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February 16-22 Kowalewski - LLWI 2003 1
B Physics and CP Violation
Bob Kowalewski
University of Victoria
Particles and the Universe
Lake Louise Winter Institute
16-22 February 2003
February 16-22 Kowalewski - LLWI 2003 2
In remembrance of
Professor Nate Rodning
U. of Alberta
(~1957 – 2002)
February 16-22 Kowalewski - LLWI 2003 3
Plan for the lectures
Lecture 1:
• Why build B factories?• Review of CKM• B production and decay,
experimentation• Calculational tools:
OPE, HQE, HQET
• |Vub| and |Vcb|
Lecture 2:
• BB oscillations
• CP violation
• Rare decays
February 16-22 Kowalewski - LLWI 2003 4
Disclaimers
• These lectures are pedagogical in nature; as such, I will not necessarily– present the very latest measurements– carefully balance CLEO/Belle/Babar/CDF/LEP…
(my own work is on BaBar; it will be obvious!)• Due to time constraints, important topics will be
omitted; in particular,– not much will be said about Bs physics– prospects for B studies at hadron machines will not
be covered
February 16-22 Kowalewski - LLWI 2003 5
Suggested reading
• The following reviews can be consulted for more detailed presentations of the material covered in these lectures:– B Decays and the Heavy Quark Expansion, M. Neubert,
hep-ph/9702375
– The Heavy Quark Expansion of QCD, A. Falk, hep-ph/9610363
– Flavour Dynamics: CP Violation and Rare Decays, A. Buras, hep-ph/0101336
– CP Violation: The CKM Matrix and New Physics, Y. Nir, hep-ph/0208080
February 16-22 Kowalewski - LLWI 2003 6
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)
February 16-22 Kowalewski - LLWI 2003 7
B decays – QCD at the boundary
• Mix of large (mb) and small momentum (ΛQCD) scales – a laboratory for testing our understanding of QCD
• Large variety of decay channels to study in detail: leptonic, semileptonic, hadronic
• High density of states → inclusive measurements (quark-hadron duality)
• Vibrant interplay between experiment and theoryD
ππ
B
February 16-22 Kowalewski - LLWI 2003 8
CP violation – a fundamental question
But really…why spend ~109 $ on B factories?
• Explore CP violation– outside of K0 system– via different mechanisms
(direct, mixing, interference)– in many different final states
• Test the CKM picture– survey the unitarity triangle– can all measurements be
accommodated in this scheme?
Pep2 / BaBar
KEKB / Belle
February 16-22 Kowalewski - LLWI 2003 9
Return on investment
B factories give us• New physics? (high risk)• Determination of
unitarity triangle (balanced growth)
• Better understanding of heavy hadrons (old economy)
PDG 1999
PDG 2002
February 16-22 Kowalewski - LLWI 2003 10
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
3 x 3 unitary matrix. Only phase differences are physical, → 3 real angles and 1 imaginary phase
February 16-22 Kowalewski - LLWI 2003 11
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)
February 16-22 Kowalewski - LLWI 2003 12
A Unitarity Triangle
plane - and
:level 5% the At
:level 1% the At
|V||V|
06.083.0A/VA
V
0018.02205.0sinV
V
tdub
2cb
cb
cus
us
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
Choice of parameters:
and , A,
February 16-22 Kowalewski - LLWI 2003 13
Surveying the unitarity triangle
• The sides of the triangle are measured in b→uℓν and b→cℓν transitions (Ru) and in Bd
0-Bd0 and Bs
0-Bs0
oscillations (Rt)
• CP asymmetries measure the angles
• Great progress on angles; need sides too!
