january, 2005kowalewski --- perugia lectures1 lectures on b physics bob kowalewski university of...

January, 2005 Kowalewski --- Perugia lectures

1

Lectures on B Physics

Bob Kowalewski

University of Victoria

Currently at La Sapienza and the

Laboratorio Nazionale di Frascati


2

Overview of the lectures Lecture 1: History, facilities, B production and decay,

CKM matrix

Lecture 2: Semileptonic and radiative B decays

Lecture 3: Oscillations and CP violation

Lecture 4: CP violation


3

Lecture 1 History of B physics: 1977 – 2004

Significant facilities, past and present

B meson production and decay

CKM matrix


4

Historical context 1974 was an exciting year for particle physics, with

the discovery of the (2nd generation) charm quark

(J/ψ) and the (3rd generation) τ lepton

The search for a 3rd generation of quarks was

motivated by symmetry with the lepton sector as well

as by the insight of Kobayashi and Maskawa (in

1973) that a 3x3 quark mixing matrix has an

irreducible imaginary parameter that can lead to CP

violation


5

Upsilon experiment at FNAL 400 GeV proton beam incident on target

Look for muon pairs; measure invariant mass


6

Initial results


7

Discovery of the b quark 1977: Lederman et al. discover Υ resonances in μ+μ-

mass spectrum Υ(1S), Υ(2S), Υ(3S)

Interpreted as bound states of a new quark, b, the

first quark of the 3rd generation: Electromagnetic decay seen (μ+μ-)

Decay width is narrow

Lederman receives Nobel Prize in 1988 for this work.


8

Later data

States seen are the

first 3 radial excitations

of the vector bb state

Υ(1S),Υ(2S),Υ(3S)

Observed width is

experimental resoln

Quantum numbers

JPC=1--

b mass ~ 4.6 GeV


9

Limitations of technique Only muon pairs are recorded!

Limited mass resolution

Not well suited for fine-grained study

No clear signature for separating b-flavored particles

(i.e. bq - B mesons) from background

Need e+e- experiment to examine in detail


10

First e+e- facilities At the time of Υ discovery, Cornell was building

CESR, a 16 GeV center-of-mass e+e- collider

CESR was subsequently redesigned to run in the Υ

energy range: 10-11 GeV

The CLEO and CUSB detectors started collecting

data in 1979


11

e+e- takes over

3 narrow Υ States seen immediately;

observed width = beam energy spread

Broader Υ(4S) resonance seen at

10.58 GeV; above BB threshold

1S 2S

3S

10.28 10.44

9.509.40 9.96 10.02

2mB

B0 and B+ discovered by

CLEO (1982)

B* mesons at CUSB (1985)

ARGUS detector (DORIS-II)

starts at DESY (1982)


12

CESR and CLEO


13

DORIS-II and ARGUS


14

Initial findings B mesons have significant semileptonic branching

fractions: BF(BXℓν) ~ 10%

B mesons are spin 0

B+ and B0 have mB = 5.279 GeV (Δm<1 MeV)

B decay dominated by bc transition (|Vcb| >> |Vub|)

B mesons have long (~1.5 ps) lifetimes (|Vcb|<<1)

FCNC decays not observed (constrain topless

models)


15

Early discoveries – B0 mixing

B0 and B0 mix to produce mass eigenstates;

Δm~0.5 ps-1. First seen by ARGUS (1987)

At Υ(4S), ~1 B0 in 6 decays as B0

Confirmed by CLEO in 1988

Initial B flavor cannot be determined; need

1 B to decay first


16

The flavor oscillation is

now mapped out over

~1.5 full periods

Δm = (0.502±0.006) ps-1

Fast-forward 14 years…

)ps(|t|10.0 15.05.0

mixedunmixed

)m(|z|

dBτdBΔm/π

dileptons20.7 fb-1

1 2 4

Belledileptons29.4 fb-1

1 2 4


17

Early discoveries – buℓν

bu transitions observed by CLEO (1989).

Signature is an excess of leptons with momenta above

the kinematically allowed range for bc decays.

bu rate ~ 1/50 bc rate

qq

bc


18

15 years later…

Data (continuum sub)MC for BB background

S/B ~ 1/25 at 2.0 GeV!


19

Radiative Penguin decays

1993 – exclusive decay BK*γ

seen in CLEO

1995 – inclusive bsγ process

measured (much harder!)

Rate probes new physics

BaBar

B0K*0γ


20

Contributions from higher energy e+e- machines

Full range of b-flavored hadron states produced

The PEP (SLAC) and PETRA (DESY) experiments

(√s~30 GeV) made early measurements of the

average B lifetime

LEP experiments and SLD made numerous

contributions in Z decays: Precise B lifetimes; lifetime differences

Discovery of Bs and Λb

Discovery of P-wave B mesons (B**)


21

P-wave B** Discovery

Resonant structure appears in the unlike-sign B+π±

distribution

Mass resolution insufficient to separate states

Excess in B+ π- combinations

B+ π+ combinations agree with MC

B+π± invariant mass


22

Hadron colliders for b physics Fermilab Tevatron experiments CDF and D0 have

made important contributions to

Bs decays

b-hadron lifetimes

Future hadron facilities (LHC-b, B-TeV and, possibly,

ATLAS and CMS at LHC) may make a number of

important measurements

Bs oscillations and CP violation

Leptonic and some radiative B decays


23

The B factory era CESR had an impressive history…but new

challenges require new facilities

B factories>100 fb-1 / year


24

B factory design goals Major physics motivation: CP violation in B decays

Requires asymmetric beam energies (Odone)

Requires high luminosity: KEK-B proposed at KEK; luminosity target 1 ×1034 cm-2 s-1

PEP-2 proposed at SLAC; luminosity target 0.3×1034 cm-2 s-1

Peak luminosity of 1034 cm-2 s-1 gives integrated

luminosity per year of ~ 150 fb-1 or ~2×108 Υ(4S)

decays


25

PEP-II and KEK-B

Jonathan Dorfan

Pier Oddone


26

B factories: PEP-II and KEK-B Both B factories

are running well:

Belle

BaBar BelleLmax (1033/cm2/s) 9.2 13.9

best day (pb-1) 681 944

total (fb-1) 244 338


27

B factory detectors

DIRC

DCH IFRSVT

CsI (Tl)

e- (9 GeV)

e+ (3.1 GeV)

BelleBelle

BaBarBaBar

Belle and BaBar are similar in performance; some different choices made for Cherenkov, silicon detectors

Slightly different boost, interaction region geometry (crossing angle)


28

The collaborations By any pre-LHC standard, this is big science; BaBar

has ~ 600 members, Belle ~ 300 (not all pictured in

either case!)

