π+
π+
π+
K–
µ+
µ–
π– π–
7-20008558A4
CP ViolationCP Violation
Stéphane WillocqUniversity of Massachusetts, Amherst
New England Particle Physics Student Retreat18-23 August 2002
S.Willocq (UMass) CP Violation - NEPPSR 2002 2
Outline
What is CP Violation? Why is it interesting?
Fundamental Symmetries
CP Violation in the Standard Model
Studies at e+ e− Asymmetric B Factories
S.Willocq (UMass) CP Violation - NEPPSR 2002 3
What is CP Violation?Observation that the Laws of Physics are not exactly the same underthe combined transformation:
Charge conjugation C particle ↔ antiparticleParity P left-handed helicity ↔ right-handed helicity
CP symmetry is conserved in strong and electromagnetic interactionsBUT weak interactions violate CP symmetry
Manifestation: different decay rates in K and B meson decays
For example, the decay rate for K0 → π− µ+ νµ is slightly higher thanthat for K0 → π+ µ− νµ (rate asymmetry = 0.3%)
S.Willocq (UMass) CP Violation - NEPPSR 2002 4
Why is CP Violation Interesting?Phenomenon discovered in 1964 but not yet well understood or tested
Understanding of the baryon - antibaryon asymmetry of the Universe
requires three ingredients: (A. Sakharov, 1967)
1. Baryon number violating reactions occur
2. CP Violation (CPV) takes place in these reactions
3. Reactions occur out of thermal equilibrium (Big Bang)
⇒ Without CPV all matter would have annihilated with antimatter after
the Big Bang
+ level of CPV needed is much higher than the Standard Model can allow
Most extensions of the Standard Model provide new sources of CPV
⇒ CPV studies are sensitive to New Physics
S.Willocq (UMass) CP Violation - NEPPSR 2002 5
Fundamental Symmetries (I)Invariance of field equations under certain transformations
→ Implies existence of underlying symmetry→ Results in conservation laws (or forbidden processes)
Examples:Invariance under translations in space
→ Conservation of momentumInvariance under translations in time
→ Conservation of energy Invariance under phase transformations
→ Conservation of electric charge
+ There are 3 important discrete symmetries: C, P and T
S.Willocq (UMass) CP Violation - NEPPSR 2002 6
Fundamental Symmetries (II)
• Charge Conjugation C– Particle ↔ Anti-particle– Charged particles not eigenstates
+ -
⟩±≠⟩=⟩ −+− eeeC |||
Neutral particles are (eigenvalue ±1)
⟩+=⟩⟩−=⟩ 00 |||| ππγγ CC
Strong and electromagnetic interactions are observed to be invariant under C
S.Willocq (UMass) CP Violation - NEPPSR 2002 7
Fundamental Symmetries (III)• Parity P
– Reflects a system through the originspatial coordinates flipped x -x but angular momentum unchanged L L
– Particles have intrinsic parity⟩−=⟩⟩−=⟩ 00 |||| ππγγ PP
Parity operation flips helicity state (left-handed → right-handed)
helicity: projection of spin vector along direction of motion
Strong and electromagnetic interactions conserve P
S.Willocq (UMass) CP Violation - NEPPSR 2002 8
Fundamental Symmetries (IV)
• Time reversal T– Reverses direction of time
t - t
• Time invariance of a reaction implies equal rate for the time-reversed reaction:
MgAlp 2427 +⇔+ α
Once again, strong and electromagnetic interactions are invariant under T
S.Willocq (UMass) CP Violation - NEPPSR 2002 9
Fundamental Symmetries (V)
• The 3 operations (C,P, and T) are connected through invariance of combined CPT for all interactions
• CPT Theorem: all quantum field theories are invariant under this combo (any order)– Consequences:
√ particles and antiparticles have same mass and lifetime
√ particles obey spin statistics (Fermi or Bose)
√ CP violation implies T violation as well
S.Willocq (UMass) CP Violation - NEPPSR 2002 10
Fundamental Symmetries (VI)BUT: weak interactions do NOT conserve either C or P
• First observation of parity violation in weak decays of 60Co (C.S.Wu et al., 1957)
• Both C and P are completely violated in charged current weak interactions (W couples only to left-handed particles)
• Combined CP operation yields same muon decay rates
observed not observedL L eR L R R eL Re eµ µµ ν ν µ ν ν− − − −→ →P
observednot
LeRLL e µννµ ++ →C
ReLRRLeRLL ee µµ ννµννµ ++−− →→ CP
S.Willocq (UMass) CP Violation - NEPPSR 2002 11
Observation of CPV in the K0 – K0 systemBefore 1964:
Strong interaction flavor eigenstates K0 (sd) and K0 (sd) are superpositionsof mass eigenstates K0
S and K0L
⇒ CP transforms matter ↔ antimatter
Physical states K0S and K0
L are eigenstatesof CP if Hamiltonian is invariant under CP
⇒
Cronin, Fitch, Christenson, Turlay(1964):
Measure K0L decay into CP=+1 state
⇒ CP violation in kaon weak decays
Other manifestations of CPV alsoobserved in kaon decays buteffects are always small, e.g.
