论文标题
任意旋转的核散射的有效理论
The effective theory of nuclear scattering for a WIMP of arbitrary spin
论文作者
论文摘要
我们介绍了一种系统的方法，以表征Galilean不变性对单核电流的近似值中任意旋转$j_χ$允许的最通用的非相关性wimp-nucleus相互作用。五个核子电流来自游离核子狄拉克双线性的非偏移性极限。我们的过程包括（1）根据$ 2J_χ+1 $不可减至的运算符产品的等级，最高为$ 2j_χ$ wimp旋转向量，以及（2）将每种wimp电流耦合到五个核子电流中的每一个。转移的动量$ Q $似乎是由旋转不变性固定的功率。对于自旋$J_χ$的w imp，我们找到了一个4+20 $j_χ$独立运算符的基础，这些操作员耗尽了所有可能的操作员，这些操作员以一努克莱恩电流的近似值驱动弹性wimp-nucleus散射。通过将完整的运营商比较与文献中已经引入的运营商进行比较，我们表明，后者的$j_χ= 1 $不是独立的，有些丢失了。我们为平方散射幅度提供了明确的公式，该公式就核反应函数而言，在文献中可用于WIMP直接检测实验中使用的大多数目标。
We introduce a systematic approach to characterize the most general non-relativistic WIMP-nucleus interaction allowed by Galilean invariance for a WIMP of arbitrary spin $j_χ$ in the approximation of one-nucleon currents. Five nucleon currents arise from the nonrelativistic limit of the free nucleon Dirac bilinears. Our procedure consists in (1) organizing the WIMP currents according to the rank of the $2 j_χ+1$ irreducible operator products of up to $2 j_χ$ WIMP spin vectors, and (2) coupling each of the WIMP currents to each of the five nucleon currents. The transferred momentum $q$ appears to a power fixed by rotational invariance. For a WIMP of spin $j_χ$ we find a basis of 4+20$j_χ$ independent operators that exhaust all the possible operators that drive elastic WIMP-nucleus scattering in the approximation of one-nucleon currents. By comparing our operator basis, which is complete, to the operators already introduced in the literature we show that some of the latter for $j_χ=1$ were not independent and some were missing. We provide explicit formulas for the squared scattering amplitudes in terms of the nuclear response functions, which are available in the literature for most of the targets used in WIMP direct detection experiments.