GET A BETTER PICTURE
Ru
Rt
February 16-22 Kowalewski - LLWI 2003 14
B meson production
• Threshold production in e+e- at Y(4S) has advantages:
– cross-section ~1.1nb, purity (bb / Σiqiqi) ~ 1/4
– simple initial state (BB in p-wave, no other particles,decay products overlap)
– “easy” to trigger, apply kinematic constraints• Role of hadron machines
– cross-sections much higher (×102)
– Bs are produced
– triggering harder, purity (b / Σiqi) ~ (few/103)
February 16-22 Kowalewski - LLWI 2003 15
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
• Asymmetric beam energies boost into lab: (βγ)4S ~0.5
on peak
off peak (q=u,d,s,c)
2mB
February 16-22 Kowalewski - LLWI 2003 16
Requirements
• High luminosity (need 108 B or more); this means L~1033-34/cm-2s-1, 30-100 fb-1/year
• Measure Δt = tB1-tB2 (need to boost Y(4S) in lab, use silicon micro-vertex detectors to measure Δz)
• Fully reconstruct B decays with good efficiency and signal/noise (need good track and photon resolution, acceptance)
• Determine B flavour (need to separate ℓ, π, K over ~full kinematic range)
February 16-22 Kowalewski - LLWI 2003 17
PEP-II and KEK-B
February 16-22 Kowalewski - LLWI 2003 18
B factories: KEK-B and PEP-II
• Both B factories are running well:
Belle
Belle BaBarLmax (1033/cm2/s) 8.3 4.6
best day (pb-1) 434 303
total (fb-1) 106 96
February 16-22 Kowalewski - LLWI 2003 19
B factory detectors• Belle and BaBar are similar in performance; some
different choice made for Cherenkov, silicon detectors• Slightly different boost, interaction region geometry
DIRC
DCH IFRSVT
CsI (Tl)
e- (9 GeV)
e+ (3.1 GeV)
BelleBelle
BaBarBaBar
February 16-22 Kowalewski - LLWI 2003 20
So e+e-→bb… then what?
February 16-22 Kowalewski - LLWI 2003 21
• Charged-current Lagrangian in SM:
• Since mb<< MW, effective 4-fermion interaction is
• CKM suppressed → 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 decayc e νe
b
b quark decay
2†
, 22 2 with
4 2CC F CC CC F
W
gG J J G
M
L
×3 for color
February 16-22 Kowalewski - LLWI 2003 22
Tree-level decays
Semileptonic ~ 26%
Leptonic < 10-4, 7,11
τ, μ, e
b
u
Hadronic ~ 73%
Colour-suppressed:
Charmonium!Vub, helicity suppressed
single hadronic current; reliable theory
Theoretical preductions tend to have large uncertainties
February 16-22 Kowalewski - LLWI 2003 23
Loop decays –significant due to large mt , sensitive to new physics
b→sg: O(10-2) b→sγ: O(10-4) b→s(d)ℓℓ: O(10-6)
γ,Z
B0 → B0: (B0→B0) / B0 = 0.18
February 16-22 Kowalewski - LLWI 2003 24
B hadron decay
• QCD becomes non-perturbative at ΛQCD ~ 0.2 GeV, and isolated b quarks do not exist.
• How does QCD modify the weak decay of b quark?
• Bound b quark is virtual and has some “Fermi momentum” – this was the basis of the parton (valence) model of B decay
• Parton model had some successes, but did not provide quantitative estimates of theoretical uncertainties.
• Modern approach – use the operator product expansion to separate short- and long-distance physics
Xh νe
e
B
February 16-22 Kowalewski - LLWI 2003 25
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
February 16-22 Kowalewski - LLWI 2003 26
OPE in B decays
• The scale μ separating short/long distance matters not … except in finite order calculations
• typically use ΛQCD << μ ~ mb << MW; αS(mb) ~ 0.22
• Wilson coefficients Ci(μ) contain weak decay and hard-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
February 16-22 Kowalewski - LLWI 2003 27
Heavy Quarks in QCD
• There is no way to avoid non-perturbative effects in calculating B hadron decay widths
• Heavy Quarks have mQ >> ΛQCD (or, equivalently, Compton wavelength λQ << 1/ΛQCD )
• Since λQ << 1/ΛQCD, soft gluons (p2 ~ ΛQCD) cannot probe the quantum numbers of a heavy quark
→ Heavy Quark Symmetry
February 16-22 Kowalewski - LLWI 2003 28
Heavy Quark Symmetry
• For mQ→∞ the light degrees of freedom 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.
• The heavy quark (atomic nucleus) acts as a static source of color (electric) charge. Magnetic (color) effects are relativistic and thus suppressed by 1/mQ
• HQ symmetry is not surprising - different isotopes of a given element have similar chemistry!