( )
( ) 1- CP 2
1
1 CP 2
1
000
000
=−=
+=+=
KKK
KKK
L
S
00 KKCP =
3
0
0
10)4.0 0.2(
)modes charged all()(
−
−+
×±
=→Γ
→Γ
L
L
KK ππ
sK
sK
L
S800
100
105 1 CP
101 1 CP −−+
−−+
×=−=→
×=+=→
τπππ
τππ3
00
00
10)12.0 27.3(
)()()()(
−
−++−
−++−
×±
=→Γ+→Γ→Γ−→Γ
νπνπνπνπ
lKlKlKlK
LL
LL
S.Willocq (UMass) CP Violation - NEPPSR 2002 12
CP Violation in the Standard Model (I)How does the SM account for CPV in Kaon decays?
• Kobayashi and Maskawa (1973) proposeexistence of 3rd family of quarks(before discovery of charm and tau)
⇒ CPV originates from an irreducible phasein the quark mixing matrix
Quark mixing matrix now calledCabibbo-Kobayashi-Maskawa (CKM) matrix
S.Willocq (UMass) CP Violation - NEPPSR 2002 13
CP Violation in the Standard Model (II)• CKM matrix originates from the fact that
weak eigenstates are different from quark mass eigenstates
• CKM matrix plays an important role in charged current weak interaction(e.g. β decay n → p e− ν involves a d → u transition)
⋅
=
⋅=
′′′
bsd
VVVVVVVVV
bsd
Vbsd
tbtstd
cbcscd
ubusud
CKM
( ) ( )
2†
2
5
8
with current 1 CK
C
M
CW
gH J JM
dJ u c t V s
b
µµ
µ µγ γ
=
= −
S.Willocq (UMass) CP Violation - NEPPSR 2002 14
CP Violation in the Standard Model (III)Properties of CKM matrix• VCKM governs probability of quark flavor-changing processes
leptons quarks
Strength of the quark-flavor changing transition is determined by VCKM
Probability ∝ |Vtd|2 ≈ 0.0001 |Vts|2 ≈ 0.0016 |Vtb|2 ≈ 0.9983
τµ
ννν τµ
e
e
bsd
tcu
+Wt
dtdgV
+Wt
s
+Wt
btsgV tbgV
? ?
S.Willocq (UMass) CP Violation - NEPPSR 2002 15
CP Violation in the Standard Model (IV)Properties of CKM matrix• How many parameters?
