# Is there a relation between the weak scale and the intermediated string scale?

http://arxiv.org/abs/hep-th/0609180v2

http://arxiv.org/abs/hep-th/0610129v2

They state that $m_s$ is proportional to $M_P/\sqrt{V}$ and that $m_{3/2}$ is proportional to $M_P/V$.

($m_s$:intermediated string scale, $m_{3/2}$ gravitino mass, $M_P$:Planck mass)

Then they claim that $V=10^{15} l_s^6$ is required to explain the weak/Planck hierarchy. I want to understand this statement, how is the weak scale related?

• Here is somethig I think could help to find the answer: fuw.edu.pl/~tok/talksII/Conlon.pdf In page 17 "With $m_s = 1011GeV$, the weak hierarchy can be naturallygenerated through TeV-scale supersymmetry." – Anthonny Feb 5 '14 at 20:08
• Sorry, the correct link is physics.rutgers.edu/het/video/conlon.pdf but the otherone seems useful also, there is a section titled weak scale. – Anthonny Feb 5 '14 at 20:41

If the supersymetry breaking scale is close to the weak scale, the problematic renormalization parameters in the scalar sector of the Standard Model are naturally limited. In supersymemtry (when all the fields are dynamic) there are powerful non-renormalization theorems. Therefore, perturbative effects affect the scalar sector only below the supersymetry breking scale $M_S$. They are therefore of order $$\delta \propto \frac{1}{16 \pi^2} \left( \frac{M_S^2}{M_\mathrm{ew}^2}\right)$$ where $M_\mathrm{ew}$ is the electroweak scale. By having $M_s \sim 1$ TeV, $\delta \sim 1$ and the small values of parameters in the scalar sector are protected by supersymmetry.
Should the susy breaking scale (or generally the scale of new physics) be large i.e. comparable to the Planck scale, the corrections are $$\delta \propto \frac{1}{16 \pi^2} \left( \frac{M_\mathrm{Pl}^2}{M_\mathrm{ew}^2} \right) \gg 1$$ Then, there is no natural reason, why the parameters at the weak scale should be so small, if their value gets huge renormalization contributions.