Volume 430 - The 39th International Symposium on Lattice Field Theory (LATTICE2022) - Particle physics beyond the Standard Model
Noether supercurrent operator mixing from lattice perturbation theory
M. Costa*, G. Bergner", H. Panagopoulos, I. Soler" and G. Spanoudes"
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Abstract
In this work we present perturbative results for the renormalization of the supercurrent operator, $S_\mu$, in ${\cal N} =1$ Supersymmetric Yang-Mills theory. At the quantum level, this operator mixes with both gauge invariant and noninvariant operators, which have the same global transformation properties. In total, there are $13$ linearly independent mixing operators of the same and lower dimensionality. We determine, via lattice perturbation theory, the first two rows of the mixing matrix, which refer to the renormalization of $S_\mu$, and of the gauge invariant mixing operator, $T_\mu$. To extract these mixing coefficients in the $\overline{MS}$ renormalization scheme and at one-loop order, we compute the relevant two-point and three-point Green’s functions of $S_\mu$ and $T_\mu$ in two regularizations: dimensional and lattice. On the lattice, we employ the plaquette gluonic action and for the gluinos we use the fermionic Wilson action with clover improvement.
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