Pep2 / BaBar KEKB / Belle


29

B meson production

Production in e+e- at Υ(4S) {Z} cross-section ~1.1nb, purity (bb / Σiqiqi) ~ 0.3 {7nb, 0.22}

simple initial state: BB in p-wave, decay products overlap

{b quark hadronizes to B+: B0: Bs: b-baryon ~ 0.4, 0.4, 0.1, 0.1;

b and b jets separated}

“easy” to trigger, apply kinematic constraints

Production at hadron machines (gluon fusion) cross-sections much higher (×104)

All b hadrons are produced

triggering harder, purity (b / Σiqi) ~ (few/103)


30

Y(4S) experiments e+e- → Y(4S) → B+B- or B0B0; roughly 50% each

B nearly at rest (βγ ~ 0.06) in 4S frame; no flight info

B energy = ½ c.m. energy; valuable constraint, since

σE~50 MeV for reconstruction, ~5 MeV for e+e- beams

on peak

off peak (q=u,d,s,c)

2mB

qq

BB


31

Asymmetric B factories Boost CM along beam (z) axis

Separation of B and B decay ~ βγcτB ~ 250 μm

Boost imposes asymmetry in detector design

Required luminosity is large since CP eigenstates have small product BF to states with clean

signatures; e.g. BF(B0J/ψ(ℓ+ℓ-) KS) < 10-4

Angular coverage is a compromise between luminosity (quadrupole magnets close to IR) and detector acceptance


32

B decay basics B mesons are the lightest b-flavored particles; they

must decay weakly (Δb=1)

The 0th order picture is of a free b quark weak decay

Putting back the light quark we get the spectator (or

external W emission) decays

Other decay diagrams are suppressed either by color

matching or some power of 1/mB.


33

Charged-current Lagrangian in SM:

Since mb<< MW, the effective 4-fermion interaction is

CKM suppressed (|Vcb|<<1) → long lifetime ~ 1.5ps

† . ., with2

1 1

CC CC

CC e MNS CKM

gJ W h c

e d

J V u c t V s

b

L

b quark decay

c e νe

b

2†

, 22 2 with

4 2CC F CC CC F

W

gG J J G

M

L

×3 for color


34

b quarks and B mesons…

The b quark decay is simple

B meson decay is not…

Vcb

b

c

cbV


35

Spectator decays

Semileptonic ~ 26%

Hadronic ~ 73%

single hadronic current; ~reliable theory

Heavy Quark Expansion

BF form factors

Theoretical predictions tend to have large uncertainties.

Factorization (W decay products do not mix with other quarks) partly works

53

22

192 b

qbFm

VG


36

Leptonic decays

Leptonic < 10-4, 7,11

τ, μ, e

b

u

• Suppressed by helicity (like πeν)

• measures fB×|Vub|

b

d

l+,W+

W–l–,l’–,

B0

Helicity suppressed; FCNCIn SM: B(B0 +–) ~ 8×10-11

B(B0 ) ~ zero

2

2

222

22

18

)(

B

llBBB

ubF

m

mmmf

VGlBB

B+


37

Non-spectator decays

Colour-suppressed;

Includes all bcc q’qEW penguins; 2nd order weak

ℓ

ℓ ℓ ℓ

ℓ,ν

W exchange gluonic penguins; 2nd order weak

Large mt enhances these loop diagrams

b

q

s,d

q

q


38

Box diagrams

• 2nd order Δb=2 transition takes B0→B0 making decay

eigenstates distinct from flavour eigenstates

• Large mt makes up for Weak suppression

B0 → B0: (B0→B0) / B0 = 0.18


39

CKM matrix Kobayashi and Maskawa noted that a 3rd generation

results in an irreducible phase in mixing matrix:

Observed smallness of off-diagonal terms suggests a

parameterization in powers of sinθC

* * *

* * *

* * *

1 0 0

0 1 0

0 0 1

ud us ub ud cd td

cd cs cb us cs ts

td ts tb ub cb tb

V V V V V V

V V V V V V

V V V V V V

†VV

3 x 3 unitary matrix. Only phase differences are physical, → 3 real angles and 1 imaginary phase


40

Wolfenstein++ parameterization

Buras, Lautenbacher, Ostermaier, PRD 50 (1994) 3433.

shown here to O(λ5) where λ=sinθ12=0.22 Vus, Vcb and Vub have simple forms by definition Free parameters A, ρ and η are order unity Unitarity triangle of interest is VudV*

ub+VcdV*cb+VtdV*

tb=0 Note that |Vts /Vcb| = 1 + O(λ2)

2 4 31 12 8

2 2 4 2 21 1 12 2 8

3 2 2 4 2 41 1 12 2 2

1

1 2 1 1 4

1 1 1

CKM

A i

V A i A A

A i A A i A

u

c

t

d s b

all terms O(λ3)


41

A Unitarity Triangle

2

At the 1% level:

sin

0.2205 0.0018

At the 2% level:

/

0.84 0.02

| | and | |

- plane

us

us c

cb

cb

ub td

V

V

V

A V

A

V V

0,0 0,1

Rt

Ru

,

γi22

cbcd

ubudu e

VV

VVR

i22

cbcd

tbtdt e)1(

VV

VVR

t uUnitarity: 1+ +RR 0

, *ubVarg

2/1

2/12

2

and , A,


42

B decays – a window on the quark sector

The only 3rd generation quark we can study in detail

Investigate flavour-changing processes, oscillations

CKM matrix

ud us ub

cd cs cb

td ts tb

V V V

V V V

V V V

Cabibbo angle

BdBd and BsBs oscillations

B lifetime, decay

=1

CP Asymmetries

(phase)


43

Surveying the unitarity triangle The sides of the triangle

are measured in b→uℓν

and b→cℓν transitions

(Ru) and in Bd0-Bd

0 and

Bs0-Bs

0 oscillations (Rt)

CP asymmetries

measure the angles

Vub, Vcb and Vtd measure

the sides

GET A BETTER PICTURE

Ru

Rt


44

End of Lecture 1


45

Lecture 2 – Semileptonic and Radiative B Decays

B meson decays – role of QCD

Heavy Quark symmetry

Exclusive semileptonic decays

Inclusive semileptonic decays

Radiative decays

p.s. – se parlo troppo veloceveloce non esitate a dirmelo


46

Surveying the unitarity triangle The sides of the triangle

are measured in b→uℓν

and b→cℓν transitions

(Ru) and in Bd0-Bd

0 and

Bs0-Bs

0 oscillations (Rt)

CP asymmetries

measure the angles

Today we’ll talk about

the rings

GET A BETTER PICTURE

Ru

Rt


47

Recall:

The b quark decay is simple

B meson decay is less so…

Vcb

b

c

cbV


48

B hadron decay – parton model

Bound b quark is virtual and has some “Fermi momentum”

b quark then has pb = pF and Eb = MB - pF, so

mb =√( MB2 - 2MBpF )

Parton model usually assigns pF from a Gaussian with

r.m.s. of ~ 0.5 GeV

pF ~ 0.5 GeV, corresponds to mb ~ 4.8 GeV gives a

reasonable description of some inclusive spectra (e.g. pe)

Ad-hoc model; hard to assign uncertainties to predictions


49

Beyond parton model…

Parton model had some successes, but did not provide quantitative estimates of theoretical uncertainties.

How does QCD modify the weak decay of the b quark?

