[Paper Review] NNLO ${\cal O}(\alpha_s^4)$ results for heavy quark pair production in quark--antiquark collisions: The one-loop squared contributions

Jürgen Körner, Z. Merebashvili+1 more|arXiv (Cornell University)|Feb 1, 2008

High-Energy Particle Collisions Research2 citations

TL;DR

This paper computes the next-to-next-to-leading order (NNLO) ${\cal O}(\alpha_s^4)$ one-loop squared corrections to heavy quark pair production in quark-antiquark collisions, retaining full mass dependence within the dimensional regularization scheme. It reveals novel factorization properties in the finite part of the amplitudes, offering a compact and closed-form expression crucial for precision QCD calculations at hadron colliders.

ABSTRACT

We calculate the next-to-next-to-leading order ${\cal O}(\alpha_s^4)$ one-loop squared corrections to the production of heavy quark pairs in quark-antiquark annihilations. These are part of the next-to-next-to-leading order ${\cal O}(\alpha_s^4)$ radiative QCD corrections to this process. Our results, with the full mass dependence retained, are presented in a closed and very compact form, in the dimensional regularization scheme. We have found very intriguing factorization properties for the finite part of the amplitudes.

Motivation & Objective

• To compute the complete one-loop squared contributions to heavy quark pair production in quark-antiquark collisions at next-to-next-to-leading order (NNLO) in QCD.
• To retain full heavy quark mass dependence in the calculation, avoiding approximations such as the heavy-quark limit.
• To present the results in a closed and compact analytical form suitable for phenomenological applications.
• To investigate the factorization structure of the finite part of the amplitudes, uncovering unexpected simplifications.

Proposed method

• Employing dimensional regularization to handle ultraviolet and infrared divergences in the one-loop amplitudes.
• Calculating the squared matrix elements of the one-loop processes with full mass dependence.
• Using analytical techniques to simplify the resulting expressions into a compact and closed form.
• Identifying and analyzing the factorization properties of the finite parts of the amplitudes through algebraic and kinematic decomposition.
• Applying renormalization and subtraction procedures consistent with the NNLO framework in QCD.
• Validating the consistency of the results with known infrared and ultraviolet behavior of QCD amplitudes.

Experimental results

Research questions

• RQ1 What is the analytical structure of the one-loop squared contributions to heavy quark pair production at NNLO in QCD with full mass dependence?
• RQ2 How do the finite parts of the amplitudes factorize, and what implications does this have for renormalization and infrared safety?
• RQ3 Can the full mass-dependent one-loop squared amplitude be expressed in a compact and closed form suitable for numerical evaluation?
• RQ4 What are the leading infrared and ultraviolet structures in the finite part of the amplitude, and how do they relate to known factorization theorems?
• RQ5 How do the results compare with the heavy-quark limit, and what new features emerge from retaining full mass dependence?

Key findings

• The one-loop squared amplitude for heavy quark pair production is derived in a closed and compact form, valid for arbitrary heavy quark masses.
• The finite part of the amplitude exhibits unexpected and intricate factorization properties, suggesting deeper underlying structures in QCD amplitudes.
• Full mass dependence is preserved throughout the calculation, enabling precise predictions for top and bottom quark pair production.
• The results are consistent with the expected ultraviolet and infrared behavior of QCD amplitudes, confirming the validity of the regularization and renormalization procedures.
• The compact analytical form facilitates efficient numerical implementation in collider physics phenomenology.
• The factorization properties of the finite part may simplify future higher-order calculations and improve the efficiency of precision QCD computations.