Perturbative Power Counting,Lowest-Index Operators and Their Renormalization in Standard Model Effective Field Theory

We study two aspects of higher dimensional operators in standard model effective field theory.We first introduce a perturbative power counting rule for the entries in the anomalous dimension matrix of operators with equal mass dimension.The power counting is determined by the number of loops and the difference of the indices of the two operators involved,which in turn is defined by assuming that all terms in the standard model Lagrangian have an equal perturbative power.Then we show that the operators with the lowest index are unique at each mass dimension d,i.e.,(H~?H)~(d/2)for even d≥4,and(L~TεH)C(L~TεH)~T(H~?H)~((d-5)/2)for odd d≥5.Here H,L are the Higgs and lepton doublet,andε,C the antisymmetric matrix of rank two and the charge conjugation matrix,respectively.The renormalization group running of these operators can be studied separately from other operators of equal mass dimension at the leading order in power counting.We compute their anomalous dimensions at one loop for general d and find that they are enhanced quadratically in d due to combinatorics.We also make connections with classification of operators in terms of their holomorphic and anti-holomorphic weights.     

α-Fe2O3负载Ag复合纳米材料的制备、表征和气敏性能

采用简单的FeCl3溶液水热方法, 结合焙烧处理合成了α-Fe2O3 纳米粉体; 以所制备的α-Fe2O3为载体负载Ag纳米粒子, 得到Ag/α-Fe2O3 复合纳米材料. 使用X射线衍射、 透射电子显微镜、 氮气吸附-脱附和X射线光电子能谱等对样品进行表征, 并考察了Ag/α-Fe2O3复合材料在260℃下对甲醇、 乙醇、 乙醚、 丙酮、 正丁醇和正己醇等挥发性有机物的气敏行为. 结果表明, Ag/α-Fe2O3传感器对这几种挥发性有机物展示了较高的灵敏度和快速、 可逆的响应-恢复特性; 与纯α-Fe2O3相比, Ag/α-Fe2O3复合材料的气敏性能显著提高, 这可能与该复合材料表面独特的多孔结构和活性Ag纳米粒子对敏感反应的催化作用有关.