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Experimental Aspects of CP Violation
Daniel Cronin-Hennessy
TASI June 2003
Daniel Cronin-Hennessy
CP
NO NO
Research Associate University of RochesterCLEO collaboration at LEPP (Cornell)
Short Bio1995 Joined CDF collaboration at Fermilab top(1.8 TeV pp collider: q q t t )
During Run 1 Focus was tests of Perturbative QCD (αs) via analysis of W boson produced in association with jets.
1999 Joined CLEO collaboration at CESR bottom(10.58 GeV e+e- collider Y(4S) BB) During CLEOIIIImproved CKM matrix element extractions with HQET
Future CLEO-c (3 GeV) charmLattice QCD , glueballs, and hybrids
GoalsHow we know what we know
Show experimental techniquesThe phenomenology used to interpret data
Accent role of Symmetry both in theory and in experiment
Connect Observables to CKM formalismConvey importance CP Violation
Authors versus Time
Carl Anderson 1933
Authors versus Time
J H Christenson 1964 J W Cronin V L FitchR Turlay
Authors versus Time
CLEO ~ 150Recent list
Authors versus TimeCDF ~ 400 1995
Authors versus Time
BaBar ~ 600
Timeline1928 1956 1972 Dirac Lee&Yang KM e+ P Violation CP viol from
mixing matrix
1933 1957 1964 1974 1977 1982 1987 1989 Anderson Wu Cronin&Fitch Brookhaven Fermilab CESR DORIS CESR
Standforde+ P(C) Viol CP Viol J/Ψ( cc) Y(bb) Bmeson BMixiing charmless
B decay(Vub)
1995 2000 2001Fermilab CERN/Fermilab KEKB/PEPIITOP Direct CP Violation CP Violation in B
Background (positron)Carl Anderson 1933Wilson Chamber- condensation around ions. Ions generated from passing charged particle.Device immersed in high B field (15 kG)14 cm diameter
Background (positron)B field into page qvXB the sign of chargeNegative particle moving down or positive particle moving up6mm 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.
Background (positron)Positive track but why not ProtonEnergy 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 studyQ < 2 QprotonM < 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
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 Dirac’s wave equation manifested negative energy solutions.These solutions were not discarded as unphysical mathematical artifacts but interpreted as antiparticle partners to the positive solutions
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 < 0.0001*observed matterObserved 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 survivedWithout this asymmetry we would not be here.
Where are the positrons (anti-protons etc) ?
Sakharov’s (1967) conditions for generating Anti-matter matter asymmetry
Baryon number violation (another story)Must be able to get rid of baryons
CP asymmetryMust 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.
Symmetries (C )
Charge conjugation (C)C changes particle to anti-particle
ExamplesCharge Conjugation on electron = positronC e- = e+ (shorthand)C p = pC π+ = π-
C ν = ν
Symmetries (P)Parity (P) Mirror symmetryInverts 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)
HelicityP Right-handed = Left-handed
Right-handed means thumbOf righthand points in direction of motion
Left-handed means thumb of left hand Points in direction of motion
ν Participates in weak interactionNo electric charge, No color charge
NEVER observedC and P in weak interactions is violatedC and P
ν RightP
P
C C
ν Left
Anti-ν Left
CP
Anti-ν Right
The τ-θ puzzle Pre – 1956
Two particles with similar characteristics (such mass and lifetime) are only different in the decays.
θ π+ π0 parity +1 (-1*-1*(-1)0)τ π+ π− π+ parity –1
Seemed obvious that if τ and θ 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.
A Test of Parity (Wu, 1957)Align Cobalt 60 nuclear spinLook for electrons from beta decay
60Co 60Ni + e- anti-νBeta decay
n p + e- anti-νd u + e- anti-ν
Electrons emitted opposite to direction of nuclear spin (parity operation would reverse direction ofelectron but not the the nuclear spin).
ν Participates in weak interactionNo electric charge, No color charge
NEVER observedC and P in weak interactions is violated
maximallyC and P ν RightP
P
C C
ν Left
Anti-ν Left
CP
Anti-ν Right
The Neutral Kaon systemK0 (d anti-s) K0 (anti-d s)Strange particles produced via strangeness conserving process.
