Fourier-positivity constraints on QCD dipole models

Bertrand G. Giraud (1) , Robi Peschanski (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

Fourier-positivity ($\mathscr{F}$-positivity), i.e. the mathematical property that a function has a positive Fourier transform, can be used as a constraint on the parametrization of QCD dipole-target cross-sections or Wilson line correlators in transverse position space $r$. They are Bessel transforms of positive transverse momentum dependent gluon distributions. Using mathematical $\mathscr{F}$-positivity constraints on the limit $r$ $\rightarrow$ 0 behavior of the dipole amplitudes, we identify the common origin of the violation of $\mathscr{F}$-positivity for various, however phenomenologically convenient, dipole models. It is due to the behavior $r^{2+ \epsilon}$, $\epsilon > 0$ softer, even slightly, than color transparency. $\mathscr{F}$-positivity seems thus to conflict with the present dipole formalism when it includes a QCD running coupling constant $\alpha$($r$).

Domains: Physics [physics]

Bertrand G. Giraud, Robi Peschanski. Fourier-positivity constraints on QCD dipole models. Physics Letters B, 2016, 760, 26-30, ⟨10.1016/j.physletb.2016.06.033⟩. ⟨cea-01299882⟩