CP Violation in B Meson Decays
Math/Physics Undergraduate
Colloquium
Daniel Marlow
Princeton University
November 19, 1999
November 19, 1999 CP Violation in B Meson Decays 1
Outline
• Introduction to Particle Physics
• P, C, CP, T and CPT
• CP Violation in the B System
• Kobayashi Maskawa Quark Mixing
• Direct CP Violation
• B mixing (matter-antimatter oscillations)
• The EPR effect
• The Tools (mainly photographs)
• The Accelerator
• The Detector
November 19, 1999 CP Violation in B Meson Decays 2
Princeton People
• PhDs: Kazu Hanagaki, Ted Liu*, DRM, Eric Prebys
• Graduate Students: Kirill Korotushenko, Jack Laiho,
Christos Leonidopoulos, Chris Mindas*, Sven Vahsen
• Undergraduates: Matt Ahart*, Tom Fertig*, Hulya
Guler*, Rachel Mandelbaum, Emma Torbert
• Technical Staff: Carl Bopp, Stan Chidzik, Bill Groom,
Bob Klemmer, Ted Lewis, Allan Nelson, Dick
Rabberman, Bill Sands, Bob Wixted*
November 19, 1999 CP Violation in B Meson Decays 3
The Standard Model
Q Leptons Quarks Q
0 ve v v u c t 2e
e 1 3
e d s b 3 e
Forces Carriers Hadrons
EM photon n ddu p uud
Weak W , Z 0 vector bosons ud - ud
Strong g gluon 0 (uu dd ) / 2
K su K 0 sd
B bu B0 b d
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Feynman Diagrams
e
Electron radiates a
photon
e
e
Electron absorbs
a photon
e
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Feynman Diagrams
e e
Electron -electron
scattering
e e
Photon is
never seen
November 19, 1999 CP Violation in B Meson Decays 6
Feynman Diagrams
W Muon radiates a W
v
boson
v
W e
ve
The W rematerializes as
e
an electron and an anti-
ve
electron neutrino.
November 19, 1999 CP Violation in B Meson Decays 7
Feynman Diagrams
e
W
ve
v
Muon decay
November 19, 1999 CP Violation in B Meson Decays 8
Feynman Diagrams
Quark transitions
u
W
u
d
d
W c
c
s
s
November 19, 1999 CP Violation in B Meson Decays 9
Parity & Charge Conjugation
What is CP?
•What is P? Answer: parity ( r r & p p )
P (r , s z ) (r , s z )
•What is C? Answer: charge conjugation.
Ce e C p p C
Note that C also flips lepton and baryon number. Note
further that neutral particles can be eigenstates of C.
November 19, 1999 CP Violation in B Meson Decays 10
Parity Falls
Until the mid-50’s, people believed that both P and C would
be conserved. However, in 1957, Wu et al., who were
pursuing ideas of Lee & Yang (inspired by experimental data
on K decays) observed parity violation in nuclear decay.
Although parity is conserved in strong and electro-magnetic
interactions it is in a sense “maximally violated” in weak
interactions.
November 19, 1999 CP Violation in B Meson Decays 11
Parity Falls
In particular, neutrinos, which are massless (or nearly so),
have a definite ``handedness’’.
• ' s are left handed S
p
• ' s are right handed. S
p
In a “symmetric” interaction, one would expect both
helicities to exist, as is the case, for example, in
electromagnetism, where photons have both left- and
right-circular polarizations.
November 19, 1999 CP Violation in B Meson Decays 12
Parity & Charge Conjugation Fall
The last hope was that the product of the two operators (i.e.
CP) would be conserved.
right-handed
P
S
p
S
p
C CP C
S
p S
P p
left-handed OK!
November 19, 1999 CP Violation in B Meson Decays 13
CP Falls
Hopes for CP conservation were dashed in 1964 by a
Princeton group led by Val Fitch and Jim Cronin, who
detected a tiny CP violating effect in neutral K decays.
This is a wonderful story, but one that we won’t go into here.
Reasons for further study:
• CP violation is “surprising”
• CP violation represents a matter-antimatter asymmetry
(we’ll see how later on) and is an essential element in
understanding the baryon-antibaryon asymmetry in
Universe.
• CP effects involving b quarks are expected to be large.
November 19, 1999 CP Violation in B Meson Decays 14
The CPT Theorem
All that is left is an operator called CPT, where “T”
stands for time-reversal.
Although the experimental tests of CPT are somewhat
limited, the CPT theorem is part of the “theoretical
bedrock” of field theory. If we assume that CPT is a
good symmetry, then
CP T
November 19, 1999 CP Violation in B Meson Decays 15
Time Reversal
In non-relativistic QM, the time-reversal operator is such
that: i i & t t
T f f *
thus
i ( kxt ) * i ( kxt )
( x, t ) 0e e 0
left-mover right-mover
As one would expect, the T operator reverses
momenta (but not positions).
