cracking the unitarity triangle — a quest in b physics — masahiro morii harvard university...
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Cracking the Unitarity Triangle— A Quest in B Physics —
Masahiro MoriiHarvard University
University of Arizona Physics Department Colloquium
7 October 2005
7 October 2005 M. Morii, Harvard 2
Outline Introduction to the Unitarity Triangle
The Standard Model, the CKM matrix, and CP violation CP asymmetry in the B0 meson decays
Experiments at the B FactoriesResults from BABAR and Belle
Angles , , from CP asymmetries |Vub| from semileptonic decays
|Vtd| from radiative-penguin decays
Current 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
The Unitarity TriangleThe Unitarity Triangle
7 October 2005 M. Morii, Harvard 3
What are we made of?
Ordinary 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”
quarksleptons
e
e u
d
0Q
1Q
13Q
23Q
strong E&M weak
u Yes Yes Yes
d Yes Yes Yes
e− No Yes Yes
e No No Yes
u
u d
e
7 October 2005 M. Morii, Harvard 4
Simplified Standard Model Strong force is transmitted by the gluon
Electromagnetic force by the photon
Weak force by the W and Z0 bosons
uu
g
dd
g
uu
dd
e−
e−
uu
Z0
dd
Z0 Z0
e−
e−
Z0
ee
du
W+
e
e−
W−
Note W± can “convert”u ↔ d, e ↔
7 October 2005 M. Morii, Harvard 5
Three generationsWe’ve got a neat, clean, predictive theory of “everything”
Why 3 sets (= generations) of particles? How do they differ? How do they interact with each other?
strong E&M weak
g W ±
Z 0
− c
s
− t
b
leptons quarks
e− u
e d1st generation
2nd generation
3rd generation
It turns out there are two “extra”
copies of particles
It turns out there are two “extra”
copies of particles
7 October 2005 M. Morii, Harvard 6
A spectrum of massesThe generations differ only by the masses The structure is mysterious
The 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 ... whose nature is unknown We are looking for it with the Tevatron,
and with the Large Hadron Collider (LHC) in the future
310
410
510
610
710
810
910
1010
1110
Part
icle
mas
s (e
V/c
2 )
1210
e
u
c
t
d
s
b
Q = 1 0 +2/3 1/3The origin of mass is one of the most urgent
questions in particle physics today
7 October 2005 M. Morii, Harvard 7
If there were no massesNothing would distinguish u from c from t
We could make a mixture of the wavefunctions and pretend it represents a physical particle
Suppose W connects u ↔ d, c ↔ s, t ↔ b
That’s a poor choice of basis vectors
u u
c c
t t
M
d d
s s
b b
N M and N are arbitrary33 unitary matrices
1 1 1
u u d d d
c c s s s
t t b b b
M M M N V
Weak interactions between u, c, t, and d, s, b are “mixed” by matrix V
7 October 2005 M. Morii, Harvard 8
Turn the masses back onMasses 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 33 unitary matrix
The Standard Model does not predict V ... for the same reason it does not predict the particle masses
ud us ub
cd cs cb
td ts tb
Wu d V V V d
c s V V V s
t b V V V b
V
Cabibbo-Kobayashi-Maskawa matrix or CKM for short
7 October 2005 M. Morii, Harvard 9
Structure of the CKM matrixThe CKM matrix looks like this
It’s not completely diagonal Off-diagonal components are small
Transition across generations isallowed but suppressed
Matrix elements can be complex Unitarity leaves 4 free parameters,
one of which is a complex phase
0.974 0.226 0.004
0.226 0.973 0.042
0.008 0.042 0.999
V
0.974 0.226 0.004
0.226 0.973 0.042
0.008 0.042 0.999
V
There seems to be a “structure”separating the generations
This phase causes “CP violation”Kobayashi and Maskawa (1973)
7 October 2005 M. Morii, Harvard 10
What are we made of, again?Dirac predicted existence of anti-matter in 1928
Positron (= anti-electron) discovered by Anderson in 1932
Our Universe contains (almost) only matter
Translation: he would like the laws of physics to be different for particles and anti-particles
e e
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
Are they?
