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Simple question: are there some notes or explicit calculations of the mass term from the paper of Zamolodchikov - Mass scale in the sine-gordon model and its reduction (1994)? I need to justify this result here:

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The perturbative calculation is a full analytical formula which has been used hundreds of times but anywe I could find the proof of it. In the paper they find the same result by using Bethe ansatz, but I would find this result not via be the ansatz (if possible).

In the paper, it is presented without providing details and I know that it is right (I used this result and compared with numerical simulations).

Thanks for your time!!

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