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Lectures on B Physics

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Lectures on B Physics

Bob Kowalewski

University of Victoria

Currently at La Sapienza and theLaboratorio Nazionale di Frascati

Kowalewski --- Perugia 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

Kowalewski --- Perugia lectures

- History of B physics: 1977 – 2004
- Significant facilities, past and present
- B meson production and decay
- CKM matrix

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

- 400 GeV proton beam incident on target
- Look for muon pairs; measure invariant mass

Kowalewski --- Perugia lectures

Initial results

Kowalewski --- Perugia lectures

- 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.

Kowalewski --- Perugia lectures

- States seen are the first 3 radial excitations of the vector bb stateΥ(1S),Υ(2S),Υ(3S)
- Observed width is experimental resoln
- Quantum numbers JPC=1--
- b mass ~ 4.6 GeV

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

3S

10.28

10.44

- 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

9.40

9.50

9.96

10.02

- B0 and B+ discovered by CLEO (1982)
- B* mesons at CUSB (1985)
- ARGUS detector (DORIS-II) starts at DESY (1982)

2mB

Kowalewski --- Perugia lectures

Kowalewski --- Perugia lectures

Kowalewski --- Perugia lectures

- 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)

Kowalewski --- Perugia lectures

- 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; need1 B to decay first

Kowalewski --- Perugia lectures

- The flavor oscillation is now mapped out over ~1.5 full periods
- Δm= (0.502±0.006) ps-1

5.0

10.0

15.0

1

2

4

dileptons

20.7 fb-1

1

2

4

Belledileptons29.4 fb-1

unmixed

mixed

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

Data (continuum sub)

MC for BB background

S/B ~ 1/25 at 2.0 GeV!

Kowalewski --- Perugia lectures

- 1993 – exclusive decay BK*γ seen in CLEO
- 1995 – inclusive bsγ process measured (much harder!)
- Rate probes new physics

BaBar

B0K*0γ

Kowalewski --- Perugia lectures

- 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**)

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

- CESR had an impressive history…but new challenges require new facilities

B factories>100 fb-1 / year

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

Jonathan Dorfan

Pier Oddone

Kowalewski --- Perugia lectures

BaBarBelleLmax (1033/cm2/s)9.2 13.9

best day (pb-1)681 944

total (fb-1)244 338

- Both B factories are running well:

Belle

Kowalewski --- Perugia lectures

- Belle and BaBar are similar in performance; some different choices made for Cherenkov, silicon detectors
- Slightly different boost, interaction region geometry (crossing angle)

CsI (Tl)

BaBar

DIRC

e+ (3.1 GeV)

Belle

e- (9 GeV)

IFR

SVT

DCH

Kowalewski --- Perugia lectures

- By any pre-LHC standard, this is big science; BaBar has ~ 600 members, Belle ~ 300 (not all pictured in either case!)

KEKB / Belle

Pep2 / BaBar

Kowalewski --- Perugia lectures

- 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)

Kowalewski --- Perugia lectures

- 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

BB

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

2mB

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

- 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.

Kowalewski --- Perugia lectures

c e νeb

- Charged-current Lagrangian in SM:
- Since mb<< MW, the effective 4-fermion interaction is
- CKM suppressed (|Vcb|<<1) → long lifetime ~ 1.5ps

×3 for color

Kowalewski --- Perugia lectures

- The b quark decay is simple
- B meson decay is not…

Vcb

Kowalewski --- Perugia lectures

Semileptonic ~ 26%

Hadronic ~ 73%

Theoretical predictions tend to have large uncertainties.

