Pseudo-PDFs and Quasi-PDFs Structure
Anatoly V. Radyushkin · 2018
Parton Densities 2/20 May 11, 1918 -R.P. Feynman's birthday Feynman diagrams, propagator, path integrals, parton model ... Original Feynman approach to PDFs f (x): infinite momentum P 3 → ∞ limit of k 3 = xP 3 momentum distributions (∼ quasi-PDFs Q(x, P 3 )) f (x) were treated as k ⊥ -integrals of more detailed f (x, k ⊥ ) distributions From the start it was understood that Q(x, P 3 → ∞) → f (x) limit exists only if f (x, k ⊥ ) rapidly decreases with k ⊥ "Transverse momentum cut-off", k 2 ⊥ ∼ 1/R 2 hadr Question 1: why Q(x, P 3 ) differs from f (x)?Question 2: how does Q(x, P 3 ) convert into f (x) when P 3 → ∞? Qualitative answer: yP 3 comes from two sources: from the motion of the hadron as a whole (xP 3 ) and from Fermi motion of quarks inside the hadron (y -x)P 3 ∼ 1/R hadr (y -x)P 3 ∼ 1/R hadr part has the same origin as transverse momentum ⇒ One should be able to relate quasi-PDFs to TMDs Pseudo-PDFs &Quasi-PDFs Parton Densities Transverse Momentum Cut-off Pseudo-distributions TMDs