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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
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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
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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
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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
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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
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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 =
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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)
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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
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Golden Decay Mode B0 àJ/ψK0
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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
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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−
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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)
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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
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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
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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
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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 = ± ±
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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+
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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
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CP Violation in B Decays Firmly Established
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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
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Constraints on Unitarity Triangle from Measurements of CKM Elements and CKM Angles
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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
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Determination of CKM Elements from Measurements
UTfit http://www.utfit.org
CKM Fitter http://ckmfitter.in2p3.fr
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Bd mixing + CPV in K mixing (εK)
~ (1 )Kε η ρ−
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Add |Vub/ Vcb|
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+ BS Mixing constraint
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+ Sin2β
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+ α constraint
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+ γ measurement
All measurements consistent, apex of (ρ,η) well defined
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Unitarity Triangle after All Constraints
Includes constraints from all CKM-related measurements
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Impact of Angle Measurements on CKM Fit
Measurements of angles dominate the constraint on the UT apex!
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Status of UT in 2007
All constraints Only angles from B and εK from Kaons