超对称保护的复合轴子：解决强CP问题的新途径
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"高质量的复合轴"
这篇论文探讨的是物理学中的强CP问题，即在量子色动力学（QCD）中，强相互作用违反了电荷共轭和宇称（CP）对称性，但这种违反的程度非常小，远低于实验观测的极限。这引发了一个重要的物理谜题，被称为“强CP问题”。标准模型无法解释这一现象，因此物理学家一直在寻找超越标准模型的理论来解决这个问题。
文章提到了最流行的解决方案之一是引入全球U（1）PQ对称性，这是一种假想的粒子——轴子（axion）的概念。轴子是一种无质量或极轻的玻色子，可以解释强CP问题。然而，这样的全局对称性可能会受到量子引力效应的影响，因为量子引力通常被认为是与全局对称性不兼容的。作者们提出了一种新的构造，通过利用超对称性和SU（N）L×SU（N）×SU（N）R×U（1）X的束缚产品规范群，保护U（1）PQ对称性免受量子引力校正的影响。在这个构造中，U（1）PQ对称性可以被保护到任意高阶，从而实现θ的绝对值小于10^-11，这对于SU(5)模型且f_a（轴子质量参数）小于3×10^11 GeV的情况是可能的。
此外，这种构造还导致了一些低能预测，如出现一个新的U（1）X规范对称性。如果X=B-L（Baryon-minus-Lepton数），这可以自然地解释MSSM（ Minimal Supersymmetric Standard Model，最小超对称标准模型）中的μ参数，使其具有大约TeV（ TeV，万亿电子伏特）量级的值。μ参数是MSSM中的关键参数，它决定了Higgs场如何与超对称伙伴相互作用，对模型的物理性质有深远影响。
关键词涉及的领域包括束缚（Confinement）、全局对称性（Global Symmetries）和自发对称性破缺（Spontaneous Symmetry Breaking），这些都是粒子物理学和场论中的核心概念。通过这些机制，理论物理学家尝试构建更复杂的模型来解释强CP问题，同时保持理论的一致性和预测能力。该研究提供了一种创新的方法，试图在考虑量子引力效应的同时，维持并利用轴子方案解决强CP问题。
JHEP11(2018)199
A lower bound f
a
& 10
9
GeV is set primarily by astrophysical observations of stellar cooling
and supernovae. In much of the parameter space, the axion provides a natural dark matter
candidate: its interactions are suppressed by the decay constant f
a
, and it can be produced
in the early universe by the misalignment mechanism [10–12]. For O(1) initial misalignment
angles, the correct relic abundance is obtained for f
a
. 10
12
GeV, though f
a
could be larger
if the misalignment was smaller. The fact that the QCD axion could also play the role of
dark matter is one of the reasons for its continued popularity as a solution to the strong
CP problem.
1.2 Axion quality problem
A closer inspection of the simple axion model presented above reveals a new set of the-
oretical difficulties, namely a hierarchy problem and a fine-tuning problem. The axion
model prefers a hierarchy between the scale of symmetry breaking f
a
and the Planck mass,
M
P
. A number of standard solutions, such as supersymmetry or compositeness, have been
proposed which would render an axion scale f
a
M
P
technically natural. However, many
axion models still suffer from a more severe fine-tuning, known as the axion quality problem.
Arguments from general relativity [13–18] suggest that non-perturbative quantum
gravitational effects do not respect global symmetries such as baryon number or U(1)
PQ
.
This is highly problematic for most axion models, which rely on U(1)
PQ
being an exact
symmetry in the α
s
→ 0 limit, explicitly broken only by the QCD anomaly. If additional
PQ-violating operators representing the short distance influence of quantum gravity such as
∆V (φ) =
|φ|
k+3
M
k
P
(λ
k
φ + λ
?
k
φ
?
) (1.8)
are present, the corresponding perturbation in V (a) can shift hai far away from the CP -
conserving value of eq. (1.6):
δV (a) ∼ λ
k
f
4
a
f
a
M
P
k
cos
∆
PQ
a
f
a
− ϕ
, (1.9)
where the phase ϕ is determined by λ
k
, and ∆
PQ
is the U(1)
PQ
charge of the operator φ.
It is convenient to describe such perturbations by defining a “quality factor” Q:
δV (a) = Qf
4
a
cos
a
f
a
− ϕ
. (1.10)
If we assume ϕ ∼ O(1) is not tuned, the measured value of
¯
θ
. 10
−11
is possible only if
δV (a) satisfies
Q . 10
−63
10
12
GeV
f
a
4
. (1.11)
Satisfying this bound requires that the theory of quantum gravity somehow produce a
severe fine-tuning in the λ
k
, such that even the dimension-12 operators in eq. (1.9) must
have λ
k
1.
In a truly compelling axion model, the U(1)
PQ
symmetry should emerge as a conse-
quence of some other underlying structure which forbids the problematic operators. For
– 3 –
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