Experimental Aspects of CP Violation

1
Experimental Aspects of CP Violation

• Daniel Cronin-Hennessy
• TASI June 2003

2

• Daniel Cronin-Hennessy

Research Associate University of Rochester CLEO
collaboration at LEPP (Cornell)
3
Short Bio

• 1995 Joined CDF collaboration at Fermilab
  top (1.8 TeV pp collider q
  q ? t t )
• During Run 1
• Focus was tests of Perturbative QCD (as) via
  analysis of W boson produced in association with
  jets.

• 1999 Joined CLEO collaboration at CESR
  bottom
• (10.58 GeV ee- collider Y(4S)?BB)
• During CLEOIII
• Improved CKM matrix element extractions with HQET

• Future CLEO-c (3 GeV)
  charm
• Lattice QCD , glueballs, and hybrids

4
Goals

• How we know what we know
• Show experimental techniques
• The phenomenology used to interpret data
• Accent role of Symmetry
• both in theory and in experiment
• Connect Observables to CKM formalism
• Convey importance CP Violation

5
Authors versus Time

• Carl Anderson 1933

6
Authors versus Time

• J H Christenson 1964
• J W Cronin
• V L Fitch
• R Turlay

7
Authors versus Time
CLEO 150 Recent list
8
Authors versus Time
CDF 400 1995
9
Authors versus Time
BaBar 600
10
Timeline
1928 1956
1972 Dirac LeeYang
KM e P Violation
CP viol from

mixing matrix

• 1933 1957 1964
  1974 1977 1982
  1987 1989
• Anderson Wu CroninFitch
  Brookhaven Fermilab CESR DORIS
  CESR
• 
  Standford
• e P(C) Viol CP Viol
  J/Y( cc) Y(bb) Bmeson
  BMixiing charmless
• 
  
  B decay(Vub)
• 1995 2000 2001
• Fermilab CERN/Fermilab KEKB/PEPII
• TOP Direct CP Violation CP Violation
  in B

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Background (positron)

• Carl Anderson 1933
• Wilson Chamber- condensation around ions. Ions
  generated from passing charged particle.
• Device immersed in high B field (15 kG)
• 14 cm diameter

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Background (positron)

• B field into page
• qvXB ? the sign of charge
• Negative particle moving down or positive
  particle moving up
• 6mm Lead plate (dark band) placed in middle of
  chamber to break up-down symmetry
• Ionization loss in lead ? radius of curvature of
  track is smaller in 2nd half of track. Positive
  charged track.

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Background (positron)

• Positive track but why not Proton
• Energy of proton (upper portion) is .3 MeV. Range
  of proton is about 5 mm at this energy. The track
  is 10 times this length (5 cm).
• Conclusions after detailed study
• Q lt 2 Qproton
• M lt 20 Melectron
• Particle (positron) identified with the
  anti-particle of electron
• Electron should be renamed negatron (from
  symmetry considerations)
• symmetry does not drive all physics

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Background (positron)

• The idea that each particle has an anti-particle
  has empirical basis
• We can reasonably ask where antimatter has gone
  if we have basis for its existence.
• Symmetry of mathematics driving the
  interpretation of physical reality
• 5 years earlier Diracs wave equation manifested
  negative energy solutions.
• These solutions were not discarded as unphysical
  mathematical artifacts but interpreted as
  antiparticle partners to the positive solutions

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Where are the anti-protons?

• Astro-physicists count photons. 3 degree cosmic
  background radiation permeates all space. It is
  the cooled (red shifted ) remnant of the early
  universe.
• Astro-physicists measure abundances hydrogen,
  helium, etc. (baryon number)
• We could detect antimatter if it were there (
  Signature photons from matter anti-matter
  annihilation not detected)
• Results
• Current limits on anti-matter lt 0.0001observed
  matter
• Observed universe Baryon number to photon number
  10-9
• For every billion photons there is one baryon
• Assuming baryon anti-baryon annihilation
  accounts for current photons in Universe ? 1
  baryon for every 1 billion baryon-antibaryon pair
  survived
• Without this asymmetry we would not be here.

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Where are the positrons (anti-protons etc) ?