9 complex elements ⇒ 18 parameters (not predicted by the theory)
However, (1) VCKM is unitary: e.g. |Vtd|2 + |Vts|2 + |Vtb|2 = 1
⇒ 9 independent parameters
(2) Quark fields can be redefined to remove 5 arbitrary phases
⇒ 4 independent parameters
3 angles + 1 phase
Note: if only 2 families of quarks ⇒ 2x2 matrix ⇒ 1 (real) independent param
⇒ no phase and no CPV
⇒ need at least 3 families of quarks to get an irreducible phase in thequark mixing matrix
1 †† == CKMCKMCKMCKM VVVV
S.Willocq (UMass) CP Violation - NEPPSR 2002 16
CP Violation in the Standard Model (V)Wolfenstein parameterization of CKM matrix
λ, A, ρ and η are fundamental parameters of the Standard Model
Expansion in powers of λ → hierarchy of transition probabilities
λ = |Vus| = 0.2196 ± 0.0023 from Kaon decay rates (s → u)A = |Vcb| / λ2 = 0.854 ± 0.041 from B → D* l ν decays & lifetime (b → c)ρ = 0.22 ± 0.10η = 0.35 ± 0.05
η ≠ 0 ⇒ non-zero phase responsible for CP violation
( )4
23
22
32
λ+
1Αλ−η−ρ−1ΑλΑλλ−λ−
η−ρΑλλλ−=
O
)i(1
)i(1 2
121
tbtstd
cbcscd
ubusud
VVVVVVVVV
from global fit to available data
S.Willocq (UMass) CP Violation - NEPPSR 2002 17
CKM Matrix Unitarity Conditions
Unitarity requires
⇒ 6 orthogonality conditions
Represented by 6 trianglesin the complex plane
Vcd V*c b
V*t s Vtb
V*c d Vcs
V*u d Vus V*t d Vts
Vud V*c d
Vus V*c sVub V*c b
λ
λ
λ5
λ5
λ
λ
V*u s VubV*c s Vcb λ2
λ2λ4
Vtb V*c b
Vtd V*c dVts V*c s λ2
λ2λ4
Vtd V*t bVud V*u b
λ3
λ3λ3
Vtb V*u b
V*t s VusVtd V*u d
λ3
λ3λ3
) and 3,2,1,(
0 3
1
*3
1
*
kjkj
VVVVi
ikiji
kiji
≠=
== ∑∑==
1Αλ−η−ρ−1ΑλΑλλ−λ−
η−ρΑλλλ−
23
22
32
)i(1
)i(1 2
121
1 †† == CKMCKMCKMCKM VVVV
S.Willocq (UMass) CP Violation - NEPPSR 2002 18
“The” Unitarity Triangle (I)
0 10
η
ρ
Vtd V*t b
|Vcd V*c b|
Vud V*u b
|Vcd V*c b| α
βγ
Unitarity condition between 1st and 3rd columns:
Condition is represented by a triangle with ~equal sides
⇒ angles α, β, γ are large and are different manifestations ofthe single CP-violating phase
0 =++ ∗∗∗tbtdcbcdubud VVVVVV
*
*
arg
td tb
ud ub
VVV
Vα
= −
*
*
arg
cd
t
cb
td bVV V
Vβ
= −
*
*
arg
ud
d c
ub
c b
VV
VV
γ
= −
S.Willocq (UMass) CP Violation - NEPPSR 2002 19
CP Violation in the Standard Model (VI)How does the CKM phase give rise to CPV?Example:
compare decay rate for
B0 → π+π− vs. B0 → π+π−
Two diagrams contribute: “Tree” “Penguin”
B → f amplitudes:
: weak phase from CKM elements involved
: phase shift due to strong interactions between final state particlesDecay rate:
Relative CKM and strong phases:
π−
B 0
W +
u,c,tg
d
b
d
u
u
d
π+
B 0
W +
d
b
d
u
d
u
π−
π+
( )
2 2 2
2 2
( )
2 cos
T Ps s
T Ps s
T PCKM CKM
T PCKM CKM
i i i if f
i i i i
M sCK
B f T P T P T P e e e e
T P e e e e
T P T P
φ φ
φ φ
δ δ
δ δ
φ δ
− −
− −
Γ → ∝ + = + +
+
+ ∆= + + ∆
TCKM
Tsi i
fT T e e δφ=PCKM
Psi i
fP P e e δφ=
CKMφ
sδ
T Ps s
T PCKM CK KM sM Cφ φ φ δ δ δ= − −∆ ∆ =
S.Willocq (UMass) CP Violation - NEPPSR 2002 20
CP Violation in the Standard Model (VII)How does the CKM phase give rise to CPV?Consider CP-conjugate B → f mode
B → f amplitudes:
Decay rate:
⇒ Rates are different for B and B decays
⇒ This kind of CPV is referred to as “direct” CPV or “CPV in decay”it requires two amplitudes with different weak (CKM) and strong phases
In general, CPV originates from a quantum mechanical interferencebetween amplitudes with different phases
TCKM
Tsi i
fT T e eφ δ−=PCKM
Psi i
fP P e eφ δ−=
( )2 2 2( ) 2 cos sf f CKMB f T P T P T P φ δΓ → ∝ + = + + + ∆∆−
2 2
2 sin sin( ) ( )( ) ( ) 2 cos cos
CKM sCP
CKM s
T PB f B fAB f B f T P T P
φ δ
φ δ
∆ ∆Γ → − Γ →= =
Γ → + Γ → + + ∆ ∆
S.Willocq (UMass) CP Violation - NEPPSR 2002 21
CP Violation in B DecaysWhy B Factories?
