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

  • #1

Main Question or Discussion Point

Hi,

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

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.
 
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