Wednesday, May 5, 2010

The Dead Man's running :P

For last couple of days I was trying to see how the Yukawa (The dead man :P) couplings of a particular model run under renormalization group evolution. Although at one loop level the equations are pretty simple, the whole sets of equations look messy since they are coupled to each other. So if there are say 23 parameters, there will be 23 coupled linear differential equations. For a complicated model where there are many parameters, lots of approximations need to be taken since we don't have as many input parameters at the electroweak scale. That's why I believe top down approach is much simpler although I never tried that. I always follow bottom up approach where I give low energy parameters as input and predict the high energy parameters. In top down approach since there are very less number of parameters, we can choose them so as to arrive at the low energy expected parameters after the running. Since I don't yet know the high energy theory properly, I can't say whether the high energy parameters I am getting after the running will fit inside a specific GUT model. May be it's time for me to switch to hard core GUT models and use the top down approach :)

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