Next-to-Leading Order QCD Corrections to the Polarized Hadroproduction of Heavy Flavors

TL;DR

The paper addresses constraining the proton's spin structure through the polarized gluon density $\Delta g$ by studying heavy-flavor production in polarized proton-proton collisions at RHIC. It delivers the first complete next-to-leading order QCD corrections to the polarized hadroproduction of heavy flavors, including virtual and real contributions and a new $gq \to Q\overline{Q} q$ channel, computed with $n=4+\varepsilon$ dimensional regularization and HVBM treatment of $\gamma_5$. The authors demonstrate a substantial reduction in renormalization and factorization scale uncertainties at NLO and provide predictions for the heavy-quark spin asymmetry $A$ that incorporate detector efficiencies, showing strong sensitivity to $\Delta g$. These results enable more reliable extraction of gluon polarization from RHIC data and have implications for addressing bottom production puzzles and potential SUSY-related processes via gluino production.

Abstract

We present the complete next-to-leading order QCD corrections to the polarized hadroproduction of heavy flavors which soon will be studied experimentally in polarized pp collisions at the BNL RHIC in order to constrain the polarized gluon density Delta g. It is demonstrated that the dependence on unphysical renormalization and factorization scales is strongly reduced beyond the leading order. The sensitivity of the heavy quark spin asymmetry to Delta g is studied, including the limited detector acceptance for experimentally observable leptons from heavy quark decays at the BNL RHIC. As a further application of our results, gluino pair production in polarized pp collisions is briefly discussed.

Figures (4)

• Figure 1: $(m^2/\alpha_s^2) \tilde{\hat{\sigma}}_{gg}$ in NLO ($\overline{\mathrm{MS}}$) and LO as a function of $\eta$ according to Eq. (\ref{['eq:totalpartonic']}), where we have set $\mu_F=\mu_R=m$ for simplicity and $4\pi\alpha_s=2.7$ as appropriate for charm production.
• Figure 2: Deviation [in $\%$] of the polarized total charm cross section in LO (dotted) and NLO (solid) from a reference choice ("0-pin" marker, see text) -- left part: as a function of $\mu_{F}$ and $\mu_{R}$ for fixed $m$; right part: as a function of $\mu_F$ and $m$ with $\mu_R=\mu_F$, here the LO result is multiplied by a factor (-1). Corresponding contour lines in steps of $20\%$ are given at the base of each plot.
• Figure 3: The NLO charm asymmetry $A$ at $\sqrt{S}=200\;\mathrm{GeV}$ for PHENIX at RHIC as a function of $x_T^{\mathrm{min}}=p_T^{\mathrm{min}}/p_T^{\mathrm{max}}$ using Eq. (\ref{['eq:eef']}). For a better separation of the curves $A$ is rescaled by $1/x_T^{\mathrm{min}}$. Recent and old sets of helicity densities are distinguished by thick and thin lines, respectively. Also shown is an estimate for the statistical error using a luminosity of ${\cal L}=320\;\mathrm{pb}^{-1}$ (see text).
• Figure 4: Ratio of the asymmetries in NLO and LO, $A(\mathrm{NLO})/A(\mathrm{LO})$, with $A(\mathrm{NLO})$ as shown in Fig. \ref{['fig:casym']}. The ratio of unpolarized cross sections $\sigma(\mathrm{LO})/\sigma(\mathrm{NLO})$ used in the calculation of $A$ is also shown for comparison (thin solid line).