Transcript Cracking the Unitarity Triangle: A Quest in B Physics

Cracking the Unitarity Triangle
— A Quest in B Physics —
Masahiro Morii
Harvard University
University of Arizona Physics Department Colloquium
7 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
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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
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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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A spectrum of masses
1012
1011
Particle mass (eV/c2)
1010
10
9
10
8
t
c
m
 The
b
u d
106
All 12 masses are inputs to the theory
 The masses come from the interaction
with the Higgs particle



103
Q = 1
Standard Model has no explanation
for the mass spectrum

e
10 4
generations differ only by the masses
 The structure is mysterious
s
107
105
 The
t
0
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+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
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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 
 c   M  c 
 
 
 t  
 t 
 d 
d 
 s   N  s 
 
 
 b 
 b 
M and N are arbitrary
33 unitary matrices
W connects u ↔ d, c ↔ s, t ↔ b
u 
u  
 d 
d 
d 
 c   M 1  c   M 1  s   M 1N  s   V  s 
 
 
 
 
 
 t 
 t  
 b 
 b 
 b 
 Suppose

Weak interactions
between u, c, t, and
d, s, b are “mixed”
by matrix V
That’s a poor choice of basis vectors
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Turn the masses back on
 Masses
uniquely define 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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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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What are we made of, again?
 Dirac

predicted existence of anti-matter in 1928
Positron (= anti-electron) discovered by Anderson 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

Translation: he would like the laws of physics to be different for
particles and anti-particles
Are they?
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10
C, P and T symmetries
 Three

particle  anti-particle
x  x, y  y, z  z
T time reversal
t  t
Not true: weak interactions do not respect C and P
Wu et al., 1957
Laws of physics are really symmetric under CP and T

 CP

C charge conjugation
P parity
Laws of physics are symmetric under C, P, and T


discrete symmetries of Nature
Wrong again: CP violation discovered in KL decays
violation makes matter and anti-matter different
Christenson et al.
1964
The SM does this with the complex phase in the CKM matrix
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Truth, the whole truth
Is the CKM mechanism the whole story of CP violation?
 CP

violation must explain how much matter is in the Universe
What’s predicted by the CKM mechanism is not enough
... by several orders of magnitude
 The
Standard Model runs into self-inconsistency at higher
energies (1-10 TeV)  New Physics must exist to resolve this

Almost all theories of New Physics introduce new sources of CP
violation (e.g. 43 of them in SUSY)
The CKM mechanism is almost certainly an
incomplete explanation of CP violation
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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*
0
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
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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
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95% CL
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Anatomy of the
 The
0
B
system
B0 meson is a bound state of b and d quarks
Particle
charge
mass
lifetime
B0  (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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Time-dependent Interference
 Starting
from a pure |B0 state, we’d get
B0
Ignoring the
lifetime
B0
50-50 mix
 Suppose
B
0
B0 and B0 can decay into a same final state fCP
B
B
t=0
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0
Two paths can interfere
 Decay probability depends on:

0
fCP


t=t
M. Morii, Harvard
the decay time t
the relative complex phase
between the two paths
16
The Golden Mode
 Consider
B0  J  K 0
J
c
c
b
Direct path
B0
b V* V d
tb
td
*
V
V
d td tb b
B
0
*
cb
V

K
d
d
d
B0
b
b
s
Vcs
d
0
K0
*
cs
Vcb V
c
Mixing path
VtdVtb
s
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* )   2b
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Time-dependent CP Asymmetry
 Quantum
interference between the direct and mixed paths
makes B0 (t )  J  K 0 and B0 (t )  J  K 0 different
 Define time-dependent CP asymmetry:
N ( B 0 (t )  J  K S0 )  N ( B0 (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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Solution:
Asymmetric
B Factory
18
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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SLAC PEP-II site
Linac
I-280
BABAR
PEP-II
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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
B0
e−
(4S)
B0
Decay products often
allow us to distinguish
B0 vs. B0
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m
e+
e
z  bg ct
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Step 1:
  Reconstruct

the signal B
decay
Step 2:
Identify the flavor
of the other B
Step 3:
Measure z  t
21
Detectors: BABAR and Belle
 Layers

of particle detectors surround the collision point
We reconstruct how the B mesons decayed from their decay
products
BABAR
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Belle
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“Rear” view of BABAR
nearA
completion.
AR
B B
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picture
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A B0 → J/ KS candidate (r-f view)
J/y KS event
−
−
Pions from
KS    
+
+
m+ +

m−
K−
Muons from
J   mm
Red tracks are from the other B,
which was probably B0
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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
7 October 2005
227 million BB events
J/ KL
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Three angles of the UT
 CP
violation measurements at the B Factories give
Angle (degree)
Decay channels
a 98.6 12.6/8.1 B0  , , 
b 21.7 1.3/1.2 B0  (cc)K0
g
63 15/12
B0  D(*)K(*)
Precision of b is 10 times
better than a and g
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CKM precision tests

