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It is known that in SUSY models, loop contributions are automatically zero leading to a technically natural solution of the Higgs mass hierarchy problem.

In many SUSY books/notes, it is often shown that, with a Lagrangian consisting chiral superfields, $$ {\cal L} = \int \left\{\Phi_i^{\dagger}\Phi_i+\left[\frac{1}{2} m_{ij}\Phi_i\Phi_j+\frac{1}{3}\lambda_{ijk}\Phi_i\Phi_j\Phi_k\right]\delta^2(\bar{\theta}) \right\}d^2\theta d^2\bar{\theta} $$$$ {\cal L} = \int \left\{\Phi_i^{\dagger}\Phi_i+\left[\frac{1}{2} m_{ij}\Phi_i\Phi_j+\frac{1}{3}\lambda_{ijk}\Phi_i\Phi_j\Phi_k\right]\delta^2(\bar{\theta}) +h.c.\right\}d^2\theta d^2\bar{\theta} $$

All the loop diagrams of the superfields are identically zero. Thus in terms of component fields, the loop contributions are canceled out.

Now, the same kind of vanishing loop contributions should be true in SUSY gauge theory as well. Without any direct/explicit calculation of the loop supergraphs, is there a simple argument/way to see how they are zero? Is that the same reason as the chiral model above, each one supergraph contains a factor of $\delta^4(\theta)$ or higher order, which is $0$ ?

Even if you provide references, your own interpretation/explanation is appreciated.

It is known that in SUSY models, loop contributions are automatically zero leading to a technically natural solution of the Higgs mass hierarchy problem.

In many SUSY books/notes, it is often shown that, with a Lagrangian consisting chiral superfields, $$ {\cal L} = \int \left\{\Phi_i^{\dagger}\Phi_i+\left[\frac{1}{2} m_{ij}\Phi_i\Phi_j+\frac{1}{3}\lambda_{ijk}\Phi_i\Phi_j\Phi_k\right]\delta^2(\bar{\theta}) \right\}d^2\theta d^2\bar{\theta} $$

All the loop diagrams of the superfields are identically zero. Thus in terms of component fields, the loop contributions are canceled out.

Now, the same kind of vanishing loop contributions should be true in SUSY gauge theory as well. Without any direct/explicit calculation of the loop supergraphs, is there a simple argument/way to see how they are zero? Is that the same reason as the chiral model above, each one supergraph contains a factor of $\delta^4(\theta)$ or higher order, which is $0$ ?

Even if you provide references, your own interpretation/explanation is appreciated.

It is known that in SUSY models, loop contributions are automatically zero leading to a technically natural solution of the Higgs mass hierarchy problem.

In many SUSY books/notes, it is often shown that, with a Lagrangian consisting chiral superfields, $$ {\cal L} = \int \left\{\Phi_i^{\dagger}\Phi_i+\left[\frac{1}{2} m_{ij}\Phi_i\Phi_j+\frac{1}{3}\lambda_{ijk}\Phi_i\Phi_j\Phi_k\right]\delta^2(\bar{\theta}) +h.c.\right\}d^2\theta d^2\bar{\theta} $$

All the loop diagrams of the superfields are identically zero. Thus in terms of component fields, the loop contributions are canceled out.

Now, the same kind of vanishing loop contributions should be true in SUSY gauge theory as well. Without any direct/explicit calculation of the loop supergraphs, is there a simple argument/way to see how they are zero? Is that the same reason as the chiral model above, each supergraph contains a factor of $\delta^4(\theta)$ or higher order, which is $0$ ?

Even if you provide references, your own interpretation/explanation is appreciated.

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mastrok
mastrok
  • 387
  • 1
  • 10

Supersymmetric cancellation of loop contributions in a SUSY gauge theory

It is known that in SUSY models, loop contributions are automatically zero leading to a technically natural solution of the Higgs mass hierarchy problem.

In many SUSY books/notes, it is often shown that, with a Lagrangian consisting chiral superfields, $$ {\cal L} = \int \left\{\Phi_i^{\dagger}\Phi_i+\left[\frac{1}{2} m_{ij}\Phi_i\Phi_j+\frac{1}{3}\lambda_{ijk}\Phi_i\Phi_j\Phi_k\right]\delta^2(\bar{\theta}) \right\}d^2\theta d^2\bar{\theta} $$

All the loop diagrams of the superfields are identically zero. Thus in terms of component fields, the loop contributions are canceled out.

Now, the same kind of vanishing loop contributions should be true in SUSY gauge theory as well. Without any direct/explicit calculation of the loop supergraphs, is there a simple argument/way to see how they are zero? Is that the same reason as the chiral model above, each one supergraph contains a factor of $\delta^4(\theta)$ or higher order, which is $0$ ?

Even if you provide references, your own interpretation/explanation is appreciated.