• Sakharovs (1967) conditions for generating
  Anti-matter matter asymmetry
• Baryon number violation (another story)
• Must be able to get rid of baryons
• CP asymmetry
• Must be imbalance in baryon violation between
  baryons and anti-baryons
• Universe must be out of thermal equilibrium
• So that time reversed process can not restore
  symmetry.

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Symmetries (C )

• Charge conjugation (C)
• C changes particle to anti-particle
• Examples
• Charge Conjugation on electron positron
• C e- e (shorthand)
• C p p
• C p p-
• C n n

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Symmetries (P)

• Parity (P) Mirror symmetry
• Inverts spatial coordinates
• x ? -x y ? -y z?-z
• Effect on other observables
• Velocity (v)
• P v - v ( reverses direction)
• Spin (s)
• P s s ( does not change)
• Helicity
• P Right-handed Left-handed

Right-handed means thumb Of righthand points in
direction of motion Left-handed means thumb of
left hand Points in direction of motion
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C and P

• n Participates in weak interaction
• No electric charge, No color charge
• NEVER observed
• C and P in weak interactions is violated

n Right
n Left
P
CP
C
C
Anti-n Right
Anti-n Left
P
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The t-q puzzle

• Pre 1956
• Two particles with similar characteristics (such
  mass and lifetime) are only different in the
  decays.
• q ?p p0 parity 1 (-1-1(-1)0)
• t ? p p- p parity 1
• Seemed obvious that if t and q are the same
  particle they should have the same intrinsic
  parity
• T.D. Lee C.N. Yang point out no evidence
  favoring parity conservation in weak decays
  must test.

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A Test of Parity (Wu, 1957)

• Align Cobalt 60 nuclear spin
• Look for electrons from beta decay
• 60Co?60Ni e- anti-n
• Beta decay
• n ? p e- anti-n
• d ? u e- anti-n
• Electrons emitted opposite to direction of
  nuclear spin (parity operation would reverse
  direction of
• electron but not the the nuclear spin).

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C and P

• n Participates in weak interaction
• No electric charge, No color charge
• NEVER observed
• C and P in weak interactions is violated
  maximally

n Right
n Left
P
CP
C
C
Anti-n Right
Anti-n Left
P
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The Neutral Kaon system

• K0 (d anti-s) K0 (anti-d s)
• Strange particles produced via strangeness
  conserving process.
• DS0 (-1 1)
• Decays weakly (violating strangeness) long lived
  and large difference in lifetimes between the
  neutral Ks
• Proposal
• Assuming CP
• K1 K0 K0 CP K1 K0 K0 K1 (CP1)
• K2 K0 K0 CP K2 K0 K0 K2
  (CP-1)
• K1 ? 2 p (CP 1)
• K2 ? 3 p (CP -1)
• Without 2 p decay open to K2 expect increased
  lifetime
• Long lived Neutral K (15 meters) Short
  lived (2.8 cm)

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CP Violation Observed
Signal K2?2p Bck K2?3p Use angle (q)
between 2p and beam axis K1 decay long before
detector Regeneration of K1 in collimator
inconsistent with vertex distribution
Spectrometer
p
Decay Volume (He)
K2
collimator
p-
57 Ft to target
Spectrometer
MK .498 MeV
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CP Violation Observed

• Christenson, Cronin, Fitch Turlay 1964
• Observed CP violating decay K2?2p 17 meters from
  production point (gt 600 times lifetime of short
  lived neutral Kaon)
• Occurred in about 1 in 500 decays.
• Interpretation Physicals states were not
  eigenstates of CP but asymmetric mixing of K0 and
  anti-particle.
• Kshort K1 e K2
• Klong K2 e K1
• Kshort (1e) K0 (1-e) K0
• Klong (1e) K0 (1-e) K0
• Asymmetric mixing at level of 0.2

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Counting Klong decays

• Part of what particle physicists do is just count
  the number of times
• a particular particle decays to a particular
  final state
• Example Given 10000 Klong particles
• 2108 times I see the Klong decay to p0 p0 p0
• 1258 times I see the Klong decay to p p- p0
• 1359 times I see the Klong decay to p- m n
• 1350 times I see the Klong decay to p m- n
• 1950 times I see the Klong decay to p- e n
• 1937 times I see the Klong decay to p e- n
• 38 times I see the Klong decay to other
• Note that p- e n and p e- n are connected by
  CP
• CP (p- e n) p e- n

