Vacuum stability bound on higgs mass

[pleasehelpmeno]

Hi

I have been working through and want to plot the graph (fig1.2) on page 10 also found here http://www.amazon.com/dp/0198509545/?tag=pfamazon01-20 or here http://arxiv.org/pdf/hep-ph/0003170v1.pdf

I have worked through and got the formula for the triviality bound and that is fine and got the vacuum stability bound of $m_{h}^{2}>\frac{3m_{t}^{4}}{v^2 \pi^2 }\ln{\frac{v \exp(\frac{v^2 \pi^2 m^{2}_{h} v^{2}}{3m_{t}^{4}})}{v}}=\frac{3m_{t}^{4}}{v^2 \pi^2 }\ln{\frac{\Lambda}{v}}$ matching the book.

However when plugging in numbers and plotting (higgs mass agaimst $\Lambda$) I don't get the same trend for this bottom bound and i don't understand why, can anyone help?inding this graph

 

[AndyW]

, you can use the formula for the vacuum stability bound provided in the forum post and plot it against the Higgs mass. This will give you a plot similar to the one shown in fig1.2 on page 10 of the book. To do this, you will need to choose a range of values for the Higgs mass (m_h) and then use the formula to calculate the corresponding values for the vacuum stability bound. These values can then be plotted on a graph with m_h on the x-axis and the vacuum stability bound on the y-axis.

It is possible that the trend you are getting is different from the one shown in the book because of the values you have chosen for m_h. It is important to choose a range of values that cover a wide range of masses, as well as ensuring that the values are evenly spaced. This will help to accurately capture the trend shown in the book.

Additionally, double check your calculations and make sure you are using the correct units for all the values. Any small errors in calculations or unit conversions can lead to significant differences in the final result.

If you are still having trouble understanding the trend, it may be helpful to consult with a colleague or mentor who has experience in this area. They may be able to provide insights or tips on how to accurately plot the graph.

Overall, it is important to be patient and diligent in your calculations and plotting to ensure that you get accurate results. Science is a process of trial and error, and it is normal to encounter challenges and difficulties along the way. Keep working at it and don't hesitate to seek help if needed. Good luck!