November 19, 1999 CP Violation in B Meson Decays 16
Time Reversal
The expectation value of an operator transformed by T is
Q K
QK dV Q dV
*
K
*
*
(Q ) dV Q dV
* *
Q *
Operators with complex phases (e.g., p and L),
are not T invariant (and therefore are not CP
invariant).
November 19, 1999 CP Violation in B Meson Decays 17
Quark Mixing
Experimentally we know that the eigenstates of the weak
Hamiltonian and the mass eigenstates are different. For
simplicity we start with a two-quark-doublet version of
nature, i.e.,
q 2 u c If the quarks acted like leptons, then
3
d
s
only vertical transitions would be
q3
1
allowed and the s quark would be stable.
s u 0
u
However, the kaon decays
in 12 ns. It appears that
K W
there are generation- d
crossing transitions. u u
November 19, 1999 CP Violation in B Meson Decays 18
Quark Mixing
Rather than saying that the strange quark is decaying
directly to an up quark, we write the following
sin d
d ' cos
s' sin
cos s
Cabibbo mixing
And say that the s-quark in the kaon has a d ' component
that can decay into a u-quark.
u c u c Q: What does
d '
s'
d
s this have to do
with CP
Weak eigenstate Mass eigenstate violation?
November 19, 1999 CP Violation in B Meson Decays 19
Quark Mixing
Ans: Nothing! (yet)
However, even before the discovery of the c-quark (and
two decades before the observation of the t-quark)
Kobayashi and Maskawa proposed a three-generation
scheme
u c t u c t
d '
s'
b'
d
s b
Weak eigenstates Mass eigenstates
November 19, 1999 CP Violation in B Meson Decays 20
Quark Mixing
d ' Vud Vus Vub d
KM
s ' Vcd Vcs Vcb s
Mixing
b' V Vts Vtb b
td
Both Cabibbo (2x2) and KM (3x3) mixing are described by
unitary transformations. In general
d ' Md where M M 1
November 19, 1999 CP Violation in B Meson Decays 21
Quark Mixing
Case Ngen Parameter(s)
Cabibbo 2 2 C
i
KM 3 3 1 , 2 , 3 , e
The essential contribution of Kobayashi and Maskawa was
the observation that only a 3x3 scheme would provide the
phase needed for T violation (and hence CP violation).
November 19, 1999 CP Violation in B Meson Decays 22
Quark Mixing
Original Kobayashi-Maskawa parameterization.
c1 s1c3 s1s3
M s1c2 c1c2 c3 s2 s3ei i
c1c2 s3 s2 c3e
s s c1s2 c3 c2 s3ei c1s2 s3 c2 c3ei
1 2
where si sin i & ci cos i
This parameterization is valid, but it is not especially
intuitive.
November 19, 1999 CP Violation in B Meson Decays 23
Quark Mixing
A more popular choice is the Wolfenstein parameterization:
Vud Vus Vub 1 2 A3 ( i )
2
V
M cd Vcs Vcb 1 2 2 A 2
Vtd Vts Vtb A3 (1 i ) A2
1
This approximation ( 1 ) reflects the theoretical
prejudice (and experimental reality) that the elements get
smaller as one moves off the diagonal.
Allowed u c t
suppressed doubly
d
s
b
suppressed
November 19, 1999 CP Violation in B Meson Decays 24
Quark Mixing
The appearance of the KM phase offers a natural
explanation for standard-model CP violation. Moreover,
there is a wealth of other (non-CP) experimental data that
supports the KM picture. However, to date there have
been no quantitative tests of its predictions regarding CP
violation.
November 19, 1999 CP Violation in B Meson Decays 25
The Unitarity Triangle
Vud Vus Vub 1 2 2 A3 ( i )
V
M cd Vcs Vcb 1 2 2 A 2
Vtd Vts Vtb A3 (1 i ) A2
1
Unitarity implies M M 1 M ik M jk ij
*
k
In particular, the V V V V V V 0
ud td us ts
*
ub tb
“d b” unitarity
relation yields Vtd Vub A3
*
November 19, 1999 CP Violation in B Meson Decays 26
The Unitarity Triangle
Like any sum of
complex numbers ,
Vtd Vub A3
*
V Vtd
2
can be plotted as a ub
triangle in the A 3
A3
complex plane.
