弹性解耦暗物质ELDER的现现象学与实验预测

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本文探讨了弹性解耦遗物（ELDER）暗物质的现象学，这是一种在宇宙早期与标准模型（SM）粒子通过弹性散射而保持相互作用的热暗物质候选者。ELDER的当前密度主要受其与SM粒子散射的横截面决定，特别是当这种散射过程由暗光子所驱动时。暗光子是一种假设中的轻媒介粒子，它在暗物质与可见世界的相互作用中起到桥梁作用。作者假设ELDER场景对电子反冲直接探测实验具有重要的预测价值，因为暗光子的存在使得暗物质与电子的相互作用成为可能。这些预测独立于暗物质的具体相互作用强度，为次GeV暗物质和暗光子的实验搜索提供了明确的目标区域。新一代的实验设备可以通过寻找ELDER现象中的特定信号来验证或排除这一理论。研究者为ELDER场景中的一些关键物理量提供了解析近似值，这些近似有助于简化理论计算并促进实验设计。文章还介绍了一个可重归一化的简单模型，这个模型将ELDER的强相互作用与暗光子耦合起来，使得理论更具可操作性。值得注意的是，该研究发表于《Journal of High Energy Physics》(JHEP)的2017年第8期，是开放获取的，这意味着读者可以自由查阅和研究。文章接收日期为2017年7月1日，接受日期为8月1日，最终发布日期为8月18日。研究团队来自美国康奈尔大学、希伯来大学和辛普森学院，以及加拿大Perimeter Institute for Theoretical Physics，展示了跨学科的合作精神和对未知领域的深入探索。总结来说，这篇论文对于理解ELDER暗物质的物理特性及其对现代物理学实验的潜在影响至关重要，它为未来的暗物质和暗光子实验提供了理论指导，推动了对宇宙中最神秘成分之一的探索。

JHEP08(2017)078

where x = m

/T , x

= m

, and t =

−n−4

n+4

. At small x, x

≈ x, corresponding to

SM and ELDER sectors in thermal equilibrium. At large x, the asymptotic form of the

solution is

≈ 3 log(x) +



n + 4



n+4



n + 3

n + 4



− 3 log

n+4



n + 4



n+4

. (2.5)

Identifying the “decoupling temperature” at which the ELDER and the SM thermally

decouple,

= m



n+4



n+4



n+3

n+4



, (2.6)

eq. (2.5) can be rewritten as x

' x

+ 3 log(x/x

), or

1 + 3

log

. (2.7)

This is precisely the behavior expected in the “cannibalization” regime [1], where ELDER

temperature decreases only slowly (logarithmically with the scale factor) as the universe ex-

pands. The physical reason is that the kinetic energy released by 3 → 2 self-annihilations

partially compensates for the energy lost when particle momenta are redshifted due to

the expansion. This regime persists until the 3 → 2 process decouples, after which the

ELDER density is frozen out. Note that the dark matter particles remain non-relativistic

throughout the cannibalization period, so that from the point of view of Cosmic Microwave

Background (CMB) and structure formation, ELDER is a Cold Dark Matter (CDM) can-

didate, consistent with observations.

The evolution of ELDER temperature throughout the kinetic decoupling and freeze-out

process is illustrated in ﬁgure 1. The ELDER-to-SM temperature ratio starts growing after

kinetic decoupling due to cannibalization, reaching the maximum value of T

/T ∼ 10 at the

time of freeze-out. It drops rapidly after freeze-out since ELDERs are non-relativistic and

∝ R

−2

, while T ∝ R

−1

, where R is the size of the universe. The analytic function (2.4)

provides an excellent approximation to the numerical solution of the Boltzmann equations

up until 3 → 2 freezeout.

We note that eq. (2.7) can also be derived by assuming instantaneous kinetic decou-

pling between the dark sector and the SM at temperature T

, and using the conservation

of comoving entropy in the dark sector after decoupling. This approach was taken, for ex-

ample, in ref. [7]. The alternative derivation presented here does not make the assumption

of instantaneous decoupling, relying instead on the approximate solution for the evolution

of T

accurate throughout the decoupling process. Apart from being better justiﬁed phys-

ically, the distinct advantage of the new derivation is that it automatically provides the

expression for T

in terms of the underlying model parameters, eq. (2.6).

In the instantaneous freeze-out approximation, the asymptotic value of the yield Y

, where s

is the entropy density today, is given by

∞

= Y

(2πx

)

−3/2

−x

(2π

/45)g

∗s,f

−3

, (2.8)

– 5 –

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