∆S=0 (-1 +1)Decays weakly (violating strangeness) long lived and large difference in lifetimes between the neutral KsProposal
Assuming CPK1 ~ K0 + K0 CP K1 = K0 + K0 = K1 (CP=1)K2 ~ K0 – K0 CP K2 = K0 – K0 = K2 (CP=-1)
K1 2 π (CP =1)K2 3 π (CP = -1)
Without 2 π decay open to K2 expect increased lifetime: Long lived Neutral K (15 meters) Short lived (2.8 cm)
CP Violation Observed
K2
57 Ft to target
collimatorDecay Volume(He)
Spectrometer
Spectrometer
π+
π−
494-509 MeV
cosθ
484-494 MeV 504-514 MeV
cosθ cosθ
Signal K2 2πBck K2 3π
Use angle (q) between 2p and beam axis
K1 decay long before detector
Regeneration of K1 in collimator inconsistent with vertex distribution
MK = .498 MeV
CP Violation Observed Christenson, Cronin, Fitch & Turlay 1964Observed CP violating decay K2 2π 17 meters from production point (> 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 + ε K2
Klong ~ K2 + ε K1
Kshort ~ (1+ε) K0 + (1-ε) K0
Klong ~ (1+ε) K0 – (1-ε) K0
Asymmetric mixing at level of 0.2%
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 π0 π0 π0
1258 times I see the Klong decay to π+ π- π0
1359 times I see the Klong decay to π- µ+ ν1350 times I see the Klong decay to π+ µ- ν1950 times I see the Klong decay to π- e+ ν1937 times I see the Klong decay to π+ e- ν
38 times I see the Klong decay to other
Note that π- e+ ν and π+ e- ν are connected by CPCP (π- e+ ν) = π+ e- ν
Counting Klong decays
Example: Given 10000 Klong particles 1950 times I see the Klong decay to π- e+ ν1937 times I see the Klong decay to π+ e- ν
If CP were an exact symmetry I expect the same number of
π- e+ ν and π+ e- ν decays.- e+ ν and π+ e- ν decays.different numbers 1950 and 1937π-) – N(KL e- ν π+ ) = 0.0033L e+ ν π-) + N(KL e- ν π+ )
CP Violation in Neutral Kaon a = amp(K0 f) a = amp(K0 f)χ = (a-a) / (a+a)η = amp(KL f )/amp(KS f)
Kshort ~ (1+ε) K0 + (1-ε) K0
Klong ~ (1+ε) K0 – (1-ε) K0
η = (1+ε) a - (1-ε)a = (a-a) + ε(a+a) = ε + χ(1+ε) a + (1-ε)a ε(a+a) + (a-a) 1+εχ
η = ε + χ(mixing) + (direct CP violation – Process dependent)
|η+-| != |η00|
Observable for Direct CP Violation
η+- /η00
= amp(KL π+π-)/amp(KS π+π-) = ε +ε’amp(KL π0π0)/amp(KS π0π0) ε – 2ε’
Actual measurement:
Γ(KL π+π-)/Γ(KS π+π-) ~ 1 + 6 Re(ε’/ε)Γ(KL π0π0)/Γ(KS π0π0)
ε’ small compared to ε. ε already small difficult measurement!
K mixing (quark mixing)K0 K0 (Standard Model)
K0 K0
s
d s
d
u,c,t
u,c,t
W W
quark mixing
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
=⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
bsd
VVVVVVVVV
bsd
tbtstd
cbcscd
ubusud
'
'
'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.
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
−−−−−−
−
132313231223121323122312
132313231223121323122312
1313121312
ccescsscesccsscsesssccessccsescscc
ii
ii
i
δδ
δδ
δ
Parameterized by 3 rotation angles(θij) and a phase (δ)Sij =sinθij
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
VVVVVVVVV
tbtstd
cbcscd
ubusud
CP Violation:3 generations required for non-Real matrixQuark mass not degenerate (u,c,t) (d,s,b)δ not 0 or π
⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜
⎝
⎛
−−−
−−
−−
1)1(2
1
)(2
1
23
22
32
ληρλ
λλλ
ηρλλλ
AiA
A
iA
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
−−−−−−
−
132313231223121323122312
132313231223121323122312
1313121312
ccescsscesccsscsesssccessccsescscc
ii
ii
i
δδ
δδ
δ
rewrite in terms of the Wolfenstein parametersA λ ρ ηTaking advantage of small value of λ2
22.0||12 ==≡ usVsλ)81.(23
2 ≈≡ AsAλ
~order λ4
)(3 ηρλ iAVub −=
)1(3 ηρλ iAVtd −−=
Unitarity Triangle
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
VVVVVVVVV
tbtstd
cbcscd
ubusud
Unitarity
ρ,η
||||
VV
cb
ub a
g bCP
Algebra
0,0 1,0
VV tbtd*
VV cbcd*
VV ubud*0*** =++ VVVVVV tbtdcbcdubud
0))1(()(1 =+−−+− ηρηρ ii
Implications of CPV via CKM matrix
At least 3 generations of quarksCharm quark not known at time of proposal2 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 (∆S=2, K0 K0) .
