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January, 2005 Kowalewski --- Perugia lectures
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Lectures on B Physics
Bob Kowalewski
University of Victoria
Currently at La Sapienza and the
Laboratorio Nazionale di Frascati
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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
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Lecture 1 History of B physics: 1977 – 2004
Significant facilities, past and present
B meson production and decay
CKM matrix
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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
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Upsilon experiment at FNAL 400 GeV proton beam incident on target
Look for muon pairs; measure invariant mass
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Initial results
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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.
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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
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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
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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
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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)
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CESR and CLEO
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DORIS-II and ARGUS
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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)
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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
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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
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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
bc
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15 years later…
Data (continuum sub)MC for BB background
S/B ~ 1/25 at 2.0 GeV!
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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
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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**)
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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
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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
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The B factory era CESR had an impressive history…but new
challenges require new facilities
B factories>100 fb-1 / year
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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
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PEP-II and KEK-B
Jonathan Dorfan
Pier Oddone
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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
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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)
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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
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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)
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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
BB
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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
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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.
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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
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b quarks and B mesons…
The b quark decay is simple
B meson decay is not…
Vcb
b
c
cbV
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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
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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+
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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
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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
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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
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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)
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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,
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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)
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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
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End of Lecture 1
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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
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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
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Recall:
The b quark decay is simple
B meson decay is less so…
Vcb
b
c
cbV
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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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
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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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
71
μπ2 ~
λ1
μG2 ~
λ2
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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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
74
OPE preliminary fit results|Vcb| measured to 2%!
January, 2005 Kowalewski --- Perugia lectures
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|…
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia 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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
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86
Radiative FCNC decays
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87
Sensitivity to new physics
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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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
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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
January, 2005 Kowalewski --- Perugia lectures
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
<<
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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).
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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)
January, 2005 Kowalewski --- Perugia lectures
100
Physicist’s Rorschack
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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!
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
109
• From the recent CKM2005 workshop:
Mother Nature has been very kind!
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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 ↑
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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!
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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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
January, 2005 Kowalewski --- Perugia lectures
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
January, 2005 Kowalewski --- Perugia lectures
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)
January, 2005 Kowalewski --- Perugia lectures
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,
January, 2005 Kowalewski --- Perugia lectures
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
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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!
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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)
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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
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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.
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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
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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
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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
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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
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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
BBAABBARARBBAABBARAR
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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
BBAABBARARBBAABBARAR
BABAR CONF-04/037
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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
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CKM constraints and sin2 and measurements
CKM fit to indirect constraints overlaid with sin2β and measurements
• Constraints on starting to have an impact
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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
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sin(2β+γ) from B0D(*)-π+ decays
Same final state reached by B0, B0 in different diagrams
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Status of sin(2β+γ) Fit determines coefficients of time-dependent terms;
further input still needed to get sin(2β+γ)
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Idea – use D0 CP eigenstates
fCP: K+K-, KSπ, π+π-
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Idea – use DCS D0 decays
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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
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D0 CP eigenstates, multibody
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Dalitz amplitude fits – wow!
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Promising, but needs more data
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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
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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!
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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
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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
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|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
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Radiative FCNC decays
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Sensitivity to new physics
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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
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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!
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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
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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
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Grazie… a Maurizio per l’invito e l’ospitalita’
a tutti voi per l’ascolto