# Homework Help: Problem with graph drawing

1. Jan 13, 2013

### dingo_d

1. The problem statement, all variables and given/known data

I need to draw the running coupling constant graph like this one:

And I have a formula:

$\frac{1}{\alpha(\mu)} = \frac{1}{\alpha(M_Z)} + \frac{b}{2\pi}\ln\frac{\mu}{M_{Z}}$

And I have the necessary data to draw $\frac{1}{\alpha_i(\mu)}-\log(\mu)$ graph (I have $\alpha_i^{-1}(M_Z)$, $b_i$, and $M_Z$).

And I plug that in in Mathematica and I cannot seem to get that graph! I tried by replacing the $\frac{1}{\alpha(\mu)}$ with y, and $\log(\mu)$ with x, and plotting that, I've tried by not changing the logarithm, and making the LogPlot, but no go.

I really don't know what I'm doing wrong :(

I looked at 3 papers on this topic, to see if I got the constants wrong, but I didn't see anything different :|

arXiv:hep-ph/0012288v2, arXiv:0711.2903v1 [hep-ph], and arXiv:hep-ph/9705479v1

EDIT:

Never mind! I reversed the sign of the b somehow... xD

Last edited: Jan 13, 2013
2. Jan 13, 2013

### Staff: Mentor

so where is your graph for comparison?

You've checked the units ofmeasure for each quantity and constant you're using?

It looks like both x and y axes are log based. Are you using the same kind of chart?

The formula is using natural log base e and it looks like the sample chart is using log base 10.

3. Jan 13, 2013

### dingo_d

I've found what I've done wrong. The b constants had reversed sign :D

Thanks anyway :D

4. Jan 13, 2013

### Staff: Mentor

That's good. Many times just explaining it helps you find your error.

5. Jan 14, 2013

### dingo_d

True that! :D

I do that sometimes with my friends, and in the midst of explaining them the issue, I find the solution :D