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QCD corrections to the hadronic production of a heavy quark pair and a W-boson including decay correlations

Simon Badger, John M. Campbell, R. K. Ellis

TL;DR

<3-5 sentence high-level summary> Problem: NLO QCD corrections to hadronic production of a heavy-quark pair in association with a W, with finite heavy-quark mass and decay correlations. Approach: analytic one-loop amplitudes using spinor-helicity with massive quarks, four-dimensional unitarity, and a comprehensive color-primitive amplitude decomposition; results include divergent parts, scalar-integral coefficients, and rational terms, implemented in the MCFM framework. Contributions: explicit expressions for primitive amplitudes A_6^{lc}, A_6^{sl}, A_6^{lf}, and A_6^{hf}, plus renormalization and implementation details, validated by unitarity checks and cross-sections against prior work. Significance: provides mass-aware, precise predictions for W bb̄ production backgrounds at the LHC and a fast, stable tool for phenomenology and Higgs searches.

Abstract

We perform an analytic calculation of the one-loop amplitude for the W-boson mediated process 0 \to d u-bar Q Q-bar l-bar l, retaining the mass for the quark Q. The momentum of each of the massive quarks is expressed as the sum of two massless momenta and the corresponding heavy quark spinor is expressed as a sum of two massless spinors. Using a special choice for the heavy quark spinors we obtain analytic expressions for the one-loop amplitudes which are amenable to fast numerical evaluation. The full next-to-leading order (NLO) calculation of hadron+hadron \to W(\to e nu) b b-bar with massive b-quarks is included in the program MCFM. A comparison is performed with previous published work.

QCD corrections to the hadronic production of a heavy quark pair and a W-boson including decay correlations

TL;DR

<3-5 sentence high-level summary> Problem: NLO QCD corrections to hadronic production of a heavy-quark pair in association with a W, with finite heavy-quark mass and decay correlations. Approach: analytic one-loop amplitudes using spinor-helicity with massive quarks, four-dimensional unitarity, and a comprehensive color-primitive amplitude decomposition; results include divergent parts, scalar-integral coefficients, and rational terms, implemented in the MCFM framework. Contributions: explicit expressions for primitive amplitudes A_6^{lc}, A_6^{sl}, A_6^{lf}, and A_6^{hf}, plus renormalization and implementation details, validated by unitarity checks and cross-sections against prior work. Significance: provides mass-aware, precise predictions for W bb̄ production backgrounds at the LHC and a fast, stable tool for phenomenology and Higgs searches.

Abstract

We perform an analytic calculation of the one-loop amplitude for the W-boson mediated process 0 \to d u-bar Q Q-bar l-bar l, retaining the mass for the quark Q. The momentum of each of the massive quarks is expressed as the sum of two massless momenta and the corresponding heavy quark spinor is expressed as a sum of two massless spinors. Using a special choice for the heavy quark spinors we obtain analytic expressions for the one-loop amplitudes which are amenable to fast numerical evaluation. The full next-to-leading order (NLO) calculation of hadron+hadron \to W(\to e nu) b b-bar with massive b-quarks is included in the program MCFM. A comparison is performed with previous published work.

Paper Structure

This paper contains 34 sections, 134 equations, 17 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Treatment of massive spinors
  3. Special choice for massive spinors
  4. Setup
  5. Colour decomposition
  6. Tree level amplitudes
  7. Decomposition of one-loop amplitudes into primitive amplitudes
  8. Structure of the calculation
  9. The results for primitive amplitude $A^{\rm lc}_6$
  10. Divergent parts
  11. Calculation of the box coefficients
  12. Calculation of $d_{1|2|3}$
  13. Calculation of $d_{1|2|34}$
  14. Calculation of $d_{1|23|4}$
  15. Calculation of triangle coefficients
  16. ...and 19 more sections

Figures (17)

  • Figure 1: Example of a partonic process contributing to $W b \bar{b}$ production
  • Figure 2: Feynman graphs that enter the calculation of the lowest order amplitude. The massive quarks are represented by the heavy (red) line, the wavy line denotes a $W$ boson and as usual the helical line denotes a gluon.
  • Figure 3: Parent diagrams for the leading colour primitive $A^{\rm lc}_6(1,2,3,4)$ and crossed box primitive $A^{\rm cb}_6(1,2,3,4)$.
  • Figure 4: Parent diagrams for the subleading colour primitive amplitude, $A^\sl_6(1,2,3,4)$.
  • Figure 5: Diagrams for the fermion loop primitives $A^{\rm lf}_6(1,2,3,4)$ and $A^{\rm hf}_6(1,2,3,4)$.
  • ...and 12 more figures