Physics Letters B 787 (2018) 182–187
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
/ from charged-Higgs-induced gluonic dipole operators
Chuan-Hung Chen
a
, Takaaki Nomura
b,∗
a
Department of Physics, National Cheng-Kung University, Tainan 70101, Taiwan
b
School of Physics, KIAS, Seoul 02455, Republic of Korea
a r t i c l e i n f o a b s t r a c t
Article history:
Received
28 May 2018
Received
in revised form 26 September
2018
Accepted
4 November 2018
Available
online 6 November 2018
Editor:
B. Grinstein
We study the effect of charged-Higgs-induced chromomagnetic operator, Q
8G
(−) ≡
¯
sσ
μν
T
a
γ
5
dG
a
μν
, on
the Kaon direct CP violation Re(
/). Using the matrix element ππ|O
8G
(−)|K
0
recently obtained by a
large N
c
dual QCD approach, we find that if the Kobayashi–Maskawa phase is the origin of CP violation,
the charged-Higgs-induced gluon penguin dipole operator in the type-III two-Higgs-doublet model can
explain the measured Re(
/) when the constraints from the relevant low energy flavor physics, such
as B(K ) = 2, B → X
s
γ , B
s
→μ
+
μ
−
, and Kaon indirect CP violation parameter , are included.
© 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
Significant recent progress in meeting the long-standing chal-
lenge
for the prediction of the Kaon direct CP violation Re(
/)
in the standard model (SM) has been made based on two results:
(i) RBC-UKQCD collaboration obtains a surprising lattice QCD result
on Re(
/) with [1,2]:
Re(
/) = 1.38(5.15)(4.59) × 10
−4
, (1)
where the numbers in brackets denote the errors. (ii) Using a large
N
c
dual QCD [3–7], the authors in [8,9]found:
Re(
/)
SM
=(1.9 ±4.5) × 10
−4
, (2)
where the non-perturbative parameters at the m
c
scale extracted
from RBC-UKQCD lattice results [1,2]are taken as:
B
(1/2)
6
(m
c
) = 0.57 ± 0.19 ,
B
(3/2)
8
(m
c
) = 0.76 ± 0.05 . (3)
Intriguingly, although the errors in both approaches are still large,
their results are consistent with each other. If we take the results
as the SM prediction, a 2σ deviation from the experimental data
of Re(
/)
exp
= (16.6 ± 2.3) ×10
−4
, measured by NA48 [10]and
KTeV [11,12], is indicated.
The
potential missing contributions in the SM could be from
long-distance (LD) final state interactions (FSIs). However, their ef-
fects
have not yet been concluded, where the LD effects obtained
*
Corresponding author.
E-mail
addresses: physchen@mail.ncku.edu.tw (C.-H. Chen), nomura@kias.re.kr
(T. Nomura).
in [13,14] cannot compensate for the insufficient Re(
/)
SM
, but
the authors in [15]obtain Re(
/)
SM
=(15 ±7) × 10
−4
when the
short-distance (SD) and LD effects are combined.
An
alternative resolution to the small Re(
/)
SM
is to in-
troduce
new physics effects, such as in [16–30]. In this work,
we investigate the effects of charged-Higgs-induced chromomag-
netic
operators (CMOs), denoted by
¯
s σ
μν
T
a
P
L(R)
d G
a
μν
, where
P
L(R)
= (1 ∓ γ
5
)/2, T
a
are the SU(3) generators and are normal-
ized
as Tr(T
a
T
b
) = 1/2δ
ab
, and G
a
μν
represents the gluon field
strength tensors. It is known that the SM gluonic dipole contribu-
tion
in chiral quark model could be in the region of Re(
/)
Q
8G
∼
(
0.2, 0.7) × 10
−4
[9,31,32]. Recently, a smaller B
CMO
-parameter,
which describes the K → ππ matrix element via CMO, is con-
sistently
obtained by the lattice QCD [33] and a large N
c
dual
QCD [14]. Thus, it can be concluded that the SM CMO contri-
bution
cannot help to resolve the Re(
/)
SM
problem. However,
CMO induced by other new effects may play an important role in
Re(
/) [35,36].
We
consider the charged-Higgs contributions to CMOs based
on the following characteristics: (a) gluon-penguin effect can be
enhanced by the top-quark mass m
t
, which arises from the top-
quark
Yukawa coupling and mass insertion in the propagator; (b) a
large tan β enhancement from Yukawa couplings could occur in
the gluon-penguin diagram, and (c) the CP violation phase can
uniquely originate from the Kobayashi–Maskawa (KM) phase of
the Cabibbo–Kobayashi–Maskawa (CKM) matrix [37,38], where the
same KM phase can be used to explain the Kaon indirect CP viola-
tion
and CP asymmetries observed in the B-meson system.
A
charged-Higgs naturally exits in a two-Higgs-doublet model
(2HDM), and its Yukawa couplings strongly depend on how the
Higgs doublets couple to fermions. Before discussing a specific
https://doi.org/10.1016/j.physletb.2018.11.006
0370-2693/
© 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.
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