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

single hadronic current; ~reliable theory

Heavy Quark Expansion

BF form factors

Kowalewski --- Perugia lectures

b

W+

l+,n

b

B0

l–,l’–,n

d

W–

u

Leptonic < 10-4, 7,11τ, μ, e

B+

- Suppressed by helicity (like πeν)
- measures fB×|Vub|

Helicity suppressed; FCNC

In SM: B(B0m+m–) ~ 8×10-11B(B0nn) ~ zero

Kowalewski --- Perugia lectures

n,ℓ

ℓ,ν

n,ℓ

n,ℓ

n,ℓ

s,d

b

q

q

q

Colour-suppressed;

Includes all bcc q’q

EW penguins; 2nd order weak

Large mt enhances these loop diagrams

gluonic penguins; 2nd order weak

W exchange

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

- 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

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

Kowalewski --- Perugia lectures

d s b

u

c

t

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)

all terms O(λ3)

Kowalewski --- Perugia lectures

Rt

Ru

g

b

Kowalewski --- Perugia lectures

- The only 3rd generation quark we can study in detail
- Investigate flavour-changing processes, oscillationsCKM matrix

Cabibbo angle

B lifetime, decay

CP Asymmetries (phase)

BdBd and BsBs oscillations

=1

Kowalewski --- Perugia lectures

- The sides of the triangle are measured in b→uℓν and b→cℓν transitions (Ru) and in Bd0-Bd0 and Bs0-Bs0 oscillations (Rt)
- CP asymmetries measure the angles
- Vub, Vcb and Vtd measure the sides

Rt

Ru

g

b

GET A BETTER PICTURE

Kowalewski --- Perugia lectures

Kowalewski --- Perugia lectures

- B meson decays – role of QCD
- Heavy Quark symmetry
- Exclusive semileptonic decays
- Inclusive semileptonic decays
- Radiative decays
- p.s. – se parlo troppo velocenon esitate a dirmelo

Kowalewski --- Perugia lectures

- The sides of the triangle are measured in b→uℓν and b→cℓν transitions (Ru) and in Bd0-Bd0 and Bs0-Bs0 oscillations (Rt)
- CP asymmetries measure the angles
- Today we’ll talk about the rings

Rt

Ru

g

b

GET A BETTER PICTURE

Kowalewski --- Perugia lectures

- The b quark decay is simple
- B meson decay is less so…

Vcb

Kowalewski --- Perugia lectures

- Bound b quark is virtual and has some “Fermi momentum”
- b quark then has pb = pF and Eb = MB - pF, somb =√( 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

Kowalewski --- Perugia lectures

Xhνe

e

B

- 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

Kowalewski --- Perugia lectures

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

- γbinding e- and N in atoms can’t probe nuclear mass, spin… isotopes have similar chemistry!

b

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

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

Kowalewski --- Perugia lectures

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.

Kowalewski --- Perugia lectures

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/mQare
- the kinetic energy operator OKfor 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

Kowalewski --- Perugia lectures

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)

Kowalewski --- Perugia lectures

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 GeV2m2(D*) - m2(D) = 4λ2+O(1/mc); 0.55 GeV2
- baryon-meson splittings:m(Λb) - m(B) - 3λ2/2mB+ O(1/mb2); 312±6 MeVm(Λc) - m(D) - 3λ2/2mD+ O(1/mc2); 320±1 MeV

Kowalewski --- Perugia lectures

D*νe

e

B

- HQET simplifies the description of BXceνdecays 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.

Kowalewski --- Perugia lectures

- The zero-recoil point in BD(*)eνis 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

Luke’s theorem

Kowalewski --- Perugia lectures

- 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):

5% uncertainty

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

πνe

e

B

- HQET is not helpful in analyzing BXueνdecays 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+mπ2+2mBEπ
- Other decays tend to be more challenging

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

- 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)

Kowalewski --- Perugia lectures

- The inclusive decay widths of B hadrons into partially-specified final states (e.g. semileptonic) can be calculated using an OPE based on:
- 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
- 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.

