How Randall-Sundrum model has solved the hierarchy problem?

[Safinaz]

I'm trying to understand how the RS model solved the hierarchy problem from this mass relation

$$ M^2_p = \frac{M^3}{k} \Large[1- e^{-2k\pi r} \Large],$$

Equ. 16 in their paper:

https://arxiv.org/abs/hep-ph/9905221

With k as large as the Planck scale, the exponential will be so small and almost has no effect, which leads to (is this correct? ), as they say in page 6, $M \approx M_p$!

So the conflict rises here, cause $M_p$ is the four dimensional effective Planck scale $\sim 10^{18}$ GeV, while $M$ is the higher 5-dimensional Planck scale assumed to be at TeV scale, so what does $M \approx M_p$ mean?

Any help is appreciated!

See also the discussion in this thread:
[The hierarchy problem][1] [1]: https://physics.stackexchange.com/q...hy-problem?noredirect=1#comment1484638_661737

 

[AndyW]

Thank you for your question. The RS (Randall-Sundrum) model is a theoretical framework that attempts to solve the hierarchy problem, which refers to the large discrepancy between the Planck scale and the electroweak scale (where the Higgs boson mass is located). This model introduces an extra dimension in addition to the three spatial dimensions we are familiar with, and it is this extra dimension that helps to explain the hierarchy between the two scales.

Equation 16 in the paper you referenced is a mass relation that arises from the geometry of the extra dimension in the RS model. This equation shows that the four-dimensional Planck mass (Mp) is related to the five-dimensional Planck mass (M) through a factor of k, which is the curvature of the extra dimension. As you correctly noted, when k is very large (on the order of the Planck scale), the exponential term in the equation becomes very small and can be neglected. This leads to the approximation of M ≈ Mp.

However, it is important to note that this approximation is only valid in the context of the RS model and its assumptions. In reality, we do not know the exact value of the five-dimensional Planck mass, and it could potentially be at a much higher energy scale than the TeV scale. The RS model simply offers a possible explanation for the hierarchy problem, but it is still an active area of research and there are other theories that attempt to solve this problem as well.

I hope this helps to clarify the concept of the hierarchy problem and the role of the RS model in addressing it. If you have any further questions, please don't hesitate to ask.