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Homework Help: Problem with graph drawing

  1. Jan 13, 2013 #1
    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:

    [itex]\frac{1}{\alpha(\mu)} = \frac{1}{\alpha(M_Z)} + \frac{b}{2\pi}\ln\frac{\mu}{M_{Z}}[/itex]

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

    And I plug that in in Mathematica and I cannot seem to get that graph! I tried by replacing the [itex]\frac{1}{\alpha(\mu)}[/itex] with y, and [itex]\log(\mu)[/itex] 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


    Never mind! I reversed the sign of the b somehow... xD
    Last edited: Jan 13, 2013
  2. jcsd
  3. Jan 13, 2013 #2


    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.
  4. Jan 13, 2013 #3
    I've found what I've done wrong. The b constants had reversed sign :D

    Thanks anyway :D
  5. Jan 13, 2013 #4


    Staff: Mentor

    That's good. Many times just explaining it helps you find your error.
  6. Jan 14, 2013 #5
    True that! :D

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