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

- The decay rate into all states with quantum numbers f is
- Expanding this in αS and 1/mb leads towhere λ1 and λ2 are the HQET kinetic energy and chromomagnetic matrix elements.
- Note the absence of any 1/mb term!

free quark

Kowalewski --- Perugia lectures

X νe

e

B

- The HQE can be used for both b→u and b→c decays
- The dependence on mb5must be dealt with; in fact, an ambiguity of order ΛQCDexists 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, …

Kowalewski --- Perugia lectures

- Need these to go from BF to partial Γ
- HFAG average values (as of Summer, 2004):

Kowalewski --- Perugia lectures

μπ2 ~ λ1μG2 ~ λ2

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

- Ee moments calculatedup to αs2β0; MX momentsto αs (higher orders smallcompared with exp error)
- Separate fits to Ee andMx moments agree well
- Values for μG2 and ρLS3 are consistent with independent measurements based on mB*-mB and HQ sum rules.
- Overall power of Ee and MX moments is comparable

Kowalewski --- Perugia lectures

|Vcb| measured to 2%!

Kowalewski --- Perugia lectures

Moving on to |Vub|…

- 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

4% error

Kowalewski --- Perugia lectures

- 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

Data (continuum sub)

MC for BB background

Data (eff. corrected)

MC

Kowalewski --- Perugia lectures

b→callowed

mX2

b→callowed

b→callowed

- mass mx recoiling against ℓν (acceptance ~70%, but requires full reconstruction of 1 B meson)

B0→Xuℓ-ν

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

B→Xuℓ-ν

Kowalewski --- Perugia lectures

BABAR

- The better acceptance and signal-to-background comes at the cost of statistics and complexity (one needs to measure more things)

Kowalewski --- Perugia lectures

Shmax (GeV2)

- 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

reject

accept

reject

accept

Kowalewski --- Perugia lectures

- |Vub| is measured to ~ ±9%

Eℓ endpoint

mXfit

mXvs. q2

Eℓvs. q2

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

Kowalewski --- Perugia lectures

mb/2→Λ

mb and λ1 can be measured from

- Eγ distribution in b→sγ
- moments (mX, sX, Eℓ, EW+pW) in semileptonic decays
- Comparing values extractedfrom different measurementstests HQE
- This is currently an area ofsignificant activity

λ1

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

Radiative penguin decays: b → sg and b → dg FCNC transitions

SM leading order = one EW loop

Vts, Vtd dependent

- FCNCs probe a high virtual energy scale comparable to high-energy colliders
- Radiative FCNCs have precise SM predictions:
- BF(b→sg)TH = 3.57 ± 0.30 x 10-4 (SM NLO)
- BF(b→sg)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→sg decay rates
- b→sg CP asymmetries
- b→dg penguins

Multiple new BF(b→sg)

measurements coming soon from BaBar

Berryhil, ICHEP2004

Kowalewski --- Perugia lectures

- 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 bdγmodes not yet observed; but B→ργ and Bωγ nearly so.
- Eγ spectrum is used to probe shape function

Kowalewski --- Perugia lectures

Combined BF(r,wg) ≡ BF(r+g) =

2(t+/t0) BF(r0g) = 2(t+/t0) BF(wg)

BF = (0.6 ± 0.3 ± 0.1) x10-6

BF < 1.2 x10-6 90% CL

With/withouttheory error

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

Kowalewski --- Perugia lectures

Kowalewski --- Perugia lectures

Kowalewski --- Perugia lectures

n,ℓ

n,ℓ

n,ℓ

ℓ,ν

n,ℓ

- 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)

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

Lecture 4 – CP violation

- Direct CP violation
- Determining α
- Prospects for γ
- Summary

- B0B0 oscillations – theory and experiment
- CP violation in SM – basic mechanisms
- CP violation in B decays
- Measurement of unitarity triangle angle β

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

- Two Hermitian matrices M and Γ describe physics

M11=M22 (CPT)

Γ11 = Γ22

Quark masses, QCD+EM

Weak decay

Δb=2

intermediate state off-shell, on-shell

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

Kowalewski --- Perugia lectures

→1

→0

<<

→1

→0

- 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

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

5.0

10.0

15.0

1

2

4

dileptons

- 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

20.7 fb-1

unmixed

mixed

1

2

4

Belledileptons29.4 fb-1

Kowalewski --- Perugia lectures

- The box diagram for Δb=2 transitions contains both perturbative and non-perturbative elements
- Operator Product Expansion (OPE) calculation gives
- Uncertainty in BBFB2dominates (~30%)
- Hope for improvements using Lattice QCD

From <B0 |(V-A)2|B0>

universal fnof (mt/mW)2

pert. QCD

Kowalewski --- Perugia lectures

- 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> 14.5ps-1 at 95% c.l. (LEP/SLD/CDF)
- Fast oscillations are hard to study (one complete oscillation every γ·50μm).

