1. science
2. physics

Why flavor matters at the LHC
Recent developments and prospects in flavor physics
Jernej F. Kamenik
07/01/2012, Heidelberg
Introduction
SM phenomenologically very successful theory
Strong theoretical arguments to consider it as effective
theory
“Flavor physics”
one of arguments to
consider SM not complete
L⌫SM = Lgauge (Aa ,
Ve↵ =
µ
2 †
+ (
†
key tool to investigate NP
beyond SM
i ) + Dµ
2
) +Y
ij
†
Dµ
i
L
j
R
Ve↵ ( , Aa ,
y ij
+
⇤
iT
L
flavor content of model
i)
j T
L
+ ...
Introduction
Ve↵ =
µ
2 †
+ (
†
2
) +Y
ij
i
L
j
R
y ij
+
⇤
iT
L
j T
L
+ ...
Beside direct searches for new d.o.f’s at high energy colliders,
main task is to understand/constrain size of additional terms in
series
Higgs & Flavor physics
Given good agreement with SM predictions
- NP may exhibit considerable mass gap
Indirect searches of NP crucial - require high precision
The SM and NP flavor puzzles
The quark Yukawa sector of SM is very particular
mu =vVLu Y u VRu†
V = VLu VLd†
md =vVLd Y d VRd†
hierarchical
aligned
“SM flavor puzzle”
The SM and NP flavor puzzles
Yu, Yd only source of global flavor symmetry breaking:
GF = SU (3)Q ⇥ SU (3)U ⇥ SU (3)D
10 physical parameters:
6 quark masses
3 CKM mixing angles
1 CP odd phase
Determine all flavor phenomena in quark sector!
The SM and NP flavor puzzles
⇤
⇤
Yu, Yd only source⇢¯ of
symmetry
breaking:
+ i¯
⌘global
= (Vud Vflavor
)/(V
V
cd
ub
cb )
GF = SU (3)Q ⇥ SU (3)U ⇥ SU (3)D
10 physical parameters:
6 quark masses
3 CKM mixing angles
1 CP odd phase
Determine all flavor phenomena in quark sector!
Generally excellent consistency!
NP effects by means of a generalization of the Fermi Theory. The
renormalizable part of a more general local Lagrangian which include
with dimension d > 4, constructed in terms of SM fields, suppressed b
The SM and NP
flavor
puzzles
scale Λ > MW :
Severe constraints on NP sources of flavor
Leff = LSM +
!
(d)
ci
(d)
O
i (SM field
(d−4)
Λ
Isidori, Nir & Perez, 1002.0900
Operator
( F = 2)
(¯
sL γ µ dL )2
approach allows us toObservables
analyse all
BoundsThis
on Λgeneral
in TeV (cbottom-up
ij = 1) Bounds on cij (Λ = 1 TeV)
Re limited
9.8 × 102
2
(¯
cL γ u L )
1.2 × 10
5.1 × 10
2
(¯bR dL )(¯bL dR ) 1.9 × 103
(¯bL γ µ sL )2
(¯bR sL )(¯bL sR )
1.6 × 104
9.0 × 10−7
3.4 × 10−9
3.2 × 105
6.9 × 10−9
2.6 × 10−11
5.6 × 10
1.0 × 10
∆mK ; "K
the
scale Λ defines
the cut-off
of the −7
effective theory. However, cor
3
3
−7
(¯
cR uL )(¯
cL uR ) 6.2 × 103
(¯bL γ µ dL )2
Im
Re
number
of parameters
(theIm
coefficients of the higher-dimensio
∆mK ; "K
of this method is the impossibility to establish
correlations of NP eff
(¯
sR dL )(¯
sL dR ) 1.8 × 104
µ
realistic ext
2.9 × 10
1.5 × 104
9.3 × 10
2
3.6 × 103
1.1 × 102
3.7 × 102
5.7 × 10−8
3.3 × 10
−6
5.6 × 10−7
1.1 × 10−8
∆mD ; |q/p|, φD
∆mD ; |q/p|, φD
6
−6
∆mBd ; SψKS
1.7 × 10−7
∆mBd ; SψKS
1.0 × 10
7.6 × 10−5
1.3 × 10−5
∆mBs
∆mBs
TABLE I: Bounds on representative dimension-six ∆F = 2 operators. Bounds on Λ are quoted assuming an
“NP flavor puzzle”
effective coupling 1/Λ2 , or, alternatively, the bounds on the respective cij ’s assuming Λ = 1 TeV. Observables
related to CPV are separated from the CP conserving ones with semicolons. In the Bs system we only quote
a bound on the modulo of the NP amplitude derived from ∆mB (see text). For the definition of the CPV
NP effects by means of a generalization of the Fermi Theory. The
renormalizable part of a more general local Lagrangian which include
with dimension d > 4, constructed in terms of SM fields, suppressed b
The SM and NP
flavor
puzzles
scale Λ > MW :
Severe constraints on NP sources of flavor
Leff = LSM +
!
