Semi-Inclusive Deeply Inelastic Scattering at Small q_T

TL;DR

This work develops a comprehensive framework for semi-inclusive deep inelastic scattering at small transverse momentum ${q_T}$ by combining fixed-order perturbative results with Sudakov resummation in impact-parameter space. It derives the Sudakov form factor coefficients, constructs a matched expression that remains valid across the entire ${q_T}$ range, and models non-perturbative contributions via a $b_*$ prescription tied to Drell–Yan and $e^+e^-$ data. The approach yields finite, well-behaved energy-distribution predictions as ${q_T} o0$ and demonstrates sizable sensitivity to non-perturbative Sudakov effects in the small-${q_T}$ region, while maintaining consistency with known results in related processes. The framework provides a robust tool for interpreting HERA data and for exploring the interplay between perturbative and non-perturbative QCD in DIS energy flows.

Abstract

Measurement of the distribution of hadronic energy in the final state in deeply inelastic electron scattering at HERA can provide a good test of our understanding of perturbative QCD. For this purpose, we consider the energy distribution function, which can be computed without needing final state parton fragmentation functions. We compute this distribution function for finite transverse momentum q_T at order alpha_s, and use the results to sum the perturbation series to obtain a result valid for both large and small values of transverse momentum.

Figures (15)

• Figure 1: Feynman diagrams for quark initiated process with a quark jet observed. The observed parton is the upper line, indicated with a dot.
• Figure 2: Feynman diagrams for quark initiated process with a gluon jet observed. The observed parton is the lower line, indicated with a dot.
• Figure 3: Feynman diagrams for gluon initiated process with a quark jet observed. The observed parton is the upper line, indicated with a dot.
• Figure 4: The hadron frame. The initial hadron $P_A$ lies along the positive $z$-axis, and the vector boson $q$ lies along the negative $z$-axis. The next-to-leading order QCD corrections can give the final state hadron $P_B$ a non-zero $x$-component.
• Figure 5: The HERA lab frame for the process: $e^-(\ell) + A(P_A) \to e^-(\ell') + B(P_B) + X$. The final state leption $e^-(\ell')$ lies in the $x$-$z$--plane, and the final state hadron $B(P_B)$ has a non-zero $y$-component if $\phi_B$ is non-zero.