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But in the physical sense, a fundamental theory means it is valid at any arbitrary energy scale. We know that non-renormalizable theories are not fundamental because they must break down at a finite cut-off; QED is not fundamental because it blows up at the Landau pole. However, QCD is asymptotically free and I see nowhere it must break down. Suppose we have only QCD in our world. There is no EW theory or gravity. do we still worry about the divergence in QCD and set off looking for a fundamental mother theory for QCD? In other words, is divergence really physical so that we must find something to cure it?