(d)
ci
(d)
O
i (SM field
(d−4)
Λ
This general bottom-up approach allows us to analyse all realistic ext
NP at TeV scale has to be approximately flavor “aligned” with SM breaking
limited number of parameters (the coefficients of the higher-dimensio
of this
methodFlavor
is the impossibility
correlations
maximal alignment
- Minimal
Violation (Yu, to
Ydestablish
remain only
sources)of NP eff
d’Ambrosio et al., hep-ph/0207036
the scale Λ defines the cut-off of the effective theory. However, cor
¯i
JµN P = Xij Q
j
Q
,
µ
Xij = a0 1 + a1 Y u† Y u + a2 Y d† Y d + . . .
even in MFV, bounds on NP scale O (few TeV)!
“NP flavor puzzle”
6
Hurth, Isidori, J.F.K. & Mescia, 0807.5039
UTFit, 0707.0636
Bs,d →
+
μ μ status
and prospects
y sensitive to FCNC scalar currents and FCNC Z penguins
Bs,d → μ+μ- status and prospects
b
μ
b
s
μ
s
μ
t
t
B
B about flavor physics beyond SM:
These modes are unique source of information
μ
• theoretically very clean (virtually no long-distance contributions)
gauge-less limit
• particularly sensitive to FCNC scalar currents and FCNC Z penguins
B
bR
sL
tL
ϕ+
tR
ϕ0
μR
μL
good approx. to the
full SM amplitude
(gaugeless limit - good approx. to full SM amplitude)
Clean probe of the Yukawa interaction
(→ Higgs sector) beyond the tree level
Clean probe of the Yukawa interaction
(→ Higgs sector) beyond tree level
ipated, in this case the dominant source of uncertainty in Bs,SM is of parametric nature.
Treating all errors as Gaussian, we obtain the final result
Bs →
(0)
Bs,SM
μ+μ- recent
= (3.23 ± 0.27) ⇥ 10
developments
9
,
(17)
which is closest to our large-mt result in the (0,0) scheme. We choose eq. (17) as our
reference value for the non-radiative branching ratio.
Updated SM prediction taking into account leading NLO EW (+ full NLO QCD)
For future reference, we illustrate the impact of the various inputs via the following
Buras et al., 1208.0934
parametric expression:
(0)
Bs,SM
= 3.2348 ⇥ 10
9
⇥
✓
Mt
173.2 GeV
◆3.07 ✓
f Bs
227 MeV
◆2 ✓
⌧B s
1.466 ps
◆
Vtb⇤ Vts
4.05 ⇥ 10
2
2
= 3.23 ± 0.15 ± 0.23fBs ⇥ 10 9 .
(18)
systematic continuos
~3% theory error.
improvement
of fBs on
In the second line of eq. (18) we have explicitly
separated
theLattice
contribution to the error
~4%) and deserves a dedicated
due to fBs , which is the most relevant source(currently
of uncertainty
discussion. + Correction factors in relating theory to experimentally accessible rate
As pointed out
in Ref. [34], incut
principle
one can
get ridincluded
of the quadratic
fBs dependence in
- Photon-energy
→ ~ -10%
(already
in exp. eff.)
B(Bs ! µ+ µ - )ΔΓ
bys normalizing
this
to yet
mB
taking
advantage of the
≠0
→observable
~ +10% (not
included
in exp.
results)
s , thereby
¯s Bs mixing amplitude, that
relatively precise lattice results on the bag parameter of the B
enters the latter linearly. Moreover, this procedure removes also the dependence on the
+µ )
(exp) the uncertainty
+1.5
9 LHCb,1211.2674
9 proposal reduced
CKM parameters.
Indeed,
in
2003
this
in
B(B
!
