february 16-22kowalewski - llwi 20031 b physics and cp violation bob kowalewski university of...

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

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In remembrance of

Professor Nate Rodning

U. of Alberta

(~1957 – 2002)


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


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


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


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)


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


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


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


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


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)


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,


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


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)


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


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)


PEP-II and KEK-B


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


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


So e+e-→bb… then what?


• 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


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


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


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


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


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


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


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!


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


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


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


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


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


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


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


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


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


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


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


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.


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


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


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


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


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+


|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


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


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


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


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


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


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


END OF LECTURE 1


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


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


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


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


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


)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


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


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%))


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


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)


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


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


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


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


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


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


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


• 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


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.


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


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


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


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


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


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


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


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


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)


Hadronic Rare B Decays: Towards sin(2)

• B-> would measure sin(2)…

• …if it weren’t for Penguin pollution!


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


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!


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


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!


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


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


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


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


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


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


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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february 16-22kowalewski - llwi 20031 b physics and cp violation bob kowalewski university of...

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