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Counting Klong decays

• Example Given 10000 Klong particles
• 1950 times I see the Klong decay to p- e n
• 1937 times I see the Klong decay to p e- n
• If CP were an exact symmetry I expect the same
  number of
• p- e n and p e- n decays.
• We observe different numbers 1950 and 1937
• d N(KL ? e n p-) N(KL ? e- n p ) 0.0033
• N(KL? e n p-) N(KL ? e- n p )

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CP Violation in Neutral Kaon

• a amp(K0 ?f) a amp(K0?f)
• c (a-a) / (aa)
• h amp(KL ? f )/amp(KS ? f)
• Kshort (1e) K0 (1-e) K0
• Klong (1e) K0 (1-e) K0
• h (1e) a - (1-e)a (a-a) e(aa)
  e c
• (1e) a (1-e)a e(aa) (a-a)
  1ec
• h e
  c
• (mixing)
  (direct CP violation Process dependent)
• ? h- ! h00

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Observable for Direct CP Violation

• h- /h00
• amp(KL?pp-)/amp(KS?pp-) e
  e
• amp(KL?p0p0)/amp(KS?p0p0)
  e 2e
• Actual measurement
• G(KL?pp-)/G(KS?pp-)
  1 6 Re(e/e)
• G(KL?p0p0)/G(KS?p0p0)
• e small compared to e. e already
  small ?
• difficult measurement!

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K mixing (quark mixing)

• K0 ? K0 (Standard Model)

s
d
u,c,t
W
W
K0
K0
d
s
u,c,t
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quark mixing

• CKM matrix relates quark mass eigenstates to weak
  eigenstates
• Fundamental Standard Model parameters must be
  measured.
• Measurement of these electro-weak parameters
  complicated by QCD (we observe hadrons not
  quarks)
• The formalism that provides a viable framework
  for extracting CKM elements is Heavy Quark
  Effective Theory HQET.

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Parameterized by 3 rotation angles(qij) and a
phase (d) Sij sinqij

• CP Violation
• 3 generations required for non-Real matrix
• Quark mass not degenerate (u,c,t) (d,s,b)
• d not 0 or p

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rewrite in terms of the Wolfenstein parameters A
l r h Taking advantage of small value of l2
order l4
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Unitarity Triangle
r,h
a
CP
g
b
0,0
1,0
Unitarity
Algebra
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Implications of CPV via CKM matrix

• At least 3 generations of quarks
• Charm quark not known at time of proposal
• 2 generations can not provide required phase
• Same mechanism that describes CPV in Kaon system
  predicts (possibly larger) CPV in B meson
  system.
• Direct CPV predicted
• In contrast to other competing mechanisms such as
  superweak (DS2, K0 ?K0) .

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Keeping Score (CKM constraints)

h
e
r
37
Observed particles

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hidden bottom

• 1977, Fermilab
• 400 GeV protons on nuclear targets
• Examined mm- pair mass
• Broad peak observed (1.2 GeV) at 9.5 GeV
• Eventually interpreted as 2 peaks
• Had observed the Y and Y.
• Bound states of bb quarks.
• PRL 39 p252 77

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The Y system

• 1980 CESR online. e e- collisions in the 10 GeV
  energy range
• Resonance structures very similar to the cc (J/y)
  observations just a few years earlier.

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The Y as a B laboratory

• ee-? U(4S) ? BB (s 1.0 nb) ee-? qq (s
  3.0 nb)
• Broad (14 MeV gtgt narrow Y,Y,Y)
• Lepton production
• Spherical topology
• Just above 2 times B meson mass (5.279 GeV).
• Bs nearly at rest

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The Y as a B laboratory
qq
BB
R2 (shape)
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B mixing

• B0 ? B0 (Standard Model)

b
d
u,c,t
W
W
B0
B0
d
b
u,c,t
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B Mixing
B0 ? D e- n B0 ? D- e n BB ? BB or
BB Signature Same sign leptons ee or
e-e- 1987 (ARGUS/DESY)
Vcb
B
D
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Observation of top