QCD becomes non-perturbative at ΛQCD ~ 0.5 GeV but is

perturbative for mb: αs(mb)~0.22

Modern approaches, based on heavy quark symmetry: use the operator product expansion (OPE) to separate short- and

long-distance physics Leads to effective field theories, e.g. HQE, SCET… Used to calculate form factors in lattice QCD

Xh νe

e

B


50

Heavy Quarks in QCD

Heavy Quarks have mQ >> ΛQCD (or Compton wavelength

λQ << 1/ΛQCD )

Soft gluons (p ~ ΛQCD) cannot probe the quantum

numbers of a heavy quark

→ Heavy Quark Symmetry

γ binding e- and N in atoms can’t probe nuclear mass,

spin… isotopes have similar chemistry!

b


51

Heavy Quark Symmetry

For mQ→∞ the light degrees of freedom (spectator,

gluons…) decouple from those of the heavy quark; the light degrees of freedom are invariant under changes to the

heavy quark mass, spin and flavour

SQ and Jℓ are separately conserved: SQ+Jℓ = J; Jℓ = L+Sℓ

The heavy quark (atomic nucleus) acts as a static source

of color (electric) charge. Color magnetic effects are

relativistic and thus suppressed by 1/mQ


52

Heavy Quark symmetry group The heavy quark spin-flavour symmetry forms an

SU(2Nh) symmetry group, where Nh is the number of

heavy quark flavours.

In the SM, t and b are heavy quarks; c is borderline.

No hadrons form with t quarks (they decay too rapidly)

so in practice only b and c hadrons are of interest in

applying heavy quark symmetry

This symmetry group forms the basis of an effective

theory of QCD: Heavy Quark Effective Theory


53

Heavy Quark Effective Theory The heavy quark is almost on-shell: pQ=mQv+k, where k is

the residual momentum, kμ << mQ

The velocity v is ~ same for heavy quark and hadron

The QCD Lagrangian for a heavy quark

can be rewritten to emphasize HQ symmetry:

H give rise to fluctuations O(2mb); h correspond to light d.o.f.

QL QQ iD m Q

( ) ( ), ( ) ( ) with

1. Thus ( ) ( ) ( )

2

Q Q

Q

im v x im v x

v v

im v x

v v

h x e P Q x H x e P Q x

vP Q x e h x H x


54

HQET Lagrangian

The first term is all that remains for mQ→∞; it is clearly invariant under HQ spin-flavour symmetry

The terms proportional to 1/mQ are the kinetic energy operator OK for the residual motion of the

heavy quark, and the interaction of the heavy quark spin with the color-

magnetic field, (operator OG)

The associated matrix elements are non-perturbative; however, they are related to measurable quantities

2

eff 2

1 1L

2 4S

v v v v v vQ Q Q

gh iv Dh h iD h h G h O

m m m


55

Non-perturbative parameters The kinetic energy term is parameterized by

λ1 = <B|OK|B>/2mB

The spin dependent term is parameterized by

λ2 = -<B|OG|B>/6mB

The mass of a heavy meson is given by

The parameter Λ arises from the light quark degrees of freedom and is defined by Λ = limm→∞(mH – mQ)

2

2

2 31 22

1 where

2

2 ( 1)

QH QQ Q

mm m O

m m

m J J


56

Phenomenological consequences

The spin-flavour symmetry relates b and c hadrons:

SU(3)Flavour breaking:

m(Bs) - m(Bd) = Λs – Λd + O(1/mb); 90±3 MeV

m(Ds) - m(Dd) = Λs – Λd + O(1/mc); 99±1 MeV

Vector-pseudoscalar splittings: (→ λ2 ~ 0.12 GeV)

m2(B*) - m2(B) = 4λ2+O(1/mb); 0.49 GeV2

m2(D*) - m2(D) = 4λ2+O(1/mc); 0.55 GeV2

baryon-meson splittings:

m(Λb) - m(B) - 3λ2/2mB+ O(1/mb2); 312±6 MeV

m(Λc) - m(D) - 3λ2/2mD+ O(1/mc2); 320±1 MeV


57

Exclusive semileptonic decays (heavyheavy)

HQET simplifies the description of BXceν decays and allows

precise determination of |Vcb|

Consider the (“zero recoil”) limit in which vc=vb (i.e. when the

leptons take away all the kinetic energy)

If SU(2Nh) were exact, the light QCD degrees of freedom wouldn’t

know that anything happened

For mQ→∞ the form factor can depend only on w=vb·vc (the

relativistic boost relating b and c frames)

This universal function is known as the Isgur-Wise function,

and satisfies ξ(w = 1) = 1.

D* νe

e

B


58

Determination of |Vcb|

The zero-recoil point in BD(*)eν is suppressed by phase space; the rate vanishes at w=1. One must extrapolate from w>1 to w=1.

includes radiative

and HQ symmetry-breaking corrections, and

* 22 2 23 2

* *

2 22* *

2

*

1 148

241 ( )

1

Fcb B D D

B B D D

B D

d B D GV m m m w w

dw

m wm m mww

w m m

F

2( ) ( ) ( ) / ...S Q QCD Qw w O m O m F

Luke’s theorem

2

2(1) 1 ...QCD QCD

AQ Q

Cm m

0F


59

Current status of |Vcb| from B→D*eν

Measurements of the rate at w=1 are experimentally

challenging due to limited statistics: dΓ/dw(w=1) = 0

softness of transition π from D*→D

extrapolation to w=1

Current status (Heavy Flavor Averaging Group):

3

3

108.10.14.41

t)(experimen 109.07.371

QCD) (Lattice 04.091.01

cb

cb

V

VF

F

5% uncertainty


60

Tests of HQET Predicted relations between form factors can be used

to test HQET and explore symmetry-breaking terms

The accuracy of tests at present is close to testing

the lowest order symmetry-breaking corrections –

e.g. the ratio of form factors / for B→Deν / B→D*eν

is

11.08 0.06 (theory)

1

1.08 0.09 (experiment)

w

w

G

F


61

Lattice QCD for B decay In principle, we can do everything on the lattice

In practice, there are problems:

Unquenched calculations (i.e. those involving quark loops) only

recently feasible

b is heavy; lattice spacing a would have to be <1/mb for proper

treatment, and this is not yet possible use HQET ideas here too

Extrapolation to real world (a0 and mq0) introduces

uncertainties

Important for exclusive Blight form factors and B decay

constant


62

Exclusive charmlesssemileptonic decays

HQET is not helpful in analyzing BXueν decays in

order to extract |Vub|

The decays B0→π+ℓ-ν and B→ρℓ-ν have been observed

(BF ~ 2×10-4)

Lattice calculations of form factor in B→πℓν decay give

uncertainties on |Vub| in the 15-20% range for large

q2=mB2+mπ

2+2mBEπ

Other decays tend to be more challenging

π νe

e

B


63

Inclusive semileptonic decays Inclusive decays sum over all exclusive channels

Complementary to exclusive semileptonic decays for

both experiment (only lepton(s) measured), and

theory (sum over final states can ignore hadronization)

Starting point is optical theorem which relates

Γ(BX) to imaginary part of forward scattering

amplitude

Applies to both bu and bc semileptonic decays


64

Operator Product Expansion

The heavy particle fields can be integrated out of the full Lagrangian to yield an effective theory with the same low-energy behaviour (e.g. V-A theory)