Keeping Score (CKM constraints)
η
ρ
ε
Observed particles:
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
τνµ
ν µe
esd
u
hidden bottom
1977, Fermilab400 GeV protons on nuclear targetsExamined µ+µ− pair massBroad peak observed (1.2 GeV) at 9.5 GeVEventually interpreted as 2 peaksHad observed the Y and Y’.Bound states of bb quarks.PRL 39 p252 ‘77
The Y system 1980 CESR online. e+ e- collisions in the 10 GeV energy range Resonance structures very similar to the cc (J/ψ) observations just a few years earlier.
The Y as a B laboratorye+e- Υ(4S) BB (σ ~ 1.0 nb) e+e- qq (σ ~ 3.0 nb) Broad (14 MeV >> narrow Y,Y’,Y’’)Lepton production Spherical topologyJust above 2 times B meson mass (5.279 GeV).B’s nearly at rest
The Y as a B laboratory
qqBB
R2 (shape)
B mixing B0 B0 (Standard Model)
B0 B0
b
d b
d
u,c,t
u,c,t
W W
B MixingB0 D+ e- ν
B0 D- e+ ν
BB BB or BB
Signature:Same sign leptonse+e+ or e-e-
1987 (ARGUS/DESY)
B DVcb
Observation of top1995 D0 and CDF at FERMILAB1.8 GeV pp collisionsIgnoring sea quarks and gluons:
(uud) + (uud)
u u t t (production)t b W (Vtb) (decay no bound states)
Observation of topTop decays fast (due to large mass). No time forbound state formation.
t t signals (t b W)b l+ ν (dilepton) b j j (lepton + jets)b l- ν b l- ν
b j j (6 jets)b j j
Background W + jet production
Observation of topLepton:
electron -(well measured in tracking and electromagnetic calorimeter)
muon - tracking chambers behind shieldingNeutrino: Large (20-30 GeV) missing transverse energy. W boson: coincidence of above with consistent transverse mass.Jets: clusters of energy in hadronic calorimeterB-jets: algorithm identifying displaced vertex from long lived b
quark (and/or) soft lepton in jet from semileptonic decay of b quark.
W and Jets
Top massW+4jet sample With b-tagged jets
Reconstruct top mass (7%).Mass top ~ 175 GeV
Currently best known quark mass (few%).
Keeping Score (CKM constraints)
)1(3 ηρλ iAVtd −−=
))1(|| 22 ηρ +−≈tdV
B0 B0
b
db
d
t
t
ε
∆md
Part II
Extractrion of a CKM matrix elementsObservation of CPV in B systemObservation of Direct CPVHow does the standard model do?
B DecaysHadronic Semileptonic Radiative
B XH B XH l ν B XH γ
B D π (K π) Exclusive Inclusive Exclusive InclusiveExperimentally B D l ν B Xc l ν B K* γ B Xs γ“Easy” B π l ν B Xu l ν
Heavy Quark Exp Heavy Quark Exp Theoretically Factorization clean
B Decay
c
u
d
b c d u
b
W
Still need QCD correctionsPerturbative Non-Perturbative
Hard gluon (Short distance) Soft gluon (Long distance)
αs Λ, λ1 & λ2
B D e ν
W
e
ν
]Dc
B[b
Just right?