µ
s
Bs
= (3.2 1.2 ) ⇥ 10
B s,SM = (3.54 ± 0.3) ⇥ 10
by a factor of three. However, given the recent progress in the direct determination of fBs
from the lattice [28,
and in the
determination
of CKM
parameters this strategy is
At 35–41]
this stage
there
is perfect
compatibility...
no longer necessary although it gives presently a very similar result [42].
Bs → μ+μ- recent developments
HCP 2012, Kyoto Nov. 2012
G. Isidori – Flavor Physics Theory
...and good agreement with SM has important implications:
...and the good agreement with SM has important implications:
E.g.II: Constraints
onon
thethe
structure
of theofA-terms
in more in
general
models
Example:
Constraints
structure
the A-terms
SUSYSUSY
models
(“Disoriented A-terms” framework → Z-mediated FCNCs)
W
b
Ytb*
s
〈ϕ〉
〈ϕ〉
W
b
A33*
Yts
tR
~
Z
Leading contribution
Leading
contrib. in to
SM
the SM amplitude
s
~
A32
tR
〈ϕ〉
〈ϕ〉
Z
Possible
O(O(
± 30%)
Possible
± 30%)corrections
corrections to Br
~< 0.5
to the for
BR m
fortRm
TeVTeV
stop < 0.5
LR mixing term still largely unknown
(mh ~125 GeV → large A33)
Measurement with σ(Br) ~ 30% provides first relevant constraint on such
couplings below stability bounds ( |A33 A32| < 3 mtL2 ) for mtL<1 TeV
Puzzling CP violation in charm decays
Puzzling CP violation in charm decays
Year ago LHCb reported first evidence of CP violation in
charm system, evidence soon after confirmed by CDF & Belle
15
aWorld
=
CP
(0.68 ± 0.15)%
(~4.3σ from 0)
Thanks to Marco Gersabeck from HFAG
Unambiguous evidence for direct CPV
af ⌘
¯0 ! f)
(D0 ! f )
(D
.
0
0
¯
(D ! f ) + (D ! f )
aCP ⌘ aK + K
a⇡ + ⇡
Totally unexpected: before LHCb result
DCPV in charm above 0.1% often
quoted as “clear signal of NP”...
Post-measurement considerations:
The observed ΔaCP is large compared to its “natural” SM expectation, but is not
large enough, compared to SM uncertainties, to be considered a clear signal of NP:
Puzzling CP violation in charm decays
ΔaCP ≈ (0.13%) Im(ΔRSM)
Heff ≈ Vcd*Vud H(d) + Vcs*Vus H(s)
Observed ΔaCP is large compared to “natural” SM expectation
matrix-element ratio:
“penguin” (disconnected)
SM
aCP
⇡
(0.13%)Im(
R
),
CKM
“tree” (connected)
suppression:
naturally expected < 1
u
SMc
RSM ⌘ RK
+
D
suppression
“disconnected”
Brod et al. '11, '12
Golden, Grinstein '89
✓ ⇤
◆
”connected”
Feldmann et al. '12
Vcs Vus
4
arg
= O( )
naturally expected <1
⇤
Vcd Vud
c.f. Grossman et al., hep-ph/0609178
d
H
d |
c|=1 +
s
H
s |
c|=1 +
peng
⇤
H
⌘
V
Vuq ,
b
q
| cq
c|=1
d
D
s
u
d
+
u
H(s)
c
s
+
b
π
d
u
u
ΔR>1 is not what we expect for mc >> ΛQCD, but is
the charm as a light quark:
CKM not impossible treating
matrix
element
possible connection with the ΔI=1/2
ruleratio:
in Kaons
H|e↵ c|=1 =
(d)
H
SM
R⇡
=0
π
π
d
d
u
π
Post-measurement considerations:
The observed ΔaCP is large compared to its “natural” SM expectation, but is not
large enough, compared to SM uncertainties, to be considered a clear signal of NP:
Puzzling CP violation in charm decays
ΔaCP ≈ (0.13%) Im(ΔRSM)
Heff ≈ Vcd*Vud H(d) + Vcs*Vus H(s)
Observed ΔaCP is large compared to “natural” SM expectation
matrix-element ratio:
0.000
CKM
suppression:
-0.002
“penguin” (disconnected)
“tree” (connected)
naturally expected
u
c
d
D
update of
J.F.K, Ligeti & Perez
< Isidori,
1
1111.4987
aCP