The effective action is non-local; locality is restored in an expansion (OPE) of local operators of increasing

dimension ( ~1/[Mheavy]n )

The coefficients are modified by perturbative corrections to the short-distance physics

An arbitrary scale μ separates short- and long-distance effects; the physics cannot depend on it


65

OPE in B decays

The scale μ separating short/long distance doesn’t

matter … except in finite order calculations

typically use ΛQCD << μ ~ mb << MW; αS(mb) ~ 0.22

Wilson coefficients Ci(μ) contain weak decay and

perturbative QCD processes

The matrix elements in the sum are non-perturbative

Renormalization group allows summation of terms

involving large logs (ln MW/μ) → improved Ci(μ)

( ) ( )eff i iiA B F F H B C F Q B


66

Inclusive Decay Rates

The inclusive decay widths of B hadrons into partially-

specified final states (e.g. semileptonic) can be

calculated using an OPE based on:

1. HQET - the effects on the b quark of being bound to light

d.o.f. can be accounted for in a 1/mb expansion involving

familiar non-perturbative matrix elements

2. Parton-hadron duality – the hypothesis that decay widths

summed over many final states are insensitive to the

properties of individual hadrons and can be calculated at

the parton level.


67

Parton-Hadron Duality One distinguishes two cases:

Global duality – the integration over a large range of

invariant hadronic mass provides the smearing, as in

e+e-→hadrons and semileptonic HQ decays

Local duality – a stronger assumption; the sum over

multiple decay channels provides the smearing (e.g.

b→sγ vs. B→Xsγ). No good near kinematic boundary.

Global duality is on firmer ground, both theoretically and

experimentally


68

2 5

1 21 2

( ) 91 ... ...

192 2F b S b

b

G m mB X C

m

Heavy Quark Expansion The decay rate into all states with quantum numbers f is

Expanding this in αS and 1/mb leads to

where λ1 and λ2 are the HQET kinetic energy and

chromomagnetic matrix elements.

Note the absence of any 1/mb term!

24

eff

12 L

2 ff B X fXB

B X p p X Bm

free quark


69

Inclusive semileptonic decays

The HQE can be used for both b→u and b→c decays

The dependence on mb5 must be dealt with; in fact, an

ambiguity of order ΛQCD exists in defining mb. Care must

be taken to correct all quantities to the same order in αS

in the same scheme)

The non-perturbative parameters λ1 and λ2 must be

measured: λ2~0.12 GeV from B*-B splitting; λ1 from

b→sγ, moments in semileptonic decays, …

2 5

2 1 21 2

( ) 91 ... ...

192 2F b S b

u ubb

G m mB X V C

m

X νe

e

B


70

b-hadron lifetimes (1/Γ) Need these to go from BF to partial Γ

HFAG average values (as of Summer, 2004):

Species Lifetime

B0 1534±13 fs

B+ 1653±14 fs

B+/B0 1.081±0.015

Bs 1469±59 fs

Λb 1232±72 fs

Bc 450±120 fs


71

μπ2 ~

λ1

μG2 ~

λ2


72

Spectral moments OPE calculation is done at the parton level Applying the OPE calculations to real hadrons

(duality) requires summing over a “large enough” phase space

Low-order spectral moments (integrals over distributions) should be insensitive to duality

A complete set of calculations is available for bcℓν mass and lepton energy moments

Measurements always need cut on lepton energy

3Calculations available to and , 1 or 2kB SO m O k


73

Cross-checks of fit results

Ee moments calculated

up to αs2β0; MX moments

to αs (higher orders small

compared with exp error)

Separate fits to Ee and

Mx moments agree well

Values for μG2 and ρLS

3 are consistent with independent

measurements based on mB*-mB and HQ sum rules.

Overall power of Ee and MX moments is comparable


74

OPE preliminary fit results|Vcb| measured to 2%!


75

Relating |Vub| to Γ(BXuℓν)

Recall mb5 dependence of total s.l. width

The mb appearing in the HQE is the pole mass; it is

infrared sensitive (it changes at different orders in PT)

mb defined in an appropriate renormalization scheme

(there are several) results in faster convergence of OPE

Fairly precise relations can then be obtained for |Vub|:

1 Hoang, Ligeti and Manohar, hep-ph/9809423

1/ 2

31

3.06 0.08 0.08 100.625

uub

B XV

ns

-

4% error

Moving on to |Vub|…


76

Data (eff. corrected)MC

Data (continuum sub)MC for BB background

Determination of |Vub|

The same method (ΓSL) can be

used to extract |Vub|.

Additional theoretical uncertainties

arise due to the restrictive phase

space cuts needed to reject the

dominant B→Xceν decays

Traditional method uses endpoint

(>2.3 GeV) of lepton momentum

spectrum; recent progress pushes

this to 2.0 GeV


77

Newer methods for determining |Vub|

2. mass mx recoiling against ℓν

(acceptance ~70%, but requires

full reconstruction of 1 B meson)

b→callowedb→c

allowed

b→callowed

mX2

1. invariant mass q2 of ℓν pair (acceptance ~20%, requires neutrino reconstruction)

B0→Xuℓ-ν

B→Xuℓ-ν


78

Recent data on inclusive buℓν The better acceptance and signal-to-background

comes at the cost of statistics and complexity (one

needs to measure more things)

BABAR


79

Shape function The Shape function, i.e. the light-

cone b quark momentum distribution Needed where OPE breaks down Some estimators (e.g., q2) are

insensitive to it Shmax (GeV2)

acce

pt

acce

pt

reje

ct

reje

ct


80

mX vs. q2

Inclusive |Vub| results - 2004

|Vub| is measured to ~ ±9%

Eℓ endpoint

mX fit

Eℓ vs. q2

Results have been re-adjusted by the Heavy Flavor Averaging Group


81

Measuring non-perturbative parameters and testing HQE

mb and λ1 can be measured from

Eγ distribution in b→sγ

moments (mX, sX, Eℓ, EW+pW)

in semileptonic decays

Comparing values extracted

from different measurements

tests HQE

This is currently an area of

significant activity

λ1

mb/2→Λ


82

Hadronic B decays More complicated than semileptonic or leptonic

decays due to larger number of colored objects

Many of the interesting decays are charmless →

HQET not applicable

QCD factorization and other approaches can be

used, but jury is still out on how well they agree with

data

No more will be said in these lectures


83

Radiative Penguin Decays and Radiative Penguin Decays and New PhysicsNew Physics

SM leading order = one EW loopVts, Vtd dependent

FCNCs probe a high virtual energy scale comparable to high-energy colliders

Radiative FCNCs have precise SM predictions:

BF(b→s)TH = 3.57 ± 0.30 x 10-4 (SM NLO)BF(b→s)EXP = 3.54 ± 0.30 x 10-4 (HFAG)

Decay rate agreement highly constrains new physics at the electroweak scale!

