NNLO QCD corrections to hadron production in DIS at finite transverse momentum

Abstract

We present the first complete calculation of hadron production in deep-inelastic scattering (DIS) at finite transverse momentum to next-to-next-to-leading order (NNLO) in perturbative QCD. To overcome the long-standing challenge of infrared divergences in semi-inclusive processes with identified final state hadrons at finite transverse momentum, we implement the recently developed $q_T$-subtraction framework based on the recoil-free jet definition. By utilizing the winner-take-all recombination scheme, we achieve a consistent factorization for hadron-jet associated production, enabling the inclusion of $\mathcal{O}(α_s^3)$ corrections. Our results demonstrate a significantly improved stabilization of the perturbative expansion and a reduction in scale uncertainties compared to previous next-to-leading order predictions. We find that the NNLO corrections are essential for a robust description of high precision multiplicity data from the ZEUS collaborations. This work provides a high precision theoretical foundation for the upcoming Electron-Ion Collider era and establishes a new benchmark for the exploration of the nucleon's three-dimensional structure.

Figures (5)

• Figure 1: Schematic definition of the kinematic variables used for the $q_T$-subtraction method in the Breit frame. The incoming virtual photon $\gamma^*$ scatters off the proton, producing an identified hadron and a leading recoiling jet ${\cal J}_k$. The blue lines along the proton direction denote beam collinear radiation. The green curved lines indicate the soft radiation. The slicing variable is defined by the azimuthal decorrelation $\delta\phi$ (or equivalently the out-of-plane momentum $p_{\rm out}$ of the hadron with respect to the beam-jet plane). The limit $\delta\phi \to 0$ corresponds to the unresolved back-to-back configuration governed by the factorization formula in Eq. (\ref{['eq:fact_phi_jet']}).
• Figure 2: Numerical stability of the total cross section with respect to the slicing parameter $\delta\phi^{\rm cut}$. The panels display the $\mathcal{O}(\alpha_s^2)$ (red) and $\mathcal{O}(\alpha_s^3)$ (blue) contributions for six representative partonic channels. Error bars indicate Monte Carlo statistical uncertainties. The solid cyan lines represent the fit to the asymptotic limit $\delta\phi^{\rm cut} \to 0$. The dashed purple lines denote the reference values of $\mathcal{O}(\alpha_s^2)$.
• Figure 3: Differential cross section as functions of the hadron momentum fraction $z$ for charged pion production at the EIC at various orders in QCD together with scale variations. Kinematic cuts, including a lower limit of 2 GeV on the hadron transverse momentum, are applied.
• Figure 4: Differential cross section as functions of the hadron transverse momentum $P_{hT}$ for charged pion production at the EIC at various orders in QCD together with scale variations.
• Figure 5: Multiplicity distribution as functions of the hadron transverse momentum $P_{hT}$ for unidentified charged hadron production at the HERA at various orders in QCD together with scale variations, compared to the ZEUS data ZEUS:1995acw.