Cracking the Unitarity Triangle — A Quest in B Physics —

Cracking the Unitarity Triangle— A Quest in B Physics —

Masahiro MoriiHarvard University

Tohoku University Physics Colloquium

21 November 2005

21 November 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 Factories Results 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


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


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 ↔


Three generations We’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


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

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


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

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


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

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


Structure of the CKM matrix The 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)


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


CP symmetry

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 it

is a mirror image of our Universe To create a matter-dominant Universe,

C charge conjugation particle anti-particle

P parity x x, y y, z z

CP symmetry must be broken

e e

One of the three necessary conditions (Sakharov 1967)


CP violation CP violation was discovered in KL decays

KL decays into either 2 or 3 pions

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

Christenson et al. (1964)

(33%)LK

(0.3%)LK 1CP

1CP

Final states have different CP eigenvalues

Nothing else?


CP violation and New Physics

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 < 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 existNew sources of CP violation almost certainly exist

Are there additional (non-CKM) sources of CP violation?


The Unitarity Triangle V†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


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


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

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


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

0B

0B

Ignoring the lifetime

0B

0BfCP

0B

t = 0 t = t

time

0pure B 0pure B 0pure B


The Golden Mode Consider

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


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

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


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

Produce ~108 B/year by colliding e+ and e− with ECM = 10.58 GeV

(4 )e e S BB (4 )e e S BB


SLAC PEP-II site

BABAR

PEP-II

I-280

Linac


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


Detectors: BABAR and Belle Layers of particle detectors surround the collision point

We reconstruct how the B mesons decayed from their decay products

BABARBABAR BelleBelle


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


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


Three angles of the UT CP 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

12.68.198.6

1.31.221.7

151263


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 as the reference

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


Angle from penguin decays The 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


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 Most 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


Strange hints Measured CP asymmetries

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 (penguin) sin 2 (tree)

Need more data!

Penguin decays

Penguin modes

Golden mode


The sides To measure the lengths of the

two sides, we must measure|Vub| ≈ 0.004 and |Vtd| ≈ 0.008 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


|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


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!


Figuring out what we see Cut 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


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 s and b cv decays Theory error has shrunk from ~15% to ~5% in the process

Fully reconstructedB hadrons

v

X

BABARpreliminaryb cv

background


Status of |Vub|

|Vub| determined to 7.6% c.f. sin2is 4.7%

|Vub| world average as of Summer 2005

Measures the length of the left side of the UT


|Vtd| – the right side

Why can’t 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

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


Radiative penguin decays Look for a different loop that does b t d

Radiative-penguin decays

New results from the B Factories:

Translated to

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

(B )

BABAR (0.6 0.3) 106

Belle (1.3 0.3) 106

Average (1.0 0.2) 106

0.18 0.03td tsV V 0.18 0.03td tsV V


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!

*

( )

( )

B

B K


The UT today

Angles from CP asymmetriesSides + KL decaysCombined


The UT today The B Factories have dramatically

improved our knowledge of theCKM 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 hidingquite skillfully


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 Xs, Xs, D0 mixing and rare D decays lepton-number violating decays

Precision measurements at the B Factories place strong constraints on

the nature of New Physicsm

H (

GeV

)

tan

Allowed byBABAR data

B b s

Two Higgs doublet model


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

Documents

Cracking the Unitarity Triangle — A Quest in B Physics —