ΔR>1 is not what we expect for mc >> ΛQCD, butSM
is
-0.004
impossible treating the charm as a light quark:
CKM not
CDF
matrix
element
ratio:
possible connection with the ΔI=1/2 rule in Kaons
DaCP
H(d)
O(4-6) values of |ΔRSM| needed
d
u
u
World aver. c
suppression
“disconnected”
-0.006
Brod et al. '11, '12
Golden, Grinstein '89
✓ ⇤
◆
”connected”
Feldmann et al. '12
D
Vcs Vus
4
arg
= O( )
u
naturally expected <1
⇤
-0.008
Vcd Vud
LHCb
-0.010
0.2
0.5
1.0
2.0
5.0
10.0
peng
⇤
H|e↵ c|=1 = d H|d c|=1 + s H|s c|=1 + RqbSM
H
⌘| Vcq
Vuq ,
d+ s+
c|=1
»DR SM »
π
u
H(s)
s
b
=0
π
π
d
d
u
π
Puzzling CP violation in charm decays
Observed ΔaCP is large compared to “natural” SM expectation
aCP ⇡ (0.13%)Im( RSM ) ,
CKM
suppression
✓ ⇤
◆
Vcs Vus
arg
= O(
⇤
Vcd Vud
4
)
SM
RSM ⌘ RK
+ R⇡SM
matrix element ratio:
“disconnected”
”connected”
naturally expected <1
c.f. Grossman et al., hep-ph/0609178
ΔRSM > 1 is not what we expect for mc >> ΛQCD, but is
not impossible treating charm quark as light:
possible connection with the ΔI=1/2 rule in Kaons
Golden & Grinstein Phys. Lett. B 222 (1989)
Brod, Kagan & Zupan 1111.5000
Brod, Grossman, Kagan & Zupan 1203.6659
Puzzling CP violation in charm decays
Observed ΔaCP is large compared to “natural” SM expectation
...but not large enough, compared to SM uncertainties, to be
considered clear signal of NP
Assuming SM does not saturate exp. value parametrize NP
contributions normalized to effective SM scale
aCP ⇡ (0.13%)Im( R
SM
)+9
X
Im(CiNP ) Im( RiNP )
i
2
2
SM
v
(0.61
±
0.17)
0.12
Im(
R
)
(10
TeV)
NP
• for Im(Ci Im(C
: )
) = NDA
=
.
2
2
NP
⇤
⇤NDA
Im( R )
Are such contributions allowed by other
flavor constraints?
Puzzling CP violation in charm decays
Isidori, J.F.K, Ligeti & Perez
1111.4987
In EFT can be estimated via “weak mixing” of operators
n
NP
T H|e↵ c|=1
(0), HSM (x)
o
c
u
Qi
q
⇒
q
W
_
Important constraints on most operators from D-D mixing
and direct CPV in K0→π+π- (ε’/ε)
CPV chromo-magnetic operators only weakly
constrained by EDMs
Gedalia, J.F.K, Ligeti & Perez
1202.5038
• Strict bounds from D meson mixing naturally
satisfied
• Easily generated in various well-motivated models
(SUSY, warped extra-dim.,....)
Giudice, Isidori & Paradisi,1201.6204
Keren-Zur et al., 1205.5803
Delaunay, J.F.K., Perez & Randall, 1207.0474
Puzzling CP violation in charm decays
Key question: how to distinguish NP vs. SM explanations?
NP explanation via chromo-magnetic operators:
Unavoidable large CPV also in the electric-dipole operators
(model-independent connection via QCD)
Isidori & J.F.K., 1205.3164
Lyon & Zwicky, 1210.6546
Fajfer & Kosnik, 1208.0759
CPV in radiative D decays (D→(P+P-)V γ; also D→(P+P-)V l+l-)
CPV asymmetries above 3% would be a clear sign of NP in dipole operators
Neutron EDM and LFV in charged leptons are
also expected to be close to present bounds,
but connection is more model-dependent
CP violation in Bs mixing?
CP violation in Bs mixing?
HCP 2012, Kyoto Nov. 2012
G. Isidori – Flavor Physics Theory
Given good consistency of global CKM fits, CPV in Bs
Given this situation, it is particularly interesting to see what happens in the b→s
Another
triangle
mixing
predicted
precisely
ΔF=2
amplitude
(CPV in Bs mixing),
where the in
SMSM
prediction
is more unitarity
precise.