7 October 2005 M. Morii, Harvard 11
C, P and T symmetriesThree discrete symmetries of Nature
Laws of physics are symmetric under C, P, and T Not true: weak interactions do not respect C and P
Laws of physics are really symmetric under CP and T Wrong again: CP violation discovered in KL decays
CP violation makes matter and anti-matter different The SM does this with the complex phase in the CKM matrix
C charge conjugation particle anti-particle
P parity x x, y y, z zT time reversal t t
Wu et al., 1957
Christenson et al.1964
7 October 2005 M. Morii, Harvard 12
Truth, the whole truth
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 magnitudeThe 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
Is the CKM mechanism the whole story of CP violation?
7 October 2005 M. Morii, Harvard 13
The Unitarity TriangleV†V = 1 gives us
Experiments measure the angles , , and the sides
* * *
* * *
* * *
0
0
0
ud us cd cs td ts
ud ub cd cb td tb
us ub cs cb ts tb
V V V V V V
V V V V V V
V V V V V V
This one has the 3 terms in the same
order of magnitude
A triangle on the complex plane
1
td tb
cd cb
V V
V V
ud ub
cd cb
V V
V V
0
*ud ubV V
*td tbV V
*cd cbV V
7 October 2005 M. Morii, Harvard 14
The UT 1998 2005
95% CL
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 Factoriesthat produce and study B mesons
in quantity
7 October 2005 M. Morii, Harvard 15
Anatomy of the B0 systemThe B0 meson is a bound state of b and d quarks
They turn into each other spontaneously
This is called the B0-B0 mixing
0 ( )B bd0 ( )B bd
Particle charge mass lifetime
0 5.28 GeV/c2 1.5 ps
0 5.28 GeV/c2 1.5 ps
Indistinguishable from the outside
0B 0B
W+
W-
b
d
d
b
7 October 2005 M. Morii, Harvard 16
Time-dependent Interference Starting from a pure |B0 state, we’d get
Suppose B0 and B0 can decay into a same final state fCP
Two paths can interfere Decay probability depends on:
the decay time t the relative complex phase
between the two paths
0B
0B
50-50 mix
Ignoring the lifetime
0B
0BfCP
0B
t = 0 t = t
7 October 2005 M. Morii, Harvard 17
The Golden ModeConsider
Phase difference is
0 0B J K0 0B J K
b
d d
scc
0B
J
0K
d
b s
d
c c
0B 0K
J
0Bd
b
b
d
s
ds
d0K
Direct path
Mixing path
*cbV csV
*csVcbV*
tbV
tdV
tdV
*tbV
*cdV
csV
csV
*cdV
* 2 *2 * 2 *2 * *arg( ) arg( ) 2 arg( ) arg( ) 2cs cb td tb cb cs cs cd cd cb td tbV V V V V V V V V V V V * 2 *2 * 2 *2 * *arg( ) arg( ) 2 arg( ) arg( ) 2cs cb td tb cb cs cs cd cd cb td tbV V V V V V V V V V V V
td tbV V
cd cbV V
7 October 2005 M. Morii, Harvard 18
Time-dependent CP AsymmetryQuantum interference between the direct and mixed paths
makes and differentDefine time-dependent CP asymmetry:
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
0 0 0 0
0 0 0 0
( ( ) ) ( ( ) )( ) sin(2 )sin( )
( ( ) ) ( ( ) )S S
CPS S
N B t J K N B t J KA t mt
N B t J K N B t J K
Solution:Asymmetric
B Factory
0 0( )B t J K0 0( )B t J K
7 October 2005 M. Morii, Harvard 19
B FactoriesDesigned 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
Produce ~108 B/year by colliding e+ and e− with ECM = 10.58 GeV
(4 )e e S BB (4 )e e S BB
7 October 2005 M. Morii, Harvard 21
Step 2:
Identify the flavorof the other B
Decay products often allow us to distinguishB0 vs. B0
Asymmetric B Factory Collide e+ and e− with E(e+) ≠ E(e−)
PEP-II: 9 GeV e− vs. 3.1 GeV e+ = 0.56
Step 1:
Reconstruct the signal B decaye− e+
Moving in the lab
(4S)
Step 3:
Measure z tz c t
e
0B
0B
7 October 2005 M. Morii, Harvard 22
Detectors: BABAR and BelleLayers of particle detectors surround the collision point
We reconstruct how the B mesons decayed from their decay products
BABARBABAR BelleBelle
7 October 2005 M. Morii, Harvard 24
J/y KS eventA B0 → J/ KS candidate (r-view)
Muons from
Pions from
Red tracks are from the other B,which was probably B0
−
+
+
−
−
+
+
K−
J
SK
7 October 2005 M. Morii, Harvard 25
CPV in the Golden Channel BABAR measured in B0 J/ + KS and related decays
J/ KSJ/ KS
227 million events227 million eventsBBsin 2 0.722 0.040(stat.) 0.023(syst.)
