论文标题
$ {\ cal n} = 1 $ sqed正规化的三环异常维度和四环$β$ function
The three-loop anomalous dimension and the four-loop $β$-function for ${\cal N}=1$ SQED regularized by higher derivatives
论文作者
论文摘要
对于$ {\ cal n} = 1 $ sqed，带有$ n_f $的口味，由较高衍生品在一般$ξ$ - 高器中正规化，我们计算了按照裸露的耦合常数定义的物质超级场景的三环异常维度，并表现出其仪表的独立性。此后，根据NSVZ方程获得了根据裸耦合常数定义的四环$β$ function，这对于所有循环中的这些重新归一化组函数都是有效的。接下来，我们计算三环异常维度和四回路$β$函数，该函数根据补充较高衍生化正则化的任意减法方案定义的定义。然后，我们构建了一个恢复正常化的处方，结果与$ \ overline {\ mbox {dr}} $ - 方案中的结果相吻合，并描述了所考虑的近似值中的所有NSVZ方案。另外，我们还证明了一个减法方案的存在，其中异常维度不取决于$ n_f $，而$β$ function仅包含$ n_f $中的第一阶的术语。该方案是借助与量子校正结构兼容的有限重新规范化，为NSVZ。在所有循环中也证明了这种NSVZ方案的存在。
For ${\cal N}=1$ SQED with $N_f$ flavors regularized by higher derivatives in the general $ξ$-gauge we calculate the three-loop anomalous dimension of the matter superfields defined in terms of the bare coupling constant and demonstrate its gauge independence. After this the four-loop $β$-function defined in terms of the bare coupling constant is obtained with the help of the NSVZ equation, which is valid for these renormalization group functions in all loops. Next, we calculate the three-loop anomalous dimension and the four-loop $β$-function defined in terms of the renormalized coupling constant for an arbitrary subtraction scheme supplementing the higher derivative regularization. Then we construct a renormalization prescription for which the results coincide with the ones in the $\overline{\mbox{DR}}$-scheme and describe all NSVZ schemes in the considered approximation. Also we demonstrate the existence of a subtraction scheme in which the anomalous dimension does not depend on $N_f$, while the $β$-function contains only terms of the first order in $N_f$. This scheme is obtained with the help of a finite renormalization compatible with a structure of quantum corrections and is NSVZ. The existence of such an NSVZ scheme is also proved in all loops.
