Cracking the Unitarity Triangle

1
Cracking the Unitarity Triangle A Quest in B
Physics

• Masahiro Morii
• Harvard University
• Tohoku University Physics Colloquium
• 21 November 2005

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 Factories
• Results from BABAR and Belle
• Angles a, b, g from CP asymmetries
• Vub from semileptonic decays
• Vtd from radiative-penguin decays
• Current status and outlook

The Unitarity Triangle
a
g
b
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
3
What are we made of?
u
u
d

• 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

strong EM weak
u Yes Yes Yes
d Yes Yes Yes
e- No Yes Yes
ne No No Yes
4
Simplified Standard Model

• Strong force is transmitted by the gluon
• Electromagnetic force by the photon
• Weak force by the W? and Z0 bosons

g
g
u
d
u
d
g
u
u
W
W-
e-
u
ne
d
5
Three generations

• Weve 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 EM weak
g g W
g g Z 0
leptons quarks
e- u
ne d
m- c
nm s
It turns out there are two extra copies of
particles
t - t
nt b
6
A spectrum of masses

• The 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

The origin of mass is one of the most urgent
questions in particle physics today
Q ?1 0 2/3 ?1/3
7
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
• Suppose W? connects u? ? d?, c? ? s?, t? ? b?
• Thats a poor choice of basis vectors

M and N are arbitrary3?3 unitary matrices
Weak interactions between u, c, t, and d, s, b
are mixed by matrix V
8
Turn the masses back on

• Masses uniquely define the u, c, t, and d, s, b
  states
• We dont know what creates masses? We dont know
  how the eigenstates are chosen? M and N are
  arbitrary
• V is an arbitrary 3?3 unitary matrix
• The Standard Model does not predict V
• ... for the same reason it does not predict the
  particle masses

or CKM for short
Cabibbo-Kobayashi-Maskawa matrix
9
Structure of the CKM matrix

• The CKM matrix looks like this ?
• Its 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

There seems to be a structureseparating the
generations
This phase causes CP violation
Kobayashi and Maskawa (1973)
10
What are we made of, again?

• Dirac predicted existence of anti-matter in 1928
• Positron ( anti-electron) discovered 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
11
CP symmetry
C charge conjugation particle ? anti-particle
P parity x ? ?x, y ? ?y, z ? ?z

• C and P symmetries are broken in weak
  interactions
• Lee, Yang (1956), Wu et al. (1957), Garwin,
  Lederman, Weinrich (1957)
• Combined CP symmetry seemed to be good
• Anti-Universe can exist as long as itis a mirror
  image of our Universe
• To create a matter-dominant Universe,

e?
e
CP symmetry must be broken
One of the three necessary conditions (Sakharov
1967)
12
CP violation

• CP violation was discovered in KL decays
• KL decays into either 2 or 3 pions
• Couldnt 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

Christenson et al. (1964)
Final states have different CP eigenvalues
Nothing else?
13
CP violation and New Physics
Are there additional (non-CKM) sources of CP
violation?

• The CKM mechanism fails to explain the amount of
  matter-antimatter 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 lt 1 TeV/c2
• Almost all theories of New Physics introduce new
  sources of CP violation (e.g. 43 of them in
  supersymmetry)
• Precision studies of the CKM matrix may uncover
  them

New sources of CP violation almost certainly exist
14
The Unitarity Triangle

• VV 1 gives us
• Experiments measure the angles a, b, g and the
  sides

This one has the 3 terms in the same order of
magnitude
A triangle on the complex plane
15
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
Factoriesthat produce and study B mesonsin
quantity
16
Anatomy of the B0 system

• The B0 meson is a bound state of b and d quarks
• They turn into each other spontaneously
• This is called the B0-B0 mixing

Particle charge mass lifetime
0 5.28 GeV/c2 1.5 ps
0 5.28 GeV/c2 1.5 ps
Indistinguishable from the outside
17
Time-dependent Interference

• Starting from a pure B0? state, the wave
  function evolves as
• 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

Ignoring the lifetime
time
fCP
t 0
t t
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The Golden Mode

• Consider
• Phase difference is

Direct path
Mixing path
19
Time-dependent CP Asymmetry

• Quantum interference between the direct and mixed
  paths makes and
  different
• Define 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

Solution Asymmetric B Factory
20
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
21
SLAC PEP-II site
Linac
I-280
BABAR
PEP-II
22
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

Moving in the lab
U(4S)
e
e-
23
Detectors BABAR and Belle

• Layers of particle detectors surround the
  collision point
• We reconstruct how the B mesons decayed from
  their decay products

