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I have a 2D sigma model with supersymmetry on the worldsheet. It has both cubic and quartic interactions and I'm interested in the one loop correction to the worldsheet masses. When I calculate this with dimensional regularization I find that everything is zero as expected. In momentum cutoff ##\Lambda## however I find terms corresponding to infinite mass renormalization. That is

Dim reg:

$$ \delta m^2 = 0 $$

while in

momentum cutoff:

$$ \delta m^2 = \alpha \Lambda^2 + \beta $$

where ##\alpha,\beta## are constants like ##1/\pi## etc.

My question is, what is the meaning of the terms popping up in the momentum cutoff? They shouldn't be physical but I feel I lack a proper argument for that statement.

Thanks a lot

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# Dimensional regularization vs momentum cutoff

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