The impact of prescriptions in phenomenological extractions of Transverse Momentum Dependent distributions

Abstract

We investigate the impact of phenomenological prescriptions in the Collins-Soper-Sterman (CSS) approach for global extractions of Transverse Momentum Distributions (TMDs). We show that fits to low-energy Drell-Yan data with different choices of $b_*$ prescription yield equally good agreement with data and similar TMDs at small partonic transverse momentum. In contrast, sizable differences emerge at intermediate transverse momentum region, significantly affecting the predictions for high-energy Drell-Yan processes. Our results demonstrate that the $b_*$ prescription represents an intrinsic source of theoretical uncertainty in the CSS approach, introducing systematic effects that influence TMD extractions and their interpretation. At the same time, our analysis emphasizes the interplay between data at different energy scales in assessing the effect of phenomenological prescriptions in TMD fits adopting the CSS framework.

Figures (9)

• Figure 1: Comparison between the definition of the $b_*(\boldsymbol{b}_T^2)$ functions in Eqs. \ref{['e:bstar_collins']}-\ref{['e:bstar_echevarria']}, represented in blue and orange, respectively. We fixed $b_{\rm max} = 2e^{-\gamma_E}$ (with $\gamma_E$ the Euler constant).
• Figure 2: Comparison between data for a selection of $Q$ bins of the E288 and E605 experiments and theoretical predictions for DY cross section differential in $|\boldsymbol{q}_{T}|$. Left column, comparison between Fit $b_*^{\rm CSS}$ (blue bands) and Fit $b_*^{\text{\scriptsize CSS-mod}}$ (light-blue bands); right column: comparison between Fit $b_*^{\rm CSS}$ and Fit $b_*^{\rm exp}$ (red bands). Lower panels: ratio between experimental data and theoretical cross section. Theoretical uncertainty bands correspond to 68% C.L., error bars on experimental data display uncorrelated uncertainties only. Single visible color bands signal complete overlap.
• Figure 3: The TMD PDF of the up quark in a proton at $\mu = \sqrt{\zeta} = Q = 4$ GeV and $x$ = 0.1 as a function of the partonic transverse momentum $|\boldsymbol{k}_\perp|$ as extracted from Fit $b_*^{\rm CSS}$ (blue band), Fit $b_*^{\rm exp}$ (red band), Fit $b_*^{\text{\scriptsize CSS-mod}}$ (light-blue band), and Fit $b_*^{\text{\scriptsize exp-mod}}$ (orange band). The uncertainty bands represent the 68% C.L.
• Figure 4: Comparison between the TMD PDF of the up quark in a proton at $\mu = \sqrt{\zeta} = Q = 4$ GeV and $x$ = 0.1 as a function of the partonic transverse momentum $|\boldsymbol{k}_\perp|$, as extracted from Fit $b_*^{\rm CSS}$ (blue curve), the perturbative (fixed order OPE at NLO) result (green curve), and the perturbative resummed (at NLL) result (brown curve). Uncertainty bands represent one-$\sigma$ error.
• Figure 5: Comparison between the TMD PDF of the up quark in a proton at $\mu = \sqrt{\zeta} = Q = 4$ GeV and $x$ = 0.1 as a function of the partonic transverse momentum $|\boldsymbol{k}_\perp|$ and the perturbative (OPE) result (green curve). Left panel: comparison between Fit $b_*^{\rm CSS}$ (blue band), Fit $b_*^{\text{\scriptsize CSS-mod}}$ (light-blue band). Right panel: comparison between Fit $b_*^{\rm CSS}$ (blue band), Fit $b_*^{\rm exp}$ (red band). Uncertainty bands represent one-$\sigma$ error.