Form factor and new EFT operators for a WIMP on a nucleon

[junhui.liao]

Hi,

On the third paragraph(right column) of page 1 of the paper, http://journals.aps.org/prc/pdf/10.1103/PhysRevC.89.065501 ,

It says on form factor, "Because the momentum transfer in the scattering is large compared to the inverse nuclear size, form factors are generally included ".

I think this means if \lambda = h / p ~ r, then a form factor should be included, as the review of "Lewin and Smith" shown. Where \lambda is the wavelength of incident a WIMP, h is plank constant, p is momentum transfer, r is the radius of a nucleon.
Q1 : Is my understanding correct ?

Beneath a little bit at same paragraph, it says "Once momentum transfers reach that point that q⃗ · ⃗x(i), where ⃗x(i) is the nucleon coordinate within the nucleus, is no longer small, not only form factors, but new operators arise. ".

The "new operators arise" under the condition of q⃗ · ⃗x(i) is not small, how small it is ?
My understanding is : h/p ~ x => p*x ~ h. So, this is to say, if the "P*x ~ h" or " q⃗ · ⃗x(i) ~ h", then one needs to consider new operators, right ?
Q2 : If yes, then essentially, if one has considered a form factor, new EFT operators should be considered at the same time, or I have misunderstood something ?

Thanks.

 

[AndyW]

Hello,

Thank you for bringing up this interesting topic. Your understanding is correct in that form factors are included in the scattering process when the momentum transfer is large compared to the inverse nuclear size. This is because at high momentum transfers, the size of the nucleus becomes relevant and needs to be accounted for in the calculations.

As for your question about the condition of q⃗ · ⃗x(i) being not small, this refers to the magnitude of the momentum transfer compared to the size of the nucleon. This condition is typically satisfied at high momentum transfers, where the size of the nucleon becomes relevant. In this case, new operators arise because the scattering process is no longer dominated by the form factors, and other factors such as the internal structure of the nucleon need to be taken into account.

In terms of your understanding, it is correct that if the momentum transfer is large enough, both form factors and new operators need to be considered for an accurate description of the scattering process. This is why it is important to carefully consider the conditions and assumptions made in the calculations.

Thank you for your interest in this topic and for your thoughtful questions. I hope this helps clarify any confusion.