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CKM Matrix and CP Violation in Standard Model
FisicadellePar,celleElementari,AnnoAccademico2014-15http://www.roma1.infn.it/people/rahatlou/particelle/
ShahramRahatlou
Measurementofsin2β.ConstraintsonCKMLecture17
2
+e-e
B0 → J/ψ Ks
CP Violation in Interference between Mixing and Decay
z
Δ zΔ t βγ c≈< >
Brec
Btag( )4sΥ
βγΥ(4S) = 0.55
zΔ-π
0sK +π
+µ-µ
Coherent BB pair
B0
B0
µ�
Κ�
Separate B0 and B0
Any CP Eigenstate
3
Time-Evolution of B Decays to CP Eigenstates
n Probability of |B0>|B0> → |fCP>|ftag> depends on n Difference Δt between decay time of the two B mesons
n Decay amplitudes
n Oscillation parameter
n Flavor of tagging neutral B meson: B0 or B0
n Convenient parameter to describe time evolution n Takes into account combined effect
of oscillation and decay
CP
CP
0f CP
0f CP
A f | H | B , t
A f | H | B , t
= 〈 〉
= 〈 〉
12 i2
12
Mq ep M
− β= − =
CP CP
CP
CP CP
f ff
f f
AAq q=p A p A
λ = η
4
Time-Dependent Decay Rates to CP Eigenstates
n Expression and complexity of λ depends on specific final states n Decay amplitudes A and A can be more or less complicated depending on
number of amplitudes contributing to total amplitude
CP CP
CP
CP CP
f ff
f f
AAq q=p A p A
λ = η
5
Time-Dependent CP Asymmetry in Interference
n CP Violation occurs if
n But even with |λ|=1 it is sufficient to have Imλ ≠ 0
| | 1q Ap A
λ = ≠
1qp= 1A
A=No CP Violation
in Mixing No Direct CP Violation
In Standard Model we expect |λ|≅1 in most of B decays
6
Simple Case with |λCP|=1
n Very simple expression for CP violating asymmetry
n Amplitude of asymmetry defined by phase difference between mixing parameter q/p and ratio of decay amplitudes
n Complex phase ΦM depends on specific final state n Can probe different angles of Unitarity triangle through different B decays
M βΦ =
7
At ϒ(4S): integrated asymmetry is zero à must do a time-dependent analysis !
This is impossible to do in a conventional symmetric
energy collider producing ϒ(4S)→BB !!
+∞
−∞
Δ =∫ CPfa d t 0
Why do We Need Time Dependence?
sin (�mB�t)
8
CPV In Interference Between Mixing and Decay
0 0Neutral B Decays into CP final state accesible by both & decays
This is CPV when 1 and 1 and the CP parameter of interest is
CPV Asymmetry is defined as :
=
Γ=
≡= CP
CP
CP
CP CP
CP
ff f
f
CP
f
f
CPf
f B B
q Ap
q ApA A
a
λ η
( ) ( )( ) ( ) ( )
( )( )
( )
20 0
20 0 2
1( ) ( ) - cos
( ) (
When B decay is dominated by a single
2sin
diagram, 1 sin
11)
= ⇒
−→ −Γ →= Δ
Γ → +Δ
+
=
Γ → +
Δ
CPCP
C
CP CP CP
PP C
fphys CP phys CPB
phy
f
s CP ph
f f f
ys f
BC
B
fP
mB t
tf B t f
m t
a m
B t f B t f
tλ λ
λ λ
λλ
Im
Im
+ 2
+ 2
≠ B0
B0
B0 fcp
B0 fcp
B0
B0 fcp fcp
CP asymm. can be very large and can be cleanly related to CKM angles
0Bϕfi
CPA eCPf
0Bϕ−
=12
2 Mi
Mie
ϕ− fiCPA e
9
Golden Decay Mode B0 àJ/ψK0
10 55
Golden Decay Mode J/ψ K0
37
*c
*ub u
b cs
-2
s*
cb cs
(V V )
Aexpect -1
V V 1Since
V V 50
=10 A
⇒; T is the dominant amplitude
Hence "Platinum" mode !
