$N_{\textrm{eff}}$对伪狄拉克中微子的限制
$N_{\textrm{eff}}$ Constraint on Pseudo-Dirac Neutrinos
AI总结：
研究通过CMB对N_eff的限制，推导出伪狄拉克中微子质量分裂的新约束，并预测未来实验可进一步提高该限制。
摘要：
在电弱对称破缺之后，我们可以为标准模型中微子写出两种类型的质量，即狄拉克或马约拉纳类型。人们常认为这两种类型的质量在中微子振荡现象中无法区分。实际上，如果中微子是伪狄拉克（严格来说仍然是马约拉纳）类型，它们会几乎最大限度地与惰性中微子混合，形成伪狄拉克对。如果这种现象在自然界中确实存在，我们实验上观察到的三种质量本征态实际上是三种质量本征态对，其中每对之间还有尚未测量的新质量分裂。虽然第一和第二质量本征态之间的新质量平方分裂受到太阳中微子实验的严格限制，即|δm_{1,2}^2| ≲10^{-11} eV^2，而第三质量本征态的相关分裂则有较弱的限制|δm_3^2| ≲10^{-5} eV^2。通过仅保留一个非零的伪狄拉克质量平方分裂，我们推导出伪狄拉克场景的有效3+1描述。然后我们利用宇宙微波背景（CMB）对中微子相对论自由度N_{eff}的限制，推导出一个新的限制|δm_3^2| < 2×10^{-6} eV^2，并显示未来的CMB-S4和CMB-HD实验可以将此限制提高一个数量级。
英文摘要：
After the electroweak symmetry breaking, we can write down two types of mass for the Standard Model neutrinos, Dirac or Majorana. It is often said that both types of mass cannot be distinguished in neutrino oscillation phenomena. This is in fact not true if neutrinos are pseudo-Dirac (strictly speaking still Majorana) where they mix almost maximally with sterile neutrinos to form pseudo-Dirac pairs. If this is indeed realized in Nature, what we observe experimentally as three mass eigenstates are actually three pairs of mass eigenstates with yet-to-be-measured new mass splitting among each pair. While the new mass squared splitting of the first and second mass eigenstates have stringent constraints from solar neutrino to be $|δm_{1,2}^2| \lesssim10^{-11}\,\textrm{eV}^{2}$, the one regarding the third mass eigenstate has a weaker constraint $|δm_3^2| \lesssim10^{-5}\,\textrm{eV}^{2}$. By keeping only one nonzero pseudo-Dirac mass squared splitting at a time, we derive an effective 3+1 description for the pseudo-Dirac scenario. Then we use the Cosmic Microwave Background (CMB) constraint on neutrino relativistic degrees of freedom $N_{\textrm{eff}}$ to derive a new constraint $|δm_3^2| < 2 \times 10^{-6}\,{\rm eV}^2$ and show that the future CMB-S4 and CMB-HD can improve this bound by an order of magnitude.
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