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Soffer's inequality and the transversely polarized Drell-Yan process at next-to-leading order

O. Martin, A. Schaefer, M. Stratmann, W. Vogelsang

TL;DR

This paper numerically tests whether Soffer's inequality for quark transversity distributions remains valid under NLO QCD evolution and uses this to bound the transverse double spin asymmetry A_TT in Drell–Yan muon-pair production. By saturating the bound at a low hadronic scale and evolving with NLO splitting functions, the authors derive upper limits on A_TT and show that the inequality is preserved for both valence and sea quarks. The results indicate maximal A_TT values of a few percent at realistic energies, with moderate NLO corrections and controlled scale dependence, providing a firm target for future transversely polarized experiments. A concurrent mathematical proof of the NLO preservation of Soffer's inequality is noted in a postscript.

Abstract

We check numerically if Soffer's inequality for quark distributions is preserved by next-to-leading order QCD evolution. Assuming that the inequality is saturated at a low hadronic scale we estimate the maximal transverse double spin asymmetry for Drell-Yan muon pair production to next-to-leading order accuracy.

Soffer's inequality and the transversely polarized Drell-Yan process at next-to-leading order

TL;DR

This paper numerically tests whether Soffer's inequality for quark transversity distributions remains valid under NLO QCD evolution and uses this to bound the transverse double spin asymmetry A_TT in Drell–Yan muon-pair production. By saturating the bound at a low hadronic scale and evolving with NLO splitting functions, the authors derive upper limits on A_TT and show that the inequality is preserved for both valence and sea quarks. The results indicate maximal A_TT values of a few percent at realistic energies, with moderate NLO corrections and controlled scale dependence, providing a firm target for future transversely polarized experiments. A concurrent mathematical proof of the NLO preservation of Soffer's inequality is noted in a postscript.

Abstract

We check numerically if Soffer's inequality for quark distributions is preserved by next-to-leading order QCD evolution. Assuming that the inequality is saturated at a low hadronic scale we estimate the maximal transverse double spin asymmetry for Drell-Yan muon pair production to next-to-leading order accuracy.

Paper Structure

This paper contains 5 sections, 19 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Preservation of Soffer's inequation by NLO evolution
  3. Upper bounds on $A_{TT}$: Framework
  4. Results
  5. Conclusions

Figures (7)

  • Figure 1: The ratio $R_q(x,Q^2)$ as defined in (\ref{['req']}) for $q=u_v,\bar{u},d_v,\bar{d}$ and several fixed values of $Q^2$.
  • Figure 2: The dynamical SU(2)-breaking in the NLO transversity densities expressed by the ratio $\delta D(x,Q^2)$ as defined in (\ref{['xxx']}) for several fixed values of $Q^2$.
  • Figure 3: NLO and LO maximal polarized Drell-Yan cross sections and asymmetries for HERA-$\vec{\rm N}$. The error bars have been calculated according to Eq. (\ref{['aerr']}) and are based on ${\cal L}=240\,\hbox{pb}^{-1}$, 70% polarisation of beam and target and 100% detection efficiency.
  • Figure 4: As in Fig. \ref{['fig3']}, but for RHIC at $\sqrt{S}=150\, \hbox{GeV}$ assuming ${\cal L}=240\,\hbox{pb}^{-1}$, 70% polarisation of each beam and 100% detection efficiency.
  • Figure 5: As in Fig. \ref{['fig4']}, but for $\sqrt{S}=500\,\hbox{GeV}$ and ${\cal L}=800\,\hbox{pb}^{-1}$.
  • ...and 2 more figures