• 1995 D0 and CDF at FERMILAB
• 1.8 GeV pp collisions
• Ignoring sea quarks and gluons
• (uud) (uud)
• u u ? t t (production)
• t ? b W (Vtb) (decay no bound states)

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Observation of top

• Top decays fast (due to large mass). No time for
• bound state formation.
• t t signals (t?b W)
• b l n (dilepton) b j j (lepton
  jets)
• b l- n b l- n
  
• b j j (6 jets)
• b j j
• Background W jet production

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Observation of top

• Lepton
• electron -
• (well measured in tracking and
  electromagnetic calorimeter)
• muon - tracking chambers behind shielding
• Neutrino Large (20-30 GeV) missing transverse
  energy.
• W boson coincidence of above with consistent
  transverse mass.
• Jets clusters of energy in hadronic calorimeter
• B-jets algorithm identifying displaced vertex
  from long lived b quark (and/or) soft lepton in
  jet from semileptonic decay of b quark.
  

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W and Jets
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Top mass

• W4jet sample
• With b-tagged jets
• Reconstruct top mass (7).
• Mass top 175 GeV
• Currently best known quark
• mass (few).

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Keeping Score (CKM constraints)
d
b

t
B0
B0
Dmd
b
d
t
e
51
Part II

• Extractrion of a CKM matrix elements
• Observation of CPV in B system
• Observation of Direct CPV
• How does the standard model do?

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B Decays

• Hadronic Semileptonic
  Radiative
• B?XH B ? XH l n
  B?XH g
• B?D p (K p) Exclusive Inclusive
  Exclusive Inclusive
• Experimentally B?D l n B?Xc l n
  B?K g B?Xs g
• Easy B? p l n B?Xu
  l n
• Heavy Quark Exp Heavy Quark Exp
  Theoretically
  
• Factorization
  clean

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B Decay

• Still need QCD corrections
• Perturbative
  Non-Perturbative
• Hard gluon (Short distance) Soft gluon
  (Long distance)
• as
  L, l1 l2

54
Heavy Quark Limit

• B meson a heavy quark light degrees of
  freedom
• lb 1/mb (mb 5GeV)
• Typical energy exchanges LQCD (.1 GeV) ll
  1/LQCD
• ll gtgt lQ ? point charge (can not resolve mass)
  flavor blind
• Chromo-magnetic moment g/(2 mQ) ? spin blind
• Heavy quark symmetry will provide relations
  between different heavy flavor mesons (B ??D) and
  mesons with different spin orientations (B??B ,
  D??D)
• LQCD is in non-perturbative regeme (no as
  expansion for bound state effects).
• Heavy Quark Effective Theory systematically
  provides symmetry breaking corrections in
  expansion (LQCD/mQ)

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• HQETOPE allows any inclusive observable to be
  written as a double expansion in powers of as
  and 1/MB

O(1/M) L energy of light degrees of
freedom O(1/M2) l1 -momentum squared
of b quark l2 hyperfine
splitting (known from B/B and D/D DM) O(1/M3)
r1, r2, t1, t2, t3, t4 (.5 GeV)3 from
dimensional considerations

• Gsl Vcb2 (A(as,,boas2)B(as)L/MB Cl1/MB2)
• L, l1 combined with the Gsl measurements ? better
  Vcb2

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b ? s g Moments
u, c, t
57
b ? s g Moments
u, c, t
Xs
58
b ? s g Moments
u, c, t
radiative tail
59
Back to CMK Elements

• Gsl (B Meson Semileptonic Decay Width)
• Calculated from B meson branching fraction and
  lifetime measurements (CLEO, CDF, BaBar, Belle
  )
• It is the first approximation to the b quarks
  decay width

DM hyperfine splitting
b quark motion increased b lifetime
Free quark decay width
Pfermi
60
Strategy

• Bound state corrections needed.
• Extract L, l1, l2 from independent observables
• L (e.g. average photon energy B?Xs g)
• l1 (e.g. width of photon energy)
• l2 (e.g. D and D mass difference)
• Once determined can be used in extraction of CKM
  elements (e.g. Vub and Vcb)
• Over constrain in order to check size of higher
  order terms

