Cracking the Unitarity Triangle
— A Quest in B Physics —
Masahiro Morii
Harvard University
MIT Department of Physics Colloquium
20 October 2005
Outline
 Introduction
to the Unitarity Triangle
The Standard Model, the CKM matrix, and CP violation
 CP asymmetry in the B0 meson decays

The Unitarity Triangle
 Experiments
at the B Factories
 Results from BABAR and Belle
 Angles a, b, g from CP asymmetries
|Vub| from semileptonic decays
 |Vtd| from radiative-penguin decays

 Current
a
g
b
status and outlook
Results presented in this talk are produced by the BABAR, Belle, and CLEO Experiments,
the Heavy Flavor Averaging Group, the CKMfitter Group, and the UTfit Collaboration
20 October 2005
M. Morii, Harvard
2
What are we made of?
e
u
u
 Ordinary
d
matter is made of electrons and up/down quarks
Add the neutrino and we have a complete “kit”
 We also know how they interact with “forces”

leptons
Q  1
Q0
20 October 2005
e

e
strong E&M weak
quarks
u
d
Q2
Q1
3
3
M. Morii, Harvard
u
Yes
Yes
Yes
d
Yes
Yes
Yes
e−
No
Yes
Yes
e
No
No
Yes
3
Simplified Standard Model
 Strong
force is transmitted by the gluon
g
u
g
d
u
 Electromagnetic
g
u
d
force by the photon
g
u
 Weak
e−
d
d
g
e−
force by the W and Z0 bosons
Z0
u
Z0
d
W−
e−
u
d
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e−
d
u
W+
Z0
e
M. Morii, Harvard
e−
Z0
e
e
Note W± can “convert”
u ↔ d, e ↔ 
4
Three generations
 We’ve
got a neat, clean, predictive theory of “everything”
1st generation
2nd generation
3rd generation
 Why
leptons
quarks
e−
u
e
d
m−
m
c
t−
t
t
strong E&M weak
g
g
s
b
W±
Z0
It turns out there
are two “extra”
copies of
particles
3 sets (= generations) of particles?
How do they differ?
 How do they interact with each other?

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5
A spectrum of masses
1012
1011
Particle mass (eV/c2)
1010
10
9
108
t
m
c
u
106
 The
b
d
e
10 4

0
20 October 2005
Standard Model has no explanation
for the mass spectrum
All 12 masses are inputs to the theory
 The masses come from the interaction
with the Higgs particle



103
Q = 1
generations differ only by the masses
 The structure is mysterious
s
107
105
 The
t
+2/3 1/3
... whose nature is unknown
We are looking for it with the Tevatron, and
with the Large Hadron Collider (LHC) in
the future
The origin of mass is one of the most urgent
questions in particle physics today
M. Morii, Harvard
6
If there were no masses
 Nothing

would distinguish u from c from t
We could make a mixture of the wavefunctions and pretend it
represents a physical particle
u  
u 
 d 
d 
 c   M  c 
 s   N  s 
M and N are arbitrary
 
 
 
 
33 unitary matrices
 t  
 t 
 b 
 b 
 Suppose W connects u ↔ d, c ↔ s, t ↔ b
u 
u  
 d 
d 
 d  Weak interactions
 c   M 1  c   M 1  s   M 1N  s   V  s  between u, c, t, and
 
 
 
 
  d, s, b are “mixed”
 t 
 t  
 b 
 b 
 b  by matrix V

That’s a poor choice of basis vectors
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7
Turn the masses back on
 Masses
uniquely define the u, c, t, and d, s, b states
We don’t know what creates masses
 We don’t know how the eigenstates are chosen
 M and N are arbitrary
 V is an arbitrary 33 unitary matrix

u 
 d  Vud
 c  
W   V  s   V
 
   cd
 t 
 b  Vtd
Vus Vub   d 
Vcs Vcb   s 
Vts Vtb   b 
Cabibbo-Kobayashi-Maskawa matrix
 The

or CKM for short
Standard Model does not predict V
... for the same reason it does not predict the particle masses
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8
Structure of the CKM matrix
0.974 0.226 0.004 
 It’s not completely diagonal
V  0.226 0.973 0.042 
 Off-diagonal components are small
0.008 0.042 0.999 
 The
CKM matrix looks like this 

Transition across generations is
allowed but suppressed
There seems to be a “structure”
separating the generations
 Matrix

elements can be complex
Unitarity leaves 4 free parameters,
one of which is a complex phase
This phase causes “CP violation”
Kobayashi and Maskawa (1973)
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9
What are we made of, again?
 Dirac

predicted existence of anti-matter in 1928
Positron (= anti-electron) discovered in 1932
e
 Our
e
Universe contains (almost) only matter
I do not believe in the hole theory, since I would like to have
the asymmetry between positive and negative electricity in the
laws of nature (it does not satisfy me to shift the empirically
established asymmetry to one of the initial state)
Pauli, 1933 letter to Heisenberg

