Cracking the Unitarity Triangle: A Quest in B Physics
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Transcript Cracking the Unitarity Triangle: A Quest in B Physics
Cracking the Unitarity Triangle
— A Quest in B Physics —
Masahiro Morii
Harvard University
Ohio State University Physics Colloquium
9 May 2006
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 B0 and Bs mixing
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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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
Q0
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e
e
strong E&M weak
quarks
u
d
Q2
Q1
3
3
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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
d
e−
force by the W and Z0 bosons
Z0
u
Z0
d
W−
e−
u
d
Z0
e−
d
u
W+
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e−
d
g
e
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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
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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
+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
33 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 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 33 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 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
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Translation: he would like the laws of physics to be different
for particles and anti-particles
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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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CP violation
CP
violation was discovered in KL decays
Christenson et al. (1964)
KL decays into either 2 or 3 pions
KL (33%) CP 1
KL (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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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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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 2006
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, the wave function evolves as
pure B 0
B
pure B0
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
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Two paths can interfere
Decay probability depends on:
B0
fCP
t=t
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the decay time t
the relative complex phase
between the two paths
17
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
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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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 ct
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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
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
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Belle
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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 mm
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
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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)
a
b
g
98.612.6
8.1
21.7 1.3
1.2
6315
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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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
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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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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
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c
b
s
K0
B0
d
d
u , c, t
W
c J /
Tree
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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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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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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
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Collaboration between
theory and experiment
plays key role
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|Vub| – the left side
determines the rate of the b u transition
Measure the rate of b uv decay ( = e or m)
|Vub|
W
b
u
Vub
The problem: b cv 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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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!
bc
bc
bu
bu
E
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bu
q2
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bc
mX
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Figuring out what we see
away b cv Lose a part of the b uv signal
2
We measure ( B X u ) f C Vub C
Cut-dependent
Cut
constant predicted
by theory
Total b uv 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
Winter
2006: Vub Vub (3.5expt 2.8model 4.1SF 4.2theory )%
7.4%
HFAG Moriond 2006 average
What happened in the last 2+1/2 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
b cv
background
BABAR
preliminary
v
Theorists
understand the b-quark motion better
Use information from b sg and b cv decays
X
Theory error has shrunk from ~15% to ~4% in the process
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Status of |Vub|
determined to 7.4%
c.f. sin2b is 4.7%
|Vub|
World Average 4.45 0.33
2/dof = 5.5/6
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Measures the length of
the left side of the UT
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|Vtd| – the right side
Why
can’t we just measure the t d decay rates?
Top quarks are hard to make
(t d ) (t b) Vtd2 Vtb2 104
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
md = (0.509 0.004) ps−1
News from the Tevatron:
ms
0.07 CDF
17 ms 21(90%CL) DØ
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B0
W
d Vtd t
17.330.42
0.21
t Vtd d
b
Vtd
Vts
M. Morii, Harvard
B0
W
b
0.008
0.208
0.007
37
Radiative penguin decays
Look
for a different loop that does b t d
g
Radiative-penguin decays
Vtd
( B g )
*
( B K g ) Vts
2
t
2
B( B K *g ) (4.0 0.2) 105
Latest results from the B Factories:
B(B g)
BABAR
Belle
t
(0.6 0.3)
106
(1.3 0.3)
106
b
B
W
Vtd
u, d
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
106
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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 )
Mixing measurements pinned down |Vtd/Vts| as precisely as sin2b
B g provides a crosscheck, with sensitivity to New Physics
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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
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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
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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
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