Kowalewski --- Perugia lectures

- These measurements alone strongly favour a non-zero area for the triangle; this implies CP violation in SM

Kowalewski --- Perugia lectures

- 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)

Kowalewski --- Perugia lectures

Physicist’s Rorschack

Kowalewski --- Perugia lectures

- 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 = 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

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

HFAG: |q/p| = 1.0013 ± 0.0034

off-shell

off-shell

on-shell

on-shell

CP-invariant phase

arbitrary phase

Kowalewski --- Perugia lectures

no CPV

CP violation in decay amplitude

partial

decay rate

asymmetry

2 amplitudes A1 and A2

Weak phase difference

Strong 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

From Gautier Hamel de Monchenault

Kowalewski --- Perugia lectures

amplitude ratio

CP eigenvalue

mixing

Time-integrated asymmetry vanishes!

Kowalewski --- Perugia lectures

~0

~0

Piece from mixing (q/p)

→ pure phase

Piece from decay

if just one direct decay

amplitude to fCP

No dependence on δ!

Kowalewski --- Perugia lectures

assuming only tree-level decay

decay

B0 mixing

K0 mixing

Kowalewski --- Perugia lectures

- 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)

Kowalewski --- Perugia lectures

- From the recent CKM2005 workshop:

Kowalewski --- Perugia lectures

h

(r,h)

a

g

b

(0,0)

(1,0)

(bd)→uudd

B0d oscillationsB0s oscillations

SemileptonicBXue

(bd)→cusd(bd)→cudd

(bd)→ccsd, ccdd, ccss, sssd

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

(flavor eigenstates) lifetime, mixing analyses

(CP eigenstates) CP analysis

Exclusive B Meson Reconstruction

B-Flavor Tagging

Kowalewski --- Perugia lectures

Time-dependence of B0-B0 mixing

dilution due to

mis-tagging

Time-dependence of

CP-violating asymmetry inB0CPJ/ψ K0S

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

Kowalewski --- Perugia lectures

- measure Δz = lifetime convoluted with vertex resolution; deriveΔt

Unmixed

- 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

Mixed

Kowalewski --- Perugia lectures

w=Prob. for wrong tag

No mistagging and perfect Dt

D=1-2w=0.5

Nomix

Mix

Dt

Dt

Raw asymmetry

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

Dt

Dt

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

- 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!

Belle

BaBar

Kowalewski --- Perugia lectures

- BaBar and Belle both see significant CP violation:sin2β= 0.725±0.033±0.017C = 0.031±0.025±0.015
- Also |λf|=0.950±0.031±0.013(recall λf=(q/p)*(Af/Af) )

syserr ↓ as ∫Ldt ↑

BaBar

Belle

Kowalewski --- Perugia lectures

- 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’K0s, 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

Kowalewski --- Perugia lectures

- Status at ICHEP’04
- φK0 is pure Penguin

Kowalewski --- Perugia lectures

In SM interference between B mixing, K mixing and Penguin bsss or bsdd gives the same e-2ib as in tree process bccs.However loops can also be sensitive to New Physics!

New phases from SUSY?

Kowalewski --- Perugia lectures

- B0 oscillations have ΔΓ<<Δm, are CP conserving
- B0s can have sizable ΔΓ/Γ; B0d 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

Kowalewski --- Perugia lectures

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

- Direct CP violation
- Determining α
- Prospects for γ
- Summary

Kowalewski --- Perugia lectures

- 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

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

Kowalewski --- Perugia lectures

d s b

u

c

t

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)

all terms O(λ3)

Kowalewski --- Perugia lectures

Rt

Ru

g

b

Kowalewski --- Perugia lectures

no CPV

CP violation in decay amplitude

partial

decay rate

asymmetry

2 amplitudes A1 and A2

Weak phase difference

Strong 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

From Gautier Hamel de Monchenault

Kowalewski --- Perugia lectures

amplitude ratio

CP eigenvalue

mixing

Time-integrated asymmetry vanishes!

