SMEFT effects on ΔF=2 FCNC
Motoi Endo (KEK)Beyond the BSM, Gunma, 2018.10.1

New physics contributions to FCNC
New physics — FCNC>~1TeV
SM
100GeVSM w/. EWSB
~1GeV
observable

Higher dimensional
operators

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Conventional FCNC calculation
Higher dimensional operators
He↵F =2 = C1 (dL,i µ dL,j )(dL,i µ dL,j )↵¯+ C2 (dR,i dL,j )(dR,i dL,j ) + C3 (dR,i dL,j )(dR,i d↵L,j )↵+ C4 (dR,i dL,j )(dL,i dR,j ) + C5 (dR,i dL,j )(dL,i d↵R,j )EFT below EWSB, i.e., top, W, Z and H are decoupled

New physics scale > O(100)GeV — SM effective field theory(SMEFT)P
Le↵ = LSM +Are SMEFT effects be negligible?
d>4
C
O
i i i

Outline
Introduction: “Are SMEFT effects be negligible?”
SMEFT in ΔF=2 FCNC
Two models:• Flavor-changing Z penguin• Left-right model
Summarysha1_base64="4d4rf0NExqXAf1AQemnya6dcVyk=">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</latexit>

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latexitZ<

Flavor-changing Z penguin: Motivation
Sensitive to physics beyond SM — cleanest probe

FC Z-penguintW±sha1_base64="1q1iJ6Wg2QzMNQjO02QEHFszQqM=">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</latexit>

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s

d
f±
W
Z

2.8σ anomaly
0

Z

ũi

u, d
s

d
f±
W

KOTO

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KL ! ⇡ ⌫ ⌫¯<latexit

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<latexit

Flavor-changing Z penguin: Motivation
Sensitive to physics beyond SM — cleanest probeLess constrained by experiments — ε’/ε0

KS ! µ + µ

⌫
d
d

s

ũi

d

ũi

f±
W

µ

Z

LHCb

Direct CP violation of KaonFirst lattice computation of hadron matrix element[RBC-UKQCD’15]

SM prediction (lattice + NLO)(✏0 /✏)SM = (1.1 ± 5.1) ⇥ 10 4[Kitahara et.al.’16]

Experimental result(✏0 /✏)exp = (16.6 ± 2.3) ⇥ 10 4

[NA48,KTeV’90-99]

New 2.8σ discrepancy(Near) future prospects
increase statistics, improve systematics, resolve δ0, …

New physics interpretation
Flavor-changing Z penguin
L=

µ
¯
(
d
sL )Zµ +L L(✏0 /✏)NP / Im

s

µ
¯
(
d
sR )ZµR R

c2W
L + s2 Im
W

Z

R

u/d

d
Not gauge invariant under SU(2)xU(1)— lose correlations among NP cont. in ``low-scale’’ EFTsha1_base64="8qoPXhxFPB/duSbdwfwwSHth0iE=">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</latexit>

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[OHD ] = (H iDµ H)(di µ dj )gLe↵ = L ZµWµ G+ + Wµ+ G
mZ<latexit(1)† !
[OHQ ] = (H iDµ H)(q i µ qj )

P

(3)
† !
a
a µ
[OHQ ] = (H iDµ H)(q i ⌧qj )†ΔF=2 transitions

EWSB
)
ΔL

ΔR
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d>4
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Z penguin in SMEFT
SM gauge symmetric, SU(2)xU(1)

✏ /✏

0

+ . . . (q L,i µ qL,j )Indirect CP violation of Kaon
i'"

✏=e

✏

SM

+✏

NP

ImhK 0 |H|K 0 i
sL/R

dL/R

sL

dL

sL

dL

t

sL

dL

t

sL

dL

t

SM

Z
dL/R

Z

sL/R

(a)

dL/R

sL/R

(b)

G−

W
dL/R

sL/R

(c)

G−

G−

W

dL/R

sL/R

(d)

G−

dL/R

sL/R

(e)

ΔL, ΔR

Figure 1. The NP contributions to ∆S = 2 process.
The blackbubble denotes the ver
Correlate
in SMEFT
tices in Eq. (2.4) originating from the dimension-6 eﬀective operators: OL and OR . The
white bubble with “SM” denotes the SM flavor-changing Z interaction. Subfigures (b)–(e)Indirect CP violation of Kaon
Experimental value
✏

