超新星1987A对次GeV暗区粒子约束：暗光子、荷电粒子与轴向粒子的研究

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"这篇文章是关于超新星1987A对次GeV暗区粒子、带电荷的粒子（如millicharged particles）、QCD轴心粒子和类似轴心粒子的约束的研究。研究者们探讨了一个费米子与暗光子耦合的模型，以及这些粒子如何在暗区中通过不同的质量关系相互作用。他们还提出了一种新的方法来判断何时这些带电荷的粒子在大的混合角度下会被捕获。研究中提出的限制排除了某些参数空间，这些空间原本不受加速器实验和直接探测搜索的约束。对于质量小于200 MeV的带电粒子，研究者设定了电荷量的排除范围，这对于理解毫微微克和质量层次的粒子尤其重要。此外，对于QCD轴心粒子和类似轴心粒子，他们应用了最新的核物理计算，考虑了能量损失的依赖性，这使得能够排除更大质量范围内的粒子。文章由JaeHyeok Chang、Rouven Essig和Samuel D. McDermott合作完成，发表在JHEP期刊上。" 本文的核心内容是研究超新星1987A对暗物质粒子的限制，这些粒子包括与暗光子耦合的费米子、millicharged particles（即带有微小电荷的粒子）、QCD轴心粒子以及类似轴心的粒子。研究者建立了一个模型，其中费米子可以与暗光子相互作用，暗区的粒子可能有不同的质量关系。特别是，他们关注了当这些粒子具有非弹性过渡时的暗区费米子。对于带电荷的粒子，研究者发展了一种新的分析工具，以确定在大混合角度下粒子是否会被超新星捕获。他们对耦合强度与粒子质量成正比的费米子进行了分析，发现对于质量小于200 MeV的粒子，电荷量在10^(-9)至少量乘以10^(-6)电子电荷之间被排除，这扩展了之前设定的边界，对质量更小的粒子产生了更强的约束。针对QCD轴心粒子和类似轴心的粒子，研究者使用了更新的核物理计算方法，并考虑了光学深度的能量依赖性，以精确计算高耦合时的能量损失。这种改进的方法允许他们排除了更大质量范围内的这些粒子，从而提供了对这类粒子更全面的理解。这篇研究对暗物质粒子物理学领域的理解做出了重要贡献，它不仅限制了暗物质粒子可能的性质，而且对未来的实验室探测和理论建模提供了有价值的指导。通过分析超新星1987A的数据，研究者能够填补了现有实验和理论研究中未覆盖的参数空间，对于深化我们对宇宙中暗物质成分的理解具有重要意义。

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JHEP09(2018)051

Sam McDermott

February 22, 2018

′

¯χ

′

•

¯χ

•

′

Figure 1. The Feynman diagram for the interaction between χ and Standard Model particles f,

which have a charge qe, where e is the electron’s charge.

We deﬁne the mass splitting ∆ ≡ m

− m

= m

+ m

. The lighter of the two Majorana

fermions, χ

, could be a DM candidate. We refer to this model as “inelastic DM” [38],

since the scattering of χ

oﬀ SM particles could be dominated by a transition from χ

the heavier state χ

. This model was studied in [39, 40] in the sub-GeV mass range of

interest in this paper. If m

= m

exactly, the elastic coupling vanishes and only inelastic

scattering is possible at tree-level. We will calculate below the SN1987A constraints for

this simple variant of the inelastic DM model. We note that even in this case χ

could

scatter elastically at one-loop, although this is highly suppressed, as we will discuss further

in section 3.3.

2.1.2 Model variation: millicharged particles

A millicharged particle is a dark-sector particle with a small electric charge. One well-

motivated way to attain such small charge is by introducing a massless dark photon, which

can be removed by a ﬁeld redeﬁnition of the SM photon. Under such a ﬁeld redeﬁnition,

dark-sector particles coupled to the A

acquire a small coupling to the SM photon, g

where  is again the kinetic-mixing parameter between SM photon and dark photon. We

deﬁne Q ≡ g

/e so that dark-sector particles charged under the dark photon have an

electric charge Qe.