3 1
The Bjorken
Triangle Vcb 1,0
A3
November 19, 1999 CP Violation in B Meson Decays 27
Direct CP Violation
Consider the CP mirror processes:
B f and B f
The CP asymmetry is defined as
( B f ) B f )
ACP
( B f ) B f )
The decay amplitudes are
i KM i KM
Af Af e and Af Af e
Note that the KM phase changes sign.
November 19, 1999 CP Violation in B Meson Decays 28
Direct CP Violation
2 2
However, Af Af f f
We see no effect! This is so even though the weak interaction
is in a sense maximally CP violating.
We need some sort of interference, two amplitudes (i.e.,
two Feynman diagrams). Consider B- - 0
u 0 d
b
u b
u
B
d
B
u 0
u u u u
add amplitudes
November 19, 1999 CP Violation in B Meson Decays 29
Direct CP Violation
The resulting amplitudes are:
i KM i S1 i KM 2 i S2
Af A1 e 1
e A2 e e
i KM i S1 i KM 2 i S2
A f A1 e 1
e A2 e e
Note that there is one more slight complication: the addition
of a strong phase (but this is a good thing).
f A1 A2 2 A1 A2 cos( KM S )
2 2
f A1 A2 2 A1 A2 cos(KM S )
2 2
November 19, 1999 CP Violation in B Meson Decays 30
Direct CP Violation
Despite its conceptual and experimental “simplicity”, there
are two problems with direct CP violation:
• Cases where there are two comparable
amplitudes that are large are (probably) rare.
• The strong phases are poorly understood,
making it difficult to extract the weak (KM)
phases that are of greatest interest.
We need a better way. Such a way, which goes by the
name of “Indirect CP Violation,” has been found and
will be the topic of all that follows.
November 19, 1999 CP Violation in B Meson Decays 31
Matter-Antimatter Oscillations
First observed in the neutral kaon (strange quark) system,
neutral meson mixing represents an oscillation between
matter and anti-matter. In the neutral B system, the reaction
proceeds by the following Feynman diagram:
*
b Vtb t Vtd d
0 0
B W W B
d Vtd t V * b
tb
November 19, 1999 CP Violation in B Meson Decays 32
Matter-Antimatter Oscillations
As a consequence, an initially pure B 0 develops in time
according to the expression given below.
B 0 (t ) e i ( mi cos 2 t B 0 i sin 2 t e 2im B 0
m m
mixing
where the KM matrix element Vtd determines m .
November 19, 1999 CP Violation in B Meson Decays 33
Indirect CP Violation
Thus for a decay B 0 f
B0 where f is a CP eigenstate, we
B 0
f have two “indistinguishable”
decay paths
Working through the ( B 0 f ) ( B 0 f )
algebra, yields a time- ACP (t )
dependent CP ( B 0 f ) ( B 0 f )
asymmetry 2 f sin( mt ) sin 2( M D )
Where M and D are the CP f f f
weak phases for the mixing and
decay diagrams, respectively and f 1
November 19, 1999 CP Violation in B Meson Decays 34
Indirect CP Violation
( B 0 f ) ( B 0 f )
ACP (t )
( B f ) ( B f )
0 0
One complication is that since CP eigenstates are
neutral, they give no information as to whether the
0 0
decaying meson was a B B
Fortunately there is a solution in the form of . . .
November 19, 1999 CP Violation in B Meson Decays 35
Quantum Weirdness
One way to make B 0 ' s is to produce B 0 B 0
pairs at an e e collider. In practice this means
making using of resonant production, i.e.,
e e Y (4S ) B 0 B 0
Where the Y ( 4 S ) is a radial excitation of a
“quarkonium” bound state. The important point is
0 0
that the B B pair is produced in a coherent
state.
November 19, 1999 CP Violation in B Meson Decays 36
Quantum Weirdness
Tagging side CP eigenstate side
t1 t0 t2 J /
l
B0 B 0 KS
Tags this particle This particle must
as a B 0 have decayed as a B0
If t1 t2 then the particle on the CP eigenstate must be a B 0.
Note that the tagging information is communicated across space
instantaneously despite the fact that the B’s could be separated
by a finite distance (a few hundred microns). This is an
instance of the EPR paradox.
November 19, 1999 CP Violation in B Meson Decays 37
The Measurement
tag
D0
e
e B0
0
z
B The times involved are too
short (~1 ps) to measure
J /
directly, instead we measure the
decay positions and convert
K0
CP these positions to times.
November 19, 1999 CP Violation in B Meson Decays 38
The Measurement
The time-dependent
asymmetry appears
mainly as a mean shift
in the z distribution
between events tagged
0
as B decays and
0
events tagged as B
decays.