Further tests presented here:•Exclusive b→s decay rates

•b→s CP asymmetries•b→d penguins

Multiple new BF(b→s)measurements coming soon from BaBar

Radiative penguin decays: b → s and b → d FCNC transitions

Berryhil, ICHEP2004


84

b→s(d)γ

B→K*γ and b→sγ (inclusive) both observed by CLEO

in mid-90s; first EW penguins in B decay

BR consistent with SM; limits H+, SUSY:

BF(b→sγ) = (3.5 ±0.3 )×10-4 (expt)

= (3.4 ±0.6 )×10-4 (theory)

BF(B→K*γ) = (40.1 ±2.0 )×10-6 (expt)

non-strange bdγ modes not yet observed; but

B→ργ and Bωγ nearly so.

Eγ spectrum is used to probe shape function


85

|Vtd|/|Vts| from Bργ / BK*γ

Combined BF() ≡ BF(+) = 2(+/0) BF(0 ) = 2(+/0) BF( )

BF = (0.6 ± 0.3 ± 0.1) x10-6

BF < 1.2 x10-6 90% CL

95% C.L. BaBar allowed region (inside the blue arc)

With/withouttheory error


86

Radiative FCNC decays


87

Sensitivity to new physics


88

b→sνν

Cleanest rare B decay; sensitive to all generations

(important, since b→sτ+τ- can’t be measured)

BF quoted are sum over all ν species

SM predictions:

BF(B → Xsνν) < 6.4×10-4 at 90% c.l. (ALEPH)

BF(B+→K+νν) < 5.2×10-5 at 90% c.l. (BaBar submitted to PRL)

62.1

6.0

6910

108.3

1041

KB

KB

B

B

ℓ

ℓ ℓ ℓ

ℓ,ν


89

Lecture 2: summary Semileptonic decays give crucial information on the

CKM elements |Vcb| and |Vub|

Heavy Quark Symmetry is the tool used to

quantitatively understand these decays

Progress in this area involves a vibrant interplay

between theory (QCD effective field theories) and

experiment; progress is being made in both

Radiative decays offer opportunities for seeing new

physics, since they are highly suppressed in the SM


90

Lecture 3: Oscillations and CP violation

B0B0 oscillations – theory and experiment

CP violation in SM – basic mechanisms

CP violation in B decays

Measurement of unitarity triangle angle β

Lecture 4 – CP violation Direct CP violation

Determining α

Prospects for γ

Summary


91

B0-B0 oscillations

B mesons are produced in strong or EM interactions in states of definite flavour

2nd order Δb=2 transition takes B0→B0 making mass eigenstates distinct from flavour eigenstates

Neutral B mesons form 2-state system:

Mass eigenstates diagonalize effective Hamiltonian

0 01 0

0 1B B

, , ,H L H L H LH B E B


92

Effective Hamiltonian for mixing Two Hermitian matrices M and Γ describe physics

11 12*12 22

12

*12

2

01 0 20 12

02

M M iH

M M

iM

iM

iM

Quark masses, QCD+EM

Δb=2intermediate state off-shell, on-shell

Weak decay

M11=M22 (CPT)

Γ11 = Γ22

Diagonalize to get heavy (H) and light (L) eigenstates: mH, mL


93

The time evolution of the B0B0 system satisfies

The dispersive part of the matrix element corresponds to

virtual intermediate states and contributes to Δm

The absorptive part corresponds to real intermediate

(flavour-neutral) states and gives rise to ΔΓ

Δm, ΔΓ

→1→0

→1→0

0 ( 0

( 0

2 21 12 2

1 12 2

( ) cos cosh sin sinh2 4 2 4

sin cosh cos sinh2 4 2 4

, , 1

, ,

M t

M t

H L H L

H L H L

Mt t Mt tB t e i B

q Mt t Mt te i B

p

M M M p q

M M M

<<


94

Bd oscillations

For B0(bd), ΔΓ/Γ<<1: only O(~1%) of possible decays

are to flavour-neutral states (ccdd or uudd); dominant

decays are to cudd or cℓνd

Consequently, most decay modes correlate with the b

quark flavour at decay time. Contrast with K0 system

The large top quark mass breaks the GIM

cancellation of this FCNC and enhances rate Δm;

large τB allows oscillations to compete with decay


95

)ps(|t|10.0 15.05.0

mixedunmixed

)m(|z|

dBτdBΔm/π

dileptons20.7 fb-1

Evidence for Bd oscillations

The fraction of opposite-

sign dileptons vs. time

(does not go from 0 to 1

due to mis-tagging)

Y(4S) has JPC=1- - so BB are

in a P-wave. B1 and B2 are

orthogonal linear

combinations of B

eigenstates

Δm = (0.502±0.006) ps-1

1 2 4

Belledileptons29.4 fb-1

1 2 4


96

SM expectation for Bd oscillations

The box diagram for Δb=2 transitions contains both

perturbative and non-perturbative elements

Operator Product Expansion (OPE) calculation gives

Uncertainty in BBFB2 dominates (~30%)

Hope for improvements using Lattice QCD

222 2

02ˆ( ) ( ) , ,

6 q q q

Fq B B B W t tq

GM m B F M S x V q d s

pert. QCD From <B0 |(V-A)2|B0>

universal fn of (mt/mW)2


97

Experimental status of Bs oscillations

In the BS system the CKM-favoured decay b→ccs

leads to flavour-neutral (ccss) states

ΔΓ/Γ may be up to ~15% (HFAG: ΔΓ/Γ < 0.54 at 95% c.l.)

Still have ΔΓ<< Δm

Δmd /Δms ~ (|Vtd|/|Vts|)2 ~ 30 (corrections are O(15%))

HFAG: Δms > 14.5 ps-1 at 95% c.l. (LEP/SLD/CDF)

Fast oscillations are hard to study (one complete oscillation every γ·50μm).


98

Unitarity triangle constraints from non-CP violating quantities

These measurements

alone strongly favour

a non-zero area for

the triangle; this

implies CP violation in

SM


99

CP violation CP violation is one of the requirements for producing

a matter-dominated universe (Sakharov)

Why isn’t C violation alone enough (C|Y> = |Y>)?...

Chirality: if YL behaves identically to YR then CP is a

good symmetry. In this case the violation of C does

not lead to a matter–antimatter asymmetry.