Angle measurements agree with the Standard Model
The CKM mechanism is responsible for the bulk of
the CP violation in the quark sector


But is it all?
We’ve measured b precisely, but a and g are much harder

One good measurement doesn’t test consistency
a
VudVub*
VcdVcb*
g
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*
td tb
*
cd cb
V V
V V
b
Next steps


Measure b with different methods
that have different sensitivity to
New Physics
Measure the sides
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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
7 October 2005
c
b
s
K0
B0
d
d
u , c, t
W

c J /
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
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29
Strange hints
 Measurements
show a
suspicious trend
sin 2b (b  sss)  sin 2b (b  ccs)
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
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The sides
 To
measure the lengths of the
two sides, we must measure
|Vub| ≈ 0.04 and |Vtd| ≈ 0.08

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
(b  u  )

(b  c  ) Vcb
Vub
2
2

1
50
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
7 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  4.0theory )%
 7.6%

HFAG EPS 2005 average
What happened in the last 2 years?
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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

BABAR
b  cv
background
preliminary
v
 Theorists
understand the b-quark motion better
 Use information from b  sg and b  c decays


X
Theory error has shrunk from ~15% to ~5% in the process
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Status of |Vub|
 |Vub|
has been measured
to 7.6%
 c.f. sin2b is 4.7%
 Fruit
of collaboration
between theory and
experiment
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36
|Vtd| – the right side
 Why
can’t we just measure the t  d decay rates?

Top is hard to make

(t  d ) (t  b)  Vtd2 Vtb2  104
 Must

use loop processes where b  t  d
Best known example: B 0 -B 0 mixing combined with Bs0 -Bs0 mixing
B0
2
oscillation frequency
Bs oscillation frequency
Vtd
md

2
ms
Vts
t Vtd d
b
B0
W
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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Radiative penguin decays
 Look

for a different loop that does b  t  d
g
Radiative-penguin decays
2
( B  [  /  ]g ) Vtd

2
*
( B  K g )
Vts

B( B  K g )  (4.0  0.2) 10

New results from B Factories:
t
Belle
B+  +g
< 1.810-6
(0.6  0.4)10-6
B0  0g
< 0.410-6
(1.2  0.3)10-6
B0  g
< 1.010-6
(0.6  0.3)10-6
B  [ /]g < 1.210-
(1.3  0.3)10-
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6
Average
Vtd
d
,
u, d
g
BABAR
6
W

u, d
Mode
95% C.L.
b
B
5
*
t
t
B
b
u, d
t
Vts s K *
W

u, d
6
B( B  [  / ]g )  (0.940.25
)

10
0.22
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38
Impact on the UT
 From
the radiative-penguin measurements
limits from the
B0/Bs mixing
Vtd
 0.18  0.03
Vts

Comparable sensitivities to |Vtd|

Promising alternative/crosscheck to the B0/Bs mixing method
Need more data!
7 October 2005
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39
The UT today
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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
 Bad
news: the Standard Model lives
Some deviations observed  require further attention
 New Physics seems to be hiding quite skillfully

 Good
news: the Standard Model lives!
New Physics at ~TeV scale affect physics at low energies
 Precision measurements at the B Factories place strong constraints
on the nature of New Physics

7 October 2005
M. Morii, Harvard
41
B Factories and New Physics

mH (GeV)
Two Higgs doublet model
In addition to the angles and the sides
of the UT, we explore:
 rare B decays into Xsg, Xs, t

Allowed by
BABAR data


b  sg
Even absence of significant effects
contributes to identifying NP

tanb
7 October 2005
D0 mixing and rare D decays
lepton-number violating decays
If we measure them precisely enough
Some of the best limits on NP
come from rare B decays
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
7 October 2005
M. Morii, Harvard
43