Penguin:: u,c,t loops
* * *P tb ts cb cs ubt usc u A =V V +V V VP V + PP
Tree
*T cb cs ccsA V V T =
* * *tb ts cb cs ub us
T P c*
cb cs
*cb
*ub u
cs
cs c t u ts
*ub us
V V
Use Unitarity relation V V V V V V to rearrange terms
A A (T P P ) (P P )
= (V V )
V V
+(V
A
V
+ +
+ = + − + −=
T ) P×
Golden Decay Mode B0 "J/ψK0
11
CPV In Interference Between Mixing and Decay: B0 àJ/ψK0
1λ
β)sin(2)Im(λ
S
S
ψK
ψK
=⇒
=⇒
L SψK ψKλ λ= −
ηCP = -1 (+1) for J/ψ K0
S(L)
( ) [ ]0 /,/ 1 sin2 sin( )tS L CPB J K e mtτψ η β−→ ∝ Δ−Γ
( ) [ ]0 /,/ 1 sin2 sin( )tS L CPB J K e mtτψ η β−→ ∝ Δ+Γ
0Bϕfi
CPA eCPf
0Bϕ−
=12
2 Mi
Mie
ϕ− fiCPA e
Same is true for a variety of B →(cc) s final states
S
S
S
*cb cs*cb cs
*cs cd*cs
*t
* *ψKB tb cbb td td
* *cd
ψK *B ψK tb cb cdtb td tdcd
Vq A V V Vλ = V VV VV V
V VV
=- = -p A V VV V VV V
2ie β−
12
Time-Dependent CP Asymmetry with a Perfect Detector
• Perfect measurement of time interval t=Δt • Perfect tagging of B0 and B0 meson flavors • For a B decay mode such as B0→ψKs with | λf|=1
sin 2β
B0 B0
Asy
mm
etry
AC
P
CPV
ACP (�t) = sin 2� sin (�m�t)
13
Charmonium+K0 CP Sample for BABAR (�02)
1 modesfη = −
( )
0 0
0 0 0 0
0
0
0 01
0 0
2
η π
+ −
+ −
+ −
→ →→ →→ →
→ →→ →
l lCP S
CP S
CP
S
CP c S
CP c S
B J/ψK { π π }B J/ψK { π π }B ψ S { or
J/ψπ π }KB χ { J/ψγ}KB { KK }K
(after tagging & vertexing)
988 signal candidates, purity 55%
1506 signal candidates, purity 94%
modes 1f −=η
1 modefη = +0 0CP LB J/ψK→
BABAR 81.3 fb�1
14
Calibration with Flavor eigenstates
sin2β = 0.017 ± 0.022
Control Sample with no expected CP asymmetry
01
( )B D π /ρ /a +∗ − + +→
B0 B0
10 times larger than signal
15
Observation of CP Violation (BaBar 2001)
B0 à J/ψ KS
B0 à ψ(2S) KS B0 à χc KS B0 à ηc KS
sin2β = 0.755 ± 0.074 B0 B0
16
BABAR Result for sin2β (July 2002)
sin2β = 0.755 ± 0.074
ηCP = -1 ηCP = +1
sin2 0 741 0 067 0 033(stat) (syst). . .β = ± ±
17
Updated (ICHEP04) sin2β results from Charmonium Modes
0( ) ( odd) modesScc K CP
−1205 on peak or 227 pairs7730 CP events (tagged signal)
fb M BB
0( ) ( even) modesLcc K CP
= + ± ±−
= = ± ±+
βλλ
2
2
sin2 0 722 0.040 0.0231 | | 0.051 0.033 0.0141 | |
.
CLimit on direct CPV
S
L
cc K cc K+
18
Belle Results on sin2β from Charmonium Modes
386M pairsBB
2
2
sin 2 0 652 0.039 0.0201 | | 0.010 0.026 0.0361 | |
= ± ±−
= = − ± ±+
.
C
βλλ
Belle 2005
BàψKS Sample
New Belle value lower than in �03 but still consistent with BaBar�04 sin2 0 728 0.056 0.023= + ± ±.β
19
CP Violation in B Decays Firmly Established
20
Lessons From sin2β Measurement With B0→J/ψK0
n In 2001, large CP Violation in B system was observed in this mode by BaBar and Belle. n First instance of CPV outside the Kaon system.
n First instance of a CPV effect which was O(1) in contrast with the Kaon system n Confirms the 1972 conjecture of Kobayashi & Maskawa. n Excludes models with approximate CP symmetry (small CPV).
n In 2007 sin2β became a precision measurement (5%) and agrees well with the constraints in the ρ-η plane from measurements of the CKM magnitudes (will be discussed in tomorrow�s lecture)
n Appears unlikely to find another O(1) source of CPV n enterprise now moves towards looking for corrections rather than
alternatives to SM/CKM picture
n Focus now shifts to measurements of time-dependent asymmetries in rare B decays n dominated by Penguin diagrams in the SM and where New Physics could
contribute to the asymmetries
21
Constraints on Unitarity Triangle from Measurements of CKM Elements and CKM Angles
22
4
3( )
( )3
21 / 22 2
(1 )
1 / 22 1
A i
O
A i
A
ACKM
λ ρ η
λ
λ ρ η
λ λ
λ λ λ
λ
+
⎛ ⎞−⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟− −⎜ ⎟⎝ ⎠
−
− −
−
=Vβ
-i
-i
γ1 11 1 1
1 1
e
e
⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠
ud us ub
CKM cd cs cb
td ts tb
V V VV V VV V V
⎛ ⎞⎜ ⎟= ⎜ ⎟⎜ ⎟⎝ ⎠
V
23
Determination of CKM Elements from Measurements
UTfit http://www.utfit.org
CKM Fitter http://ckmfitter.in2p3.fr
24
Bd mixing + CPV in K mixing (εK)
~ (1 )Kε η ρ−
25
Add |Vub/ Vcb|
26
+ BS Mixing constraint
27
+ Sin2β
28
+ α constraint
29
+ γ measurement
All measurements consistent, apex of (ρ,η) well defined
30
Unitarity Triangle after All Constraints
Includes constraints from all CKM-related measurements
31
Impact of Angle Measurements on CKM Fit
Measurements of angles dominate the constraint on the UT apex!
32
Status of UT in 2007
All constraints Only angles from B and εK from Kaons