Can the result on cross section of some process be dependent on the renormalization scheme used?
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If one calculates it to all orders, it shouldn't. In particular, if the coupling constant is small, the $O(g^k)$ accuracy calculation of the cross section obtained in different schemes can differ at most by $o(g^k)$, negligible amounts. However, when one truncates the cross section at some order, the results may really depend on the renormalization scheme by subleading, higher-order terms. Physically, cross sections are measurable so a valid theory must predict unequivocal values for it. And a renormalization scheme doesn't really "change the theory". |
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