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Register a new userProcess dependence of the gluon Sivers function in inclusive $pp$ collisions: phenomenology
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Within the so-called color gauge invariant generalized parton model, a TMD scheme including initial- (ISI) and final-state (FSI) interactions, we present a phenomenological analysis of available SSA data for pion and $D$-meson production in $pp$ collisions. This allows us, for the first time, to put a preliminary constraint on the two universal types of gluon Sivers function entering the model. Predictions for SSAs in $J/psi$ and direct photon production, as well as a comparison with the simpler generalized parton model (without ISIs and FSIs), are also presented.
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Within a generalized parton model approach, with inclusion of spin and intrinsic transverse momentum effects, we show how the latest, highly precise, midrapidity data on the transverse single spin asymmetry measured in $pptopi^0, X$ by the PHENIX Collaboration at RHIC [1], can be used to get a first estimate on the still poorly known gluon Sivers distribution. To this end we also adopt the present information on the quark Sivers functions, as extracted from semi-inclusive deeply inelastic scattering data. This analysis updates a previous study by some of us where a first bound on this distribution was obtained [2].
We study the transverse single-spin asymmetries for $p^uparrow pto pi, X$ and $p^uparrow pto gamma, X$ within the so-called color gauge invariant generalized parton model (CGI-GPM) which, in addition to spin and transverse momentum effects, includes initial and final state interactions with the polarized proton remnants. We compute all relevant contributions, focusing in particular on the process dependence of the gluon Sivers function, which, for these processes, can always be expressed as a linear combination of two independent, universal terms. This study extends and completes a previous one, where only quark initiated partonic processes were considered. We then perform a combined phenomenological analysis of RHIC data on transverse single-spin asymmetries in $p^uparrow pto pi, X$ and $p^uparrow pto D, X$, putting the first preliminary constraints on these two gluon Sivers functions. We show how their size can be estimated by means of these data, and use our results to provide predictions for the process $p^uparrow pto J/psi,X$, comparing them with data, and $p^uparrow pto gamma, X$, for which experimental information will soon become available. Corresponding estimates within the simpler GPM approach, without initial and final state interactions and with a single universal gluon Sivers function, are also given, showing that a clear discrimination between these two models is, for the moment, not possible.
In this contribution, we will present a short overview of the transverse momentum dependent (TMD) approach as a tool for studying the 3-dimensional structure of hadrons in high-energy (un)polarized hadron collisions. We will then summarize the present status of a running research programme that aims at constraining the poorly known transverse momentum dependent gluon Sivers function, through the study of single spin asymmetries in quarkonium (mainly $J/psi$), pion, and $D$-meson production in polarized proton-proton collisions at RHIC. Finally, we will shortly discuss perspectives for this field of research, emphasizing in particular its role in the physics programme of LHC in the fixed-target setup and NICA.
We consider the transverse single-spin asymmetry (SSA) for $J/psi$ production in $p^uparrow p to J/psi + X$ within a TMD approach in non-relativistic QCD. Extending a previous study [1], we employ here the color-gauge invariant generalized parton model (CGI-GPM), in which spin and intrinsic transverse momentum effects are taken into account, together with leading-order initial- and final-state interactions (ISIs and FSIs). We find that, even when the heavy-quark pair is produced in a color-octet state, ISIs and FSIs lead to a nonvanishing SSA, allowing, in principle, to test the process dependence of the gluon Sivers function (GSF). We show that of the two independent contributions, due to the so-called $f$- and $d$-type GSFs, appearing in the CGI-GPM, the $d$-type one turns out to be dynamically suppressed. Therefore, as already found adopting the Color-Singlet Model approach for the $J/psi$ formation [2], only the $f$-type GSF could play a role in phenomenology. A comparison with the corresponding results obtained in the generalized parton model, without the inclusion of ISIs and FSIs, is also carried out.
We study the process dependence of the Sivers function by considering the impact of color-gauge invariant initial and final state interactions on transverse spin asymmetries in proton-proton reactions within the framework of the transverse momentum dependent (TMD), generalized parton model. To this aim, we consider the azimuthal distribution of leading pions inside a fragmenting jet as well as single inclusive jet asymmetry in polarized proton proton collisions. In contrast to single inclusive pion production, in both cases we can isolate the Sivers contribution and thereby study its process dependence. The predictions for the Sivers asymmetry obtained with and without inclusion of color gauge factors are comparable in size but with opposite signs. We conclude that both processes represent unique opportunities to discriminate among the two approaches and test the universality properties of the Sivers function in hadronic reactions.
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