[Paper Review] Weak Corrections to Hadronic Observables

Y. Kurihara, Stefano Moretti+2 more|ArXiv.org|Jul 13, 2004

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper computes one-loop weak corrections to hadronic processes at high-energy colliders, focusing on three-jet production, $Z/\gamma$+jet, and $b$-quark pair production. Using helicity amplitudes and gauge-invariant loop calculations, it finds that weak corrections—particularly $\alpha_s^2\alpha_{\text{EW}}$ contributions—can induce parity-violating asymmetries comparable in magnitude to leading-order QCD effects, with significant enhancements at LHC energies due to Sudakov logarithms.

ABSTRACT

We illustrate one-loop weak corrections to three-jet production in $e^+e^-$ at $\sqrt{s}=M_Z$, to the production of a $Z$ or $γ$ in association with a hard jet at hadron colliders and to the production cross section of two $b$-jets at Tevatron and Large Hadron Collider (LHC).

Motivation & Objective

• To assess the quantitative impact of one-loop weak corrections on key hadronic observables at $e^+e^-$, $p\bar{p}$, and $pp$ colliders.
• To isolate genuinely weak, gauge-invariant contributions from electromagnetic effects in processes involving $Z$, $\gamma$, and $W$ bosons.
• To evaluate the role of Sudakov logarithms $\alpha_W \log^2(\sqrt{\hat{s}}/M_W^2)$ in enhancing weak corrections at high-energy scales.
• To study parity-violating asymmetries, such as the forward-backward $b$-quark asymmetry, as probes of new physics beyond the Standard Model.
• To compare the relative importance of $gg$- and $q\bar{q}$-initiated one-loop weak corrections at Tevatron and LHC energies.

Proposed method

• Calculates helicity amplitudes $\mathcal{A}^{(G)}_{\lambda_1,\lambda_2,\sigma}$ for $V + q \to g + q$ processes, preserving fermion helicity via Dirac structures with odd numbers of $\gamma$-matrices.
• Uses the Chisholm identity in four-dimensional regularization to handle spinor structures in loop amplitudes.
• Evaluates virtual weak corrections via one-loop self-energy and vertex diagrams, including $W$ and $Z$ exchange with longitudinal polarization components.
• Applies $\overline{\text{MS}}$-regularized QCD and QED loops with full dependence on the Higgs mass ($M_H = 115$ GeV) in self-energy corrections.
• Computes cross sections and asymmetries using NLO PDFs (GRV94) and two-loop $\alpha_s$ running for $\alpha_s^3$ terms.
• Compares contributions from $\alpha_{\text{EW}}^2$, $\alpha_s^2\alpha_{\text{EW}}$, and $\alpha_s^3$ subprocesses in inclusive and differential distributions.

Experimental results

Research questions

• RQ1 How significant are one-loop weak corrections—especially $\alpha_s^2\alpha_{\text{EW}}$ terms—to $b$-quark pair production at Tevatron and LHC?
• RQ2 To what extent do Sudakov logarithms $\alpha_W \log^2(\sqrt{\hat{s}}/M_W^2)$ enhance weak corrections in high-energy hadronic processes?
• RQ3 How do weak corrections affect the forward-backward $b$-quark asymmetry, and can they be distinguished from tree-level weak or QCD effects?
• RQ4 Why are $gg$-initiated weak corrections more dominant at the LHC than at the Tevatron, and how do they compare to $q\bar{q}$-initiated ones?
• RQ5 Can weak corrections induce parity-violating effects large enough to be measurable and useful for testing new physics beyond the Standard Model?

Key findings

• One-loop weak corrections of order $\alpha_s^2\alpha_{\text{EW}}$ contribute approximately -2% to the leading $\alpha_s^2$ cross section at high transverse momentum in $b\bar{b}$ production at the LHC.
• The $\alpha_s^2\alpha_{\text{EW}}$ corrections to the $b$-quark forward-backward asymmetry are comparable in magnitude to $\alpha_s^3$ corrections and are of opposite sign to the tree-level weak contribution over most of the $p_T$ spectrum.
• At the LHC, $gg$-initiated $\alpha_s^2\alpha_{\text{EW}}$ corrections dominate over $q\bar{q}$-initiated ones, unlike at Tevatron where both are comparable.
• Sudakov logarithms enhance weak corrections more effectively at LHC energies than at Tevatron, due to the larger ratio $\sqrt{\hat{s}}/M_W^2$.
• The forward-backward asymmetry is of order -4% at the $Z$ resonance and fractions of a percent elsewhere, making it measurable at Run 2 and beyond.
• Weak corrections induce parity-violating effects that are not only large but also opposite in sign to tree-level weak contributions, offering a sensitive probe for new physics such as right-handed currents or contact interactions.