Are non-renormalizable theories less predictive than renormalizable theories? Non-renormalizable field theories contain non-renormlizable operators whose couplings have negative mass dimension (for example, Fermi coupling in the Fermi theory of weak interaction). These couplings provide an energy scale $\Lambda$ built into the theory, and it is said that the predictions above energy $E\geq \Lambda$, is not reliable. 


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*How does one understand whether the predictions of a nonrenormalizable theory, below $\Lambda$ are reliable but bound to fail above $\Lambda$?

*Consider a renormalizable theory such as the Standard model. There is no built-in length scale. Therefore, if its predictions are tested at energy $E=E_1$, can we not claim that it's predictions, will be perfectly reliable to arbitrarily high energies (for example, $E=10^{16}\times E_1$), if there is no new physics that enter in between. 

*Such a claim may be (or must be?) false for a nonrenormalizable theory. Isn't it? 
 A: *

*The effective lagrangian is usually written as an expansion in inverse powers of the energy cut-off $\Lambda$. That means that observables at some energy $E$ will be computed as the first terms of an expansion in powers of $E/\Lambda$. When $E\gtrsim\Lambda$, higher powers contribute more than lower ones and the calculations using the effective theory are no longer valid.

*The Standard Model does indeed have a built-in length scale, but it doesn't matter for this discussion. In the case of the Standard Model (as in any other renormalizable theory) we can of course claim that it is reliable to arbitrarily high energies if new physics don't arise in between. But notice that this is almost by definition of new physics! The statement "there is no new physics" means that "old physics" remain valid.

*For a non-renormalizable theory the logic is the same, so the same statement can be made, with the extra advantage that the theory itself tells you at which maximum energy scale the new physics are expected to appear.
A: A renormalizable theory is determined by a fixed number of parameters; once these are determined, all of its predictions are determined (though not necessarily easily calculable) at every energy. 
A nonrenormalizable theory requires at higher and higher energies more and more counterterms and corresponding parameters that must be determined to make definite predictions at a fixed accuracy, and depending on the behavior of the resulting higher order terms, the asymptotic expansion may break down completely above some energy. Given a fixed number of terms, we still have an infinite family of theories with these low order terms, which have different behavior at higher energies. Thus the theory is not predictive enough at high energies.
The above holds for any quantum field theory, irrespective of its realization in Nature. Whether the predictions of a specific (renormalizable or unrenormalizable) theory are matched by Nature is a completely different matter and can be decided only by comparing the predictions with experiment. The latter is also needed to adjust the constants on which the predictions depend.
