Vivek Sharma

University of California at San Diego

http://vsharma.ucsd.edu/marialaach05.pdf

CP Violation in B Decays

CP Violation in B Decays

2

Outline Of The Four Lectures

• Brief history of discrete symm. violation & KM Conjecture• CKM Matrix, Unitarity triangle & the special place of B mesons• Primer on B physics (to understand CPV discussion better)• Quantum entanglement in (4S)B0 B0 Need for Asymmetric

energy colliders : PEP-II and KEK-B• Critical features of BaBar & Belle for CPV measurements• Three types of CPV in B system : SM predictions• Techniques in time-dependent CPV measurements• Observables and hot new experimental results on CP violation • Synthesis and summary of current experimental observations • Future experimental directions

Lectures intended for beginning graduate students in Particle and Particle Astrophysics kept simple and intuitive

3

Suggested Reading• BaBar Physics Book available online at

– http://www.slac.stanford.edu/pubs/slacreports/slac-r-504.html• J. Silva’s lecture notes on CP Violation from Prague summer school 2004:

– hep-ph/0410351 • Z. Ligeti’s SLAC Summer School Lectures 2002

– hep-ph/0302031• Review articles on CP Violation, CKM Matrix and B Mixing in the Particle

Data Book – http://pdg.lbl.gov/

• B Physics at the Tevatron: Run II and Beyond :– hep-ph/0201071 Discovery Potential of a Super B factory:– http://www.slac.stanford.edu/pubs/slacreports/slac-r-709.html

• LHC-b “reoptimized” Detector TDR :– http://lhcb.web.cern.ch/lhcb/TDR/reoptdr.pdf

• Textbooks: – CP Violation: Branco,Lavoura,Silva; Published by Clarendon Press– CP Violation by Bigi & Sanda; Published by Cambridge Press– Heavy Quark Physics: Manohar & Wise; Published by Cambridge

4

Outline of Lectures: Lecture 1• Brief History of Symmetry violations

– Thru the looking glass With Alice :P, C and CP mirrors

– CP Violation in Kaon system

– The KM conjecture and the rise of three quark generations

• The CKM Matrix and Unitarity Triangles

– “The” Unitarity Triangle in B system

• Three surprising discoveries that made B physics exciting

• Prolific environments of b flavored hadrons

• A quick primer on general B hadron properties (to understand the CP discussion better)

• CP Violation as a Quantum Phenomenon

• B0 Meson time evolution and the special case of (4S)B0 B0

• The need for an Asymmetric energy collider

5

Three Important Discrete Symmetries That Usually Work

• Parity, P

– Parity reflects a system through the origin. Convertsright-handed coordinate systems to left-handed ones.

– Vectors change sign but axial vectors remain unchanged

• x x , L L

• Charge Conjugation, C

– Charge conjugation turns a particle into its anti-particle

• e e K K

• Time Reversal, T

– Changes, for example, the direction of motion of particles

• t t

Gravitational, E&M and Strong Interaction indistinguishable under these transformations : but NOT Weak Interaction

6

A Shocker : Weak Interaction Violates Parity !

C.S.Wu

Observation of a spatial asymmetry in

the -decay electrons from 60Co 60Ni e1956 • Cold 60Co inside a Solenoidal B Field

• 60Co nuclei spin aligned with B field direction

•60Co undergoes decay …….electron emitted• Measure electron intensity w.r.t B field dir.

• Result:Electrons preferentially emitted opposite spin dir. ev

1 - cos c

I( ) = B

Ve

The fore-aft asymmetry of intensity Weak interaction violated Parity

7

Alice’s New Adventures Through The “Looking Glass” !

See Wigner, Adair ’s Articles (~1965) in Scientific American

Real World Mirror World

8

Weak Interaction and a Journey Through The Symmetry Mirror Worlds With Alice !

