论文标题
三循环验证新算法用于计算$β$功能的超对称理论的$ {\ cal n} = 1 $ sqed的$β$功能
Three-loop verification of a new algorithm for the calculation of a $β$-function in supersymmetric theories regularized by higher derivatives for the case of ${\cal N}=1$ SQED
论文作者
论文摘要
我们验证了一种最近提出的方法，用于获得$ {\ cal n} = 1 $ supersymmetric仪表理论的$β$ - 功能，这是通过显式计算正规化的。根据这种方法，可以通过计算特殊修改的真空超图，而不是大量的两点超级图，可以找到$β$功能。结果是以双重衍生物相对于循环动量的某种积分的形式产生的。在这里，我们比较了$ {\ cal n} = 1 $ sqed的三环$β$ function在常规$ξ$ - 高架中获得的结果，并在此方法的帮助下，并借助标准计算。它们的巧合证实了新方法的正确性以及用于推导其推导的一般论点。我们还验证，在考虑的近似值中，NSVZ关系对于根据裸耦合常数定义的重新归一化组函数和根据HD+MSL方案中重新归一化的耦合常数定义的函数有效。
We verify a recently proposed method for obtaining a $β$-function of ${\cal N}=1$ supersymmetric gauge theories regularized by higher derivatives by an explicit calculation. According to this method, a $β$-function can be found by calculating specially modified vacuum supergraphs instead of a much larger number of the two-point superdiagrams. The result is produced in the form of a certain integral of double total derivatives with respect to the loop momenta. Here we compare the results obtained for the three-loop $β$-function of ${\cal N}=1$ SQED in the general $ξ$-gauge with the help of this method and with the help of the standard calculation. Their coincidence confirms the correctness of the new method and the general argumentation used for its derivation. Also we verify that in the considered approximation the NSVZ relation is valid for the renormalization group functions defined in terms of the bare coupling constant and for the ones defined in terms of the renormalized coupling constant in the HD+MSL scheme, both its sides being gauge-independent.
