb  
Vtb 
Vus Vub  d 
 
Vcs Vcb  s 

Vts Vtb 
b
 
  sin qC  sin q12  0.23
Magnitude of elements shown only, no information of phase
Niels Tuning (20)
Approximately diagonal form
• Values are strongly ranked:
– Transition within generation favored
– Transition from 1st to 2nd generation suppressed by sin(qc)
– Transition from 2nd to 3rd generation suppressed bu sin2(qc)
– Transition from 1st to 3rd generation suppressed by sin3(qc)
CKM magnitudes
d
u
c
t
s


3
b
3
2
Why the ranking?
We don’t know (yet)!
If you figure this out,
you will win the nobel
prize
2
=sin(qc)=0.23
Niels Tuning (21)
Intermezzo: How about the leptons?
• We now know that neutrinos also have flavour oscillations
– Neutrinos have mass
– Diagonalizing Ylij doesn’t come for free any longer
• thus there is the equivalent of a CKM matrix for them:
– Pontecorvo-Maki-Nakagawa-Sakata matrix
vs
Niels Tuning (22)
Intermezzo: How about the leptons?
• the equivalent of the CKM matrix
– Pontecorvo-Maki-Nakagawa-Sakata matrix
vs
• a completely different hierarchy!
Niels Tuning (23)
Intermezzo: How about the leptons?
• the equivalent of the CKM matrix
– Pontecorvo-Maki-Nakagawa-Sakata matrix
vs
• a completely different hierarchy!
ν1
ν2
ν3
See eg. PhD thesis R. de Adelhart Toorop
d
s
b
Niels Tuning (24)
Intermezzo: what does the size tell us?
H.Murayama, 6 Jan 2014, arXiv:1401.0966
Neutrino mixing due to ´anarchy´:
`quite typical of the ones obtained by randomly
drawing a mixing matrix from an unbiased
distribution of unitary 3x3 matrices´
Harrison, Perkins, Scott,
Phys.Lett. B530 (2002) 167,
hep-ph/0202074
Neutrino mixing due to
underlying symmetry:
Niels Tuning (25)
Back to business: quarks
We discussed magnitude.
Next is the imaginary part !
Niels Tuning (26)
Quark field re-phasing
Under a quark phase transformation:
id i
iu i
d

e
d Li
Li
Li
Li
and a simultaneous rephasing of the CKM matrix:
u e u
 e u

V 


e c
e t
  Vud

  Vcd
  Vtd

the charged current
Vus Vub   e d

Vcs Vcb  
Vts Vtb  

J CC
 uLi Vij d Lj
Degrees of freedom in VCKM in
Number of real parameters:
Number of imaginary parameters:
Number of constraints (VV† = 1):
Number of relative quark phases:
Total degrees of freedom:
Number of Euler angles:
Number of CP phases:
e  s


 or
e b 


V j  exp i  j    V j
is left invariant.
3
N generations
9
+ N2
9
+ N2
-9
- N2
-5
- (2N-1)
----------------------4
(N-1)2
3
N (N-1) / 2
1
(N-1) (N-2) / 2
2 generations:
 cos q sin q 
VCKM  

  sin q cos q 
No CP violation in SM!
This is the reason
Kobayashi and Maskawa
first suggested a 3rd
family of fermions!
Niels Tuning (27)
First some history…
Niels Tuning (28)
Cabibbos theory successfully correlated many decay rates
• There was however one major exception which Cabibbo
could not describe: K0  + – Observed rate much lower than expected from Cabibbos rate
correlations (expected rate  g8sin2qccos2qc)
s
d
cosqc
u
sinqc
W
W

+
-
Niels Tuning (29)
The Cabibbo-GIM mechanism
• Solution to K0 decay problem in 1970 by Glashow,
Iliopoulos and Maiani  postulate existence of 4th quark
– Two ‘up-type’ quarks decay into rotated ‘down-type’ states
– Appealing symmetry between generations
u
c
W+
d’=cos(qc)d+sin(qc)s
 d '   cos q c
   
 s'    sin q c
W+
s’=-sin(qc)d+cos(qc)s
sin q c  d 
 
cos q c  s 
Niels Tuning (30)
The Cabibbo-GIM mechanism
Phys.Rev.D2,1285,1970
…
…
…
Niels Tuning (31)
The Cabibbo-GIM mechanism
• How does it solve the K0  +- problem?
– Second decay amplitude added that is almost identical to original
one, but has relative minus sign  Almost fully destructive
interference
– Cancellation not perfect because u, c mass different
s
d
cosqc
u
d
+sinqc
-sinqc
c
cosqc