J/ KLJ/ KL
7 October 2005 M. Morii, Harvard 26
Three angles of the UTCP violation measurements at the B Factories give
Angle (degree) Decay channels
B
BccK
BD(*)K(*)
Precision of is 10 times better than and
Precision of is 10 times better than and
7 October 2005 M. Morii, Harvard 27
CKM precision tests Angle measurements agree with the Standard Model
But is it all? We’ve measured precisely, but and are much harder
One good measurement doesn’t test consistency
Next steps Measure with different methods
that have different sensitivity to New Physics
Measure the sides
Next steps Measure with different methods
that have different sensitivity to New Physics
Measure the sides
*
*tb
cb
td
cd
V
V V
V
*
*ubud
cd cb
V
V V
V
The CKM mechanism is responsible for the bulk of the CP violation in the quark sector
7 October 2005 M. Morii, Harvard 28
Penguin decaysThe Golden mode is Consider a different decay
e.g., b cannot decay directly to s The main diagram has a loop
The phase from the CKM matrix is identical to the Golden Mode
We can measure angle in e.g.B0 KS
b ccs
b sss
Tree
0Kb
c
sc
d
0B
/J
d
Penguin
0Kb
s
ss
d
0B
d
gW
, ,u c t , ,u c ttop is the main
contributor
7 October 2005 M. Morii, Harvard 29
New Physics in the loopThe loop is entirely virtual
W and t are much heavier than b It could be made of heavier particles
unknown to usMost New Physics scenarios predict
multiple new particles in 100-1000 GeV 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 t
b s
t t
b s
Comparing penguins with trees is a sensitive probe for New PhysicsComparing penguins with trees is a sensitive probe for New Physics
7 October 2005 M. Morii, Harvard 30
Strange hintsMeasurements show a
suspicious trend
Naive average of penguins give sin2 = 0.50 0.06
Marginal consistency from the Golden Mode(2.6 deviation)
sin 2 ( ) sin 2 ( )b sss b ccs
Need more data!Golden Mode
Penguin decays
7 October 2005 M. Morii, Harvard 31
The sidesTo measure the lengths of the
two sides, we must measure|Vub| ≈ 0.04 and |Vtd| ≈ 0.08 The smallest elements – not easy!
Main difficulty: Controlling theoretical errors due to hadronic physics Collaboration between
theory and experiment plays key role
*
*tb
cb
td
cd
V
V V
V
*
*ubud
cd cb
V
V V
V
Vtd
Vub
7 October 2005 M. Morii, Harvard 32
|Vub| – the left side
|Vub| determines the rate of the b u transition Measure the rate of b uv decay ( = e or )
The problem: b cv decay is much faster
Can we overcome a 50 larger background?
ubVb
u
W 22 5
2( )
192F
ub b
Gb u V m
22 5
2( )
192F
ub b
Gb u V m
cbVb
c
W 2
2
( ) 1
( ) 50ub
cb
Vb u
b c V
2
2
( ) 1
( ) 50ub
cb
Vb u
b c V
7 October 2005 M. Morii, Harvard 33
Use mu << mc difference in kinematics
Signal events have smaller mX Larger E and q2
Detecting b → uℓv
2q
b c
b u
uX
B
u quark turns into 1 or more hardons
q2 = lepton-neutrino mass squaredq2 = lepton-neutrino mass squared
mX = hadron system massmX = hadron system mass
E = lepton energyE = lepton energy
E
b c
b u
Xm
b cb u
Not to scale!Not to scale!
