What values do the six quark mass achieve when they run up to Planck energy?

Question

Let us assume that the standard model is correct up to Planck mass, without supersymmetry or other changes. (Yes, this is a big assumption.) If we continue the running of quark masses with energy, due to renormalization, what are the mass values we get for the six quarks at Planck energy?

I am especially interested in understanding whether the sequence of mass values remains the same also at Planck energy, or whether some quarks "catch" up with others, such as up and down quarks. Any literature on this issue would also be very welcome.

Comments

Table IV of http://arxiv.org/abs/0712.1419 extrapolates up to 2 x 10^16 GeV. But these masses are somewhat fictitious. What really runs are the Yukawa couplings, and the mass in the table is the yukawa times the VEV of the Higgs field after electroweak symmetry breaking. But at such high scales, electroweak symmetry is restored, and the VEV and the mass are zero. But the yukawa couplings are nonzero. So the values in the table are at least a proxy for something real.

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Thank you; the first author has a few other, more recent papers on the arxiv that are worth reading. Unfortunately they have no data for the Planck energy.