⇢¯ + i¯
⌘ s =)
_ Bs ψBφ(f
0
0.10
Bs K
Bs
⇤
⇤
(Vub Vus
)/(Vcb Vcs
)
L
at C
ed
lud
exc
S
C
i
d
a
excluded area has CL > 0.95
.95
>0
0.05
Bs
So far, no signs of deviations
from
SM...
So
far, no the
signs of
deviations from the SM...
md & ms
SM
Sψφ
0.00
md
= -sin(ϕs )
= 0.041 ± 0.01
Vub
N
s
-0.05
sin 2
CKM
K
fitter
Winter 12
-0.10
-0.10
s
-0.05
0.00
0.05
Bs
⇢¯Bs + i ⌘¯Bs = arg
⇣
⇤
Vub Vus
⇤
Vcb Vcs
0.10
⌘
d
c
m
=b,c,SLM
q
q
q
q [(Pq
q=b,c,SLM
· Pq ) + (Pq · Pq )]
We recall the basic ingredients in the determination0 of Absl fr
Py mention that
another
observable
is introduced in Ref. [3] by considering AS restric
+
+
¯
¯
[(Pq · Pq ) (Pq charge
· Pq )]asymmetry according to Ref. [2] and applicable to the m
q=b,c,SLM
of dimuons with a large enough muon
impact parameter. We
refrain from study
.
(8)
values
quoted
in
the
latter
reference
for
our
numerical analysis
+ ¯+
¯
[(Pqbecause
· Pq ) +
(P
Pq )]of knowledge concerning the experimental inputs a
q ·lack
she
observable
of
our
s
q=b,c,SLM
DØ experiment of a sizable
like-sign
dimuonAASL
charge
[1–3]
dimuon charge
asymmetry
and theasymmetry
inclusive muon
charge as
CP violation in B mixing?
asls
required, but we highlight that it could be analyzed0 along the same lines as what
heoretical
interest.
If interpreted
as considering
originating Afrom
mixing-induced
CP
observable
is introduced
in Ref. [3] by
++
S restricted
0
N
N
n+
for AS .
= ++
,
a= +
euark
enough
muon
impact
parameter.
...except
persistent
Asl anomaly
decays,
the
observed
value
ofWe
Ref.refrain
[3] from Astudying
N
+N
n
our lack of knowledge concerning the experimental inputs and
b
++,
+, ) denote the number of events with two m
where
N
(n
A
=
(
0.787
±
0.172
±
0.093)%
,
(1)
ht
that
it
could
be
analyzed
along
the
same
lines as what we
role ofsl the semileptonic CP asymmetries
0.02
0
S
-0.02
B
D
passing the kinematic selections.
SM and material-related
b
4 [4]
There
are
various
detector
processes
co
nce
of
CP
violation
in
semileptonic
b
and
c
quark
aS +0.15
and
A
can
be
direc
dimuon
asymmetry
by D0
ASLwithincharge
S
xpected
the standard
model (SM)
Asl decays,
= ( 3.96
)
·
10
0.04
b
reconstructed
muons
are
classified
into
two
categories:
“short
terms
of
A
,
a
linear
combination
of
the
wrong-sign
semileptonic
flavor
specific
asy
D0,
1106.6308 other hand,sl recent measurements of CP violation in
wrong
signcharge
semilepSame-sign
dimuon
asymmetry yield
0.02
2:
decays
of b, c, ⌧inand
from
electromagnetic
decays
of short-lived
eptonic
CP
asymmetries
e
B
mesons
measuring
CP
-violation
their
respective
mixings
3
8.5 ± 2.8) · 10 [2010] ! ( 7.4 ±
HCbd,sIf
and
DØtocollaborations
[6, 7] from decays of charged( kaons
due
CPV in BL)s,dcoming
mixing
and pions as well as
Linear comb. of semileptonic (flavour specifi
+
¯
can
separate
the
contribution
from
short
aS to
the inclu
emileptonic b and c quarks decays,
aS(Band
A can be(B
directly
¯ q (t)!`
µ +muons
X)
(B
⌫X ) (Bq (t)!`
⌫X )
q q !