+
s
-
+
Niels Tuning (32)
Quark field re-phasing
Under a quark phase transformation:
id i
iu i
d

e
d Li
Li
Li
Li
and a simultaneous rephasing of the CKM matrix:
u e u
 e u

V 


e c
e t
  Vud

  Vcd
  Vtd

Vus Vub   e d

Vcs Vcb  
Vts Vtb  
e  s


 or
e b 


V j  exp i  j    V j
In other words:
Niels Tuning (33)
Quark field re-phasing
Under a quark phase transformation:
id i
iu i
d

e
d Li
Li
Li
Li
and a simultaneous rephasing of the CKM matrix:
u e u
 e u

V 


e c
e t
  Vud

  Vcd
  Vtd

the charged current
Vus Vub   e d

Vcs Vcb  
Vts Vtb  

J CC
 uLi Vij d Lj
Degrees of freedom in VCKM in
Number of real parameters:
Number of imaginary parameters:
Number of constraints (VV† = 1):
Number of relative quark phases:
Total degrees of freedom:
Number of Euler angles:
Number of CP phases:
e  s


 or
e b 


V j  exp i  j    V j
is left invariant.
3
N generations
9
+ N2
9
+ N2
-9
- N2
-5
- (2N-1)
----------------------4
(N-1)2
3
N (N-1) / 2
1
(N-1) (N-2) / 2
2 generations:
 cos q sin q 
VCKM  

  sin q cos q 
No CP violation in SM!
This is the reason
Kobayashi and Maskawa
first suggested a 3rd
family of fermions!
Niels Tuning (34)
Intermezzo: Kobayashi & Maskawa
Niels Tuning (35)
Timeline:
• Timeline:
– Sep 1972: Kobayashi & Maskawa predict 3 generations
– Nov 1974: Richter, Ting discover J/ψ: fill 2nd generation
– July 1977:
Ledermann discovers Υ: discovery of 3rd generation
Niels Tuning (36)
From 2 to 3 generations
• 2 generations: d’=0.97 d + 0.22 s
 d '   cos q c
   
 s'    sin q c
(θc=13o)
sin q c  d 
 
cos q c  s 
• 3 generations: d’=0.97 d + 0.22 s + 0.003 b
• NB: probabilities have to add up to 1: 0.972+0.222+0.0032=1
–  “Unitarity” !
Niels Tuning (37)
From 2 to 3 generations
• 2 generations: d’=0.97 d + 0.22 s
 d '   cos q c
   
 s'    sin q c
(θc=13o)
sin q c  d 
 
cos q c  s 
• 3 generations: d’=0.97 d + 0.22 s + 0.003 b
Parameterization used by Particle Data Group (3 Euler angles, 1 phase):
Possible forms of 3 generation mixing matrix
• ‘General’ 4-parameter form (Particle Data Group) with
three rotations q12,q13,q23 and one complex phase d13
– c12 = cos(q12), s12 = sin(q12) etc…
0
1

0
c
23

0 s
23

0   c13

s 23   0
c 23   eid s13
0 e  id s13   c12

1
0    s12
0
c13   0
s12
c12
0
0

0
1 
• Another form (Kobayashi & Maskawa’s original)
– Different but equivalent
• Physics is independent of choice of parameterization!
– But for any choice there will be complex-valued elements
Niels Tuning (39)
Possible forms of 3 generation mixing matrix
 Different parametrizations! It’s about phase differences!
Re-phasing V:
KM
PDG
3 parameters: θ, τ, σ
1 phase:
φ
Niels Tuning (40)
Quark field re-phasing
Under a quark phase transformation:
id i
iu i
d