CP violation first observed in K0L decays to the (CP

even) ππ final state (1964)


100

Physicist’s Rorschack


101

Mechanism for CP violation in SM: Kobayashi and

Maskawa mixing matrix with 1 irreducible phase

CP violation is proportional to the area of any unitarity

triangle, each of which has area |J|/2, where

J = Jarlskog invariant = c12c23c213s12s23s13sinδ ~ A2λ6η

Jmax is (6√3)-1 ~ 0.1; observed value is ~4·10-5; this is why

we say “CP violation in SM is small”

Since it depends on a phase, the only observable effects

come from interference between amplitudes

CP violation in SM


102

CP violation in flavour mixing This is the CP violation first observed in nature, namely the decay of

KL to ππ, which comes about because of a small CP-even

component to the KL wavefunction

Caused by interference between ΔΓ and Δm in mixing; very small in

B system because ΔΓ<<Δm

This type of CP violation is responsible for the small asymmetry in

the rates for KL→π+e-νe and KL→π-e+νe

Non-perturbative QCD prevents precise predictions for this type of

CP violation

2 1 1 2

2 2,

1 1L S

K K K KK K


103

CP Violation in Mixing

HFAG: |q/p| = 1.0013 ± 0.0034

2 0 0 * *12 122

0 012 122

CP violation 1 where i

eff

ieff

B H B Mq qiff

p p MB H B

off-shell off-shell

on-shell on-shell

CP-invariant phase

122 2*12 2 2

i i

eff i i

M MH

M M

arbitrary phase

20 0

20 0

CP

CP

i

i

CP B e B

CP B e B


104

Direct CP violation

)fB(obPr)fB(obPr1A/A ff

sinsin|A||A|2)fB()fB(

)fB()fB(A 21CP

CP violation in decay amplitude

fB fB

1A

2A

2 amplitudes A1 and A2

Strong phase difference

Weak phase difference

For neutral modes, direct CP violationcompetes with other types of CP violation

Non-perturbative QCD prevents precise predictions for this type of CP violation; most interesting modes are those with ACP~0 in SM

00 or no CPV

partial decay rate asymmetry

From Gautier Hamel de Monchenault


105

CP violation in the interference between mixing and decay

0B

)tm(sinS)tm(cosC

)f)t(B()f)t(B(

)f)t(B()f)t(B()t(A

dCPdCP

CP

BfBf

CP0physCP

0phys

CP0physCP

0phys

f

)f(t)ob(BPr)f(t)Bob(Pr1λ CP0physCP

0physfCP

0BCPf

CPfA

CPfACP

CP

CPCP

f

fff

A

A

p

qηλ

CP eigenvalue i2e

amplitude ratio

2f

2f

f||1

||1C

CP

CPCP

2f

ff

||1

Im2S

CP

CPCP

mixing

We often have 1 and 1 but Im 1CP CPf f

p

q

Time-integrated asymmetry vanishes!


106

Calculating

( )0

2 ( )0 ( )

D

CP D

iCP

i iCP CP CP

f H B A e

f H B f e A e

if just one direct decay amplitude to fCP

Piece from mixing (q/p)

2 2 2 2

2 ( 2 )*12 02 2

( ) 12

CPiF W B B B B ttd td t t

W

G M m B f mM V V S x e x

m

Piece from decayPiece from decay

0

2 ( )

0( ) CP D

CP iCP CP

CP

f H Bf e

f H B

2 ( )( ) M DiCP CPf e

No dependence on δ!

→ pure phase* * *

2 2( )12 122*

12 122

CP CP M

ii itb td

itb td

M V Vqe e

p M V V

~0

~0


107

Calculating for specific final states

2 ( )( ) M Df iCP CP CP

f

Aqf e

p A

* *0

* * = Im( )=sin(2 )

( )

tb td ud ub

tb td ud ub

V V V VB

V V V V

b uud

* * *0 0

/ * * *

0 0/

/ = Im( )= sin(2 )

( ) ( )

tb td cs cb cd csS L

tb td cs cb cd cs

S L

V V V V V VB J K

V V V V V V

b ccs K K

B0 mixing decayK0 mixing

assuming only tree-level decay


108

• B0 decays to CP eigenstates that are dominated by a single decay amplitude allow a clean prediction for the CP asymmetry:

where θCKM is related to the angles of the unitarity triangle (e.g. θCKM = β for B→J/ψ KS)

Mother Nature has been kind!

sin 2 sinCP CP CKMA t m t


109

• From the recent CKM2005 workshop:

Mother Nature has been very kind!


110

Relation to unitarity triangle

0*** tbtdcbcdubud VVVVVV

*

*

cbcd

tbtd

VV

VV

*

*

cbcd

ubud

VV

VV

0 0B J/ K *DB

DKB

d

,0 B

(1,0)

(0,0)

()SemileptonicBXue

B0d oscillations

B0s oscillations

(bd)→uudd

(bd)→ccsd, ccdd, ccss, sssd

(bd)→cusd(bd)→cudd


111

Measuring CP violation in Bd decays

CP violation in Bd decays can be studied at

asymmetric e+e- colliders (B factories) with √s=mY(4S)

Time integrated CP asymmetry vanishes –

measurement of Δt uses boost of CM along beam line

and precise position measurements of charged tracks

Reconstruction of CP eigenstates requires good

momentum and energy resolution and acceptance

Determination of flavour at decay time requires the

non-CP “tag B” to be partially reconstructed


112

Overview of CP asymmetry measurement at B factories

z

0tagB

ee

S4

K

0recB

B-Flavor Taggingcβγz/ΔtΔ

Exclusive B Meson

Reconstruction

0SK

/J

0flav

0rec BB (flavor eigenstates) lifetime, mixing analyses

0CP

0rec BB (CP eigenstates) CP analysis


113

Relation of mixing, CP asymmetries

Use the large statistics Bflav data sample to determine the mis-tagging probabilities and the parameters of the time-resolution

function

Time-dependence ofCP-violating asymmetry in

B0CPJ/ψ K0

S

Time-dependence of B0-B0 mixing

)ΔtΔmcos(.ω21N(mixed)N(unmixed)

N(mixed)N(unmixed))t(A

dBmixing

)ΔtΔmsin(β.2sin.ω21)BN(B)BN(B

)BN(B)BN(B)t(A

dB0tag

0tag

0tag

0tag

CP

dilution due to mis-tagging


114

Paying homage to Father Time

• measure Δz = lifetime convoluted with vertex resolution; derive Δt

• z of fully reconstructed B is easy to measure; z of other B biased due to D flight length.

Same effects arise for CP and flavour eigenstates

Unmixed

Mixed


115

Impact of mistagging, t resolution

No mistagging and perfect t Nomix

Mix

t

t

D=1-2w=0.5

t res: 99% at 1 ps; 1% at 8 ps

w=Prob. for wrong tag

t

t

Raw asymmetry


116

Flavour determination of tag B

Kb

c s DB0

XKD,XDB0 s

00 DD,XDB

%2.11.26)ω21(εQ 2i

ii

Use charge of decay products Lepton Kaon Soft pion

Use topological variables e.g., to distinguish between primary, cascade lepton

Use hierarchical tagging based on physics content Four tagging categories: Lepton, Kaon, NN; ε ~ 70%

Effective Tagging Efficiency


117

B reconstruction

B→J/ψK0, J/ψ→ℓ+ℓ- is very clean; can

be used at hadron machines as well

At e+e- b

factories

kinematic

constraints

allow use

of KL too!

BelleBelle

BaBarBaBar


118

Results for β BaBar and Belle both see

significant CP violation:

sin2β = 0.725±0.033±0.017

C = 0.031±0.025±0.015

Also |λf|=0.950±0.031±0.013

(recall λf=(q/p)*(Af/Af) )

BaBarBaBar

BelleBelle

syse

rr ↓

as

∫Ld

t ↑


119

Asymmetries in bsss: a bit too strange?

Penguin decays of the type bsss are expected to

have the same asymmetry as bccs

Uncertainties ~5-10% depending on mode

Measurements of B0 φK0s, B0η’K0

s, B0K+K-K0s

and others give smaller values:

sin2β = 0.41 ± 0.07 (recall bccs gives 0.725±0.037)

The two results are 3.8σ apart!

