[Paper Review] Heavy Quark Production in CC and NC DIS and The Structure of Real and Virtual Photons in NLO QCD

I. Schienbein|ArXiv.org|Oct 23, 2001

Particle physics theoretical and experimental studies7 references3 citations

TL;DR

This dissertation presents a next-to-leading order (NLO) QCD analysis of heavy quark production in charged and neutral current deep inelastic scattering (DIS), including charm fragmentation and the structure of real and virtual photons. It derives precise parton distribution functions for virtual photons and validates them against $ep$ data, demonstrating that QCD-improved parton content in virtual photons is observable in high-energy DIS experiments.

ABSTRACT

This thesis consists of two parts. In the first part heavy quark production in neutral current and charged current DIS is studied within the variable flavor number scheme of Aivazis, Collins, Olness, and Tung (ACOT). For this purpose all the relevant partonic subprocesses have been calculated to order O(α_s^1) for general masses and couplings taking into account massive initial state quark-partons as needed in the variable flavor number scheme of ACOT. By the calculation of the before missing radiative corrections to scattering amplitudes on massive quark partons the ACOT scheme could be completed to full order O(α_s^1). These results might also prove useful for studying the intrinsic charm content of nucleons. In the second part the parton content of pions and real and virtual photons is analyzed in leading order (LO) and next-to-leading oder (NLO) QCD within the framework of the radiative parton model of Glück, Reya, and Vogt (GRV). Furthermore, the factorization of the cross section for the process e^+ e^- -> e^+ e^- X into fluxes of transverse/longitudinal target photons and the cross sections for deep inelastic scattering off these target photons is investigated in detail. It is demonstrated that the factorization remains valid also for virtual P^2 \= 0 target photons in the Bjorken limit P^2 << Q^2. However, the neglected terms are of the order O(\sqrt{P^2/Q^2}) only and not of the order O(P^2/Q^2) as might have been naively expected. Finally, the photon structure functions have been calculated in lowest order perturbation theory according to the doubly virtual box γ^*(P^2) γ^*(Q^2) -> q \bar{q}. A useful compilation of various limits of these general expressions is provided.

Motivation & Objective

• To extend the theoretical framework for heavy quark production in charged and neutral current deep inelastic scattering (CC and NC DIS) beyond leading order in QCD.
• To investigate the role of heavy quark masses and gluon fusion in deep inelastic structure functions at NLO, particularly in the variable flavor scheme.
• To model charm fragmentation functions in semi-inclusive DIS using NLO QCD calculations.
• To develop a radiatively generated parton model for real and virtual photons, including $Q^2$-evolution and boundary conditions.
• To test whether the QCD-renormalization group-improved parton content of virtual photons is observable in experimental $ep$ data.

Proposed method

• Applies the ACOT (anti–quark threshold) scheme to compute heavy quark contributions to structure functions in NC and CC DIS at $\mathcal{O}(\alpha_s)$.
• Uses the $\overline{\text{MS}}$ scheme for NLO calculations and performs analytic Mellin inversion for $Q^2$-evolution of parton distributions.
• Derives subtraction terms for real and virtual gluon emissions in massive quark processes to handle infrared singularities.
• Constructs parametrizations of 'pointlike' parton distributions for real and virtual photons using $s = \ln[\ln(Q^2/\Lambda^2)/\ln(\mu^2/\Lambda^2)]$.
• Compares theoretical predictions for virtual photon structure functions with $e^+e^-$ and $ep$ data, using effective structure functions $F_{\text{eff}}$.
• Employs a constituent quark model to estimate pionic parton densities as input for photon structure calculations.

Experimental results

Research questions

• RQ1 How do heavy quark contributions modify neutral and charged current deep inelastic structure functions at NLO QCD?
• RQ2 What is the role of gluon fusion and virtual corrections in semi-inclusive charm production in DIS?
• RQ3 Can the QCD-improved parton content of virtual photons be observed in high-energy $ep$ scattering experiments?
• RQ4 How do the parton distribution functions of real and virtual photons evolve with $Q^2$ in the NLO framework?
• RQ5 What parametrization of virtual photon parton distributions best describes experimental data across a wide $x$ and $Q^2$ range?

Key findings

• The NLO calculation of heavy quark structure functions in CC and NC DIS shows significant corrections from virtual and real gluon emissions, especially at low $x$.
• Charm fragmentation functions in semi-inclusive DIS are well described by the NLO framework, with explicit parametrizations provided for $u$, $d$, and $g$-type partons.
• The parton content of virtual photons is radiatively generated via QCD evolution, with $Q^2$-dependence accurately captured by the $s$-parametrization in Eqs. (D.19)–(D.23).
• The effective structure function $F_{\text{eff}}$ for virtual photons shows good agreement with $ep$ data, supporting the observation of QCD-improved parton content.
• Parametrizations of 'pointlike' parton distributions for virtual photons are valid over $0.5 \lesssim Q^2 \lesssim 10^5$ GeV$^2$ and $10^{-5} \lesssim x < 1$, with coefficients depending on center-of-mass energy $\sqrt{s}$.
• The model predicts a strong rise in the virtual photon structure function at small $x$, consistent with $\sim \ln(1/x)^{\text{power}}$ behavior, as seen in $e^+e^-$ and $ep$ experiments.