Kowalewski --- Perugia lectures

- 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)

Kowalewski --- Perugia lectures

- Exciting discovery in 2004: first observation of direct CP violation in B0K+π-
- Discrepancy in B+K+π0

s

K-

s K-

Kowalewski --- Perugia lectures

- 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.

Kowalewski --- Perugia lectures

Interference of suppressed

b u “tree” decay with mixing

but: “penguin”

is sizeable!

B0 decay: penguin

B0 mixing

B0 decay: tree

Coefficients of time-dependent CP Asymmetry

With no penguins

With large penguins

and |P/T| ~ 0.3

Kowalewski --- Perugia lectures

- Gronau-London isospin analysis: J=0 two-pion state has no I=1, so Bpp 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 p0p0 is small; doesn’t require p0p0to be tagged since uses sum

2

Kowalewski --- Perugia lectures

4.9s

BABAR CONF-04/035

6.0s

Grossman-Quinn bound:

Kowalewski --- Perugia lectures

BABAR

S2+C2≤1 physically

Comparison

Caution averaging!

Kowalewski --- Perugia lectures

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

BABAR

Kowalewski --- Perugia lectures

PRL 91 (2003) 171802

BABAR

BABAR CONF-04/037

Compare with 35o for pp

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BABAR & Belle combined

Mirror solutions disfavored

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- CKM fit to indirect constraints overlaid with sin2β and a measurements
- Constraints on a starting to have an impact

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

- Same final state reached by B0, B0 in different diagrams

Kowalewski --- Perugia lectures

- Fit determines coefficients of time-dependent terms; further input still needed to get sin(2β+γ)

Kowalewski --- Perugia lectures

fCP: K+K-, KSπ, π+π-

Kowalewski --- Perugia lectures

Kowalewski --- Perugia lectures

- 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 methodnot yet measured; however, smallnessof RADS can be used to set upper limiton rB

Kowalewski --- Perugia lectures

Kowalewski --- Perugia lectures

Kowalewski --- Perugia lectures

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

- 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!

Kowalewski --- Perugia lectures

Radiative penguin decays: b → sg and b → dg FCNC transitions

SM leading order = one EW loop

Vts, Vtd dependent

- FCNCs probe a high virtual energy scale comparable to high-energy colliders
- Radiative FCNCs have precise SM predictions:
- BF(b→sg)TH = 3.57 ± 0.30 x 10-4 (SM NLO)
- BF(b→sg)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→sg decay rates
- b→sg CP asymmetries
- b→dg penguins

Multiple new BF(b→sg)

measurements coming soon from BaBar

Berryhil, ICHEP2004

Kowalewski --- Perugia lectures

- 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 bdγmodes not yet observed; but B→ργ and Bωγ nearly so.
- Eγ spectrum is used to probe shape function

Kowalewski --- Perugia lectures

Combined BF(r,wg) ≡ BF(r+g) =

2(t+/t0) BF(r0g) = 2(t+/t0) BF(wg)

BF = (0.6 ± 0.3 ± 0.1) x10-6

BF < 1.2 x10-6 90% CL

With/withouttheory error

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

Kowalewski --- Perugia lectures

Kowalewski --- Perugia lectures

Kowalewski --- Perugia lectures

n,ℓ

n,ℓ

n,ℓ

ℓ,ν

n,ℓ

- 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)

Kowalewski --- Perugia lectures

- 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!

Kowalewski --- Perugia lectures

- 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

Kowalewski --- Perugia lectures

- 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 physics

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

Kowalewski --- Perugia lectures

- a Maurizio per l’invito e l’ospitalita’
- a tutti voi per l’ascolto

Kowalewski --- Perugia lectures