Time-reversal odd fragmentation and distribution functions in pp and ep single spin asymmetries

TL;DR

This work develops a formal framework to quantify time-reversal odd (T-odd) quark distribution and fragmentation functions, specifically $f_{1T}^{ perp}$ and $H_1^ perp$, by linking light-front quark correlators to observable spin-dependent effects. Using parametrizations fit to $p^ p$ data and established fragmentation inputs, the authors extract $k_T$-dependent moments and relate them to measurable angular asymmetries through weighted integrals. They estimate the ratios $H_1^ perp/D_1$ (about 8% under typical cuts) and $f_{1T}^{ perp}/f_1$ (about 7–8%), consistent with DELPHI results and offering predictions for $ep^$ scattering. The results show that T-odd effects, while small, are potentially detectable and provide a practical framework for extracting these soft functions from experimental data.

Abstract

We present some estimates of T-odd fragmentation and distribution functions, $H_1^\perp$ and $f_{1T}^{\perp}$, evaluated on the basis of a fit on experimental data in p$^\uparrow$p. Assuming the T-odd fragmentation function to be responsible for the single spin asymmetry in pion production in p$^\uparrow$p, we find the ratio $H_1^{\perp}/D_1$ to be in good agreement with the experimental results from DELPHI data on Z -> 2$-jet decay. We use our estimates to make predictions for ep$^\uparrow$.

Figures (4)

• Figure 1: Pictorial representation of the various kinds of distribution functions
• Figure 2: Pictorial representation of the various kinds of fragmentation functions
• Figure 3: The $(\bm k_{ T}^2/2M^2)$-moment of the T-odd distribution function, $f_{1T}^{\perp \, (1)\, u}(x)$, solid line, and $f_{1T}^{\perp \, (1) \, d}(x)$, dashed line, evaluated from Eq. ( \ref{['f(1)']}).
• Figure 4: The T-odd fragmentation function first moment, $H_{1}^{\perp \, (1)\,\hbox{\small fav}}(z)$, as it can be evaluated from Eq. ( \ref{['H(1)']}).