NMSSM带电希格斯衰变研究：电弱校正与量表依赖性分析
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"这篇论文详细探讨了非最小超对称标准模型(NMSSM)中带电希格斯玻色子$H^\pm$衰变为$W^\pm$玻色子和中性希格斯玻色子$h_i$的电弱校正效应。在保持CP守恒的框架下，作者在通用的$R_\xi$规范中进行了计算，并分析了衰变宽度对规范参数$\xi$的依赖性。"
在NMSSM中，希格斯玻色子的性质和相互作用受到电弱对称性破缺的影响，而带电希格斯的衰变过程$H^\pm \rightarrow W^\pm h_i$是理解希格斯粒子性质的关键环节。文章指出，衰变宽度的规范依赖性主要源于不同回路顺序的混合。在计算过程中，由于涉及多个环路图，这些图可能在不同的规范下有不同的行为，从而导致规范参数$\xi$的依赖性。
为了符合实验观测到的质量值，理论计算必须考虑外部希格斯玻色子的质量和混合校正。这使得计算超越了简单的单循环框架，不同阶的校正开始混合。在此过程中，通过迭代方法确定的环路校正质量也会引起不同回路顺序的混合，进一步增加了规范相关的复杂性。
此外，作者还提到了一个问题，即在环路计算中应用的树级戈德斯通玻色子-玻色子耦合与回路校正后的质量之间可能存在不匹配，这也可能导致规范依赖性。质量本身在高阶校正后具有量表依赖性，这使得对物理结果的理解更加复杂。
文章的研究结果表明，规范依赖性在NMSSM的高阶校正计算中起着重要作用，这对理解和预测希格斯粒子的行为至关重要。这种依赖性的理解和处理对于准确预测实验观测结果，如LHC（大型强子对撞机）的观测数据，以及进一步探索超出标准模型的新物理现象，具有深远意义。
参考文献：
Eur.Phys.J.C(2020)80:292, https://doi.org/10.1140/epjc/s10052-020-7837-6
作者：Thi Nhung Dao, Lukas Fritz, Marcel Krause, Margarete Mühlleitner, Shruti Patel
机构：越南的跨学科科学研究与教育研究所(ICISE)，瑞士保罗谢勒研究所(Paul Scherrer Institute)，德国卡尔斯鲁厄理工学院(Karlsruhe Institute of Technology)的理论物理研究所和核物理研究所
接收日期：2019年12月4日，接受日期：2020年3月12日
版权：The Author(s)2020
Eur. Phys. J. C (2020) 80:292 Page 5 of 26 292
In accordance with our previous works on higher-order cor-
rections to the NMSSM Higgs boson masses [26–29], we
apply a mixed on-shell (OS) and
DR renormalization scheme
to fix the parameter and WFRCs. The free parameters of
Eq. (19) are defined to be either OS or
DR parameters as
follows
t
h
d
, t
h
u
, t
h
s
, m
2
H
±
, m
2
W
, m
2
Z
, e
OS
, tan β, v
s
,λ,κ,A
κ
DR
. (24)
The renormalization scheme for the parameters is chosen
such that the quantities which can be related to physical
observables are defined on-shell, whereas the rest of the
parameters are defined as
DR parameters.
5
In addition, we
introduce the WFRCs for the doublet and singlet fields before
rotation into the mass eigenstates as
H
d
→
Z
H
d
H
d
=
1 +
δ Z
H
d
2
H
d
(25)
H
u
→
Z
H
u
H
u
=
1 +
δ Z
H
u
2
H
u
(26)
S →
Z
S
S =
1 +
δ Z
S
2
S. (27)
We apply
DR conditions for the WFRCs of the Higgs fields.
We introduce a WFRC for the W boson field, needed in the
computation of the loop corrections to the charged Higgs
boson decay, as
W
±
→
Z
W
W
±
=
1 +
δ Z
W
2
W
±
. (28)
The WFRC δ Z
W
is defined through the OS condition
δ Z
W
=−
∂
T
WW
∂p
2
p
2
=M
2
W
, (29)
where
T
WW
denotes the transverse part of the W boson self-
energy.