• CPV effects expected to be much larger in some B decay modes than
those observed in kaon decays
Modes involving quark transitions between 3rd and 1st families:
these elements have large imaginary parts ⇒ large weak phases
• CPV phenomenology much richer (many more decay modes)
• Some CPV measurements are particularly clean both theoretically
and experimentally, e.g., CPV in B0 → J/ψ K0s decays
⇒ Opportunity to test the Standard Model in a clean and new waye+ e- B Factories operating at SLAC (BaBar) and KEK (Belle) since 1999hadron collider experiments (CDF and D0) will also contribute soon
( i ) and ( i )td ubV V3 3= Αλ 1− ρ − = Αλ ρ −η η
S.Willocq (UMass) CP Violation - NEPPSR 2002 22
B0 – B0 SystemAs in the neutral kaon system, Heavy and Light mass eigenstates are superpositions of flavor eigenstates
System characterized bymass difference ∆m = mH – mL
width difference ∆Γ = ΓL – ΓH
Different time evolution for BH and BL
leads to B0 ↔ B0 oscillations withfrequency ∆m (a.k.a. “mixing”)
00
00
BqBpB
BqBpB
H
L
−=
+=
timLL
timHH
LL
HH
etBtB
etBtB )2/(
)2/(
)0( )(
)0()(Γ−−
Γ−−
==
==
2 tdtbd VVm ∗∝∆
b
d,s
W
t d,s
b
W
t
Vtd,ts
Vtd,ts
b
d,s
t
W d,s
b
t
W
Vtd,ts
Vtd,ts
B0 B0
S.Willocq (UMass) CP Violation - NEPPSR 2002 23
3 Classes of CP Violation (I)Need 2 amplitudes with different phase structure contributing to the same decay
→ 3 different ways to achieve this:1) CP violation in decay (a.k.a. direct CP violation)
two amplitudes with different weak phases & different strong phasese.g. compare BR(B+ → K+π0) and BR(B− → K−π0) but strong phases are not known
2) CP violation in mixing (a.k.a. indirect CP violation)
Need relative phase between mass and width parts of mixing matrixCP-violating asymmetries expected to be small in Standard Model
1||||
need ≠BHfBHf
fB 2≠ fB 2
1 need ≠pq
fB0 B0 2≠ fB0 B0 2
S.Willocq (UMass) CP Violation - NEPPSR 2002 24
3 Classes of CP Violation (II)3) CP violation in interference between decays with and without mixing
Final state f is a CP eigenstate (e.g. J/ψ K0s or π+ π−)
need to have CPV (no strong phases needed!)
which can happen even if → only need weak phase
+ asymmetries can be large & do NOT require unknown strong phase+ small theoretical uncertainties in some cases (e.g. J/ψ K0
s)⇒ most promising way to study CPV via measurements of the angles α, β, γ
≠
fB0 B0
fB0 2
+
fB0 B0
2
+fB0
0 ||
|| arg 0
0
≠
BHf
BHfpq
1||
|| and 1 0
0
==BHf
BHfpq
S.Willocq (UMass) CP Violation - NEPPSR 2002 25
CP Violation in B0 → J/ψ K0s Decays (I)
W
b
d
c
c
d
s
Vcb*
Vcs
B0
J/ψ
K0
W
b
d c
c
d
s
Vcb*
Vcs
B0
J/ψ
K0
WW
t
t
b
d
Vtd
Vtd
Ks0
Ks0
Vtb*
Vtb*
Consider B0 decays into CP eigenstates⇒ Interference between amplitudes for decay with and without mixing
β : weak (CKM) phase from B mixing
( ) ( ) tmfB dfCP∆−∝→Γ sin Im1 0 λ ( ) ( ) tmfB dfCP
∆+∝→Γ sin Im1 0 λ
B0
B0
fmixing
B0
B0
fmixing
β
λ
2*
*
0
0
||
||
i
tdtb
tdtb
f
eVVVV
pq
BHf
BHfpq
CP
−==
=
S.Willocq (UMass) CP Violation - NEPPSR 2002 26
CP Violation in B0 → J/ψ K0s Decays (II)Expect large CP asymmetry
Standard Model fit yields sin 2β = 0.75 ± 0.09 S.Mele, PRD59, 113011 (1999)
Small branching ratio
BR(B0 → J/ψ K0) = (8.9 ±1.2) x 10-4