February 16-22 Kowalewski - LLWI 2003 29
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
February 16-22 Kowalewski - LLWI 2003 30
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:
• In Q rest frame, h(H) correspond to upper(lower) components of the Dirac spinor Q(x)
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
February 16-22 Kowalewski - LLWI 2003 31
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
February 16-22 Kowalewski - LLWI 2003 32
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
February 16-22 Kowalewski - LLWI 2003 33
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 MeVm(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/mb
2); 312±6 MeV m(Λc) - m(D) - 3λ2/2mD+ O(1/mc
2); 320±1 MeV
February 16-22 Kowalewski - LLWI 2003 34
Exclusive semileptonic decays
• HQET simplifies the description of BXceν decays and allows better determinations 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
February 16-22 Kowalewski - LLWI 2003 35
BD*eν form factors
• The HQET matrix element for BD*eν decays is
• The form factors hV … are related in HQET:
• ξ must be measured; predicted relations can be tested!
1 2 3
* *'
* *'
( , ) ( ) ( ) ;
( , ) ( ) ( )( 1) ( ) ( )
v V
v A A A
D v c b B v h w i v v w v v
D v c b B v h w w v h w v h w v
ε
1 3
2 2
( ) ( ) ( ) ( );
2 (1 )( ) ( ) 0 as
V A A
B DA Q
B D
h w h w h w w
m m wh w w m
m m
February 16-22 Kowalewski - LLWI 2003 36
Determination of |Vcb|• The zero-recoil point in BD(*)eν is suppressed by
phase space; the rate vanishes at w=1, requiring an extrapolation 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 theorem2
2(1) 1 ...QCD QCD
AQ Q
Cm m
0F
February 16-22 Kowalewski - LLWI 2003 37
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 (PDG 2002):
3
3
1 0.91 0.04 (Lattice QCD, sum rules)
1 38.3 1.0 10 (experiment)
(42.1 1.1 1.9) 10
cb
cb
V
V
F
F
5% error
February 16-22 Kowalewski - LLWI 2003 38
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
February 16-22 Kowalewski - LLWI 2003 39
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); large backgrounds from e+e-→qq events
• Prospects for calculating the form factor in B→πℓν decay on the Lattice are good; current uncertainties are in the 15-20% range on |Vub|
• Not yet very constraining
π νe
e
B
February 16-22 Kowalewski - LLWI 2003 40
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.
February 16-22 Kowalewski - LLWI 2003 41
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
February 16-22 Kowalewski - LLWI 2003 42
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
February 16-22 Kowalewski - LLWI 2003 43
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
February 16-22 Kowalewski - LLWI 2003 44
The upsilon expansion1
• The mb appearing in the HQE is the pole mass; it is infrared sensitive (changes at different orders in PT)
• Instead, one can expand both Γ(B→Xf) and mY(1S) in a perturbation series in αS(mb) and substitute mY(1S) for mb in Γ(B→Xf) – this is the upsilon expansion
• There are subtleties in this – the expansion must be done to different orders in αS(mb) in the two quantities
• The resulting series is well behaved and gives
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
February 16-22 Kowalewski - LLWI 2003 45
Semileptonic B decay basics
• BF(B→Xℓ-ν) ~ 10.5%
• Γ(b→cℓ-ν) is about ~60 times Γ(b→uℓ-ν) (not shown)• Leptons from the cascade b→c→ℓ+ have similar rate
but softer momentum spectrum, opposite charge
b→ℓ- b→ℓ+
February 16-22 Kowalewski - LLWI 2003 46
|Vcb| from inclusive s.l. B decays
higher orders in mb, αS
Knowledge of λ1, λ2
• ΓSL = τB×BFSL ≅ Γ(B→Xcℓν) ∝ |Vcb|2
• Using (from PDG2002)τ(B0) = 1542±16 fs, τ(B+) = 1674±18 fs, BF(B→Xcℓν) = (10.38±0.32)% along with the aforementioned theoretical relation,
|Vcb| = (40.4±0.5exp±0.5±0.8th)·10-3
• Compatible with D*ℓν result; 3rd best CKM element
February 16-22 Kowalewski - LLWI 2003 47
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 methods usesendpoint of lepton momentumspectrum; acceptance ~10%leading to large extrapolationuncertainty
February 16-22 Kowalewski - LLWI 2003 48
Better(?) 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
February 16-22 Kowalewski - LLWI 2003 49
Shape function• The Shape function, i.e. the
distribution of the b quark mass within the B
• Some estimators (e.g., q2) are insensitive to it Sh
max (GeV2)
acce
pt
acce
pt
reje
ct
reje
ct
February 16-22 Kowalewski - LLWI 2003 50
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 measurementstests HQE
• This is currently an area ofsignificant activity
mb/2→Λ
λ1
February 16-22 Kowalewski - LLWI 2003 51
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
February 16-22 Kowalewski - LLWI 2003 52
Surveying the unitarity triangle
• The sides of the triangle are measured in b→uℓν and b→cℓν transitions (Ru) and in Bd
0-Bd0 and Bs
0-Bs0
oscillations (Rt)
• CP asymmetries measure the angles
• Great progress on angles; need sides too!