W
b c
u
d]π
]DB[
B D π
Very difficult
Heavy Quark LimitB meson ~ a heavy quark + “light degrees of freedom”
λb ~ 1/mb (mb ~ 5GeV)
Typical energy exchanges ~ ΛQCD (.1 GeV) λl ~ 1/ΛQCDλl >> λQ point charge (can not resolve mass) flavor blindChromo-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*)
ΛQCD is in non-perturbative regeme (no αs expansion for bound state effects).
Heavy Quark Effective Theory systematically provides symmetry breaking corrections in expansion (ΛQCD/mQ)
HQET+OPE allows any inclusive observable to be written as a double expansion in powers of as and 1/MB:
)1()(),( 322
21
2
22
MO
ME
MD
MC
MBAObservable sss +++
Λ+
Λ+= λλααα
O(1/M) Λ energy of light degrees of freedomO(1/M2) λ1 -momentum squared of b quark
λ2 hyperfine splitting (known from B/B* and D/D* DM)O(1/M3) ρ1, ρ2, τ1, τ2, τ3, τ4 ~(.5 GeV)3 from dimensional considerations
Gsl = |Vcb|2 (A(as,,boas2)+B(as)Λ/MB+ Cλ1/MB
2+…)
Λ, λ1 combined with the Gsl measurements better |Vcb|2
b s γ Moments
⎟⎟⎠
⎞⎜⎜⎝
⎛+−
+++−
−−−−
Λ−−−= )1(
9433
123313))(175.1954.01()(620.0385.01
2 47
222
34321
3212
02
0M
OCMM
CMMM
mEBBDBB
ss
B
ssb ρττττρρπαβ
πα
παβ
πα
γ
u, c, t
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛+
+−
−−+
Λ−++
−=− )1(
123
1232))(05412.005083.0()(01024.000815.0
12 4321
3212
02
0212
2
MO
MMMMMEE
BBB
ss
B
ss
BB
ττρρπα
βπα
πα
βπαλ
γγ
b s γ Momentsu, c, t
Xs
⎟⎟⎠
⎞⎜⎜⎝
⎛+−
+++−
−−−−
Λ−−−= )1(
9433
123313))(175.1954.01()(620.0385.01
2 47
222
34321
3212
02
0M
OCMM
CMMM
MEBBDBB
ss
B
ssB ρττττρρπαβ
πα
παβ
πα
γ
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛+
+−
−−+
Λ−++
−=− )1(
123
1232))(05412.005083.0()(01024.000815.0
12 4321
3212
02
0212
2
MO
MMMMMEE
BBB
ss
B
ss
BB
ττρρπα
βπα
πα
βπαλ
γγ
b s γ Moments
radiative tail
u, c, t
⎟⎟⎠
⎞⎜⎜⎝
⎛+−
+++−
−−−−
Λ−−−= )1(
9433
123313))(175.1954.01()(620.0385.01
2 47
222
34321
3212
02
0M
OCMM
CMMM
MEBBDBB
ss
B
ssB ρττττρρπαβ
πα
παβ
πα
γ
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛+
+−
−−+
Λ−++
−=− )1(
123
1232))(05412.005083.0()(01024.000815.0
12 4321
3212
02
0212
2
MO
MMMMMEE
BBB
ss
B
ss
BB
ττρρπα
βπα
πα
βπαλ
γγ
Back to CMK Elements
Γsl (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
b quark motion –increased b lifetime
Free quarkdecay width
∆M hyperfine splitting
)]/1(29
21[
192||)( 3
22
21
3
522
Bbb
bubFus MOradiative
mmmVGlXB ++−+=→Γ λλ
πνl
Pfermi
)]/1(474.7185.3946.0648.11[192
||)3689.0()( 322
21
2
2
3
522
BBBBB
BcbFcs MO
MMMMMVGlXB +−−
Λ−
Λ−=→Γ λλ
πνl
StrategyBound state corrections needed.Extract Λ, λ1, λ2 from independent observables
Λ (e.g. average photon energy B Xs γ)λ1 (e.g. width of photon energy)λ2 (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
Photon Energy Moments
Always require high energy photon 2.0 < Eγ < 2.7 GeV
|cos θ| < 0.7Naïve strategy: Measure Eγ spectrum for ON and OFF resonance and subtract But, must suppress hugecontinuum background![veto is not enough]
π0 γγ and η γγThree attacks:
Shape analysisPseudoreconstructionLeptons
Photon Energy Moments
Photon Energy Moments
Photon Energy Moments
Photon Energy Moments
HQET Predictions for moments of (inclusive) Hadronic Mass, Photon Energy & Lepton Energy
B Xc l νB Xc l νB Xs γ
6 constraints for 2 parameters
Consistency Among Observables
Λ and λ1 ellipse extracted from 1st moment of B Xs γ photon energy spectrum and 1st moment of hadronic mass2 distribution(B Xc λν). We use the HQET equations in MS scheme at order 1/MB
3 and αs2 βo.
