Collins azimuthal asymmetries of hadron production inside jets

TL;DR

The paper addresses Collins azimuthal asymmetries of hadrons produced inside jets in transversely polarized proton-proton collisions to access quark transversity and Collins fragmentation functions at RHIC.It employs a hybrid LO framework: collinear jet production combined with TMD fragmentation inside the jet, incorporating TMD evolution via a Sudakov-based formalism and the b_* prescription, using global extractions of h_1 and H_1^⊥ from SIDIS and e+e− data.The authors demonstrate that the Collins fragmentation function is universal across SIDIS, e+e−, and jet-in-pp processes and show good agreement with STAR measurements at 200 and 500 GeV, with evolution effects being small within current uncertainties.Both evolving and non-evolving treatments yield compatible results given current data precision, underscoring the robustness of the TMD framework and highlighting the need for higher-precision measurements to constrain evolution effects and large-x transversity.

Abstract

We investigate the Collins azimuthal asymmetry of hadrons produced inside jets in transversely polarized proton-proton collisions. Recently, the quark transversity distributions and the Collins fragmentation functions have been extracted within global analyses from data of the processes semi-inclusive deep inelastic scattering and electron-positron annihilation. We calculate the Collins azimuthal asymmetry for charged pions inside jets using these extractions for RHIC kinematics at center-of-mass energies of 200 and 500 GeV. We compare our results with recent data from the STAR Collaboration at RHIC and find good agreement, which confirms the universality of the Collins fragmentation functions. In addition, we further explore the impact of transverse momentum dependent evolution effects.

Figures (5)

• Figure 1: Illustration of the relevant kinematic variables for the azimuthal angular distribution of hadrons inside jets in transversely polarized $p^\uparrow p$ collisions. The incident polarized proton has momentum $P_A$ and its transverse polarization vector is denoted by $S_T$. The unpolarized proton has momentum $P_B$. The transverse momentum of the hadron inside the jet relative to the (standard) jet axis is denoted by $j_\perp$. The azimuthal angles of $S_T$ and $j_\perp$ are defined with respect to the reaction plane and are denoted by $\phi_S$ and $\phi_H$, respectively.
• Figure 2: The Collins azimuthal spin asymmetry $A_{UT}^{\sin(\phi_S - \phi_H)}$ for pions produced inside jets $pp\to(\text{jet}\,\pi^{\pm})+X$ with TMD evolution using the extracted TMDs of Kang:2015msa. We show our results as a function of $z_h$ compared to the preliminary STAR data of Adkins:2016uxvAschenauer:2016ourAschenauer:2015eha at $\sqrt{s}=200$ GeV (dashed black lines, solid black circles for $\pi^+$, open black circles for $\pi^-$) and $\sqrt{s}=500$ GeV Adamczyk:2017wld (solid red lines, solid red squares for $\pi^+$, open red squares for $\pi^-$). We have $\langle p_T\rangle = 12.9$ (31.0) GeV for the average jet transverse momentum at $\sqrt{s} = 200$ (500) GeV. The averaged hadron transverse momentum with respect to the (standard) jet axis is given by $\langle j_\perp\rangle = 1.3$ GeV and the jet rapidity is integrated over the range $0<\eta<1$. The error bands are computed using results of Ref. Kang:2015msa.
• Figure 3: Same as Fig. \ref{['fig:withTMD']}, but here our results are presented without TMD evolution using the TMDs of Ref. Anselmino:2015sxa as input.
• Figure 4: The Collins azimuthal spin asymmetry $A_{UT}^{\sin(\phi_S - \phi_H)}$ at $\sqrt{s}=500$ GeV Adamczyk:2017wld for pions produced inside jets $pp\to(\text{jet}\,\pi^{\pm})+X$ as a function of the pion momentum $j_\perp$ for $\langle z_h\rangle = 0.13$ (left panel) and $\langle z_h\rangle = 0.37$ (right panel). Solid lines correspond to calculations that take into account TMD evolution using the extracted TMDs of Ref. Kang:2015msa and the dashed lines correspond to extraction of TMDs without TMD evolution of Ref. Anselmino:2015sxa. We have $\langle p_T\rangle = 31$ GeV for the average jet transverse momentum and the jet rapidity is integrated over the range $0<\eta<1$. The error bands are computed using results of Refs. Kang:2015msaAnselmino:2015sxa.
• Figure 5: Unpolarized $pp\to(\text{jet}\,\pi^{+})+X$ cross-section at $\sqrt{s}=500$ GeV as a function of the pion momentum $j_\perp$ for $\langle z_h\rangle = 0.37$. Solid lines correspond to calculations that take into account TMD evolution using the extracted TMDs of Ref. Kang:2015msa and the dashed lines correspond to extraction of TMDs without TMD evolution of Ref. Anselmino:2015sxa. We have $\langle p_T\rangle = 31$ GeV for the average jet transverse momentum and the jet rapidity is integrated over the range $0<\eta<1$.