We will derive below the constraints from SN1987A on millicharged particles, which

update bounds presented in [31]. These bounds are equally applicable for DM particles that

couple to an “ultralight”, massive dark-photon mediator, with a mass below the typical

momentum transfer in DM production and scattering processes, i.e. so long as the mediator

mass can be neglected in the calculations [15].

2.2 Dark-sector particle production in the proto-neutron star

Dark photons and particles charged under U(1)

can be produced in the proto-neutron

star through the kinetic mixing between the SM photon and the dark photon, see ﬁgure 1.

The total luminosity in dark-sector particles is L

dark

= L

+ L

(note that L

denotes

the total luminosity in χ and ¯χ), and the criterion L

dark

= L

determines the boundary

of constraints, where L

= 3 × 10

erg / s is the neutrino luminosity at one second [2].

The dominant production mechanisms for DM particles are through bremsstrahlung (via

an oﬀ- or on-shell A

) during neutron-proton collisions and through SM photon decay in

the plasma, shown in the left and middle panels, respectively, of ﬁgure 2. For on-shell A

– 6 –

JHEP09(2018)051

production, bremsstrahlung dominates, while for χ production both bremsstrahlung and

SM photon decay are important, with the latter dominating by a factor of a few.

Before discussing the calculation of L

dark

, it is worth making some general comments

on the DM production in the supernova. We then describe the calculation of L

and L

in section 2.3 and section 2.4, respectively, leaving detailed formulae to the appendices.

Due to plasma eﬀects in the proto-neutron star interior, we ﬁnd it convenient to calcu-

late scattering amplitudes in the gauge boson interaction basis, as in [18]. With this choice,

all Feynman diagrams describing the interaction of DM with electrically charged particles

such as the proton implicitly contain the diagram of ﬁgure 1, for which the amplitude is

M = −eJ

iK

νρ





= eg



− m

+ im

+ Π





T µν

− Π

Lµν

− Π



(2.5)

where K

= (ω,

k) is the momentum four-vector of the intermediate state (carried by both

the SM photon and the dark photon), Π

is the self-energy of the dark photon in a plasma

of DM particles, P

T µν

and P

Lµν

are the transverse and longitudinal projection operators

of the SM polarization states, respectively, and Π

and Π

are polarization tensors of the

SM photon from thermal eﬀects. The dark photon absorptive width Γ

is dominated by its

decay width to DM when this decay is on shell,

1 −

1 +



− 2m



+ O(

) ≡ Γ

+ O(

) . (2.6)

In principle, the presence of the dark photon self-energy Π

suggests that we should include

separate longitudinal and transverse projection operators for the dark photon like we do

for the SM photon. However, Π

is negligible on the lower boundary of the excluded

parameter space where we calculate dark-sector production rates, since the dark-sector

particles free stream. The eﬀect of Π

is only important near the upper boundary where

the dark-sector number densities can be very high. However, as we discuss in more detail

below, in this part of parameter space it is safe to assume that number densities are simply

given by a thermal distribution inside some radius, so their exact production rate will not

be important. Thus, we will not use Π

in any explicit calculation.

The dark sector luminosity admits two kinds of resonances, as can be seen in eq. (2.5):

the on-shell peak from the dark photon propagator, attained for K

= m

, and the “ther-

mal peak,” at K

= Π

L,T

from the SM photon propagator. The on-shell peak dominates

if m

 ω

p,0

, the thermal peak dominates if m

 ω

, and both peaks can be attained for

∼ ω

. Thus for m

& ω

, oﬀ-shell DM production is suppressed, and the lower bounds

are same as the dark photon only case. However, oﬀ-shell DM production dominates for

 ω

p,0

, so the low- bounds at small m

are stronger than the bound from the A

-only

case, which decouples like m

due to suppression by thermal eﬀects [18, 20]. With the

inclusion of dark sector fermions, the production rate for dark-sector particles becomes

independent of their mass, so the lower bound is ﬂat.

– 7 –

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