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 λν 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.
CLEOPreliminary
Vcb
In MS scheme, at order 1/MB3
and αs2βo
Λ= 0.35 + 0.07 + 0.10 GeVλ1= -.236 + 0.071 + 0.078 GeV2
|Vcb|=(4.04 + 0.09 + 0.05 + 0.08) 10-2
Γsl Λ, λ1 Theory
)]/1(474.7185.3946.0648.11[192
||)3689.0()( 322
21
2
2
3
522
BBBBB
BcbFcs MO
MMMMMVGlXB +−−
Λ−
Λ−=→Γ λλ
πνl
Global Analysis: hep-ph/0210027 Bauer,Ligeti,Luke & Manohar
Moment CLEO DELPHI(prelim) BABAR(prelim)
<(m2H- <m2
H>)3 > 2.97±0.67±0.48
<m2H - m2
D> 0.251±0.023±0.062 (El>1.5GeV) 0.534±0.041±0.074 Versus EL<(m2
H- <m2H>)2 > .576±0.048±0.163 (El > 1.5GeV) 1.23±0.16±0.15
<Ey> 2.346±0.032± 0.011
<(Εγ− <Εγ>)2> 0.0226±0.0066±0.0020
<Eλ> 1.7810+0.0007+0.0009 (El > 1.5 GeV) 1.383±0.012± 0.009
<(Ελ− <Ελ>)2> 0.192 ± 0.005± 0.008
<(Ελ− <Ελ>)3> 0.029 ±0.005±0.006
R0 0.6187+0.0014 +0.0016 (El > 1.5 GeV)
|Vub| from Lepton Endpoint (using b s γ )
|Vub| from b→ u λ νWe measure the endpoint yieldLarge 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 sγ to understand Fermi momentum and apply to b→ uλν for improved measurement of|Vub|
Kagan-NeubertDeFazio-Neubert
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.
Convolute with light cone shape function.
b g s g(parton level)
B g Xs g(hadron level)
b g u l n(parton level)
B g Xu l n(hadron level)
Fraction of b ® ulnspectrum above 2.2 is
0.13 ± 0.03
|Vub| from Lepton Endpoint (using b s γ )
|Vub| = (4.08 + 0.34 + 0.44 + 0.16 + 0.24)10-3
The 1st two errors are from experiment and 2nd from theory
Method for partial inclusion ofsubleading corrections: Neubert
•Published•With subleading corrections
Subleading corrections large C. Bauer, M. Luke, T. MannelA. Leibovich, Z. Ligeti, M. Wise
CLEO
PRL 88 231803 ‘02
|Vub| measurements
Keeping Score (CKM constraints)
)(3 ηρλ iAVub −=
)(|| 22 ηρ +≈ubVε
|Vub|
∆md
CP Violation Measurement in B SystemApproximately 4 decades after observation of CPV in Kaon System
Three quark generation model well establishedconstraints from B mixing and CKM element magnitudes nicely consistentK meson and B meson measurements consistentNO 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.
