The Sivers asymmetry in hadronic dijet production

Abstract

We study the single spin asymmetry in the back-to-back dijet production in transversely polarized proton-proton collisions. Such an asymmetry is generated by the Sivers functions in the incoming polarized proton. We propose a QCD formalism in terms of the transverse momentum dependent parton distribution functions, which allow us to resum the large logarithms that arise in the perturbative calculations. We make predictions for the Sivers asymmetry of hadronic dijet production at the kinematic region that is relevant to the experiment at the Relativistic Heavy Ion Collider (RHIC). We further compute the spin asymmetries in the selected positive and negative jet charge bins, to separate the contributions from u- and d-quark Sivers functions. We find that both the sign and size of our numerical results are roughly consistent with the preliminary results from the STAR collaboration at the RHIC.

QCD evolution of the gluon Sivers function in heavy flavor dijet production at the Electron-Ion Collider

“…In the third line of eq. (2.8), J Q and S c Q are the massive quark jet and collinear-soft functions, which differ from the corresponding functions utilized in light jet production [24][25][26][27][28]. In sections 2.5 and 2.6, we present their explicit calculations at next-to-leading order (NLO).…”

“…In figure 2, the soft poles are represented by red lines. We note that for both the polarized and unpolarized cases, the hard functions can be expressed as matrices in color space [28]. For more complicated processes, the relationship between the polarized and unpolarized hard matrices is non-trivial.…”

“…However, after taking into account the evolution between the JHEP05(2021)286 soft and collinear-soft function, one finds that the φ b integral is divergent in some phase space region. In order to avoid such divergences we apply methods in [24,28] where one first performs an averaging over the φ b angle in both soft and collinear-soft function. We note that this method does not change the RG invariance as shown in eqs.…”

“…A similar idea is used to study single inclusive jet production in the Breit frame at the EIC in [22,23]. Recently, following the same Soft-Collinear Effective Theory (SCET) framework utilized in [24][25][26][27][28], the TMD factorization formula for light flavor dijet production at the EIC has been derived [29], where the azimuthal-angle-dependent soft function, describing the interaction between two final-state jets through the exchange of low-energy gluons, is analytically calculated at one-loop order. For HF jet production in the kinematic region of comparable jet and heavy quark masses, a new effective theory framework is needed.…”

“…Such resummation could be included multiplicatively by using the parton shower algorithm developed recently for massive particles[61]. Note that the fitting function used in[27,28] to capture the effects of NGLs is only an approximation for HF jet production, as finite heavy quark mass corrections are not included.…”