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Photon Energy Moments

• Always require high energy photon 2.0 lt Eg lt 2.7
  GeV cos q lt 0.7
• Naïve strategy Measure Eg spectrum for ON and
  OFF resonance and subtract
• But, must suppress huge continuum
  background!veto is not enough
• p0? gg and h? gg
• Three attacks
• Shape analysis
• Pseudoreconstruction
• Leptons

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Photon Energy Moments
63
Photon Energy Moments
64
Photon Energy Moments
65
Photon Energy Moments
66
HQET Predictions for moments of (inclusive)
Hadronic Mass, Photon Energy Lepton Energy
B?Xc l n
B?Xc l n
B?Xs g
6 constraints for 2 parameters
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Consistency Among Observables
CLEO Preliminary

• L and l1 ellipse extracted from 1st moment of
  B ?Xs g photon energy spectrum and 1st moment of
  hadronic mass2 distribution(B ?Xc ln). We use the
  HQET equations in MS scheme at order 1/MB3 and
  as2 bo.
• MS Expressions A. Falk, M. Luke, M. Savage,
• Z. Ligeti, A. Manohar, M. Wise, C. Bauer
• The red and black curves are derived from the new
  CLEO results for B ?X ln lepton energy moments.
• MS Expressions M.Gremm, A. Kapustin, Z. Ligeti
  and M. Wise, I. Stewart (moments) and I. Bigi,
  N.Uraltsev, A. Vainshtein(width)
• Gray band represents total uncertainty for the
  2nd moment of photon energy spectrum.

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Vcb
In MS scheme, at order 1/MB3 and as2bo L
0.35 0.07 0.10 GeV l1 -.236 0.071 0.078
GeV2 Vcb(4.04 0.09 0.05 0.08) 10-2
Gsl L, l1 Theory
69
Global Analysis hep-ph/0210027
Bauer,Ligeti,Luke Manohar
70
Vub from Lepton Endpoint (using b ?s g )

• Vub from b? u l n
• We measure the endpoint yield
• Large extrapolation to obtain Vub
• High E cut leads to theoretical difficulties (we
  probe the part of spectrum most influenced by
  fermi momentum)

• GOAL Use b ? sg to understand Fermi momentum
  and apply to b? uln for improved measurement of
  Vub
• Kagan-Neubert
• DeFazio-Neubert

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B g lightquark shape function, SAME (to lowest
order in LQCD/mb) for b g s g a B g Xs g and b g
u ln a B g Xu ln.
B g Xs g (hadron level)
b g s g (parton level)
Convolute with light cone shape function.
B g Xu l n (hadron level)
b g u l n (parton level)
Fraction of b uln spectrum above 2.2 is 0.13
0.03
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Vub from Lepton Endpoint (using b ? s g )
Vub (4.08 0.34 0.44 0.16
0.24)10-3 The 1st two errors are from
experiment and 2nd from theory

• Subleading corrections large
• C. Bauer, M. Luke, T. Mannel
• A. Leibovich, Z. Ligeti, M. Wise

CLEO

• Method for partial inclusion of subleading
  corrections Neubert

• Published
• With subleading corrections

PRL 88 231803 02
73
Vub measurements
74
Keeping Score (CKM constraints)

Dmd
Vub
e
75
CP Violation Measurement in B System

• Approximately 4 decades after observation of CPV
  in Kaon System
• Three quark generation model well established
• constraints from B mixing and CKM element
  magnitudes nicely consistent
• K meson and B meson measurements consistent
• NO CP violation yet observed in B meson system!
• By 1999 CLEO experiment has accumulated
  luminosity larger than all other collider
  experiments combined. Ten Million BB pairs.
• Still no hope of measuring CP violation as
  predicted by SM.
• SM predicts direct CPV and CPV in mixing small.
  Best first measurement is
• interference between decays to CP eigenstates
  with and without mixing.