20 October 2005
Translation: he would like the laws of physics to be different
for particles and anti-particles
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10
CP symmetry
C charge conjugation
P parity
C
particle  anti-particle
x  x, y  y, z  z
and P symmetries are broken in weak interactions

Lee, Yang (1956), Wu et al. (1957), Garwin, Lederman, Weinrich (1957)
 Combined

 To
CP symmetry seemed to be good
Anti-Universe can exist as long as it
is a mirror image of our Universe
e
e
create a matter-dominant Universe,
CP symmetry must be broken
One of the three necessary conditions (Sakharov 1967)
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11
CP violation
 CP

violation was discovered in KL decays
Christenson et al. (1964)
KL decays into either 2 or 3 pions
K L       (33%) CP  1
K L     (0.3%)
CP  1
Final states have different
CP eigenvalues
Couldn’t happen if CP was a good symmetry of Nature
 Laws of physics apply differently to matter and antimatter

 The

complex phase in the CKM matrix causes CP violation
It is the only source of CP violation in the Standard Model
Nothing else?
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12
CP violation and New Physics
Are there additional (non-CKM) sources of CP violation?
 The
CKM mechanism fails to explain the amount of matterantimatter imbalance in the Universe

... by several orders of magnitude
 New
Physics beyond the SM is expected at 1-10 TeV scale
e.g. to keep the Higgs mass < 1 TeV/c2
 Almost all theories of New Physics introduce new sources of CP
violation (e.g. 43 of them in supersymmetry)

New sources of CP violation almost certainly exist

Precision studies of the CKM matrix may uncover them
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13
The Unitarity Triangle
 V†V
= 1 gives us
VudVus*  VcdVcs*  VtdVts*  0
V V  VcdV  V V  0
*
ud ub
*
cb
*
td tb
VusVub*  VcsVcb*  VtsVtb*  0
A triangle on the
complex plane

VudVub
VcdVcb
VudVub*
a
VtdVtb
VcdVcb
VtdVtb*
g
This one has the 3
terms in the same
order of magnitude
b

1
VcdVcb*
 Experiments measure the angles a, b, g and the sides
0
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14
The UT 1998  2005
 We
did know something about how the UT looked in the last
century

By 2005, the allowed region for the apex has shrunk to about 1/10
in area
The improvements
are due largely to
the B Factories
that produce and
study B mesons
in quantity
20 October 2005
95% CL
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15
Anatomy of the
 The
0
B
system
B0 meson is a bound state of b and d quarks
Particle
charge
mass
lifetime
B 0  (bd )
B 0  (bd )
0
5.28 GeV/c2
1.5 ps
0
5.28 GeV/c2
1.5 ps

They turn into each other spontaneously
B0

Indistinguishable
from the outside
B0
b
W+
d
d
W-
b
This is called the B0-B0 mixing
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16
Time-dependent Interference
 Starting
from a pure |B0 state, the wave function evolves as
pure B 0
B
pure B 0
pure B 0
Ignoring the
lifetime
0
B0
time
 Suppose
B0
B0 and B0 can decay into a same final state fCP
B0
t=0
20 October 2005
Two paths can interfere
 Decay probability depends on:

B0
fCP


t=t
M. Morii, Harvard
the decay time t
the relative complex phase
between the two paths
17
The Golden Mode
 Consider
B0  J  K 0
J
c
b
Direct path
B0
b V* V d
tb
td
*
V
V
d td tb b
B
0
Vcb*
d
d
d
d
B0
b

K
Vcb V
s
b
0
K0
*
cs
c
Mixing path
c
Vcs s
VtdVtb
VcdVcb
d V* V s
cd
cs
*
V
V
s cs cd d
K0
c
J
Phase difference is
arg(VcsVcb* )  arg(Vtd2Vtb*2VcbVcs*Vcs2Vcd*2 )  2 arg(VcdVcb* )  arg(VtdVtb* )   2 b
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18
Time-dependent CP Asymmetry
 Quantum
interference between the direct and mixed paths
makes B0 (t )  J  K 0 and B 0 (t )  J  K 0 different
 Define time-dependent CP asymmetry:
N ( B 0 (t )  J  K S0 )  N ( B 0 (t )  J  K S0 )
ACP (t ) 
 sin(2b )sin(mt )
0
0
0
0
N ( B (t )  J  K S )  N ( B (t )  J  K S )