B0B0
=B0 fB0 f
Time dependent asymmetry
CP Violation Measurement in B SystemRecall B mesons produced via symmetric e+e- 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 e+e- asymmetric collisions.Enter BaBar and Belle
KEKBElectrons 8 GeVPositrons 3 GeV
PEPIIElectron at 9 GeVPositrons at 3.1 GeV
4 fb-1/week 10 Million BB pairs in 3 weeks
PEPII
CP Violation Measurement in B System
Symmetric e+e- collisions at Y(4S)β is ~ .05 (∆z ~ .025 mm)
With BaBar parametersβ is ~ .5 (∆z ~ .25 mm)Resolution ~ .15 mm
CP Violation Measurement in B System
CP Final state (example):B J/ψ Kshort (BR = 0.05%)
J/ψ l+ l- (e+e-, µ+µ-) (BR 11%) Kshort π+ π- , π0 π0 (BR ~100%)
Second “Tagging” B Provides second vertex (∆z)Provides flavor tag (65% eff in tagging)
High momentum leptons B0 (B0) l+ (l-)Kaon charge (K+, K-)Soft pion (D+* D0 π+)
88 Million BB pairs 740 B0 tags and 766 B0 tags
CP Violation Measurement in B System
MES
MES: Beam Energy substituted masssqrt(Ebeam
2-pB2)
Consistent with known MB
DE: Ebeam-EBB candidate energy consistent
with expected B meson energy
All in CM frame
∆E
CP Violation Measurement in B System
Observable: ∆z = γβc∆t
))(())((
))(())((00
00
ftft
ftft
BBBB
aphysphys
physphys
f→Γ+→Γ
→Γ−→Γ=
AA
f
f
fcp pqηλ = BBB qpL
00 += BBB qpL
00 −=
A is amplitude for decay:Even with |q/p| and |A/A| ~ 1 CP Violation possiblevia interference with and without mixing Im(λ)=0
)sin(Im~1
)sin(Im2)cos()1(
||||
2
2
tf
ttf mmma Bf
BfB
f ∆+
∆−∆−= λ
λλλ
AA
f
f
fcp pqηλ = f =J/ψ Kshort
b Vcb c
cψ
s K0Vcs*
ηρηρλii
VV
VVVV
VVVV
VVVV
td
td
tbtd
tbtd
cdcs
cdcs
cscb
cscb
+−−−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−
11~~~ **
*
*
*
*
*
B0 B0
Vtb Vtd
K0 K0
Vsc Vcd
Connection to ρ−η planeρ,η
0,0 1,0
β
((1-ρ)2+η2)1/2
(1-ρ)
η2222
22
)1()1(2
)1()1(
11~
ηρηρ
ηρηρ
ηρηρλ
+−−
++−−−
=+−−− i
ii
)2sin()sin()cos(2)1()1(
)1(2)Im(2222
βββηρ
ηηρ
ρλ ==+−+−
−=
Results
)sin()2sin(~)sin(Im~ tt mma BBff ∆∆ βλ
BaBar and Belle averageSin(2β)=0.734 + 0.055
Keeping Score (CKM constraints)
BaBar and Belle averageSin(2β)=0.734 + 0.055
β
Sin(2β)
ε
|Vub|
∆md
CP Violation observed.Constraints consistentwith previous measurements
ρ−η Constraints Including Uncertainties
ρ−η Constraints Including Uncertainties
Bottom plot shows constraints With ~few% theoretical uncertainties required to see“beyond” standard model.
Direct CP ViolationNo (unambiguous) measurement of direct CP violation from B mesons
Direct CP Violation has been observed in Kaon system.
Direct CP Violation (Kaon)Re(ε’/ε)Requires very accurate measurementsof 4 processesKlong π+ π-
Klong π0 π0
Kshort π+ π-
Kshort π0 π0
Observable for Direct CP Violation
η+- /η00
= amp(KL π+π-)/amp(KS π+π-) = ε +ε’amp(KL π0π0)/amp(KS π0π0) ε – 2ε’
Actual measurement:
Γ(KL π+π-)/Γ(KS π+π-) ~ 1 + 6 Re(ε’/ε)Γ(KL π0π0)/Γ(KS π0π0)
ε’ small compared to ε. ε already small difficult measurement!
Direct CP Violation
NA31 NA48 CERN
E731 E832 FermiLab
KTeV
Vacuum beam = Klong
Regenerator beam = Klong+ρKshort
CsI Cal Resolution = 0.7% (15GeV)Position Resolution = 1 mm (can identify parent beam)
Klong π0 π0 (2.5 M events)
SystematicsAcceptance difference for Klong& Kshort Must be well modelled.
Accounting for Klong component in Regenerator beam
Re(ε’/ε) Results
Direct CP violation observed
Superweak Theory fails
SM Model predictions consistent but has large uncertainties
Re(ε’/ε) Results
SummaryStandard Model performance
Excellent3 quark generations well establishedCP Violation in B mesons observedDirect CP violation in Kaons observedCKM constraints in quantitative agreement no known significant
deviationsThe 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?