ΔL

εK

Im ∆ LΔR

4 ×10 -6εK

2 ×10 -6

KL→μμ

ε’/ε

0

1σ
2σ

-2×10 -6

3

3

= (2.12 ± 0.18) ⇥ 10

4×10 -6

2×10 -6| = (2.228 ± 0.011) ⇥ 10

Im ∆ R

SM

SM

|✏

exp

0

-2 ×10 -6

chiral enhancement-4×10 -6

-4 ×10 -6-4 ×10 -6

L=-2 ×10 -6

0Re ∆ Lµ¯(dsL )Zµ +L L

2 ×10 -6

4 ×10 -6µ¯(dsR )ZµR R-4 ×10 -6-2 ×10 -6

0Re ∆ R

2 ×10 -6

4 ×10 -6

[ME,Kitahara,Mishima,Yamamoto]SUSY scenario[ME,Mishima,Ueda,Yamamoto]Left-handed contribution by Wino mediation
SM s

SUSY

t
W±

u, d
Z

d

ũi
f±
W

Z

Flavor and CP violation in squark trilinear couplings)!
(H † iDµ H)(q i µ qj )† !
(H iDµa H)(q i ⌧ a µ qj )V = (TU )i3 Hu ũiL t̃⇤RHow large can SUSY be?

[ME,Mishima,Ueda,Yamamoto]

Maximum SUSY contribution to ε’/ε(ϵ�/ϵ)����

�����

ε’/ε
1σ

�����

2σ

�� × ��-��� × ��-������∼ [���]mW̃ = mq̃���

= 1 TeV= 2 TeV= 3 TeVε’/ε discrepancy is explained when mq̃ . 4 TeV

Outline
Introduction: “Are SMEFT effects be negligible?”
SMEFT in ΔF=2 FCNC
Two models:• Flavor-changing Z penguin — tight constraint on RH coupling• Left-right model
SummaryScale uncertainty
New (heavy) and SM (light) particle contributions

SM(W)

SM (t)

conventional
NP (heavy)

SM (t)“low-scale” EFT(t, W, … decoupled)

Q. In which scale operators should be matched?

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Left-right symmetric model
SU(3)CxSU(2)LxSU(2)RxU(1)B-L v
R

Lint '

SU(3)CxSU(2)LxU(1)Y

Flavor-changing interactions
Left- and right-handed W bosons
gL
gR
µ
µ
Lint = p (VL )ij ūi µ PL dj WL + p (VR )ij ūi µ PR dj WR
2
2

Higgs fields: Φ~(Hu, Hd) & ΔR (ΔL)

p h
i
2 ¯ †
†
0
0 ⇤
¯
d(VL Mu VR )PR d H + d(VR Mu VL )PL d (H )vc2

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Yt (VL⇤ )3i (VR )3j<latexit

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ΔF=2 transitions: tree level

Heavy Higgs exchange
d¯0R

H0
1
Yt2
⇠
(
)
(
)
LR
ij
RL
ij
2
2
cos 2 mHdR

Input at a scale of heavy Higgs boson massΔF=2 transitions: one-loop level
Left- and right-handed W bosons (mH > mWR)
q0

q

t

q0

q

W L W
W
L

q0

q
A

VL

t

q0

VR

q
B

q0

q
WL

+

WHR

R

q0

q

WL

WR

WR

q0

H
q

C

q0

q
D

gauge invariance

he four classes of leading LR diagrams contributing to the neutral meson mixings. A,B,C,D identify the box diagra
diated tree-level amplitude, the one-loop self-energy and vertex renormalizations, respectively. The diagrams drpresentatives of each class and all allowed contractions among external and internal states are understood. In cla
all diagrams which do not contain the HWL WR vertex (with the longitudinal components of the gauge bosons)Rg for large MH , analogously to H exchange in the box A.

Which matching scale ~ W ? EWSB??

—
Match
LR
onto
SMEFT
operators
frameworks for quite specific patterns of the modelhe LR model. The destructive interference be-

e cc and ct amplitudes, achieved by a given conn of the relevant LR phases, is in fact more eﬃn estimated in the past. As a consequence, given

phases, which we discuss in detail.
We discuss finally the foreseen improvements folling from the constraints on B = 2 observables inΔF=2 transitions: one-loop level
Charged Higgs ~ neutral Higgs at one-loopt
H± = heavy

WL
VL

t

Yt V R

Take account in SMEFT analysis

Matching on SMEFT at LR scale
ΔF=1 operators at tree level
t

t

WL

WR

VL

t

VR

ΔF=2 operators at one-loop level

H±

WL

VL

t

Yt V R

Flow chart
Matching at LR scale: tree
µ = µLR

==

R

FF
==
11

=

+

+
+

F =2

+

one-loop+=

SMEFT RGE
F =2
from LR to EWSB
tree

-loop matching

one-loop matching

WL

F =1

+...