We can measure the angle of the UT
 What
do we have to do to measure ACP(t)?
Step 1: Produce and detect B0  fCP events
 Step 2: Separate B0 from B0
 Step 3: Measure the decay time t

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M. Morii, Harvard
Solution:
Asymmetric
B Factory
19
B Factories
 Designed
specifically for precision measurements of the CP
violating phases in the CKM matrix
SLAC PEP-II
KEKB
Produce ~108 B/year by
colliding e+ and e− with
ECM = 10.58 GeV
e  e   (4S )  BB
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20
SLAC PEP-II site
Linac
I-280
BABAR
PEP-II
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21
Asymmetric B Factory

Collide e+ and e− with E(e+) ≠ E(e−)

PEP-II: 9 GeV e− vs. 3.1 GeV e+  bg = 0.56
m  
Moving in the lab
e−
B0
e+
(4S)
B0
Decay products often
allow us to distinguish
B0 vs. B0
20 October 2005
m
e
z  bg ct
M. Morii, Harvard
Step 1:
  Reconstruct

the signal B
decay
Step 2:
Identify the flavor
of the other B
Step 3:
Measure z  t
22
Detectors: BABAR and Belle
 Layers

of particle detectors surround the collision point
We reconstruct how the B mesons decayed from their decay
products
BABAR
20 October 2005
Belle
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23
A B0 → J/ KS candidate (r-f view)
J/y KS event
−
−
Pions from
K S    
+
+
m+ +

m−
K−
Muons from
J   mm
Red tracks are from the other B,
which was probably B0
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24
CPV in the Golden Channel
 BABAR
measured in B0  J/ + KS and related decays
sin 2b  0.722  0.040(stat.)  0.023(syst.)
J/ KS
20 October 2005
227 million BB events
J/ KL
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25
Three angles of the UT
 CP
violation measurements at the B Factories give
Angle (degree)
a
b
g
98.6 12.6
8.1
21.7 1.3
1.2
6315
12
Decay channels
B0  , ,

B0  (cc)K0
B0  D(*)K(*)
Precision of b is 10 times
better than a and g
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26
CKM precision tests
 Measured
angles agree with what we knew before 1999
The CKM mechanism is responsible for the bulk of
the CP violation in the quark sector

But is it all?
 We
look for small deviation from the CKM-only hypothesis by
using the precise measurement of angle b as the reference
a
VudVub*
VcdVcb*
g
20 October 2005
*
tb
*
cb
VtdV
VcdV
b
Next steps


Measure b with different methods
that have different sensitivity to
New Physics
Measure the sides
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27
Angle b from penguin decays
Golden mode is b  ccs
 Consider a different decay
e.g., b  sss
 The
b cannot decay directly to s
 The main diagram has a loop

u, c, t
top is the main
contributor
The phase from the CKM matrix is
identical to the Golden Mode
can measure angle b in e.g.
B0  f  KS
 We
20 October 2005
s
b
K0
B0
d
d
u, c, t
W

c J /
c
Tree
M. Morii, Harvard
Penguin
b
g
s
f
s
s K0
B0
d
d
28
New Physics in the loop
 The
loop is entirely virtual
W and t are much heavier than b
 It could be made of heavier particles
unknown to us
t
t

New Physics scenarios predict
multiple new particles in 100-1000 GeV
b
b
Lightest ones close to mtop = 174 GeV
 Their effect on the loop can be as big as the SM loop
 Their complex phases are generally different

W
t
 Most
s
t


s
Comparing penguins with trees is a sensitive probe for New Physics
20 October 2005
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29
Strange hints
 Measured
CP asymmetries
show a suspicious trend
sin 2b (penguin)  sin 2b (tree)
Penguin decays
Naive average of penguins
give sin2b = 0.50  0.06
 Marginal consistency from
the Golden Mode
(2.6s deviation)

Need more data!
Golden mode
Penguin modes
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30
The sides
 To
measure the lengths of the
two sides, we must measure
|Vub| ≈ 0.004 and |Vtd| ≈ 0.008

V V
V V
g
The smallest elements – not easy!
Vub
VtdVtb*
VcdVcb*
b
 Main
difficulty: Controlling
theoretical errors due to
hadronic physics

Vtd
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a
*
ud ub
*
cd cb
M. Morii, Harvard
Collaboration between
theory and experiment
plays key role
31
|Vub| – the left side
determines the rate of the b  u transition
 Measure the rate of b  uv decay ( = e or m)
 |Vub|

