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Register a new userGeneral helicity formalism for Single and Double Spin Asymmetries in p p --> pion + X
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M. Anselmino
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We consider within a generalized QCD factorization approach, the high energy inclusive polarized process p p --> pion + X, including all intrinsic partonic motions. Several new spin and k_T-dependent soft functions appear and contribute to cross sections and spin asymmetries. We present here formal expressions for transverse single spin asymmetries and double longitudinal ones. The transverse single spin asymmetry, A_N, is considered in detail, and all contributions are evaluated numerically. It is shown that the azimuthal phase integrations strongly suppress most contributions, leaving at work mainly the Sivers effect.
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Predictions for the single transverse spin asymmetry A_N in semi-inclusive DIS processes are given; non negligible values of A_N may arise from spin effects in the fragmentation of a polarized quark into a final hadron with a transverse momentum k_T with respect to the jet axis, the so-called Collins effect. The elementary single spin asymmetry of the fragmenting quark has been fixed in a previous paper, by fitting data on p(transv. polarized) + P -> pion + X, and the predictions given here are uniquely based on the assumption that the Collins effect is the only cause of the observed single spin asymmetries in p(transv. polarized) + p -> pion + X. Eventual spin and k_T dependences in quark distribution functions, the so-called Sivers effect, are also discussed.
Results are presented from data recorded in 2009 by the PHENIX experiment at the Relativistic Heavy Ion Collider for the double-longitudinal spin asymmetry, $A_{LL}$, for $pi^0$ and $eta$ production in $sqrt{s} = 200$ GeV polarized $p$$+$$p$ collisions. Comparison of the $pi^0$ results with different theory expectations based on fits of other published data showed a preference for small positive values of gluon polarization, $Delta G$, in the proton in the probed Bjorken $x$ range. The effect of adding the new 2009 pz data to a recent global analysis of polarized scattering data is also shown, resulting in a best fit value $Delta G^{[0.05,0.2]}_{mbox{DSSV}} = 0.06^{+0.11}_{-0.15}$ in the range $0.05<x<0.2$, with the uncertainty at $Delta chi^2 = 9$ when considering only statistical experimental uncertainties. Shifting the PHENIX data points by their systematic uncertainty leads to a variation of the best-fit value of $Delta G^{[0.05,0.2]}_{mbox{DSSV}}$ between $0.02$ and $0.12$, demonstrating the need for full treatment of the experimental systematic uncertainties in future global analyses.
Some estimates for the transverse Single Spin Asymmetry, A_N, in the inclusive processes l p(transv. pol.) --> h X, given in a previous paper, are expanded and compared with new experimental data. The predictions are based on the Sivers distributions and the Collins fragmentation functions which fit the azimuthal asymmetries measured in Semi-Inclusive Deep Inelastic Scattering (SIDIS) processes (l p(transv. pol.) --> l h X). The factorisation in terms of Transverse Momentum Dependent distribution and fragmentation functions (TMD factorisation) -- i.e., the theoretical framework in which SIDIS azimuthal asymmetries are analysed -- is assumed to hold also for the inclusive process l p --> h X at large P_T. The values of A_N thus obtained agree in sign and shape with the data. Some predictions are given for future experiments.
We suggest inclusive hadron production in ultra-peripheral proton-nucleus collisions (UPCs) $p^uparrow A to h AX$ as a new channel to investigate single spin asymmetries (SSAs), in particular, to test the assumed dominance of the contribution from twist-three fragmentation functions. The UPC cross sections are obtained by considering the photoproduction limit of semi-inclusive deep inelastic scattering (SIDIS). In particular, we find simple formulas for the polarized UPC cross sections in the collinear twist-three framework. We then numerically calculate the fragmentation contribution to SSA in $p^uparrow A to pi A X$ at $sqrt{s} = 200$ GeV and find a few percent asymmetry in the forward region.
We present estimates of transverse single-spin asymmetry in prompt photon production in the scattering of low virtuality photons off a polarized proton target and discuss the possibility of using this as a probe to get information about the gluon Sivers function (GSF). Using a generalized parton model (GPM) framework, we estimate the asymmetries at electron-ion collider energy ($sqrt{s}$ =140 GeV) taking into account both direct and resolved photon processes and find that the dominant contribution, up to $10%$, comes from quark Sivers function (QSF) while the contribution from GSF is found to be up to $2%$. However, upon taking into account the effects of the process-dependent initial and final state interactions through the color-gauge invariant generalized parton model approach we find that the situation is significantly changed, with near zero contributions from the QSFs and up to a $1%$ level contribution from the textit{f}-type GSF. Our results indicate that this process may be useful for distinguishing between GPM and color-gauge invariant generalized parton models and can be used as a good probe of textit{f}-type GSF.
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