cracking the unitarity triangle - harvard university · slac pep-ii kekb produce ~108 b/year by...

Cracking the Unitarity Triangle— A Quest in B Physics —

Masahiro MoriiHarvard University

Ohio State University Physics Colloquium9 May 2006

9 May 2006 M. Morii, Harvard 2

Outlinen Introduction to the Unitarity Triangle

n The Standard Model, the CKM matrix, and CP violationn CP asymmetry in the B0 meson decays

n Experiments at the B Factoriesn Results from BABAR and Belle

n Angles a, b, g from CP asymmetriesn |Vub| from semileptonic decaysn |Vtd| from B0 and Bs mixing

n Current status and outlook

g

a

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

The Unitarity Triangle


What are we made of?

n Ordinary matter is made of electrons and up/down quarksn Add the neutrino and we have a complete “kit”n We also know how they interact with “forces”

quarksleptons

e

e ud0Q =

1Q =

13Q =

23Q = +

strong E&M weaku Yes Yes Yesd Yes Yes Yese− No Yes Yesne No No Yes

u

u d

e


Simplified Standard Modeln Strong force is transmitted by the gluon

n Electromagnetic force by the photon

n Weak force by the W± and Z0 bosons

uu

g

dd

g

uu

g

dd

g

e−g

e−

uu

Z0

dd

Z0 Z0

e−e−

Z0

nene

du

W+

nee−

W−Note W± can “convert”

u↔ d, e↔ n


Three generationsn We’ve got a neat, clean, predictive theory of “everything”

n Why 3 sets (= generations) of particles?n How do they differ?n How do they interact with each other?

strong E&M weak

g gW±

Z 0

µ− cnµ s

t − tnt b

leptons quarkse− une d

1st generation

2nd generation

3rd generation

It turns out there are two “extra”

copies of particles


A spectrum of massesn The generations differ only by the masses

ç The structure is mysteriousn The Standard Model has no explanation

for the mass spectrumn All 12 masses are inputs to the theoryn The masses come from the interaction

with the Higgs particlen ... whose nature is unknownn 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

Parti

cle

mas

s (eV

/c2 )

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 massesn Nothing would distinguish u from c from t

n We could make a mixture of the wavefunctions and pretend it represents a physical particle

n Suppose W± connects u¢↔ d¢, c¢↔ s¢, t¢↔ b¢

n That’s a poor choice of basis vectors

u uc ct t

=Md ds sb b

= N M and N are arbitrary3´3 unitary matrices

1 1 1

u u d d dc c s s st 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 onn Masses uniquely define the u, c, t, and d, s, b states

n We don’t know what creates massesè We don’t know how the eigenstates are chosenè M and N are arbitrary

n V is an arbitrary 3´3 unitary matrix

n The Standard Model does not predict Vn ... 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 dc s V V V st b V V V b

±=V

Cabibbo-Kobayashi-Maskawa matrix or CKM for short


Structure of the CKM matrixn The CKM matrix looks like this è

n It’s not completely diagonaln Off-diagonal components are small

n Transition across generations isallowed but suppressed

n Matrix elements can be complexn Unitarity leaves 4 free parameters,

one of which is a complex phase

0.974 0.226 0.0040.226 0.973 0.0420.008 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?n Dirac predicted existence of anti-matter in 1928

n Positron (= anti-electron) discovered in 1932

n Our Universe contains (almost) only matter

n 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 havethe asymmetry between positive and negative electricity in thelaws of nature (it does not satisfy me to shift the empiricallyestablished asymmetry to one of the initial state)

Pauli, 1933 letter to Heisenberg


CP symmetry

n C and P symmetries are broken in weak interactionsn Lee, Yang (1956), Wu et al. (1957), Garwin, Lederman, Weinrich (1957)

n Combined CP symmetry seemed to be good n Anti-Universe can exist as long as it

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

C charge conjugation particle « anti-particleP parity x ® -x, y ® -y, z ® -z

CP symmetry must be broken

e- e+

One of the three necessary conditions (Sakharov 1967)