B0
B0

f
B0
f
B0
Time dependent asymmetry
76
CP Violation Measurement in B System

• Recall B mesons produced via symmetric ee-
  collisions yields B mesons nearly at rest (Y(4S)
  2 MB)
• Require fast B mesons (displaced vertex) to
  extract time of decay.
• Hadronic collider produce boosted B meson but
  statistics low.
• Require simple design change for ee- ?
  asymmetric collisions.
• Enter BaBar and Belle

KEKB Electrons 8 GeV Positrons 3 GeV
PEPII Electron at 9 GeV Positrons at 3.1 GeV
4 fb-1/week ? 10 Million BB pairs in 3 weeks
77
PEPII
78
CP Violation Measurement in B System

• Symmetric ee- collisions at Y(4S)
• b is .05 (Dz .025 mm)
• With BaBar parameters
• b is .5 (Dz .25 mm)
• Resolution .15 mm

79
CP Violation Measurement in B System

• CP Final state (example)
• B? J/y Kshort (BR 0.05)
• J/y? l l- (ee-, mm-) (BR 11)
• Kshort? p p- , p0 p0 (BR 100)
• Second Tagging B
• Provides second vertex (Dz)
• Provides flavor tag (65 eff in tagging)
• High momentum leptons ? B0 (B0) ? l (l-)
• Kaon charge (K, K-)
• Soft pion (D? D0 p)
• 88 Million BB pairs ? 740 B0 tags and 766 B0 tags

80
CP Violation Measurement in B System

• MES Beam Energy substituted mass
• sqrt(Ebeam2-pB2)
• Consistent with known MB
• DE Ebeam-EB
• B candidate energy consistent with expected B
  meson energy
• All in CM frame

MES
DE
81
CP Violation Measurement in B System

• Observable Dz gbcDt

A is amplitude for decay Even with q/p and
A/A 1 CP Violation possible via interference
with and without mixing ? Im(l)0
82
f J/y Kshort
b Vcb c
Vtb Vtd
Vsc Vcd
y
c
B0
B0
K0
K0
Vcs
s
K0
83
Connection to r-h plane
r,h
((1-r)2h2)1/2
h
b
0,0
1,0
(1-r)
84
Results
BaBar and Belle average Sin(2b)0.734 0.055
85
Keeping Score (CKM constraints)

CP Violation observed. Constraints
consistent with previous measurements
Dmd
Sin(2b)
BaBar and Belle average Sin(2b)0.734 0.055
Vub
e
b
86
r-h Constraints Including Uncertainties
87
r-h Constraints Including Uncertainties
Bottom plot shows constraints With few
theoretical uncertainties? required to
see beyond standard model.
88
Direct CP Violation

• No (unambiguous) measurement of direct CP
  violation from B mesons
• Direct CP Violation has been observed in Kaon
  system.

89
Direct CP Violation (Kaon)

• Re(e/e)
• Requires very accurate measurements
• of 4 processes
• Klong ? p p-
• Klong ? p0 p0
• Kshort ? p p-
• Kshort ? p0 p0

90
Observable for Direct CP Violation

• h- /h00
• amp(KL?pp-)/amp(KS?pp-) e
  e
• amp(KL?p0p0)/amp(KS?p0p0)
  e 2e
• Actual measurement
• G(KL?pp-)/G(KS?pp-)
  1 6 Re(e/e)
• G(KL?p0p0)/G(KS?p0p0)
• e small compared to e. e already
  small ?
• difficult measurement!

91
Direct CP Violation
NA31 ? NA48 CERN E731 ? E832
FermiLab
92
KTeV
Vacuum beam Klong Regenerator beam
KlongrKshort CsI Cal Resolution 0.7
(15GeV) Position Resolution 1 mm (can identify
parent beam) Klong ? p0 p0 (2.5 M
events) Systematics Acceptance difference for
Klong Kshort Must be well modelled.
93
Accounting for Klong component in Regenerator beam
94
Re(e/e) Results
Direct CP violation observed Superweak Theory
fails SM Model predictions consistent but has
large uncertainties
95
Re(e/e) Results
96
Summary

• Standard Model performance
• Excellent
• 3 quark generations well established
• CP Violation in B mesons observed
• Direct CP violation in Kaons observed
• CKM constraints in quantitative agreement no
  known significant deviations
• The math works but do we understand the source of
  CP violation?
• Understanding of Higgs sector and mass generation
  may help
• If the Standard Model continues in its success
  how do we explain the quantity of observed matter?