W
b


u
Vub
The problem: b  cv decay is much faster

W
b

GF2
2
5
(b  u  ) 
V
m
ub
b
192 2
Vcb


c
2
(b  u  )
1


(b  c  ) Vcb 2 50
Vub
Can we overcome a 50 larger background?
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32
Detecting b → uℓv

Use mu << mc  difference in kinematics

B
Xu
u quark turns into
1 or more hardons

E = lepton energy
q2 = lepton-neutrino mass squared
mX = hadron system mass
Signal events have smaller mX  Larger E and q2
Not to scale!
bc
bc
b u
b u
E
20 October 2005
b u
q2
M. Morii, Harvard
bc
mX
33
Figuring out what we see
away b  cv  Lose a part of the b  uv signal
2
 We measure ( B  X u  )  f C  Vub  C
Cut-dependent
 Cut
constant predicted
by theory
Total b  uv rate
Fraction of the signal that pass the cut
requires the knowledge of the b quark’s motion
inside the B meson  Theoretical uncertainty
 Predicting fC

Theoretical error on |Vub| was ~15% in 2003
 Summer
2005: Vub Vub  (3.3expt  2.9model  4.7SF  4.0 theory )%
 7.6%

HFAG EPS 2005 average
What happened in the last 2 years?
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34
Progress since 2003
 Experiments
combine E, q2, mX to maximize fC
Fully reconstructed
B  hadrons
Recoil-B technique improves precisions
 Loosen cuts by understanding background better

b  cv
background
BABAR
preliminary
v
 Theorists
understand the b-quark motion better
 Use information from b  sg and b  cv decays


X
Theory error has shrunk from ~15% to ~5% in the process
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35
Status of |Vub|
|Vub| world average as of Summer 2005
determined to 7.6%
 c.f. sin2b is 4.7%
 |Vub|
Measures the length of
the left side of the UT
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36
|Vtd| – the right side
 Why
can’t we just measure the t  d decay rates?
Top quarks are hard to make
2
2
4
 (t  d ) (t  b)  Vtd Vtb  10

 Must

use loop processes where b  t  d
Best known example: B 0 -B 0 mixing combined with Bs0 -Bs0 mixing
B0
oscillation frequency
Bs oscillation frequency
Vtd
md

ms
Vts
2
2
b
B0 W
t Vtd d
W
B0
b
d Vtd t
md = (0.509  0.004) ps−1
0
0
 Bs -Bs mixing is being searched for at Tevatron (and LEP+SLD)


ms > 14.5 ps-1 at 95 C.L. (Lepton-Photon 2005)
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37
Radiative penguin decays
 Look

for a different loop that does b  t  d
Vtd
( B  g )

*
( B  K g ) Vts
2
t
B( B  K *g )  (4.0  0.2) 105

New results from the B Factories:
B(B  g)
BABAR
Belle
t
2


g
Radiative-penguin decays
(0.6  0.3) 
106
(1.3  0.3) 
106
b
B
W

Vtd d 
u,d
u,d
g
t
B
b
u,d
t
s
*
V
K

ts
W
u,d
Vtd 0.2)
Vts  0.18  0.03
Translated
Averageto (1.0
106
20 October 2005
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38
Impact on the UT
 We
can now constrain the right side of the UT
B0/Bs mixing
( B  g )
( B  K *g )
Comparable sensitivities to |Vtd|
 Promising alternative/crosscheck to the B0/Bs mixing method

Need more data!
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39
The UT today
Sides
Combined
+CP
KL asymmetries
decays
Angles
from
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40
The UT today
 The
B Factories have dramatically
improved our knowledge of the
CKM matrix
All angles and sides measured
with multiple techniques
 New era of precision CKM
measurements in search of NP

 The

Standard Model is alive
Some deviations observed 
require further attention
New Physics seems to be hiding
quite skillfully
20 October 2005
M. Morii, Harvard
41
Constraining New Physics
 New
Physics at ~TeV scale should affect low-energy physics
Effects may be subtle, but we have precision
 Even absence of significant effects helps to identify NP

 In
D0 mixing and rare D decays
 lepton-number violating decays

Precision measurements at the B
Factories place strong constraints on
the nature of New Physics
Two Higgs doublet model
mH (GeV)
addition to the UT, we explore:
 rare B decays into Xsg, Xs, t
Allowed by
BABAR data
b  sg
tanb
20 October 2005
M. Morii, Harvard
42
Outlook
 The
B Factories will pursue increasingly precise measurements
of the UT and other observables over the next few years
 Will the SM hold up?

Who knows?
 At
the same time,
we are setting a tight
web of constraints on
what New Physics
can or cannot be
What the B Factories achieve in the coming years will provide a
foundation for future New Physics discoveries
20 October 2005
M. Morii, Harvard
43