Azimuthal asymmetries for hadron distributions inside a jet in hadronic collisions

TL;DR

Addresses azimuthal asymmetries of leading pions inside jets in hadronic collisions using a generalized TMD parton model with spin and intrinsic motion, under a factorization hypothesis for large-pT jets. It derives the leading-twist azimuthal modulations from TMD distribution and fragmentation functions (Sivers, Boer-Mulders, transversity, Collins) and provides RHIC-relevant phenomenology under both maximized bounds and SIDIS/DY/e+e- parameterizations. The results show that Sivers and Collins-type effects can produce observable asymmetries with distinct quark versus gluon jet signatures, and forward kinematics enhance sensitivity to large-x transversity, offering a test bed for TMD factorization and universality. Overall, the study outlines how jet+π observables can disentangle initial-state motion effects and jet origins, guiding future experimental and theoretical work in the TMD framework.

Abstract

Using a generalized parton model approach including spin and intrinsic parton motion effects, and assuming the validity of factorization for large-pT jet production in hadronic collisions, we study the azimuthal distribution around the jet axis of leading unpolarized or (pseudo)scalar hadrons, namely pions, produced in the jet fragmentation process. We identify the observable leading-twist azimuthal asymmetries for the unpolarized and single-polarized case related to quark and gluon-originated jets. We account for all physically allowed combinations of the transverse momentum dependent (TMD) parton distribution and fragmentation functions, with special attention to the Sivers, Boer-Mulders, and transversity quark distributions, and to the Collins fragmentation function for quarks (and to the analogous functions for gluons). For each of these effects we evaluate, at central and forward rapidities and for kinematical configurations accessible at BNL-RHIC, the corresponding potentially maximized asymmetry (for pi+ production), obtained by saturating natural positivity bounds (and the Soffer bound for transversity) for the distribution and fragmentation functions involved and summing additively all partonic contributions. We then estimate, for both neutral and charged pions, the asymmetries involving TMD functions for which parameterizations are available. We also study the role of the different mechanisms, and the corresponding transverse single spin asymmetries, for large-pT inclusive jet production.

Figures (7)

• Figure 1: (color online). Kinematical configuration for the process $A(S_A)B\to {\rm jet}+\pi+X$ in the hadronic c.m. reference frame.
• Figure 2: (color online). Maximized quark-originated ($\cos\phi_\pi^H$) and gluon-originated ($\cos2\phi_\pi^H$) asymmetries (solid-red and dashed-green lines respectively) for the unpolarized $pp\to {\rm jet}+\pi^+ + X$ process, at $\sqrt{s}=200$ GeV c.m. energy in the central (left panel) and forward (right panel) rapidity region as a function of $p_{{\rm j}\,T}$, from $p_{{\rm j}\,T}=2$ GeV up to the maximum allowed value, adopting the Kretzer FF set. Slightly lower(similar) values are obtained for quark(gluon) asymmetries when using the DSS set.
• Figure 3: (color online). Maximized total (solid red line), quark-originated (dashed green line) and gluon-originated (dotted blue line) Sivers asymmetry for the $p^\uparrow p\to {\rm jet}+\pi^+ + X$ process, at $\sqrt{s}=200$ GeV c.m. energy in the central (left panel) and forward (right panel) rapidity region as a function of $p_{{\rm j}\,T}$, from $p_{{\rm j}\,T}=2$ GeV up to the maximum allowed value, adopting the Kretzer FF set. Similar results, with some differences in the total size and in the relative weight of the quark and gluon contributions are obtained adopting the DSS set of fragmentation functions and considering different c.m. energies.
• Figure 4: (color online). The estimated quark and gluon contributions to the Sivers asymmetry for the $p^\uparrow p\to {\rm jet}+\pi + X$ process, obtained adopting respectively the parametrization sets SIDIS 1 (quark contribution: solid red line; gluon contribution: dashed green line) and SIDIS 2 (quark contribution: dotted blue line; gluon contribution: dot-dashed cyan line), at $\sqrt{s}=200$ GeV c.m. energy in the forward rapidity region and as a function of $p_{{\rm j}\,T}$, from $p_{{\rm j}\,T}=2$ GeV up to the maximum allowed value. The dotted black vertical line delimits the region beyond which the SIDIS parameterizations for the quark Sivers function are presently plagued by large uncertainties. Similar results are obtained when considering different c.m. energies.
• Figure 5: (color online). Maximized quark (solid red line) and gluon (dashed green line) Collins(-like) asymmetries for the $p^\uparrow p\to {\rm jet}+\pi^+ + X$ process, at $\sqrt{s}=200$ GeV c.m. energy in the central (left panel) and forward (right panel) rapidity region as a function of $p_{{\rm j}\,T}$, from $p_{{\rm j}\,T}=2$ GeV up to the maximum allowed value, adopting the Kretzer FF set. Notice the difference in the scale between the two panels. Similar results, with some differences in the total size and in the relative weight of the quark and gluon contributions are obtained adopting the DSS set of fragmentation functions and considering different c.m. energies.