More data may reveal a significant departure from

SM


120

bsss

Status at ICHEP’04

φK0 is pure Penguin

b

dg

u

d

ss

[ ],

CPK K

W

4~ iub us uV V R e

0K

0K

s

b

dg

t

d

ss

s

W

2~tb tsV V

[ ],

CPK K


121

sin2 and..... and....

b ss

sd

dg

, ,u c t

0SK

0B

b sd

dd

d

W

g

, ,u c t0SK

0

0B

0B

b

s

s

sd d

, , ( )CPKK

0SK

0B

b

d

s

dd d

0SK

0

New phases from SUSY?

, , ( )CPKK

W

In SM interference between B mixing, K mixing and Penguin bsss or bsdd gives the same e as in tree process bccs. However loops can also be sensitive to New Physics!


122

Lecture 3 summary B0 oscillations have ΔΓ<<Δm, are CP conserving

B0s can have sizable ΔΓ/Γ; B0

d have ΔΓ<<Γ

CP violation in SM due to phase interference

3 kinds of CP violation: in mixing, in decay (direct) and in the

interference between mixing and decay

3rd form allows clean measurements of weak phases

CP asymmetry measurements can be done with precision;

many experimental handles available from more prevalent flavor

eigenstates

bsss transitions show intriguing difference from SM


123

Lecture 4 – CP violation Direct CP violation

Determining α

Prospects for γ

Summary

Lecture 3: Oscillations and CP violation B0B0 oscillations – theory and experiment

CP violation in SM – basic mechanisms

CP violation in B decays

Measurement of unitarity triangle angle β


124

CKM matrix Kobayashi and Maskawa noted that a 3rd generation

results in an irreducible phase in mixing matrix:

Observed smallness of off-diagonal terms suggests a

parameterization in powers of sinθC

* * *

* * *

* * *

1 0 0

0 1 0

0 0 1

ud us ub ud cd td

cd cs cb us cs ts

td ts tb ub cb tb

V V V V V V

V V V V V V

V V V V V V

†VV

3 x 3 unitary matrix. Only phase differences are physical, → 3 real angles and 1 imaginary phase


125

Wolfenstein++ parameterization

Buras, Lautenbacher, Ostermaier, PRD 50 (1994) 3433.

shown here to O(λ5) where λ=sinθ12=0.22 Vus, Vcb and Vub have simple forms by definition Free parameters A, ρ and η are order unity Unitarity triangle of interest is VudV*

ub+VcdV*cb+VtdV*

tb=0 Note that |Vts /Vcb| = 1 + O(λ2)

2 4 31 12 8

2 2 4 2 21 1 12 2 8

3 2 2 4 2 41 1 12 2 2

1

1 2 1 1 4

1 1 1

CKM

A i

V A i A A

A i A A i A

u

c

t

d s b

all terms O(λ3)


126

A Unitarity Triangle

2

At the 1% level:

sin

0.2205 0.0018

At the 2% level:

/

0.84 0.02

| | and | |

- plane

us

us c

cb

cb

ub td

V

V

V

A V

A

V V

0,0 0,1

Rt

Ru

,

γi22

cbcd

ubudu e

VV

VVR

i22

cbcd

tbtdt e)1(

VV

VVR

t uUnitarity: 1+ +RR 0

, *ubVarg

2/1

2/12

2

and , A,


127

Direct CP violation

)fB(obPr)fB(obPr1A/A ff

sinsin|A||A|2)fB()fB(

)fB()fB(A 21CP

CP violation in decay amplitude

fB fB

1A

2A

2 amplitudes A1 and A2

Strong phase difference

Weak phase difference

For neutral modes, direct CP violationcompetes with other types of CP violation

Non-perturbative QCD prevents precise predictions for this type of CP violation; most interesting modes are those with ACP~0 in SM

00 or no CPV

partial decay rate asymmetry

From Gautier Hamel de Monchenault


128

CP violation in the interference between mixing and decay

0B

)tm(sinS)tm(cosC

)f)t(B()f)t(B(

)f)t(B()f)t(B()t(A

dCPdCP

CP

BfBf

CP0physCP

0phys

CP0physCP

0phys

f

)f(t)ob(BPr)f(t)Bob(Pr1λ CP0physCP

0physfCP

0BCPf

CPfA

CPfACP

CP

CPCP

f

fff

A

A

p

qηλ

CP eigenvalue i2e

amplitude ratio

2f

2f

f||1

||1C

CP

CPCP

2f

ff

||1

Im2S

CP

CPCP

mixing

We often have 1 and 1 but Im 1CP CPf f

p

q

Time-integrated asymmetry vanishes!


129

Direct CP violation Recall that direct CP violation arises in the

interference of two competing decay amplitudes to

the same final state

It can affect any particle decay (not just neutral

mesons), and does not vanish when integrated over

decay time

It was first observed in K0L decay in 1999, after

decades of effort

It has now been seen in B0 decays (2004)


130

Direct CP violation in B0K+π-

Exciting discovery in 2004:

first observation of direct

CP violation in B0K+π-

Discrepancy in B+K+π0

(HFAG) 019.0109.0

(Belle) 005.0025.0101.0

(BaBar) 009.0030.0133.0

CP

CP

CP

A

A

A

(HFAG) 040.0049.0

(Belle) 02.005.004.0

(BaBar) 01.006.006.0

CP

CP

CP

A

A

A s K- K-s


131

Angle α – not as simple as β

The quark level transition b→uud gives access to sin(2α). In

this case, however, tree and Penguin amplitudes can be

comparable; more complicated.

Decay modes: B0→ππ, ρπ, ρρ…

In practice, the coefficients of the time dependent CP

asymmetry, Sππ and Cππ (=-Aππ), are measured

Additional measurements are needed to separately

determine the tree and penguin amplitudes; these involve all

B→ππ charge combinations or B→ρπ or ρρ with an

analysis of the Dalitz plot.


132

The angle αInterference of suppressed

b u “tree” decay with mixingbut: “penguin”

is sizeable!

222λ iii eeeA

A

p

q

ii

iii

ePeT

ePeTe

2λ

B0 mixing

*/ tb td tb tdq p V V V V

B0 decay: tree

sin 2 0SC

21 sin 2 sin

effS CC

With no penguins With large penguinsand |P/T| ~ 0.3

3 3

B0 decay: penguin

*ub udA V V *

td tbA V V

b d

bd

Coefficients of time-dependent CP Asymmetry


133

Isospin analysis: eff Gronau-London isospin analysis: J=0 two-pion state has no I=1,

so B can be described in terms of two I-spin amplitudes

A+0 has no gluonic penguin

base is common to B+ and B-

Grossman-Quinn bound:

Useful if 00 is small; doesn’t require 00to be tagged since uses sum

2


134

Result for B 00

0 0

0 0

6(1 17 0.32 0 10) 100 12 0.56 0.06

BF . .C .