e
d Li
Li
Li
Li
and a simultaneous rephasing of the CKM matrix:
u e u
 e u

V 


e c
e t
  Vud

  Vcd
  Vtd

the charged current
Vus Vub   e d

Vcs Vcb  
Vts Vtb  

J CC
 uLi Vij d Lj
Degrees of freedom in VCKM in
Number of real parameters:
Number of imaginary parameters:
Number of constraints (VV† = 1):
Number of relative quark phases:
Total degrees of freedom:
Number of Euler angles:
Number of CP phases:
e  s


 or
e b 


V j  exp i  j    V j
is left invariant.
3
N generations
9
+ N2
9
+ N2
-9
- N2
-5
- (2N-1)
----------------------4
(N-1)2
3
N (N-1) / 2
1
(N-1) (N-2) / 2
2 generations:
 cos q sin q 
VCKM  

  sin q cos q 
No CP violation in SM!
This is the reason
Kobayashi and Maskawa
first suggested a 3rd
family of fermions!
Niels Tuning (41)
Cabibbos theory successfully correlated many decay rates
• Cabibbos theory successfully correlated many decay
rates by counting the number of cosqc and sinqc terms in
their decay diagram
g cos qC
g


  n  pe    g cos q
    pe    g sin q
    e e   g 4

0
4
e

purely leptonic
semi-leptonic, S  0
2
C
e
4
g sin qC
2
C
semi-leptonic, S  1

A
2
i
i
Niels Tuning (42)
Wolfenstein parameterization
3 real parameters:
A, λ, ρ
1 imaginary parameter: η
Wolfenstein parameterization
3 real parameters:
A, λ, ρ
1 imaginary parameter: η
Exploit apparent ranking for a convenient parameterization
• Given current experimental precision on CKM element values,
we usually drop 4 and 5 terms as well
– Effect of order 0.2%...
 d
 
s 
 b 
 L

2
1


2


2


1
2
 3
2
A

1

r

i
h

A







A  r  ih  
 d 
 
2
A
 s 
 b 
1
  L


3
• Deviation of ranking of 1st and 2nd generation ( vs 2)
parameterized in A parameter
• Deviation of ranking between 1st and 3rd generation,
parameterized through |r-ih|
• Complex phase parameterized in arg(r-ih)
Niels Tuning (45)
~1995 What do we know about A, λ, ρ and η?
• Fit all known Vij values to Wolfenstein parameterization
and extract A, λ, ρ and η
• Results for A and  most precise (but don’t tell us much
about CPV)
– A = 0.83,  = 0.227
• Results for r,h are usually shown in
complex plane of r-ih for easier interpretation
Niels Tuning (46)
Deriving the triangle interpretation
• Starting point: the 9 unitarity constraints on the CKM
matrix
 V *ud V *cd V *td   Vud
 *

*
* 
V V   V us V cs V ts   Vcd
 V *ub V *cb V *tb   Vtd


Vus Vub   1 0 0 
 

Vcs Vcb    0 1 0 
Vts Vtb   0 0 1 
• Pick (arbitrarily) orthogonality condition with (i,j)=(3,1)
V V V V V V  0
*
ub ud
*
cb cd
*
tb td
Niels Tuning (47)
Deriving the triangle interpretation
• Starting point: the 9 unitarity constraints on the CKM
matrix
– 3 orthogonality relations
 V *ud V *cd V *td   Vud
 *

*
* 
V V   V us V cs V ts   Vcd
 V *ub V *cb V *tb   Vtd


Vus Vub   1 0 0 
 

Vcs Vcb    0 1 0 
Vts Vtb   0 0 1 
• Pick (arbitrarily) orthogonality condition with (i,j)=(3,1)
V V V V V V  0
*
ub ud
*
cb cd
*
tb td
V Vub  V Vcb  V V  0
*
ud
*
cd
*
td tb
Niels Tuning (48)
Deriving the triangle interpretation
• Starting point: the 9 unitarity constraints on the CKM
matrix
 V *ud V *cd V *td   Vud
 *

