Collins-type fragmentation energy correlator in semi-inclusive deep inelastic lepton-hadron scattering

TL;DR

This work introduces fragmentation energy correlators (FECs) as boost-invariant, nonperturbative extensions of fragmentation functions that encode transverse fragmentation dynamics. It establishes a collinear factorization framework for SIDIS with energy-tagged observables, detailing RC and RH factorization regions and providing a systematic subtraction scheme for double counting. Focusing on Collins-type quark FECs, it derives the leading-twist azimuthal modulations and constructs the full set of hard coefficients, verifying consistency at next-to-leading order in the quark non-singlet channel. A boost-invariant reformulation using the Λ_F variable allows clean extraction of FECs in both large-p_{hT} and p_{hT}-integrated regimes, connecting to TMDFFs and enabling direct phenomenological studies of transverse fragmentation and chiral symmetry breaking with SIDIS data.

Abstract

We initiate a systematic study of fragmentation energy correlators (FECs), which generalize traditional fragmentation functions and encode non-perturbative information about transverse dynamics in parton fragmentation processes. We define boost-invariant, non-perturbative FECs and derive a corresponding collinear factorization formula. A spin decomposition of the FECs is carried out, analogous to that of transverse-momentum-dependent fragmentation functions. In this work we focus particularly on the Collins-type quark FEC, which is sensitive to chiral symmetry breaking and characterizes the azimuthal asymmetry in the fragmentation of a transversely polarized quark. We perform a next-to-leading-order calculation of the corresponding hard coefficient in semi-inclusive deep-inelastic scattering for the quark non-singlet component, thereby validating the consistency of our theoretical framework.

Figures (6)

• Figure 1: Breit frame for the energy-tagged SIDIS in Eq. \ref{['eq:sidis']}.
• Figure 2: Leading regions (a) $R_C$ and (b) $R_H$ of the energy-tagged SIDIS in Eq. \ref{['eq:two-stage']}. The cross vertex ($\otimes$) indicates the energy flow, which is in the same collinear subgraph $J_1$ as the measured hadron $h$ in $R_C$, but is in a separate collinear subgraph $J_2$ in $R_H$. We are using cut diagram notation here: to the left of the cut is the amplitude $\mathcal{M}^X$, and to the right is its complex conjugate. Lines crossed by the cut stand for the final-state particles; they are put on shell with phase space integrated out, except for the observed hadron $h$ and energy flow weighting factor.
• Figure 3: LO diagrams of the $q + \gamma^* \to q + g$ scattering amplitude.
• Figure 4: An illustration for the energy-tagged SIDIS with $\bm{p}_{hT}$ integrated. The kinematics shown here corresponds to the LO QCD process, where the recoiled quark moves along $-\hat{z}_B$ in the Breit frame.
• Figure 5: LO (a) and NLO (b)--(d) diagrams of the $q \to q$ scattering amplitude in Eq. \ref{['eq:hard-qq-X0']}. Inclusion of the counterterm diagrams (not shown) for (b)--(d) is understood.