A mechanism for the T-odd pion fragmentation function

TL;DR

The paper addresses how to access nucleon transversity h1 by generating a leading-twist T-odd Collins fragmentation function H_1^⊥ through gauge-link-induced rescattering. Using a one-gluon exchange mechanism within a spectator model, it derives H_1^⊥(z,k_⊥), calibrates it against D_1, and predicts measurable SIDIS azimuthal asymmetries: a sin(φ+φ_S) single-spin asymmetry of ~10–15% for π^+ and a few-percent cos(2φ) asymmetry under HERMES kinematics. The results support using T-odd fragmentation functions to probe transversity and highlight the role of initial/final state interactions in generating leading-twist effects. The approach aligns with prior Sivers and h1^⊥ work and reinforces gauge-link phases as a robust mechanism for spin-dependent phenomena in hard processes.

Abstract

We consider a simple rescattering mechanism to calculate a leading twist $T$-odd pion fragmentation function, a favored candidate for filtering the transversity properties of the nucleon. We evaluate the single spin azimuthal asymmetry for a transversely polarized target in semi-inclusive deep inelastic scattering (for HERMES kinematics). Additionally, we calculate the double $T$-odd $\cos2φ$ asymmetry in this framework.

Figures (5)

• Figure 1: Figure depicts $h_1^\perp\star H_1^\perp$$\cos 2\phi$ asymmetry. The momenta flow to the quark-pion vertex is shown. The momentum $q$ is the loop integration variable. The $T$-odd distribution and fragmentation functions in this approach are obtained from cutting the spectators.
• Figure 2: The weighted analyzing power $H_1^{\perp (1)}(z)/D_1(z)$ as a function of $z$.
• Figure 3: The kinematics of semi-inclusive DIS: $k_1$ ($k_2$) is the 4-momentum of the incoming (outgoing) charged lepton, where $q=k_1-k_2$, is the 4-momentum of the virtual photon. $P$ ($P_h$) is the momentum of the target (observed) hadron. The scaling variables are $x=Q^2/2P\cdot q$ , $y=P\cdot q/P\cdot k_1$ , and $z=P\cdot P_h/P\cdot q$. The momentum $k_{1T}$ ($P_{h\perp}$) is the incoming lepton (observed hadron) momentum component perpendicular to the virtual photon momentum direction. $\phi_s$ and $\phi$ are the azimuthal angles, of the target spin projection $S_{\mathbf T}$ and $P_{h\perp}$ respectively.
• Figure 4: Upper Panel: The ${\langle \frac{P_{h\perp}}{M_h} \sin(\phi+\phi_s) \rangle}_{ UT}$ asymmetry for $\pi^+$ production as a function of $x$ . Lower Panel: The ${\langle \frac{P_{h\perp}}{M_h} \sin(\phi+\phi_s) \rangle } _{ UT}$ asymmetry for $\pi^+$ production as a function of $z$.
• Figure 5: Upper Panel: The ${\langle \frac{P^2_{h\perp}}{MM_h} \cos2 \phi \rangle}_{ UU}$ asymmetry for $\pi^+$ production as a function of $x$. Lower Panel: The ${\langle \frac{P^2_{h\perp}}{MM_h} \cos2\phi \rangle}_{ UU}$ asymmetry for $\pi^+$ production as a function of $z$.