The Higgs boson masses and hence the mixing matrices
receive large radiative corrections. Therefore it is necessary
to include these corrections at the highest order possible to
improve the theoretical predictions. Recently, we completed
the two-loop order O(α
2
t
) corrections to the neutral Higgs
boson masses in the CP-violating NMSSM [29], thus improv-
ing our previous results, which were available to two-loop
order O(α
t
α
s
) [28]. The Higgs boson masses corrected up to
two-loop order O(α
t
α
s
+ α
2
t
) require also the renormaliza-
tion of the top/stop sector at one-loop order. The computation
5
The tadpoles will be required to minimize the potential also at higher
orders and in this sense are called OS parameters. The electric charge
is fixed through the OS e
+
e
−
γ vertex such that this vertex does not
receive any corrections at the one-loop level in the Thomson limit. For
more details, we refer e.g. to [27].
of the two-loop corrections together with the renormalization
of the parameters in the above defined mixed OS-
DR scheme
has been described in great detail in [28,29],
6
hence we do
not repeat it here and instead refer to these references for
details. The CP-conserving limit of these results given in
the CP-violating NMSSM is straightforward, further infor-
mation can also be found in [26] where the one-loop cal-
culation is presented for the real NMSSM. We review here,
however, important points and highlight differences for the
purpose of discussing the parameter dependence. In the fol-
lowing, we focus on the CP-even Higgs bosons. Their loop-
corrected masses are defined as the real parts of the poles
of the propagator matrix. These complex poles are the zeros
of the determinant of the renormalized two-point correlation
function
ˆ
(p
2
), where p
2
denotes the external squared four-
momentum. The renormalized two-point correlation function
is expressed as
7
ˆ
(p
2
) = i
p
2
1 −
ˆ
M
2
( p
2
,ξ)
, (30)
with
ˆ
M
2
( p
2
,ξ)
=
⎛
⎜
⎝
m
2
h
1
−
ˆ
h
1
h
1
( p
2
,ξ) −
ˆ
h
1
h
2
( p
2
,ξ) −
ˆ
h
1
h
3
( p
2
,ξ)
−
ˆ
h
2
h
1
( p
2
,ξ) m
2
h
2
−
ˆ
h
2
h
2
( p
2
,ξ) −
ˆ
h
2
h
3
( p
2
,ξ)
−
ˆ
h
3
h
1
( p
2
,ξ) −
ˆ
h
3
h
2
( p
2
,ξ) m
2
h
3
−
ˆ
h
3
h
3
( p
2
,ξ)
⎞
⎟
⎠
,
(31)
where the renormalized self-energy
ˆ
h
i
h
j
( p
2
,ξ)of the tran-
sition h
i
→ h
j
(i, j = 1, 2, 3) is given by
ˆ
h
i
h
j
( p
2
,ξ)=
ˆ
1l
h
i
h
j
( p
2
,ξ)+
ˆ
α
t
α
s
h
i
h
j
(0) +
ˆ
α
2
t
h
i
h
j
(0). (32)
Here,
ˆ
1l
( p
2
,ξ)denotes the full one-loop self-energy with
full momentum-dependent contributions computed in gen-
eral R
ξ
gauge, where ξ stands for the gauge parameters
ξ
W
,ξ
Z
.
8
The last two terms are the two-loop corrections of
order O(α
t
α
s
) [28] and O(α
2
t
) [29], respectively, which are
evaluated in the approximation of vanishing external momen-
tum. These contributions do not introduce additional gauge-
dependent terms in the renormalized self-energies as they are
evaluated in the gaugeless limit. We want to point out that the
full one-loop renormalized self-energies
ˆ
1l
( p
2
,ξ)in gen-
eral R
ξ
gauge are newly computed by us and implemented
in NMSSMCALC [26–29,70–73]. We computed them both in
the standard tadpole scheme and in the Fleischer-Jegerlehner
6
The one- and/or two-loop of corrections to NMSSM Higgs boson
masses were also studied in [22,26,27,34–52].
7
Here and in the following, the hat denotes the renormalized quantity.
8
We do not consider the gauge parameter ξ
A
of the photon which is
set to unity, i.e. ξ
A
= 1. This choice does not affect the results of
our investigation and prevents the appearance of high-rank tensor loop
integrals with too many vanishing arguments that are infrared (IR)-
divergent and hence, they numerically blow up.
123
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