SMEFT RGEtree-level matchingF = 2

one-loopµ = MWL

F =2

+

FF==
2 2

one-loop matching

WL+

SMEFT RGE

F =2

FF= =
2 1

=

H0

µ = MW
FL= 1
F =1

=

F F= =
2 2

SMEFT RGERGE+
= SMEFT

F =1

+

++

F =1
WR
H±

LR

WL

one-loop

He↵F =2

He↵
FF =2
=2

tree-level matching

EWSB matchingF = 2 RGE

F =2

tree-levΔF=1 → ΔF=2 in SMEFT

+ λmj
t

!

(1)
(1)
(3)
(3)
)imij + (Cqq
)ijim + (Cqq
)imij + (Cqq
)i
(Cqq

3 %
ij $
αλ
αλij
(3)
(3)
(3)
t
im
(C
)
+
(C
λ
− 2t (CHq )ij I2 (xt , µW ) +t
Hq mj
Hq )im λ2πsW4πsW m=1

one-loop matching

t

t
W, G

VCKM

ij
ij
αλ
2αλ
(8)
(8)
t
t
=
(C
)
I
(x
,
µ
)
+
(C
(C4 )1–loop
33ij
1
t
W
ij
qd )33ij J(xt )πs2W ud
πs2W
#
3 '
$
α
(8)
(8)
mj
im
λ
(C
)
+
λ
(C
−
t
t
qd mjijqd )imij K(xt , µW ),22πsW m=1
#
ij '
2αλt
1
(1)
(8)
(C
=
)
−
(C
(C5 )1–loop
33ij
ij
ud
ud )33ij − (CHd )ij I1 (xt , µW )
2
πsW
2Nc
#
ij '
1
4αλt
(1)
(8)
(C
)
−
(C
+
33ij
qd
qd )33ij J(xt )
2
πsW
2Nc
3 '
!
"
$
α
1
(1)
(8)
(C
− 2
λim
)
−
(C
)mjij
mjij
qd
πsW m=1 t
2Nc qd
#
"
!
1
(1)
(8)
+ λmj
K(xt , µW ),
)
−
(C
(C
imij
t
qd
qd )imij
2Nc

where the parameters are defined as

cf. scale(μ) dependence
—
RGE
m2
ij
xt ≡

t
,
2
MW

λt ≡ Vti∗ Vtj .

preliminary]Here, Vij is the CKM matrix, and [ME,Kitahara,Ueda,sW = sin θW with the
Weinberg an

Flow chart: conventional caseMatching at LR scale: tree
µ = µLR

==

R

FF
==
11

=

+

+
+

+

one-loop=

SMEFT RGE
F =2
from LR to EWSBSMEFT RGEtree-level matchingF = 2“low-scale”tree-level
RGE matching-loop matching

one-loop matching

WL

F =1

+...

FF==
2 2

one-loopµ = MWL

F =2

+

+

F =2

one-loop matching

WL+

SMEFT RGE

F =2

FF= =
2 1

=

H0

µ = MW
FL= 1
F =1

=

F F= =
2 2

SMEFT RGERGE+
= SMEFT

F =1

+

++

F =1
WR
H±

LR

WL

one-loop

He↵F =2

He↵
FF =2
=2

EWSB matchingF = 2 RGE

F =2

tree-lev

Result: Wilson coefficients
one-loop top contribution
4

conventional
μ = mtδC4 [%]

20-2-4

μ = mWR-6-8-10mH = 6mWR
1

510

50 100WR mass [TeV]

C5 [10-12 GeV-2]

1
10 -1

SMEFT

10 -2
10 -3
10 -4
1

μ = mWRμ = mt510

50 100WR mass [TeV][ME,Kitahara,Ueda, preliminary]Result: B meson mass difference
one-loop top contribution

δ(ΔMBq) [%]

5
0
-5
-10
-15

mH = 6mWR
1

510

50 100WR mass [TeV][ME,Kitahara,Ueda, preliminary]Summary
SMEFT effects becomes important in LHC era.
In Z-penguin models, we obtain correlations, providing tightconstraint on RH flavor-changing Z coupling.
In left-right symmetric model, SMEFT is necessary for
reducing scale uncertainty.