BABAR
Belle
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J/y KS event
A B0 ? J/y KS candidate (r-f view)
p -
p -
m
p
Pions from
p
K-
p
Muons from
m-
Red tracks are from the other B,which was
probably B0
25
CPV in the Golden Channel

• BABAR measured in B0 ? J/y KS and related decays

227 million events
J/y KS
J/y KL
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Three angles of the UT

• CP violation measurements at the B Factories give

Angle (degree) Angle (degree) Decay channels
a B0 ? pp, rp, rr
b B0 ? (cc)K0
g B0 ? D()K()
Precision of b is 10 times better than a and g
27
CKM precision tests

• Measured angles agree with what we knew before
  1999
• 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

The CKM mechanism is responsible for the bulk of
the CP violation in the quark sector

• Next steps
• Measure b with different methods that have
  different sensitivity to New Physics
• Measure the sides

a
g
b
28
Angle b from penguin decays

• The Golden mode is
• Consider a different decaye.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 b in e.g.B0 ? f KS

Tree
Penguin
top is the main contributor
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New Physics in the loop

• The loop is entirely virtual
• W and t are much heavier than b
• It could be made of heavier particlesunknown to
  us
• Most New Physics scenarios predictmultiple 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

Comparing penguins with trees is a sensitive
probe for New Physics
30
Strange hints

• Measured CP asymmetries show a suspicious trend
• Naive average of penguins give sin2b 0.50 ?
  0.06
• Marginal consistency from the Golden Mode(2.6s
  deviation)

Penguin decays
Penguin modes
Golden mode
Need more data!
31
The sides

• To measure the lengths of thetwo sides, we must
  measureVub 0.004 and Vtd 0.008
• The smallest elements not easy!

a
g
b
Vub

• Main difficulty Controlling theoretical errors
  due to hadronic physics
• Collaboration between theory and experiment plays
  key role

Vtd
32
Vub the left side

• Vub determines the rate of the b ? u transition
• Measure the rate of b ? u?v decay (? e or m)
• The problem b ? c?v decay is much faster
• Can we overcome a 50? larger background?

33
Detecting b ? ulv

• Use mu ltlt mc ? difference in kinematics
• Signal events have smaller mX ? Larger E? and q2

E? lepton energy
q2 lepton-neutrino mass squared
u quark turns into 1 or more hardons
mX hadron system mass
Not to scale!
34
Figuring out what we see

• Cut away b ? c?v ? Lose a part of the b ? u?v
  signal
• We measure
• Predicting fC requires the knowledge of the b
  quarks motion inside the B meson ? Theoretical
  uncertainty
• Theoretical error on Vub was 15 in 2003
• Summer 2005
• What happened in the last 2 years?

Cut-dependentconstant predictedby theory
Total b ? u?v rate
Fraction of the signal that pass the cut
HFAG EPS 2005 average
35
Progress since 2003

• Experiments 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 ? sg and b ? c?v decays
• Theory error has shrunk from 15 to 5 in the
  process

Fully reconstructedB ? hadrons
BABARpreliminary
b ? c?vbackground
v
X
?
36
Status of Vub
Vub world average as of Summer 2005

• Vub determined to ?7.6
• c.f. sin2b is ?4.7

Measures the length of the left side of the UT
37
Vtd the right side

• Why cant we just measure the t ? d decay rates?
• Top quarks are hard to make
• Must use loop processes where b ? t ? d
• Best known example mixing combined
  with mixing
• Dmd (0.509 ? 0.004) ps-1
• mixing is being searched for at
  Tevatron (and LEPSLD)
• Dms gt 14.5 ps-1 at 95 C.L. (Lepton-Photon 2005)

B0 oscillation frequency
Bs oscillation frequency
38
Radiative penguin decays

• Look for a different loop that does b ? t ? d
• Radiative-penguin decays
• New results from the B Factories
• Translated to ?

B(B ? rg)
BABAR (0.6 ? 0.3) ? 10?6
Belle (1.3 ? 0.3) ? 10?6
Average (1.0 ? 0.2) ? 10?6
39
Impact on the UT

• We can now constrain the right side of the UT
• Comparable sensitivities to Vtd
• Promising alternative/crosscheck to the B0/Bs
  mixing method

B0/Bs mixing
Need more data!
40
The UT today
Angles from CP asymmetries
Sides KL decays
Combined
41
The UT today

• The B Factories have dramaticallyimproved our
  knowledge of theCKM matrix
• All angles and sides measuredwith multiple
  techniques
• New era of precision CKMmeasurements in search
  of NP
• The Standard Model is alive
• Some deviations observed ?require further
  attention

New Physics seems to be hidingquite skillfully
42
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 addition to the UT, we explore
• rare B decays into Xsg, Xs??-, tn
• 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
43
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 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