Part I : Spatial Inversion as in a Regular Mirror

e-

e-

“ P ” Mirror World

B

e-

e-

Alice’s World

B

Alice CAN differentiate between her world and the Parity Mirror World

9

Alice Can differentiate between her world and the Charge Mirror World !

e-

e-

Alice’s World

e+

e+

“ C ” Mirror World

The C Mirror changes particles to anti-particles and Vice-Verca

But maintains the orientation of objects it reflects

Anti-Co Nuclei have Magnetic properties Opposite of Co

So they are aligned opposite B field direction

Anti-Co Nuclei emit positrons in direction of the Nuclear Spin

10

e-

e-

Alice’s World

e+

e+

“ CP ” Mirror World

Alice Cannot differentiate between her world and the CP-Mirror World !

The CP Mirror changes particles to anti-particles and Vice-Versa, flips the orientation of objects it reflects

Anti-Co Nuclei emit positrons in direction of the Nuclear Spin

11

Paradise Lost, Paradise Regained ?

• While P & C Mirror Symmetry are each shattered

• The combined CP Mirror seemed OK (1957)

• Is CP the Universal Mirror ?

• Will Alice be trapped forever in the Mirror World ?

Luckily for Alice, the totally unexpected happened !

!

12

CP Violation in Kaon System !• CP conservation implies

CP 1

CP 1

CP violation in KL decay observed in 1964

0.2% ofthe time!

Theory in Turmoil ? How to explain this tiny CP Violation?Many models proposed …most fell by the way of experiments but One conjecture survived and grew in stature !

13

What The Discoverers Of Kaon CP Violation Said

1980 Nobel Lecture

These Lectures Examine CP Violation in the Context of

the Standard Model developed since then

14

What Was Known about Quarks and Leptons Then

?u

d s

Three Quarks for Muster Mark !…Joyce

e

e

Cabibbo Angle(Flavor mixing

c'

cd cos sd n si flavor Weak state

flavor Mass eigenstate

15

The Kobayashi-Maskawa Paradigm for CP Violation

• Proposed a “daring” explanation for CP violation in K decay:

• CP violation appears in the charged current weak interaction of quarks

• There is a single source of CP Violation Complex Quantum

Mechanical Phase in inter-quark coupling matrix

• Need at least 3 Generation of Quarks (then not known) to facilitate

this

• CP is NOT an approximate symmetry, it’s MAXIMALLY violated !

1972 Two Young Postdocs at that time !

16

Since then, Experiments ShowThree generations : no more, no less !

Generations of Quarks and Leptons Circa 2002

c tu

bd s

e

e

Just Enough to Make CP Violation Possible

17

Number of Light Neutrino Families: LEP@CERN

Width of the Z resonance

18

The Weak Interaction Couplings of Quarks

• The coupling strength at the weak vertexis given by gVij

– g is the universal Fermi weak coupling

– Vij depends on which quarks are

involved

– For leptons, the coupling is just g• For 3 generations, the Vij can be written as

a 3x3 complex unitary matrix (CKM)

• View this matrix as rotating the quark

states from a basis in which they are mass

eigenstates to one in which they are Weak

eigenstates

ud us ub

CKM cd cs cb

td ts tb

V V V

V V V

V V V

V

bW

cgVcb

ud us ub

cd cs cb

td ts tb

d V V V d

s V V V s

b V V V b

19

CP Violation In SM With 3 Generations

• The CKM matrix 33 complex unitary matrix

• Requires 4 independent parameters to describe it:

– 3 real numbers & 1 complex non-trivial phase

• The existence of the complex coupling (phase) gives rise to CP violation

– If only 2 quark generations 22 matrix is all real No CP violation

• Some Expectations:

– CP violation is the result of interference between different decay amplitudes involving weak phase

– CP violation is “built” into the Standard Model with 3 generations or more …or so Kobayashi-Maskawa wondered

20

CP Violation In SM With 3 Generations

• The CKM matrix 33 complex unitary matrix

• Requires 4 independent parameters to describe it:

– 3 real numbers & 1 complex non-trivial phase

• The existence of the complex coupling (phase) gives rise to CP violation

– If only 2 quark generations 22 matrix is all real No CP violation

• Some Expectations:

– CP violation is the result of interference between different decay amplitudes involving weak phase

