[Paper Review] T-odd quark fragmentation function and transverse spin asymmetries in the pion production

K. Suzuki|arXiv (Cornell University)|Feb 21, 2000

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper proposes that T-odd quark fragmentation functions—generated by non-perturbative final-state interactions—can probe the chiral-odd transversity distribution $ h_1(x) $ of the nucleon. Using a Nambu-Jona-Lasinio model toy framework and fitting to existing $ \vec{p}+p \to \pi + X $ data, it estimates the T-odd fragmentation function and predicts transverse single-spin asymmetries in semi-inclusive deep inelastic scattering. The key result is that pion cloud effects strongly suppress the $ d $-quark transversity distribution $ h_1^d(x) $, reducing its tensor charge by ~40%, while axial charge remains nearly unchanged.

ABSTRACT

We study the time-reversal odd quark fragmentation function and its consequences on the hard processes. T-odd quark fragmentation function may arise, although QCD is T-invariant, from the non-perturbative dynamics in the fragmentation process. Assuming the factorization, we extract the T-odd fragmentation function from the inclusive pion production in the transversely polarized proton-proton collision. We then estimate the single spin asymmetry $A_{OT}$ of the semi-inclusive deep inelastic scattering with unpolarized lepton and the transversely polarized proton. We also discuss the meson cloud effects on the transversity distribution $h_1(x)$ of the nucleon. Asymmetry for the $π^-$ production is found to be much smaller than the naive expectation, since the $d$-quark transversity is considerably suppressed by the pion cloud effects

Motivation & Objective

• To establish a connection between T-odd quark fragmentation functions and the chiral-odd transversity distribution $ h_1(x) $, which is inaccessible via deep inelastic scattering.
• To extract the T-odd fragmentation function from existing data on transverse single-spin asymmetries in $ \vec{p}+p \to \pi + X $ collisions.
• To predict transverse spin asymmetries in semi-inclusive deep inelastic scattering off transversely polarized protons for future experimental verification.
• To investigate the role of meson cloud Fock components in modifying the transversity distribution $ h_1(x) $, particularly for $ d $-quarks.
• To demonstrate that the ratio of $ \pi^+ $ and $ \pi^- $ single-spin asymmetries cancels T-odd fragmentation function uncertainties, enabling clean extraction of $ h_1^u(x)/h_1^d(x) $.

Proposed method

• A toy model based on the Nambu-Jona-Lasinio framework is used to simulate non-perturbative quark hadronization, incorporating effective four-quark interactions to generate T-odd fragmentation functions.
• The T-odd fragmentation function $ H_1^{\perp}(z,k_\perp,s_\perp) $ is derived from the matrix element involving $ \gamma^+ \gamma^5 \gamma_\perp \cdot s_\perp $, encoding transverse quark spin dependence.
• The fragmentation function is extracted by fitting to experimental analyzing powers in $ \vec{p}+p \to \pi^a + X $, assuming factorization and using the $ \vec{p}+p $ data as input.
• Perturbative time-ordered diagrams in the infinite momentum frame are used to compute meson-baryon splitting functions $ P(y)_{N\pi} $, $ \delta P_{N\pi}(y) $, and $ \sigma P_{N\pi}(y) $, which describe nucleon-to-nucleon+meson Fock state transitions.
• The transversity distribution $ h_1(x) $ is modified by including pion cloud contributions via the splitting functions, with the axial-vector pion-nucleon coupling used to compute the spin-dependent components.
• The ratio $ A_{OT}^+ / A_{OT}^- $ in semi-inclusive DIS is derived to cancel T-odd fragmentation function dependence, enabling direct access to $ h_1^u(x)/h_1^d(x) $.

Experimental results

Research questions

• RQ1 Can T-odd quark fragmentation functions be extracted from existing $ \vec{p}+p \to \pi + X $ data, and what do they imply for the transversity distribution?
• RQ2 How do meson cloud Fock components modify the transversity distribution $ h_1(x) $, particularly for $ d $-quarks?
• RQ3 What is the predicted magnitude of transverse single-spin asymmetries in semi-inclusive DIS off transversely polarized protons?
• RQ4 Can the ratio of $ \pi^+ $ and $ \pi^- $ asymmetries eliminate uncertainties from T-odd fragmentation functions?
• RQ5 To what extent does the pion cloud suppress the $ d $-quark tensor charge compared to its axial charge?

Key findings

• The T-odd quark fragmentation function $ H_1^{\perp} $ is generated via non-perturbative final-state interactions in the hadronization process, consistent with time-reversal odd phase differences.
• The $ d $-quark transversity distribution $ h_1^d(x) $ is suppressed by approximately 40% due to pion cloud effects, while the axial charge $ g_1^d(x) $ remains nearly unchanged.
• The splitting function relation $ P(y)_{N\pi} + \delta P_{N\pi}(y) = 2\sigma P_{N\pi}(y) $ leads to a strong suppression of $ h_1^d(x) $ compared to $ g_1^d(x) $, especially at small $ x $.
• The ratio $ A_{OT}^+ / A_{OT}^- $ in semi-inclusive DIS cancels the T-odd fragmentation function dependence, allowing direct extraction of $ h_1^u(x)/h_1^d(x) $ without fragmentation function uncertainties.
• The $ \pi^- $ single-spin asymmetry $ A_{OT}^{-} $ is significantly suppressed compared to $ A_{OT}^+ $, providing a clean experimental test of the meson cloud model.
• The model's prediction of a small $ h_1^u(x)/h_1^d(x) $ ratio at small $ x $, due to $ h_1^d(x) $ suppression, is consistent with lattice QCD results on the tensor charge.