Low-derivative operators of the Standard Model effective field theory via Hilbert series methods

被引:115
作者
Lehman, Landon [1 ]
Martin, Adam [1 ]
机构
[1] Univ Notre Dame, Dept Phys, Nieuwland Sci Hall, Notre Dame, IN 46556 USA
基金
美国国家科学基金会;
关键词
Gauge Symmetry; Effective field theories; Global Symmetries; Standard Model; EFFECTIVE LAGRANGIANS; EQUATIONS;
D O I
10.1007/JHEP02(2016)081
中图分类号
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号
摘要
In this work, we explore an extension of Hilbert series techniques to count operators that include derivatives. For sufficiently low-derivative operators, we conjecture an algorithm that gives the number of invariant operators, properly accounting for redundancies due to the equations of motion and integration by parts. Specifically, the conjectured technique can be applied whenever there is only one Lorentz invariant for a given partitioning of derivatives among the fields. At higher numbers of derivatives, equation of motion redundancies can be removed, but the increased number of Lorentz contractions spoils the subtraction of integration by parts redundancies. While restricted, this technique is sufficient to automatically recreate the complete set of invariant operators of the Standard Model effective field theory for dimensions 6 and 7 (for arbitrary numbers of flavors). At dimension 8, the algorithm does not automatically generate the complete operator set; however, it suffices for all but five classes of operators. For these remaining classes, there is a well defined procedure to manually determine the number of invariants. Assuming our method is correct, we derive a set of 535 dimension-8 N-f = 1 operators.
引用
收藏
页码:1 / 31
页数:31
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