QCD corrections to polarization of J/ψand Υat Fermilab Tevatron and CERN LHC

TL;DR

This work provides a detailed calculation of NLO QCD corrections to the polarization of directly produced J/psi and, for the first time, Upsilon in hadron collisions at Tevatron and LHC within the color-singlet NRQCD framework. Using virtual and real corrections with a two-cutoff phase space slicing method, the authors obtain finite results for cross sections and polarization observables, and they analyze transverse momentum distributions and polarization parameters. The key finding is a dramatic shift from LO's transverse-dominated to NLO's longitudinal-dominated polarization for J/psi (and a similar trend for Upsilon), though data still require color-octet contributions for full agreement. The paper also details color-factor handling, Upsilon treatment, and numerical setups, and it calls for including NLO corrections to color-octet states to resolve the polarization puzzles and better match experimental results.

Abstract

In this work, we present more detail of the calculation on the NLO QCD corrections to polarization of direct J/psi production via color singlet at Tevatron and LHC, as well as the results for Upsilon for the first time. Our results show that the J/psi polarization status drastically changes from transverse polarization dominant at LO into longitudinal polarization dominant in the whole range of the transverse momentum $p_t$ of J/psi when the NLO corrections are counted. For Upsilon production, the p_t distribution of the polarization status behaves almost the same as that for J/psi except that the NLO result is transverse polarization at small p_t range. Although the theoretical evaluation predicts a larger longitudinal polarization than the measured value at Tevatron, it may provide a solution towards the previous large discrepancy for J/psi and Upsilon polarization between theoretical predication and experimental measurement, and suggests that the next important step is to calculate the NLO corrections to hadronproduction of color octet state J/psi^(8) and Upsilon^(8). Our calculations are performed in two ways, namely we do and do not analytically sum over the polarizations, and then check them with each other.

Figures (10)

• Figure 1: Leading order Feynman diagrams for $g + g \rightarrow {J/\psi} + g$. The other five diagrams can be obtained by permutation the places of gluons.
• Figure 2: One-loop diagrams for $g g \rightarrow {J/\psi} g$. Group (a) and (b) are counter-term diagrams of the quark-gluon vertex and corresponding loop diagrams, Group (c) are the quark self-energy diagrams and corresponding counter-term ones. More diagrams can be obtained by permutation of external gluons.
• Figure 3: Feynman diagrams for first three real correction processes. (a) is for $gg \rightarrow {J/\psi} + gg$ and (b) is for $gg \rightarrow {J/\psi} + q\overline{q}$ while (c) is for $gq(\overline{q}) \rightarrow {J/\psi} + gq(\overline{q})$. More diagrams can be obtained by all possible permutation of gluons.
• Figure 4: Feynman diagrams for real correction process $gg \rightarrow {J/\psi} + c\overline{c}$. More diagrams can be obtained by reversing the arrow of charm quark line and/or exchanging the places of gluons.
• Figure 5: Total cross section of ${J/\psi}$ production at Tevatron and LHC, as function of the renormalization and factorization scale with $\mu_r=\mu_f=\mu$ and $\mu_0=\sqrt{(2m_c)^2+p_t^2}$.