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Gluon Sivers function in dijet production at the EIC

Miguel G. Echevarria, Patricia Andrea Gutierrez García, Ignazio Scimemi

Abstract

The transverse-momentum-dependent (TMD) factorization theorem for dijet production in deep-inelastic scattering is used here to make predictions of the gluon Sivers function. We revise the previously studied unpolarized case and develop the formalism for a transversely polarized target. We study the impact of TMD evolution in two different schemes and we use the current extractions of the evolution kernel at N$^3$LO to make predictions for the future Electron-Ion Collider (EIC). The results strongly depend on the TMD gluon distributions and their evolution kernel. Big values of the Sivers asymmetry at the EIC are predicted, between 5-50$\%$

Gluon Sivers function in dijet production at the EIC

Abstract

The transverse-momentum-dependent (TMD) factorization theorem for dijet production in deep-inelastic scattering is used here to make predictions of the gluon Sivers function. We revise the previously studied unpolarized case and develop the formalism for a transversely polarized target. We study the impact of TMD evolution in two different schemes and we use the current extractions of the evolution kernel at NLO to make predictions for the future Electron-Ion Collider (EIC). The results strongly depend on the TMD gluon distributions and their evolution kernel. Big values of the Sivers asymmetry at the EIC are predicted, between 5-50
Paper Structure (26 sections, 110 equations, 8 figures, 5 tables)

This paper contains 26 sections, 110 equations, 8 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Notation and kinematics
  3. Factorization for the dijet cross section in SIDIS
  4. Gluon channel
  5. Quark/anti-quark channels
  6. Weighted cross section and Sivers asymmetry
  7. Operator definitions
  8. Renormalization group equations and evolution kernels
  9. Evolution kernel for the soft and collinear-soft function: ${\cal M}$-scheme
  10. Scale fixing and non-perturbative effects
  11. Final expression of the unpolarized hadronic tensor
  12. Final expression of the hadronic tensor for Sivers function measurement
  13. $\cal M$-function scheme at one loop
  14. The quark and gluon CS-kernels for evolution
  15. Sivers function models
  16. ...and 11 more sections

Figures (8)

  • Figure 1: Planes and angles for dijet production in SIDIS in the Breit frame
  • Figure 2: Dijet hard processes at leading order, from delCastillo:2020omr. Here $f=q,\;\bar{q}$.
  • Figure 3: Unpolarized cross-section using CCS-scheme (left) and $\mathcal{M}$-scheme. (center). We show separately gluon-channel (red), quark-channel contributions and final result (green). In the left plot we show the comparison of unpolarized cross-section in $\mathcal{M}$- and CCS-schemes, respectively, in red and blues lines. The band corresponds to hard function uncertainty.
  • Figure 4: Sivers weighted cross-section using CCS-scheme (left) and $\mathcal{M}$-scheme. (center). We show separately gluon-channel (red), quark-channel contributions and final result (green). In the left plot we show the comparison of Sivers weighted cross-section in $\mathcal{M}$- and CCS-schemes, respectively, in red and blues lines. The band corresponds to hard function uncertainty.
  • Figure 5: Sivers asymmetry in CCS-scheme (green) and $\mathcal{M}$-scheme (red).
  • ...and 3 more figures