CP violationn CP violation was discovered in KL decays

n KL decays into either 2 or 3 pions

n Couldn’t happen if CP was a good symmetry of Natureè Laws of physics apply differently to matter and antimatter

n The complex phase in the CKM matrix causes CP violationn 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

n The CKM mechanism fails to explain the amount of matter-antimatter imbalance in the Universen ... by several orders of magnitude

n New Physics beyond the SM is expected at 1-10 TeV scalen e.g. to keep the Higgs mass < 1 TeV/c2

n Almost all theories of New Physics introduce new sources of CPviolation (e.g. 43 of them in supersymmetry)

n Precision studies of the CKM matrix may uncover them

New sources of CP violation almost certainly exist

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


The Unitarity Trianglen V†V = 1 gives us

n Experiments measure the angles a, b, g 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 VV V V V V VV 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 VV V

ud ub

cd cb

V VV V

0

*ud ubV V

*td tbV V

*cd cbV V


The UT 1998 à 2006

95% CL

The improvements are due largely to the B Factoriesthat produce and study Bmesons

in quantity

n We did know something about how the UT looked in the last centuryn By 2005, the allowed region for the apex has shrunk to about 1/10

in area


Anatomy of the B0 systemn The B0 meson is a bound state of b and d quarks

n They turn into each other spontaneously

n This is called the B0-B0 mixing

0 ( )B bd=0 ( )B bd=

Particle charge mass lifetime

0 5.28 GeV/c2 1.5 ps0 5.28 GeV/c2 1.5 ps

Indistinguishable from the outside

0B 0B

W+

W-

b

d

d

b


Time-dependent Interferencen Starting from a pure |B0ñ state, the wave function evolves as

n Suppose B0 and B0 can decay into a same final state fCP

n Two paths can interferen Decay probability depends on:

n the decay time tn 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 Moden Consider

n Phase difference is

0 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*

tbVtdV

tdV

*tbV

*cdVcsV

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= =

td tbV V

cd cbV V


Time-dependent CP Asymmetryn Quantum interference between the direct and mixed paths

makes and differentn Define time-dependent CP asymmetry:

n We can measure the angle of the UT

n What do we have to do to measure ACP(t)?n Step 1: Produce and detect B0 ® fCP eventsn Step 2: Separate B0 from B0

n Step 3: Measure the decay time t

0 0 0 0

0 0 0 0

( ( ) ) ( ( ) )( ) sin(2 )sin( )( ( ) ) ( ( ) )

S SCP

S S

N B t J K N B t J KA t mtN 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 Factoriesn 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

(4 )e e S BB+ +


SLAC PEP-II site

BABAR

PEP-II

I-280

Linac


Step 2:Identify the flavorof the other BDecay products often

allow us to distinguishB0 vs. B0

Asymmetric B Factoryn Collide e+ and e− with E(e+) ≠ E(e−)

n PEP-II: 9 GeV e− vs. 3.1 GeV e+ à bg = 0.56

Step 1:Reconstruct the signal Bdecaye− e+

Moving in the lab

U(4S)

Step 3:Measure Dz è Dtz c t=

e

+ +

0B

0B


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

n We reconstruct how the B mesons decayed from their decay products

BABAR Belle


J/y KS eventA B0 → J/y KS candidate (r-f view)

Muons from

Pions from

Red tracks are from the other B,which was probably B0

p −

p +

µ+

µ−

p −

p +

p +

K−

J +

SK+


CPV in the Golden Channeln BABAR measured in B0 ® J/y + KS and related decays

J/y KS

227 million eventsBBsin 2 0.722 0.040(stat.) 0.023(syst.)= ± ±

J/y KL


Three angles of the UTn CP violation measurements at the B Factories give

Angle (degree) Decay channels

aB0 ® pp, rp, rr

b B0 ® (cc)K0

g B0 ® D(*)K(*)

Precision of b is 10 times better than a and g

12.68.198.6+

1.31.221.7+

151263+


CKM precision testsn Measured angles agree with what we knew before 1999

n But is it all?n We look for small deviation from the CKM-only hypothesis by

using the precise measurement of angle b as the reference

g

a

b

Next stepsn Measure b with different methods

that have different sensitivity to New Physics

n Measure the sides

*

*tb

cb

td

cd

VV VV

*

*ubud

cd cb

VV VV

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


Angle b from penguin decaysn The Golden mode is n Consider a different decay

e.g., n b cannot decay directly to sn The main diagram has a loop

n The phase from the CKM matrix is identical to the Golden Mode

n We can measure angle b in e.g.B0 ® f + KS

b ccs

b sss

Tree

0Kb

c

sc

d

0B

/J

d

Penguin

0Kb

s

ss

d

0Bd

gW

, ,u c t , ,u c ttop is the main

contributor


New Physics in the loopn The loop is entirely virtual

n W and t are much heavier than bn It could be made of heavier particles

unknown to usn Most New Physics scenarios predict

multiple new particles in 100-1000 GeVn Lightest ones close to mtop = 174 GeVn Their effect on the loop can be as big as the SM loopn 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 Physics


Strange hintsn Measured CP asymmetries

show a suspicious trend

n Naive average of penguins give sin2b = 0.50 ± 0.06

n Marginal consistency from the Golden Mode(2.6s deviation)

sin 2 (penguin) sin 2 (tree)<

Need more data!