q ! µ S X)
q
D
-0.04
D
asls
DØ, 9
-0.0
SM
b
d
s a = ( 0.24 ± 0.54 ± 0.33)%
a0SL =
6= 0 =) C
72
±
0.17)%
[DØ]
,
[LHCb]
,
(2)
¯ (t)!` ⌫X
A
=
f
a
+
f
a
,
a
=
,
(
B
)+
(B
(t)!`
⌫X
)
sl
s
d
sl
sl wrong-sign
sl
sl
ombination
of the
semileptonic
flavor specific asym-
¯q ! µ+ X) + Discrepancy
(B
(B
X)SM
(
q f!(aµ from
a
=
+
) +expectation
fK aK +AfSL⇡ a=⇡ +
2
S S
g CP -violation
in
their
respective
mixings
:
Model
(fragmentation)
fractionsdeterminationsStandard
xpectations.production
Furthermore,
recent precise
of
the
CP
asymB Factory W.A.
fs the fractions of Bd and where
Bs mesons
contributing
to-0.02
the asymmetry,
whichdetection
depend
is
the
charged
asymmetry
related
to
muon
decaysetting.
[8], which
are
consistent
with
SM
predictions,
severely
DØalready
B !µD X
¯q !
(The
B
µ+ X)
(B
!
µ
X)
ental
values
used
by
the
DØ
collaboration
are
either
taken
from avera
q
q
ground
L
processes,
f
(f
,
f
)
the
fraction
of
muons
from
⇡
p
K
DØ
A
,tationasl
=
,
(9)
ofLEP
the(value
(1)(B
inmisidentifications),
terms
of
non-standard
CP-violating
con¯q ! in
[2], or at
[3].
B
µ+Eq.
X)decays,
+
!
µ
X)
DØ A 95% C.L.
q
and
-0.04 aK (a⇡ , ap ) the corresponding
b
While the
large
observed
Adirectly
still originate
from
new-1 CP-violating
resence
of CP
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B(B!D
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B(Bstatistical
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LFU in (semi)leptonic B decays
General requirements in EFT:
• no tree-level down quark / charged lepton FCNCs
• no LFU violations in pion, kaon sectors
A number of possibilities:
}
require flavor alignment
Fajfer, J.F.K., Nisandzic & Zupan,
1206.1872
modification of left-hand current - preferred in MFV
Predict monotop signature at LHC
Andrea et al., 1106.6199
J.F.K. & Zupan, 1107.0623
chirality flipping scalar operators - require non-MFV
Example: generic 2HDM
severe bounds from FCNCs
see also Crivellin, Greub & Kokulu
1206.2634
30
Conclusions
Success of SM in describing flavor-changing processes
implies that large new sources of flavor symmetry breaking
at TeV scale are excluded.
However, there are sectors of the theory that are just
starting to be tested
• Measurement of Bs,d → μ+μ- probes the Higgs Yukawa sector at loop level
• If due to NP, observed ΔaCP points towards new flavor sources in uR sector
- interesting implications for radiative charm decays
• D0 Asl measurement inconsistent with LHCb measured CPV in Bs mixing
- implications for (direct) semileptonic B (and D) asymmetries
• If confirmed, observed LFU violations in B decays point towards new charged
current interactions of 3rd gen. matter fields
31
- interesting top, tau physics at LHC
Backup
CPV in |Δc|=2
¯ 0i
• CPV in Mixing |D1,2 i = p|D0 i ± q|D
m1 + m2
m⌘
,
2
m2 m1
x⌘
,
⌘
1
y⌘
2
+
2
2
2
,
1
.
• Experimentally accessible mixing quantities:
• x,y (CP conserving)
Cannot be estimated accurately within SM
NP contributions are predictable
• flavor specific time-dependent CPV decay asymmetries [sensitive to q/p]
af (t) ⌘
¯ 0 (t) ! f )
(D0 (t) ! f )
(D
,
0
0
¯
(D (t) ! f ) + (D (t) ! f )
CPV in |Δc|=2
¯ 0i
• CPV in Mixing |D1,2 i = p|D0 i ± q|D
m1 + m2
m⌘
,
2
m2 m1
x⌘
,
⌘
1
y⌘
2
+
2
2
2
,
1
.
CPV in |Δc|=2
¯ 0i
• CPV in Mixing |D1,2 i = p|D0 i ± q|D
m1 + m2
m⌘
,
2
m2 m1
x⌘
,
x, y ⇠ 1%
⌘
1
y⌘
2
+
2
2
2
,
1
.
| | . 20