– CP violation is “built” into the Standard Model with 3 generations or more …or so Kobayashi-Maskawa wondered

qW -

pgVqp

qW +

pgV*qp

quark decay

anti-quark decay

| | | | | |

| | | | | |

| | | | | |

Vud us

CKM cd cs c

tbi

b

s

i

te

V V

V V V

V

e

V

ub

td

V

V

Complex phases CP violation

21

Measurement of CKM Element Magnitudes

( 0.05%) ( 0.4%) ( 13%)

( 5.4%) ( 11.0%) ( 3.6%)

0.9738 0.2196 0.004

.224 0.97 0.041

0.01 0.0

( 100%) ( 17.0%) ( 29%

47 0.94

)

V V Vud us ub

V V Vcd cs cb

V V Vtd ts tb

p n

e-

eK

e-

b u

e-

b c

e-

D K

l+

t b

l+

l

c

d

22

A Convenient Parameterization of CKM Matrix Wolfenstein, saw interesting pattern with 4 numbers

2

2 2

0.22

0.80

0.35

tan arg ?

us

cb

ub cb

ub

V

A V

V V

V

4

23

2

2 2

31 / 2

1

( )

( )

(1

/ 2

1)

VCKM

A i

O

A

A

Ai

β

-i

-i

γ1 1

1 1 1

1 1

e

e

u

d

t

c

bs

Relative magnitudes

ud us ub

cd cs cb

td ts tb

V V V

V V V

V V V

VCKM

The four parameters are given by CPV phases in this parametrization

23

The (Many) Unitarity TrianglesUnitarity condition of CKM Matrix orthonormality of rows & columns

various relationship between elements, three of them are interesting for understanding SM predictions for CP violation

Each relation requires sum of three complex quantities to vanish

can be represented in the complex plane as a triangle

known as Unitarity Triangles

With the knowledge of |Vij| magnitudes, its instructive to draw the triangles

* * ;( , , ) ( , , )

jk ikV V V Vij ijik kj

i u c t i d s b

24

Three Unitarity Triangles drawn to Common scale

Experimentally hard to measure small numbers easier to measure larger numbers as in (c)

ds

sb

db

One side is much shorter than the othertwo triangle collapses on a line

All sides of comparable length (3) All angles are large

25

“The” CKM Unitarity Triangle In B Decays

0ud ub cd cb td tbV V V V V V

Rescaling, aligning

2

1

3

*arg ,

*

*arg ,

*

*arg

*

V Vtd tb

V Vud ub

V Vcd cb

V Vtd tb

V Vud ub

V Vcd cb

Angles of Unitarity Triangle

All lengths involve b decays Large CP Asymmetries predicted , UT angles

26

Is CKM Matrix the (only) Source of CP Violation?

• Observed CP violation in Kaon decays is consistent with the KM conjecture but this could have been a fluke (post-prediction) !

– needs new& many rigorous experimental tests

• KM paradigm quantitatively predicts large CP violating asymmetries in the decays of the B meson system

• In addition, New Physics sources of CP violating phases which can substantially alter the CPV asymmetries in B decays– B Mesons provide a good laboratory for searches for NP– emphasis on experimental observables which have “clean” theoretical interpretation

Large B mass helps !

27

1980s: When b quark Became Special !

With CPV measurements at B factories currently in full swing, It is perhaps useful to look back at the three surprising experimental results which have paved the way towards measurement of CP Violation in B meson decays

1. B Lifetime (1983)

2. B0 Oscillation (1986)

3. bu Transitions (1988)

28

The Large Lifetime of B Mesons

• 1983: MAC and MARKII detectors at SLAC

• Measure signed impact parameter of leptons in semileptonic b hadron decay

• Impact Parameter Resolution

– MAC ~ 600 micron

– MARK II ~ 200 micron

• Results

– MAC : 1.8 +- 0.6 +- 0.4 ps

– MARKII: 1.2+.45-.36+-.3ps

• Confirmed by TASSO & JADE @PETRA

• Subsequently measured very precisely at LEP@CERN

decay

B lifetime 1.6ps !!

29

DESY’s discovery: The Large B0B0 Oscillation Rate

• Mixing rate depends on Top quark mass

• Inspired by PEP/PETRA non-observation of the top quark, many theorist assured as that “Top could not be heavier than 40-50 GeV..conservatively speaking” !!