Penguin decays

Penguin modes

Golden mode


The sidesn To measure the lengths of the

two sides, we must measure|Vub| ≈ 0.004 and |Vtd| ≈ 0.008n The smallest elements – not easy!

n Main difficulty: Controlling theoretical errors due to hadronic physicsn Collaboration between

theory and experiment plays key role

g

a

b

*

*tb

cb

td

cd

VV VV

*

*ubud

cd cb

VV VV

Vtd

Vub


|Vub| – the left siden |Vub| determines the rate of the b ® u transition

n Measure the rate of b ® uℓv decay (ℓ = e or µ)

n The problem: b ® cℓv decay is much faster

n Can we overcome a 50´ larger background?

l

ubVb

u

W 22 5

2( )192

Fub b

Gb u V m=l

l

cbVb

c

W2

2( ) 1( ) 50

ub

cb

Vb ub c V

ll


n Use mu << mc à difference in kinematics

n Signal events have smaller mX à Larger Eℓ and q2

Detecting b → uℓv

2q

b c

b u

l

uX

Bu quark turns into 1 or more hardons

q2 = lepton-neutrino mass squared

mX = hadron system mass

Eℓ = lepton energy

El

b c

b u

Xm

b cb u

Not to scale!


Figuring out what we seen Cut away b ® cℓv à Lose a part of the b ® uℓv signal

n We measure

n Predicting fC requires the knowledge of the b quark’s motion inside the B meson è Theoretical uncertaintyn Theoretical error on |Vub| was ~15% in 2003

n Winter 2006:

n What happened in the last 2+1/2 years?

2( )u C ub CB X f V× =lTotal b ® uℓv rate

Fraction of the signal that pass the cut

Cut-dependentconstant predicted

by theory

expt model SF theory(3.5 2.8 4.1 4.2 )%

7.4%ub ubV V =

= HFAG Moriond 2006 average


Progress since 2003n Experiments combine Eℓ, q2, mX to maximize fC

n Recoil-B technique improves precisionsn Loosen cuts by understanding background better

n Theorists understand the b-quark motion bettern Use information from b ® sg and b ® cℓv decaysn Theory error has shrunk from ~15% to ~4% in the process

Fully reconstructedB ® hadrons

ℓv

X

BABARpreliminaryb ® cℓv

background


Status of |Vub|

n |Vub| determined to ±7.4%n c.f. sin2b is ±4.7%

Measures the length of the left side of the UT

World Average 4.45 ± 0.33c2/dof = 5.5/6


|Vtd| – the right siden Why can’t we just measure the t ® d decay rates?

n Top quarks are hard to maken

n Must use loop processes where b ® t ® dn Best known example: mixing combined with mixing

n Dmd = (0.509 ± 0.004) ps−1

n News from the Tevatron:

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

Vmm V

B0 oscillation frequency

Bs oscillation frequency

0.420.2117.33 0.07sm+= ±

17 21(90%CL)sm< <CDF

DØ

0.0080.0070.208td

ts

VV

+=


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

n Radiative-penguin decays

n

n Latest results from the B Factories:

n Translated to è

W

t t

b dtdV,u d,u d

B

W

t t

b stsV

,u d,u d

B *K

2

2*

( )( )

td

ts

VBB K V* 5( ) (4.0 0.2) 10B K = ± ×B

B(B ® rg)BABAR (0.6 ± 0.3) ´

10-6

Belle (1.3 ± 0.3) ´10-6

Average (1.0 ± 0.2) ´10-6

0.18 0.03td tsV V = ±


Impact on the UTn We can now constrain the right side of the UT

n Mixing measurements pinned down |Vtd/Vts| as precisely as sin2bn B ® rg provides a crosscheck, with sensitivity to New Physics

*

( )( )BB K

B0/Bs mixing


The UT todayAngles from CP asymmetriesSides + KL decaysCombined


The UT todayn The B Factories have dramatically

improved our knowledge of theCKM matrix n All angles and sides measured

with multiple techniquesn New era of precision CKM

measurements in search of NPn The Standard Model is alive

n Some deviations observed èrequire further attention

New Physics seems to be hidingquite skillfully


Constraining New Physics n New Physics at ~TeV scale should affect low-energy physics

n Effects may be subtle, but we have precisionn Even absence of significant effects helps to identify NP

n In addition to the UT, we explore:n rare B decays into Xsg, Xsℓ+ℓ-, tnn D0 mixing and rare D decays n lepton-number violating decays

Precision measurements at the BFactories place strong constraints on

the nature of New Physicsm

H(G

eV)

tanb

Allowed byBABAR data

b ® sg

Two Higgs doublet model


Outlookn The B Factories will pursue increasingly precise measurements

of the UT and other observables over the next few yearsn Will the SM hold up?

n Who knows?n 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

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