Unitarity & EFT: Exploring Finite Amplitude Theory

[ChrisVer]

Hi all... As far as I understand, the concept of "unitarity" is pretty close to that of perturbation; in that it tells you that your amplitudes are finite with energy scale (one solution the Higgs gave in e.g. the Vector Boson Scattering).
However, since an EFT comes with a natural cut-off, why do people try to justify their validity using unitarity arguments? I mean, you are safe from an explosive amplitude by your EFT's scale.
Thanks.

 

[Dr.AbeNikIanEdL]

the concept of "unitarity" is pretty close to that of perturbation

I don't understand what you mean by that.

it tells you that your amplitudes are finite with energy scale (one solution the Higgs gave in e.g. the Vector Boson Scattering)

It does tell you that the S-matrix is unitary. For that the amplitudes must not grow too much, it is not necessarily enough that they stays finite.

(one solution the Higgs gave in e.g. the Vector Boson Scattering).

This solution also only works for a not too heavy Higgs. Thats why you basically knew something would be found at the LHC: A Higgs with mass larger than 1TeV or so will not work, because unitarity would be violated earlier.

However, since an EFT comes with a natural cut-off, why do people try to justify their validity using unitarity arguments? I mean, you are safe from an explosive amplitude by your EFT's scale.

So it is not enough to have an energy cutoff somewhere, you need it early enough so your amplitudes are not already too large when reaching it.