• Definitive results from ARGUS(1987) showed B mixing to be large, if we could calculate better, could have shown that top quark is as heavy as it really is !

0 0d d

0 0 0 0d d d d

P (B B )

P (B B ) P(B B )

0.17 0.05 !!

d

ARGUS

30

Vub: The Magnitude of bu Transition

• Must have Vub0 for SM with 3 generations to accommodate CP

Violation seen in K0 decays and expect CP violation in B decays

• The magnitude has too be just-right for measurable CP asymmetries in B decays

• No theory could predict the magnitude of bu transition

• Observed excess of leptops beyond bcl kinematic endpoint Vub0.

• Thus, stage was set for probing CP violation in B decays all over the world

| / |~0.08 0.02V Vub cb

bu lbcl

31

CPV Studies in B decays is a Worldwide effort

ATLASCLEO

BBAABBARAR

BELLE

199919991999

2001

2007

2002

Primary GoalPrimary GoalPrimary GoalPrimary Goal

Precision measurements of charged weak interactions

as a test of the CKM sector of the Standard Model and aprobe of the origin of the

CP violation

2002

An Express B Meson Primer

Where are the b hadrons produced copiously ?

What does the Environment Look Like ?

33

Where the B’s are : In Electron-Positron Collisions

34

(4S)

Ebeam= 5.29 GeV

e+ e-

Ebeam= 5.29 GeV

e

e

b

b

(4 )S

0B0B

Enough energy to barely produce 2 B mesons, nothing else!B Mesons produced with ~ 300 MeV momentumMoving very slowly, don’t travel much before decay

The Upsilon resonances as seen in e+ e- Collisions

35

The Magnificent Z Resonance

All types of B hadrons produced in Z bb hadronization

Average B momentum ~ 35 GeV ()B 7 (highly relativistic)

LEP/SLD Program ended in ‘95, made important contributions to b physics

36

In pp Collisions at the Tevatron (& LHC soon !)

Tevatron

37

Where the B’s are: In pp collisionsAt the Tevatron

38

Advantages And Disadvantages of (4S) Machines• Advantages:

– Low interaction rate (~102 Hz) , possible to trigger on, and record, essentially every BB event

– High Signal/Background

– Events clean to interpret, mean multiplicity~11

– One B and one B produced per event (and nothing else)

– Clean environment Possible to reconstruct 0 & capability to make measurements in many different channels

– Happening now !

• Disadvantages:

– Low cross-section, produce ~108 BB /year (107 seconds)

– Only Bd and Bu mesons produced, Not enough energy to make BsBs mesons or b baryons

/ 0.22hadronBB

39

• Advantages:

– HUGE bb cross-section ! b=100b (Tevatron), x5 (LHC)

– Bs mesons produced (1/3 of Bd rate)

– Long B decay distance (~mm) before decay

– Very energetic particle in the final state

• Disadvantages:

– Very high multiplicity event

– poor S/N0.002 (Tevatron)--0.006 (LHC)

– Difficulty in triggering and recording (need lifetime trigger)

– High interaction rate (~20,000,000 Hz!)

– Possible asymmetries in production rates of B Vs B– Tevatron luminosity finally improving, LHC experiments begin >

2008 (future)

Advantages And Disadvantages of Hadron Colliders

40

Characteristic Parameters of (4S) Machines & Hadron Colliders

Ultimately both environments are complementary and essential for complete understanding of the CPV

Phenomenon

Because (4S) Machines are currently producing exciting results at a furious pace, I will concentrate on that environment during these lectures and comment on Interesting measurements from Hadron machines at the

end

B Meson Properties

(To follow the CP Violation Discussion Better)

42

Some Lowest B Hadron Masses and Lifetimes

Particle, I(JP) Mass ( in MeV/c2) Lifetime =1/ (in10-12 s)

B0d =(bd) , I(JP)=½ (0-) 5279.4 0.5 1.536 0.014 & (c

=460m)

B- = (bu), I(JP)=½ (0-) 5279.0 0.5 1.671 0.018 & (c =501m)

