Azimuthal Spin Asymmetries in Semi-Inclusive Production from Positron-Proton Scattering

TL;DR

The paper investigates azimuthal single-spin asymmetries in semi-inclusive deep inelastic scattering to access spin-dependent distribution and fragmentation functions, focusing on the dominant but largely unknown functions $h_{1L}^{\perp(1)}(x)$, $h_L(x)$, $H_1^{\perp(1)}(z)$, and $\tilde{H}(z)$. It analyzes two extreme theoretical scenarios—one neglecting interaction-dependent terms and the other neglecting a specific T-odd distribution—and employs parameterizations from BL99 with multiple parton distribution function sets (BBS, LSS_(BBS), MRST-LSS) to compute weighted cross-section integrals for the asymmetries. The study finds that the $\sin(2\phi^l_h)$ asymmetry is generally suppressed relative to $\sin(\phi^l_h)$ and that predictions can differ by about a factor of two depending on the PDF set, illustrating the current data’s limited constraining power on the underlying functions. The results underscore the need for more comprehensive measurements across wider kinematic ranges to disentangle the twist-2 and twist-3 spin structure of the nucleon and the associated fragmentation dynamics.

Abstract

The recent measurements of azimuthal single spin asymmetries by the HERMES collaboration at DESY may shed some light on presently unknown fragmentation and distribution functions. We present a study of such functions and give some estimates of weighted integrals directly related to those measurements.

Figures (5)

• Figure 1: The distribution functions $h_1^u(x)$ and $h_1^d(x)$ as obtained by using the MRST-LSS, BBS and LSS$_{(BBS)}$ sets of distribution functions. The curves in the positive quadrant correspond to the $u$ flavour, whereas the curves in the negative quadrant correspond to the $d$ flavour.
• Figure 2: The distribution functions $h_L^u(x)$, $h_L^d(x)$ and $h_{1L}^{\perp (1) u}(x)$, $h_{1L}^{\perp (1) d}(x)$, as obtained by using the MRST-LSS, BBS and LSS$_{(BBS)}$ sets of distribution functions respectively, under the approximation $\tilde{h}_L(x) =0$.
• Figure 3: The distribution functions $\overline h_L^u(x)$ and $\overline h_L^d(x)$, as obtained under the approximation $h_{1L}^{\perp (1)}(x)=0$, by using the MRST-LSS, BBS and LSS$_{(BBS)}$ sets of distribution functions.
• Figure 4: A three-dimensional view of $-\sum _{a,\bar{a}} e^2_a x_B h_{1L}^{\perp(1)a} (x_B) H_1 ^{\perp (1) a} (z_h)$, relevant for the $\sin (2\phi^l _h)$ asymmetry in $\pi^+$ production, under the approximation $\tilde{h}_L(x)= \overline h_L =0$, as obtained by using the BBS set of distribution functions.
• Figure 5: A three-dimensional view of $-\sum _{a,\bar{a}} e^2_a \Bigl[x_B h_{1L}^{\perp(1)a} (x_B) \tilde{H} ^a (z_h)/z - x_B^2 h_L^a (x_B) H_1^{\perp (1) a}(z_h)\Bigr]$, relevant for the $\sin (\phi^l _h)$ asymmetry in $\pi^+$ production, as obtained by using the BBS set of distribution functions, under the approximation $\tilde{h}_L = \overline h_L = 0$ (on the left) and under the approximation $h_{1L}^{\perp (1)}(x)=0$ (on the right).