GET A BETTER PICTURE
Ru
Rt
February 16-22 Kowalewski - LLWI 2003 53
END OF LECTURE 1
February 16-22 Kowalewski - LLWI 2003 54
Plan for the lectures
Lecture 1:
• Why build B factories?• Review of CKM• B production and decay,
experimentation• Calculational tools:
OPE, HQE, HQET
• |Vub| and |Vcb|
Lecture 2:
• BB oscillations
• CP violation
• Rare decays
February 16-22 Kowalewski - LLWI 2003 55
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 decay 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
February 16-22 Kowalewski - LLWI 2003 56
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
February 16-22 Kowalewski - LLWI 2003 57
Δm, ΔΓ• 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
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
→1→0
→1→0
February 16-22 Kowalewski - LLWI 2003 58
Bd oscillations
• For B0(bd), ΔΓ/Γ<<1: only O(~1%) of possible decays are to flavour-neutral states (ccd or uud); dominant decays are to cud or cℓν
• Consequently, most decay modes correlate with the b quark favour at decay time. Contrast with K0 system
• Therefore most decay modes are not CP eigenstates (which are necessarily flavour-neutral)
• The large top quark mass breaks the GIM cancellation of this FCNC and enhances rate Δm/Γ; large τB allows oscillations to compete with decay
February 16-22 Kowalewski - LLWI 2003 59
)ps(|t|10.0 15.05.0
mixedunmixed
)m(|z|
dBτdBΔm/π
dileptons20.7 fb-1
Evidence for Bd oscillations
• The fraction of like-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 = (0.489±0.008) ps-1
1 2 4
Belledileptons29.4 fb-1
1 2 4
February 16-22 Kowalewski - LLWI 2003 60
SM expectation for Bd oscillations
• The box diagram for Δb=2 transitions contains both perturbative and non-perturbative elements
• 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
February 16-22 Kowalewski - LLWI 2003 61
Experimental status of Bs oscillations
• In the BS system the CKM-favoured decay b→ccs leads to flavour-neutral (ccss) states, so ΔΓ/Γ may be as large as ~15% (but we still have ΔΓ<< Δm)
• Note Γ(Bs)= Γ(Bd) to O(1%)
• Δm/Γ is much larger than for Bd, since |Vts|2/|Vtd|2~30
• Fast oscillations are hard to study (need superb spatial resolution: one complete oscillation every γ·50μm).
• Current limit (PDG2002): Δms > 13 ps-1 at 95% c.l.
• Δmd /Δms ~ (|Vtd|/|Vts|)2 (corrections are O(15%))
February 16-22 Kowalewski - LLWI 2003 62
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
February 16-22 Kowalewski - LLWI 2003 63
February 16-22 Kowalewski - LLWI 2003 64
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)
February 16-22 Kowalewski - LLWI 2003 65
CP violation in SM• 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, whereJ = Jarlskog invariant = c12c23c2
13s12s23s13sinδ ~ 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”
• Massive neutrinos imply that the same mechanism for CP violation exists in lepton mixing (MNS) matrix
• Since it depends on a phase, the only observable effects come from interference between amplitudes
February 16-22 Kowalewski - LLWI 2003 66
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
• 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
February 16-22 Kowalewski - LLWI 2003 67
CP Violation in Mixing• Compare mixing for particle and antiparticle
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-conserving 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
February 16-22 Kowalewski - LLWI 2003 68
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
February 16-22 Kowalewski - LLWI 2003 69
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
February 16-22 Kowalewski - LLWI 2003 70
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
February 16-22 Kowalewski - LLWI 2003 71
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
February 16-22 Kowalewski - LLWI 2003 72
• 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
February 16-22 Kowalewski - LLWI 2003 73
Angle α – not as simple
• 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, …• 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 with an analysis of the Dalitz plot.