November 19, 1999 CP Violation in B Meson Decays 39
The KEK-B Asymmetric e e Collider
KEK-B is a recently
completed accelerator
situated in Tsukuba City,
Japan.
ee
It is designed to produce
an order of magnitude
more luminosity
(collisions per unit cross
section) than any existing
machine.
November 19, 1999 CP Violation in B Meson Decays 40
Ring Parameters
HER e- LER e+
Parameter Design Achieved Design Achieved
Beam Current 1100 mA 514 mA 2600 mA 532 mA
Single Bunch
Current .22 mA 4 mA .52 mA 2.3 mA
Number of
5000 800 5000 1024
Bunches
x / y @ IP 33/1 cm 100/1.1 cm 33/1 cm 100/1 cm
Injection
100% 80% 100% 80%
Efficiency
November 19, 1999 CP Violation in B Meson Decays 41
Electron Source
November 19, 1999 CP Violation in B Meson Decays 42
The Linac
November 19, 1999 CP Violation in B Meson Decays 43
The Storage Rings
RF Cavity
Stations
November 19, 1999 CP Violation in B Meson Decays 44
The Storage Rings
Arc Section
November 19, 1999 CP Violation in B Meson Decays 45
The “IR”
Where matter and anti-matter collide!
November 19, 1999 CP Violation in B Meson Decays 46
The Magnet
November 19, 1999 CP Violation in B Meson Decays 47
The BELLE Collaboration
• About 200 physicists
• About 50 institutions
• Countries: Australia,
China (both!), India, Japan,
Korea, Poland, Russia,
Ukraine, United States
November 19, 1999 CP Violation in B Meson Decays 48
Cosmic Ray
How I spent my
sabbatical year!
November 19, 1999 CP Violation in B Meson Decays 49
Meters to Microns
November 19, 1999 CP Violation in B Meson Decays 50
The Magnet
November 19, 1999 CP Violation in B Meson Decays 51
The Silicon Vertex Detector
November 19, 1999 CP Violation in B Meson Decays 52
The Central Drift
Chamber
November 19, 1999 CP Violation in B Meson Decays 53
The Aerogel
Silica aerogel is a
very low-density
glass that provides
just the right index
of refraction to
produce Cerenkov
light.
In the momentum range
of interest pions emit
Cerenkov light while
the somewhat heavier
kaons don’t.
November 19, 1999 CP Violation in B Meson Decays 54
The Cesium Iodide
Detector
Upper management looks on
anxiously while $35M worth
of salt is craned into place.
Each scintillator crystal is read
by two photodiodes.
November 19, 1999 CP Violation in B Meson Decays 55
K_L Muon Detector
The muon detectors,
which are the largest, are
made from standard
soda-lime float glass
(window glass).
An endcap module is
installed.
November 19, 1999 CP Violation in B Meson Decays 56
Data Acquisition
The tip of
the
electronic
iceberg.
November 19, 1999 CP Violation in B Meson Decays 57
Key Belle Milestones
• Early 1990’s - Japanese groups begin working.
• January 1994 - Collaboration forms.
• April 1995 - TDR Submitted.
…lots of work by lots of people in lots of places...
• Dec 18, 1998 - Belle detector completed (including SVD)
• Jan 26, 1999 - First cosmic ray with full detector.
• May 1, 1999 - Belle rolled into place.
• June 1, 1999 - First hadronic event!!!!!
• June 1999 About 1200 hadron events obtained before
vacuum pipe mishap.
• July 1999 More data (30K events) and lots learned.
November 19, 1999 CP Violation in B Meson Decays 58
June 1, 1999: Our First Hadronic Event
November 19, 1999 CP Violation in B Meson Decays 59
More Fun: SVD Included
November 19, 1999 CP Violation in B Meson Decays 60
First J/y Candidate
• J/yee
– M(ee) = 3.1 GeV
November 19, 1999 CP Violation in B Meson Decays 61
SVD Performance
November 19, 1999 CP Violation in B Meson Decays 62
SVD Performance
November 19, 1999 CP Violation in B Meson Decays 63
CsI EM Calorimeter Performance
0 Reconstruction
E 50 MeV
Reconstruction
November 19, 1999 CP Violation in B Meson Decays 64
Physics from the First Runs: Energy Scan
November 19, 1999 CP Violation in B Meson Decays 65
Lepton-pair Spectrum
November 19, 1999 CP Violation in B Meson Decays 66
B Mixing
November 19, 1999 CP Violation in B Meson Decays 67
Conclusions & Outlook
• We will soon have new measurements of CP
violation.
• The experiments are highly complex and large in
scale and can only be carried out by large
scientific and technical teams.
• The fun of data analysis is now beginning.
November 19, 1999 CP Violation in B Meson Decays 68