BR(J/ψ → l+ l−) = (5.9 ±0.1) x 10-2
⇒ combined BR ≈ 10-4 for e & µ modes+ Need to reconstruct J/ψ → e+ e−, µ+ µ− and K0s → π+ π−
(account for detector and selection efficiency ~50%)⇒ Requires very large sample of B mesons
∆t / τ
-1
-0.5
0
0.5
1
0 1 2 3 4 5 6
True
Asy
mm
etry
tm
ta
d sin 2sin )K J/ψB()K J/ψB()K J/ψB()K J/ψB( )( 0
s00
s0
0s
00s
0
K J/ s
∆=→Γ+→Γ→Γ−→Γ
=
β
ψ
S.Willocq (UMass) CP Violation - NEPPSR 2002 27
e+ e− B FactoriesGOAL: Produce 30-100 million B B events/year to study CP violation in B decaysviae+ e- → ϒ(4s) → B0 B0 (50%)
B+ B− (50%)
High signal-to-background ratio σbb / σhadrons ≈ 0.22 with σbb= 1.05 nbClean events <# tracks> ≈ 11 & able to reconstruct π0 and γNo fragmentation products (low combinatorial background)Strong kinematical constraints (pϒ(4s) and pB
*) for background suppression
S.Willocq (UMass) CP Violation - NEPPSR 2002 28
ϒ(4s) → B0 B0
B0 B0 system in coherent L=1 state
B0 and B0 evolve IN PHASE⇒ always one B0 and one B0
until one of them decaysat time t = t tag
Other B continues to evolve until it decays at time t = t CP
Consider other B decays into CP eigenstate fCP
If Btag is B0 at time ttag then probability to observe other B decay into fCP is
with ∆t = tCP - ttag
if Btag is B0 at time ttag then
ϒ(4s)B0
B0
t tag
t tag
t CP
[ ]tmef dft
CP∆∆+Γ= ∆Γ−
+ sin )Im(1 41 λ
Btag
BCP
[ ]tmef dft
CP∆∆−Γ= ∆Γ−
− sin )Im(1 41 λ
S.Willocq (UMass) CP Violation - NEPPSR 2002 29
ϒ(4s) → B0 B0
∆ t / τ0
0.1
0.2
0.3
0.4
0.5
-4 -3 -2 -1 0 1 2 3 4
Dec
ay P
roba
bilit
y
f+
f+
f-
f-
∆t / τ
-1
-0.5
0
0.5
1
-4 -3 -2 -1 0 1 2 3 4
True
Asy
mm
etry
Different time evolution for B0(t = ttag) → fCP and B0(t = ttag) → fCP decaysAsymmetry depends on ∆t = tCP – ttag (NB: ∆t can be > 0 or < 0)
ϒ(4s) rest frame: B mesons produced nearly at restpB* = 340 MeV/c
→ avg distance traveled before decay <L*> = 30 µm (given τB = 1.55 ps)⇒ Symmetric e+ e− collider (e.g. CESR) does not allow time reconstruction⇒ Need unequal beam energies to boost ϒ(4s) system and measure ∆t
S.Willocq (UMass) CP Violation - NEPPSR 2002 30
S.Willocq (UMass) CP Violation - NEPPSR 2002 31
PEP-II B Factory @ SLAC
• E(e+) = 3.1 GeV and E(e−) = 9.0 GeV ⇒ βγ = 0.55 ⇒ <L> = 260 µm• Peak luminosity = 3.0 x 1033 cm-2 s-1 (design)
4.6 x 1033 cm-2 s-1 (achieved)• Number of bunches = 800• Positron current = 1775 mA, Electron current = 1060 mA• IP beam sizes = 150 µm in x, 5 µm in y
S.Willocq (UMass) CP Violation - NEPPSR 2002 32
PEP-II B Factory @ SLAC
S.Willocq (UMass) CP Violation - NEPPSR 2002 33
BABAR Collaboration @ SLACCollaboration meeting @ SLAC July 2002
9 Countries76 Institutions550 Physicists
July 2002
S.Willocq (UMass) CP Violation - NEPPSR 2002 34
BABAR Detector @ PEP-II
Cherenkov Detector (DIRC)
Silicon Vertex Tracker (SVT)
Instrumented Flux Return (IFR)CsI Calorimeter (EMC)
Superconducting Coil (1.5T)
Drift Chamber (DCH)
e- (9.0 GeV)
e+ (3.1 GeV)
S.Willocq (UMass) CP Violation - NEPPSR 2002 35
1. Fully reconstruct B decay to CP eigenstate (eigenvalue ηCP = ±1)2. Determine B0 or B0 flavor of the other (tagging) B meson3. Reconstruct decay vertices of both B mesons
∆z = zCP – ztag <∆z> = 260 µm∆t = ∆z / (γ β c) SIGNED!