B0s =(bs), I(JP)=0(0-) 5369.6 2.4 1.461 0.057 & (c

=438m)

b = (bud), I(JP)=0(1/2+) 5624.0 9.0 1.229 0.080 & (c =368m)

43

Mass Measurement: Reconstruct All p in Decay

44

ps Lifetime Measurement is a Distance Measurement

Measure distance between production and decayMeasure B momentumFit proper time distribution to exponetial detector resolution

c 2000 mmeasurable by silicon detectors

proper time distribution

A Z0 bb event

Many Ways That a B Mesons Transform or Decay

(Introduction to the Jargon relevant for CPV discussion)

46

B0 B0 Oscillation

Start with a pure beam of B0 mesons

a B0 component automagically develops with time

B00B

Pro

babi

lity

Oscillation rate dominated by tt(off-shell) intermediate states

Scope for heavy New Physics particles to contribute additionally (e.g. SUSY)

QM Two-state system

time-dependent oscillation

47

W

Annihilation W-Exchange

“Tree Level” Diagrams For B Hadron Decays

Spectator

W-

Semileptonic

W-

Color Suppressed

W-

48

Radiative Penguin EW Penguin

Penguin Decays of B Mesons

Gluonic Penguin

49

Penguins Observed in B Decay !! (1993)

CLEOBK*

Important window to New Physics

50

Penguins In B Decays?

51

Summary of b-quark Decay

u c t

d s b

52

CP Violation • CP violation can be observed by comparing decay rates of

particles and antiparticles

• The difference in decay rates arises from a different interference term for the matter vs. antimatter process. Analogy to double-slit experiment:

1A

2A

1A

2A

CP Viola io( t) n) ( a f a f

source1A

2A

Classical double-slit experiment:Relative phase variation due to different path lengths: interference pattern in space

53

CP Violation Is a Quantum Phenomenon

• CPV is due to Quantum interference between > two amplitudes

• Phases of QM amplitudes is the key • Need to consider two types of phases

– CP-conserving phases: don’t change sign under CP (Sometimes called strong phases since they can arise from strong, final-state interactions)

– CP-violating phases: these do change sign under CP transformation

(originate in the Weak interaction sector)

54

How can CP asymmetries arise ?

• Suppose a decay can occur through two different processes, with amplitudes A1 and A2.

• First, consider the case in which there is a (relative) CP-violating phase between A1 and A2 only. 1 2A A A

1 2A A A

1 1A A2A

2A

2

2

2

1 2

1 2

i

i

A A a e

A A a e

No CP asymmetry!(Decay rate is different from what is would be without the phase)

55

How can CP asymmetries arise ?

• Next, introduce a relative CP-conserving phase in addition to the relative CP-violating phase

• Now have a CP asymmetry1 2A A A

1 2A A A

1 1A A

2A

2A2

2 2

2 2

( )1 2

( )1 2

i

i

A A a e

A A a e

22

A A

56

Definition of CP Asymmetry

To extract the CP-violating phase from an observed CP asymmetry, we need to know the value of the CP-conserving phase difference

2 2

1 2 1 2 1 22 2 22

1 2 1 2 1 2 1 2

2 sin( )sin( )

cos( )cos( )

A A A AAsymmetry

A A A AA A

B system: extraordinary laboratory for quantum interference experiments: many final states, multiple “paths” Lots of channels for CP Violation

End of Lecture 1

Tomorrow:

QM of neutral B Mesons & EPR at (4S)

CPV Observables and requirements

Asymmetric Energy Colliders and Detectors–requirements–performance

58

A Convenient Parameterization of CKM Matrix • Wolfenstein, saw a pattern with 4 numbers

• The four parameters are given by: and the CPV phases in this parametrization

2

2 2

0.22

0.80

0.35

tan arg ?

us

cb

ub cb

ub

V

A V

V V

V

β

-i

-i

γ1 1

1 1 1

1 1

e

e

2

2 2

3

3 2

1 / 2 ( )

(1 )

1 / 2

1CKM A

A i

A i A

Vu

d

t

c

bs

Relative magnitudes