7 October 2005 M. Morii, Harvard 34
Figuring out what we seeCut away b cv Lose a part of the b uv signal
We measure
Predicting fC requires the knowledge of the b quark’s motion inside the B meson Theoretical uncertainty Theoretical error on |Vub| was ~15% in 2003
Summer 2005:
What happened in the last 2 years?
2( )u C ub CB X f V
Total b uv rate
Fraction of the signal that pass the cut
Cut-dependentconstant predicted
by theory
expt model SF theory(3.3 2.9 4.7 4.0 )%
7.6%
ub ubV V
expt model SF theory(3.3 2.9 4.7 4.0 )%
7.6%
ub ubV V
HFAG EPS 2005 average
7 October 2005 M. Morii, Harvard 35
Progress since 2003Experiments combine E, q2, mX to maximize fC
Recoil-B technique improves precisions Loosen cuts by understanding background better
Theorists understand the b-quark motion better Use information from b s and b c decays Theory error has shrunk from ~15% to ~5% in the process
Fully reconstructedB hadrons
v
X
BABARpreliminary
b cvbackground
7 October 2005 M. Morii, Harvard 36
Status of |Vub|
|Vub| has been measured to 7.6% c.f. sin2is 4.7%
Fruit of collaboration between theory and experiment
7 October 2005 M. Morii, Harvard 37
|Vtd| – the right side
Why can’t we just measure the t d decay rates? Top is hard to make
Must use loop processes where b t d Best known example: mixing combined with mixing
md= (0.509 0.004) ps−1
mixing is being searched for at Tevatron (and LEP+SLD) ms > 14.5 ps-1 at 95 C.L. (Lepton-Photon 2005)
2 2 4( ) ( ) 10td tbt d t b V V
tdV
tdV
b
b
d
d
t
t
W0B 0BW
0 0-B B 0 0-s sB B2
2tdd
s ts
Vm
m V
B0 oscillation frequency
Bs oscillation frequency
0 0-s sB B
7 October 2005 M. Morii, Harvard 38
Radiative penguin decaysLook for a different loop that does b t d
Radiative-penguin decays
New results from B Factories:
W
t t
b d
tdV
,u d,u d
B ,
W
t t
b s
tsV
,u d,u d
B*K
2
2*
( [ / ] )
( )td
ts
VB
B K V
* 5( ) (4.0 0.2) 10B K B
Mode BABAR Belle
B+ + < 1.810-6 (0.6 0.4)10-6
B0 0 < 0.410-6 (1.2 0.3)10-6
B0 < 1.010-6 (0.6 0.3)10-6
B [/]
< 1.210-
6
(1.3 0.3)10-695% C.L. 0.25 6
0.22( [ / ] ) (0.94 ) 10B BAverage
7 October 2005 M. Morii, Harvard 39
Impact on the UT From the radiative-penguin measurements
Comparable sensitivities to |Vtd| Promising alternative/crosscheck to the B0/Bs mixing method
limits from the B0/Bs mixing
limits from the B0/Bs mixing
0.18 0.03td
ts
V
V 0.18 0.03td
ts
V
V
Need more data!
7 October 2005 M. Morii, Harvard 41
The UT todayThe B Factories have dramatically
improved our knowledge of theCKM matrix All angles and sides measured
with multiple techniquesBad 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 42
B Factories and New Physics m
H (
GeV
)
tan
Allowed byBABAR data
B b s
Two Higgs doublet model
In addition to the angles and the sides of the UT, we explore: rare B decays into Xs, Xs, D0 mixing and rare D decays lepton-number violating decays
Even absence of significant effects contributes to identifying NP If we measure them precisely enough
Some of the best limits on NP come from rare B decays
7 October 2005 M. Morii, Harvard 43
OutlookThe B Factories will pursue increasingly precise measurements
of the UT and other observables over the next few yearsWill the SM hold up?
Who knows?At the same time,
we are setting a tightweb 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