February 16-22 Kowalewski - LLWI 2003 74
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
(bd)→cusd(bd)→cudd
February 16-22 Kowalewski - LLWI 2003 75
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
February 16-22 Kowalewski - LLWI 2003 76
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
February 16-22 Kowalewski - LLWI 2003 77
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
0S
0CP K/JB
Time-dependence ofCP-violating asymmetry in
mixing00 BB Time-dependence of
)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
February 16-22 Kowalewski - LLWI 2003 78
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
February 16-22 Kowalewski - LLWI 2003 79
Impact of mistagging, t resolutionNo 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
February 16-22 Kowalewski - LLWI 2003 80
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
February 16-22 Kowalewski - LLWI 2003 81
B reconstruction
• B→J/ψK0, J/ψ→ℓ+ℓ- is very clean; can be used at hadron machines as well
• At e+e- bfactorieskinematicconstraintsallow useof KL too!
BelleBelle
BaBarBaBar
February 16-22 Kowalewski - LLWI 2003 82
Results for sin2β• BaBar and Belle both see
significant CP violation:
• syserr ↓ as ∫Ldt ↑BaBarBaBar
BelleBelle
sin 2 0.719 0.074 0.035 (Belle)
sin 2 0.741 0.067 0.034 (BaBar)
February 16-22 Kowalewski - LLWI 2003 83
Hadronic Rare B Decays: Towards sin(2)
• B-> would measure sin(2)…
• …if it weren’t for Penguin pollution!
February 16-22 Kowalewski - LLWI 2003 84
Hadronic Rare B Decays: B→, B→K+
B→B→
B→KB→K++
mES
6(4.7 0.6 0.2) 10
6(17.9 0.9 0.7) 10
Both modes peak at B mass; need ΔE and particle ID
E=EB - ECM/2
February 16-22 Kowalewski - LLWI 2003 85
CP Asymmetry in B→
BaBarBaBar
BelleBelle
0.08 0.07
2 2
0.02 0.34 0.05 (BaBar)
1.23 0.41 (Belle)
.30 0.25 0.04 (BaBar)
.77 0.27 0.08 (Belle)
1 Physical region
S
S
C
A
S C
Hot topic!
February 16-22 Kowalewski - LLWI 2003 86
CP violation in Bs decays
• The Bs system is as good a place to study CP violation as Bd; however, Bs production is suppressed
• Presence of spectator s quark → different set of unitarity angles are accessible
• 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
February 16-22 Kowalewski - LLWI 2003 87
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!
February 16-22 Kowalewski - LLWI 2003 88
Rare decays
• Window on new physics – look for modes highly suppressed in SM
• FCNC decays, forbidden at tree level: b→s(d)γ, b→s(d)ℓ+ℓ-, b→s(d)νν
• Leptonic decays: B0→ℓ+ℓ-, B+→ℓ+ν
• New physics can enhance rates, produce CP asymmetries, modify F/B asymmetries
• Ratio of b→d / b→s FCNC decays measures |Vtd|2/|Vts|2
Z ℓ ℓ b Vts
q Xs
b ℓ Vub
u fB ν
February 16-22 Kowalewski - LLWI 2003 89
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) = (3.3 ±0.4 )×10-4 (expt) = (3.29±0.33)×10-4 (theory) BF(B→K*γ) = (4.1 ±0.3 )×10-5 (expt)
• non-strange modes (e.g. B→ργ) not yet observed; limits ~ 10-5 and improving
• Photon spectrum also used to probe shape function
February 16-22 Kowalewski - LLWI 2003 90
b→s(d)ℓℓ (or νν)
• Replace ℓ↔ν to get graphs for b→sνν• Presence of W, Z give sensitivity to new physics that
does not couple to γ• New heavy particles at EW scale (from SUSY, etc.)
can give significant rate changes w.r.t. SM prediction
February 16-22 Kowalewski - LLWI 2003 91
B→Xsℓℓ
• B→K(*)ℓℓ observed by Belle and BaBar
• No surprises yet,sensitivity is stillimproving
1.4 61.1
7
* 6
( ) 6.1 1.4 10 (Belle)
( ) 7.6 1.8 10 (BaBar+Belle)
( ) 3.0 10 at 90% c.l. (BaBar)
sBF B X
BF B K
BF B K
+ -
+ -
+ -
veto J/ψ region
February 16-22 Kowalewski - LLWI 2003 92
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) < 2.4×10-4 at 90% c.l. (CLEO)
< 9.4×10-5 at 90% c.l. (BaBar prelim)
0.8 51.0
1.2 60.6
( ) 4.1 10
( ) 3.8 10
sBF B X
BF B K
February 16-22 Kowalewski - LLWI 2003 93
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
February 16-22 Kowalewski - LLWI 2003 94
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