4. Extract sin 2β with unbinned maximum likelihood fit (value hidden to avoid bias)
Experimental effects: Dilution D = (1 – 2w) and resolution function R(∆t)σ(sin 2β) ∝ 1 / (N εtag D2)1/2
sin 2β (Blind) Analysis at BaBar
)(sin )2sin(- )()()()()( CP tmD
tFtFtFtFt dCP ∆∆≅
∆+∆∆−∆
=∆Α−+
−+ βη
[ ] )(sin 2sin )(1 )( ||41 tRtmDetF dCP
t ∆⊗∆∆−±Γ=∆ ∆Γ−± βη
−π
+π+µ
−µ
0B
0B0D
−π+µ
−K
−πµυ
)4( sΥ
LB
HBe+
e−
∆z = ∆tβγc
S.Willocq (UMass) CP Violation - NEPPSR 2002 36
Exclusive B Reconstruction (I)
Exploit two kinematical constraints:→ Beam energy substituted mass
resolution ~ 2.6 MeV/c2
dominated by beam energy spread
→ Energy difference
resolution ~10-40 MeV dependingon decay modesuppress background from other B decays
*2 *2ES beam Brecm E p= −
**beamBrec EEE −=∆
Signal regionmES:[mB -3σ, mB +3σ]
∆E:[0 -3σ, 0 +3σ]
mES (GeV/c2)
∆E
(MeV
)∆E
mES
S.Willocq (UMass) CP Violation - NEPPSR 2002 37
Exclusive B Reconstruction (II)Full reconstruction of B decay into→ CP-odd eigenstates: ηCP = -1
• B0 → J/ψ K0s
J/ψ → e+ e−, µ+ µ−
• B0 → ψ(2s) K0s
ψ(2s) → e+ e−, µ+ µ−, J/ψ π+ π−
• B0 → χc1 K0s
χc1 → J/ψ γ• B0 → ηc K0
s
ηc → K0s K+ π− , K+ K− π0
with K0s → π+ π− (and π0 π0 for J/ψ mode)
→ CP-even eigenstates: ηCP = +1
• B0 → J/ψ K0L
→ CP-mixed eigenstates:• B0 → J/ψ K*0 (K*0 → K0
s π0)
BELLE J/ψ K0L
1506 signal candidates,purity 94%
988 signal candidates,purity 55%
S.Willocq (UMass) CP Violation - NEPPSR 2002 38
Candidate for B0 → J/ψ K0s with J/ψ → e+ e− and K0
s → π+ π−
S.Willocq (UMass) CP Violation - NEPPSR 2002 39
Candidate for B0 → J/ψ K0s with J/ψ → e+ e− and K0
s → π+ π−Candidate for B0 → J/ψ K0s with J/ψ → e+ e− and K0
s → π+ π−
S.Willocq (UMass) CP Violation - NEPPSR 2002 40
Need to tag B0 or B0 flavor of other (Btag) mesonBCP has flavor opposite that of Btag at t = ttag
Examine all charged particles in the event not included in BCP reco
Ingredients:• Lepton charge (B → l+ X vs. B → l− X )• Kaon charge (b →c →s transition ⇒ B → K+ X vs. B → K− X) • Slow pion charge (B → D*− X ⇒ slow π− )• Cascade lepton charge
Flavor Tagging (I)
−π
+π+µ
−µ
0B
0B0D
−π+µ
−K
−πµυ
)4( sΥ
LB
HBe+
e−
∆z = ∆tβγc
BCP
Btag
S.Willocq (UMass) CP Violation - NEPPSR 2002 41
Flavor Tagging (II)Tag performance extracted directly from data:• reconstruct one B decay to flavor eigenstate D*− l+ νl, D(*)− π+, D(*)− ρ+, …• tag the rest of the event and measure both mistag rate w and ∆md
2.7 ± 0.331.5 ± 0.920.0 ± 0.3Inclusive
28.1 ± 0.765.5 ± 0.5All
6.7 ± 0.420.9 ± 0.819.8 ± 0.3Kaon II
10.7 ± 0.410.0 ± 0.716.7 ± 0.2Kaon I
7.9 ± 0.33.3 ± 0.69.1 ± 0.2Lepton
Q (%)w (%)εtag (%)Method
EffectivenessQ = ε (1 – 2w)2
= ε D2
S.Willocq (UMass) CP Violation - NEPPSR 2002 42
Proper Time Difference ∆t = ∆z / (γ β c)Measure decay vertex positions for BCP and Btag along boost direction
→ BCP vertex:* Geometric & kinematic fit σz ~ 65 µm