*
* 
V V   V us V cs V ts   Vcd
 V *ub V *cb V *tb   Vtd


Vus Vub   1 0 0 
 

Vcs Vcb    0 1 0 
Vts Vtb   0 0 1 
• Pick (arbitrarily) orthogonality condition with (i,j)=(3,1)
V V V V V V  0
*
ub ud
*
cb cd
*
tb td
Niels Tuning (49)
Visualizing the unitarity constraint
• Sum of three complex vectors is zero 
Form triangle when put head to tail
(Wolfenstein params to order 4)
Vtb*Vtd  1  A3 (1  r  ih )
Vub* Vud  A3 ( r  ih )
Vcb* Vcd  A2  ( )
Niels Tuning (50)
Visualizing the unitarity constraint
• Phase of ‘base’ is zero  Aligns with ‘real’ axis,
Vtb*Vtd  1  A3 (1  r  ih )
Vub* Vud  A3 ( r  ih )
Vcb* Vcd  A2  ( )
Niels Tuning (51)
Visualizing the unitarity constraint
• Divide all sides by length of base
(r,h)
Vtb*Vtd
 (1  r  ih )
*
VcbVcd
Vub* Vud
 ( r  ih )
*
VcbVcd
(0,0)
Vcb* Vcd
1
*
VcbVcd
(1,0)
• Constructed a triangle with apex (r,h)
Niels Tuning (52)
Visualizing arg(Vub) and arg(Vtd) in the (r,h) plane
• We can now put this triangle in the (r,h) plane
Vub* Vud
 ( r  ih )
*
VcbVcd
Vtb*Vtd
 (1  r  ih )
*
VcbVcd
Niels Tuning (53)
“The” Unitarity triangle
• We can visualize the CKM-constraints in (r,h) plane
β
• We can correlate the angles β and γ to CKM elements:
 Vcb*Vcd 
  arg  *     arg Vcb*Vcd   arg Vtb*Vtd   2  arg Vtd 
 VtbVtd 
Deriving the triangle interpretation
• Another 3 orthogonality relations
 Vud

VV †   Vcd
V
 td
Vus Vub   V *ud V *cd V *td   1 0 0 
 *


*
* 
Vcs Vcb   V us V cs V ts    0 1 0 
Vts Vtb   V *ub V *cb V *tb   0 0 1 
• Pick (arbitrarily) orthogonality condition with (i,j)=(3,1)
V Vtd  V V  V V  0
*
ud
*
us ts
*
ub tb
Niels Tuning (56)
The “other” Unitarity triangle
• Two of the six unitarity triangles have equal sides in O(λ)
• NB: angle βs introduced. But… not phase invariant definition!?
Niels Tuning (57)
The “Bs-triangle”: βs
• Replace d by s:
Niels Tuning (58)
The phases in the Wolfenstein parameterization
Niels Tuning (59)
The CKM matrix
• Couplings of the
charged current:
• Wolfenstein
parametrization:
• Magnitude:
 Vud

 Vcd
V
 td
 d '   Vud
  
 s '    Vcd
 b'  V
   td
 d
 
s 
 b 
 L
Vus Vub  d 
 
Vcs Vcb  s 

Vts Vtb 
 b 

2
1


2


2


1
2
 3
2
 A 1  r  ih   A


W
b
gVub
u

A 3  r  ih  
 d 
 
A 2
 s 
 b 
1
  L


• Complex phases:
Vus Vub 

Vcs Vcb  
Vts Vtb 
Niels Tuning (60)
Back to finding new measurements
• Next order of business: Devise an experiment that measures
arg(Vtd) and arg(Vub).
– What will such a measurement look like in the (r,h) plane?
CKM phases
Fictitious measurement of  consistent with CKM model
Vtb*Vtd
 (1  r  ih )
*
VcbVcd
Vub* Vud
 ( r  ih )
*
VcbVcd


Niels Tuning (61)
Consistency with other measurements in (r,h) plane
Precise measurement of
sin(2β) agrees perfectly
with other measurements
and CKM model
assumptions
The CKM model of CP
violation
experimentally
confirmed with high
precision!
Niels Tuning (62)
What’s going on??
• ???
•
Edward Witten, 17 Feb 2009…
See “From F-Theory GUT’s to the LHC” by Heckman and Vafa (arXiv:0809.3452)