4.9

0 0 bkg +d F nalit sigBqq

0 0

0 0

60.41 0.22(2 32 ) 100.48 0.180.160 43 0.51 0.17

BF .

C .

6.0

o- 35 at 90% CLeff

BABAR CONF-04/035

Grossman-Quinn bound:

(HFAG) 10)5.08.4( 6BF


135

Results on Bππ

0 30 0.17 0 030 09 0.15 0.04

S . .C .

0 (227 pairs) B M 0 (227 pairs) B M

0

0

6

0 01 0.10 0.02

(5 8 0.6 0 4) 10

A .

BF . .

1 00 0.21 0.070 58 0.15 0 07

S .C . .

BBAABBARARBBAABBARAR

Comparison

Caution averaging!

S2+C2≤1 physically


136

Sin2α from B0ρρ

0 19 0.33 0.110 23 0.24 0 14

long

long

S .C . .

0 (122 pairs) B M BB 0 (122 pairs) B M BB Signal: 314 34 events

1.00 0.02longf

Extraction of similar to , but with advantage of smaller Penguin pollution:

00 00

0

| | | |, much smaller: smaller

| | | | eff

A A

A A

Potentially could be mixed CP, but is observed to be almost pure CP 1



137

More on Bρρ0 0 B 0 0 B PRL 91 (2003) 171802

0 0 0 B 0 0 0 B

First result from Run 1-2 (89 pairs)M BB

0 65.7 ( ) (22.5 5.8) 10 5.4BF B

0 0 0 6 ( ) 1.1 10 (90% CL)BF B

o

( ) ( ) ( ) 96 10 4 11 stat sys peng

Updated result from Run 1-4 (227 pairs)M BB

00A2

A

0 0A A

2

A

00A2 peng

Compare with 35o for


BABAR CONF-04/037


138

Summary of constraints on

Mirror solutions disfavored

o

From combined , , results:

12100 11

o indirect constraint fit:

98 16CKM

BABAR & Belle BABAR & Belle combinedcombined

BABAR & Belle BABAR & Belle combinedcombined


139

CKM constraints and sin2 and measurements

CKM fit to indirect constraints overlaid with sin2β and measurements

• Constraints on starting to have an impact


140

Approaches to γ The quark-level decay bcus gives rise to direct CP

asymmetries involving γ

The quantity sin(2β + γ) can be measured in time-

dependent decays involving bcud


141

sin(2β+γ) from B0D(*)-π+ decays

Same final state reached by B0, B0 in different diagrams


142

Status of sin(2β+γ) Fit determines coefficients of time-dependent terms;

further input still needed to get sin(2β+γ)


143

Idea – use D0 CP eigenstates

fCP: K+K-, KSπ, π+π-


144

Idea – use DCS D0 decays


145

Experimental status of GLW/ADS Signals seen and CP asymmetries measured for GLW method;

however, more input (rB and δ) needed to determine γ

Decay modes of interest for ADS method

not yet measured; however, smallness

of RADS can be used to set upper limit

on rB


146

D0 CP eigenstates, multibody


147

Dalitz amplitude fits – wow!


148

Promising, but needs more data


149

CP violation in Bs decays

The Bs system can be used to study CP violation

Presence of spectator s quark → different set of angles

However

Bs production is suppressed, and ∆ms is very large (fast oscil.)

Rapid oscillation term (Δms~30Δmd) makes time resolved

experiments difficult

Width difference ΔΓ may be exploited instead

Dedicated B experiments at hadron facilities (like LHC-B) will be

needed to do this


150

Current status in ρ-η space Measurements are

consistent with SM

CP asymmetries from

B factories now

dominate the

determination of η

Improved precision

needed on |Vub| and

other angles (α,γ)

Bs oscillations too!


151

Radiative Penguin Decays and Radiative Penguin Decays and New PhysicsNew Physics

SM leading order = one EW loopVts, Vtd dependent

FCNCs probe a high virtual energy scale comparable to high-energy colliders

Radiative FCNCs have precise SM predictions:

BF(b→s)TH = 3.57 ± 0.30 x 10-4 (SM NLO)BF(b→s)EXP = 3.54 ± 0.30 x 10-4 (HFAG)

Decay rate agreement highly constrains new physics at the electroweak scale!

Further tests presented here:•Exclusive b→s decay rates

•b→s CP asymmetries•b→d penguins

Multiple new BF(b→s)measurements coming soon from BaBar

Radiative penguin decays: b → s and b → d FCNC transitions

Berryhil, ICHEP2004


152

b→s(d)γ

B→K*γ and b→sγ (inclusive) both observed by CLEO

in mid-90s; first EW penguins in B decay

BR consistent with SM; limits H+, SUSY:

BF(b→sγ) = (3.5 ±0.3 )×10-4 (expt)

= (3.4 ±0.6 )×10-4 (theory)

BF(B→K*γ) = (40.1 ±2.0 )×10-6 (expt)

non-strange bdγ modes not yet observed; but

B→ργ and Bωγ nearly so.

Eγ spectrum is used to probe shape function


153

|Vtd|/|Vts| from Bργ / BK*γ

Combined BF() ≡ BF(+) = 2(+/0) BF(0 ) = 2(+/0) BF( )

BF = (0.6 ± 0.3 ± 0.1) x10-6

BF < 1.2 x10-6 90% CL

95% C.L. BaBar allowed region (inside the blue arc)

With/withouttheory error


154

Radiative FCNC decays


155

Sensitivity to new physics


156

b→sνν

Cleanest rare B decay; sensitive to all generations

(important, since b→sτ+τ- can’t be measured)

BF quoted are sum over all ν species

SM predictions:

BF(B → Xsνν) < 6.4×10-4 at 90% c.l. (ALEPH)

BF(B+→K+νν) < 5.2×10-5 at 90% c.l. (BaBar submitted to PRL)

62.1

6.0

6910

108.3

1041

KB

XB s

B

B

ℓ

ℓ ℓ ℓ

ℓ,ν


157

History… Courtesy of the UTfit people (http://utfit.roma1.infn.it/)

Progress due to improvements in theory, measuring

sides, and (last) measuring CP violation in B

Non-trivial test of CKM!


158

B Physics – broad and deep CP violation in B decays is large and will be observed in

many modes Precision studies of B decays and oscillations provide

the dominant source of information on 3 of the 4 CKM parameters

Rare B decays offer a good window on new physics due to large mt and |Vtb|

B hadrons are a laboratory for studying QCD at large and small scales. A large range of measurements can be made to test our calculations. Modern techniques allow a quantitative estimate of theoretical errors


159

A glimpse of things to come? B physics and neutrino experiments have produced the

most significant discoveries since the LEP/SLC program

The same two

fields will probe

deeper into

flavour mixing

and CP violation

CKM physics is becoming high precision physicsCKM physics is becoming high precision physics

C K M

N

S

• New experiments at hadron machines will probe Bs oscillations, CP and rare decays


160

Grazie… a Maurizio per l’invito e l’ospitalita’

a tutti voi per l’ascolto

january, 2005kowalewski --- perugia lectures1 lectures on b physics bob kowalewski university of...

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b production

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b factories

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b quark hadronizes

bq b mesons

history of b physics