→ Btag vertex:* Fit remaining tracks* Use beam spot constraint* Iterate to remove trks with large χ2 (minimize bias from charm decays)* Include resultant K0
s trajectory and BCP momentum vectorσz ~ 110 µm
→ dominates ∆z resolution + introduces δz ~ 25 µm bias from charm
C PBta gB
∆ z
e+e-
S.Willocq (UMass) CP Violation - NEPPSR 2002 43
sin 2β Measurement• BaBar 88 x 106 BB pairs: sin 2 0.741 0.067 ( ) 0.033 ( )stat systβ = ± ±
ηCP = -1 ηCP = +1
S.Willocq (UMass) CP Violation - NEPPSR 2002 44
sin 2β Measurement with Lepton Tags Only• 220 lepton-tagged ηf = -1 events
= ±sin2 0 79 0 11β . .
98% purity3.3% mistag rate
20% better ∆t resolution
S.Willocq (UMass) CP Violation - NEPPSR 2002 45
World sin 2β Measurements
World average
sin 2β = 0.734 ± 0.055
In excellent agreementwith value determinedindirectly from otherB and K decay measurements:sin 2β = 0.75 ± 0.09S.Mele, PRD59, 113011 (1999)
S.Willocq (UMass) CP Violation - NEPPSR 2002 46
Search for CP violation in charmlessB decays (b → u or b → s transitions)
→ measure decay rate asymmetry
No evidence for direct CPV yetUncertainties at the 5-40% level
(similar results from CLEO and BELLE)
Most precise for B0 → K+π− with
CP Violation in Decay
)()()()(
fBfBfBfBACP →Γ+→Γ
→Γ−→Γ=
0.102 0.050 (stat) 0.016 (syst)
CPA = − ±±
fB 2≠ fB 2
CP Violation in decay:
S.Willocq (UMass) CP Violation - NEPPSR 2002 47
CP Violation in Mixing
CP Violation in mixing:
Measure asymmetry in semileptonic decays
BaBar: aSL = 0.005 ± 0.012(stat) ± 0.014(syst)
| q / p | = 0.998 ± 0.006(stat) ± 0.007(syst)
Consistent with small predicted violation
40 0
40 0
1 /( ) ( )( ) ( ) 1 /
l lSL
l l
q pB l X B l XaB l X B l X q p
ν νν ν
+ −
+ −
−Γ → − Γ →= =
Γ → + Γ → +
fB0 B0 2≠ fB0 B0 2
Rate of “wrong” sign leptons(from mixing)
t (ps)∆ 0 2 4 6 8 10 12
Sam
e-si
gn
Dile
pto
n A
sym
met
ry
-0.4
-0.3
-0.2
-0.1
-0
0.1
0.2
0.3
0.4
BABAR
⇒
S.Willocq (UMass) CP Violation - NEPPSR 2002 48
“The” Unitarity Triangle (II)Without sin 2β, ρ and η poorly constrained by expt (large theory uncertainties)
|Vub| = |A λ3 (ρ – iη)|B → Xu l ν decays (b → u)
|Vtd| = |A λ3 (1 – ρ – iη)|B0 – B0 oscill. freq. (d → t)CPV in Kaon decaysεK measurement (s → c)
All constraints are consistentwith one another
GOAL:Stringent test of SMvia precise measurements ofthe sides and angles ofthe unitarity triangle
S.Willocq (UMass) CP Violation - NEPPSR 2002 49
“The” Unitarity Triangle (III)
εK
sin2β
ρ_
η_
We can now check the consistency of the CKM picture of CPVCompare constraints from:
1. CPV in the kaon system (εK)2. CPV in b → ccs (e.g. B0 → J/ψ K0
s)3. |Vub| and |Vtd| from b → u decay rate and B mixing frequency
Excellent consistencybetween the differentobservables
CKM matrixprovides coherentframework (so far…)
0 1-1
1
0
S.Willocq (UMass) CP Violation - NEPPSR 2002 50
“The” Unitarity Triangle (IV)Possible situation in 2007 showing inconsistency between the measurement of the sides and of the angles of the triangle:
Assume uncertainties of 3% in |Vcb|, 10% in |Vub|, <1% in ∆md and ∆ms
Assume uncertainties of 1% in sin 2β, 5o in α and 10o in γ
Inconsistency between constraints might look like:
S.Willocq (UMass) CP Violation - NEPPSR 2002 51
SummaryCP Violation:
New window into the Standard Model of Particle Physics,relevant to matter-antimatter asymmetry of the Universe,sensitive to New Physics
CKM quark mixing matrix for 3 families of quarks contains an irreducible
phase that induces CP violation in weak charged current interactions
B Factories have observed (large) CP violation for the first time outside of the neutral kaon system (B0 → J/ψ K0
s decays)
Current data is in excellent agreement with the CKM picture of CPV
Probing of the SM continues with larger data samples at the B Factoriesand begins at the Fermilab Tevatron
S.Willocq (UMass) CP Violation - NEPPSR 2002 52
Additional Slides
S.Willocq (UMass) CP Violation - NEPPSR 2002 53
CP Violation in the Standard Model (I)(Electroweak) Standard Model:• Three families of quarks and leptons
arranged in left-handed doublets andright-handed singlets
• Local gauge invariance underU(1)Y ⊗ SU(2)L symmetry groups yieldselectromagnetic and weak interactions
• Field equations (Lagrangian) describe electromagnetic (LEM), charged current weak (LCC), and neutral current weak (LNC) interactions,also “Yukawa” interactions between Higgs field φ and fermions(LY to provide mass to the fermions)
family 1for , , , , stRRR
L
e
L
edued
u
ν
S.Willocq (UMass) CP Violation - NEPPSR 2002 54
CP Violation in the Standard Model (II)Higgs coupling to fermions:For the first family we have
Note: separate terms for up-type quarks (Q = +2/3 e) and
down-type quarks (Q = -1/3 e)
After spontaneous symmetry breaking, we obtain quark mass terms
−=
=
=
=
+++=
−
+
φ
φφ
φ
φφ
ν
φφφ
, , , where
.. *0
0c
LL
L
e
Rc
LuRLdReY
du
Qe
L
chuQgdQgeLgL
( ) ( )R
DL
R
ULY
bsd
M bsdtcu
Mtcu
+
= ~~ massquark L
S.Willocq (UMass) CP Violation - NEPPSR 2002 55
CP Violation in the Standard Model (III)Quark mass matrices:In general, mass matrices are not diagonal
⇒ Need to diagonalize those with matrices Vup and Vdown
⇒ Redefine quark eigenstates to get
( ) ( )R
downRD
downLL
R
upRU
upLLY
bsd
VM Vbsdtcu
VMVtcu
+
= ††massquark L
DU MM ~ and ~
( ) ( )R
DL
R
ULY
bsd
Mbsdtcu
Mtcu
+
= massquark L
S.Willocq (UMass) CP Violation - NEPPSR 2002 56
CP Violation in the Standard Model (IV)Charged-current Weak Interaction:Redefinition of quark mass eigenstates has non-trivial consequence:
→ Eigenstates for weak interactions (d’, s’, b’) are linear combinations ofmass eigenstates (d, s, b):
→ Unitary transformation matrix is Cabibbo-Kobayashi-Maskawa(CKM) mixing matrix
( )
( ) ..'''
2
.. 2
†
chWbsd
tcug
chWbsd
VVtcug
L
L
L
downL
upLLCC
+
γ=
+
γ=
+µ
µ
+µ
µL
⋅
=
⋅=
′′′
bsd
VVVVVVVVV
bsd
Vbsd
tbtstd
cbcscd
ubusud
CKM
† downL
upLCKM VVV =
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