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Towards a fully massive five-flavour scheme

Frank Krauss, Davide Napoletano

TL;DR

This work develops a fully massive five-flavour scheme (5FMS) by extending the Catani–Seymour subtraction formalism to massive initial-state quarks, enabling NLO predictions with heavy-quark masses in the initial state while preserving the resummation properties of the massless five-flavour scheme. It derives phase-space mappings, dipole structures, and integrated subtraction terms for massive initial-state emissions, and implements MC@NLO matching within the SHERPA framework. The approach is validated through bottom-quark fusion production of a scalar A, comparing 5FMS with the traditional 5FS and against the DIRE parton shower; mass effects are found to be small in many regions but can be relevant near thresholds or in specific observables. The results demonstrate that 5FMS provides a practical, fully differential, mass-aware extension of VFNS suitable for LHC phenomenology and beyond.

Abstract

In this work we explore first necessary steps to contruct a fully massive version of a variable flavour number scheme. In particular we focus, as an example, on an extension of the five-flavour scheme, where instead of neglecting explicit initial state quark mass effects, we retain all massive dependence, while keeping the resummation properties of the massless five-flavour scheme. We name this scheme five-flavour-massive (5FMS) scheme. Apart from consistently modified parton distribution functions, we provide all the ingredients that are needed to implement this scheme at MC@NLO accuracy, in a Monte Carlo event generator. As proof of concept we implement this scheme in SHERPA, and perfom a comparison of the new scheme with traditional ones for the simple process of scalar particle production in bottom quark fusion.

Towards a fully massive five-flavour scheme

TL;DR

This work develops a fully massive five-flavour scheme (5FMS) by extending the Catani–Seymour subtraction formalism to massive initial-state quarks, enabling NLO predictions with heavy-quark masses in the initial state while preserving the resummation properties of the massless five-flavour scheme. It derives phase-space mappings, dipole structures, and integrated subtraction terms for massive initial-state emissions, and implements MC@NLO matching within the SHERPA framework. The approach is validated through bottom-quark fusion production of a scalar A, comparing 5FMS with the traditional 5FS and against the DIRE parton shower; mass effects are found to be small in many regions but can be relevant near thresholds or in specific observables. The results demonstrate that 5FMS provides a practical, fully differential, mass-aware extension of VFNS suitable for LHC phenomenology and beyond.

Abstract

In this work we explore first necessary steps to contruct a fully massive version of a variable flavour number scheme. In particular we focus, as an example, on an extension of the five-flavour scheme, where instead of neglecting explicit initial state quark mass effects, we retain all massive dependence, while keeping the resummation properties of the massless five-flavour scheme. We name this scheme five-flavour-massive (5FMS) scheme. Apart from consistently modified parton distribution functions, we provide all the ingredients that are needed to implement this scheme at MC@NLO accuracy, in a Monte Carlo event generator. As proof of concept we implement this scheme in SHERPA, and perfom a comparison of the new scheme with traditional ones for the simple process of scalar particle production in bottom quark fusion.

Paper Structure

This paper contains 15 sections, 56 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Catani--Seymour subtraction for massive initial states
  3. Nomenclature
  4. Massive II dipoles: initial state splitter with initial state spectator
  5. Phase space
  6. Dipole formulae for initial-final configurations
  7. MC@NLO matching
  8. Sudakov form factor
  9. Initial-Initial configurations
  10. Initial-Final configurations
  11. Physical kinematics
  12. Initial-Initial configurations
  13. Initial-Final configurations
  14. Results
  15. Conclusions

Figures (2)

  • Figure 1: The $p_\perp$ spectrum of the scalar boson $A$ for various combinations of $m_A$ and $\tan\beta$, in the 5FS and in the 5FMS, fixed-order predictions.
  • Figure 2: The $p_\perp$ spectrum of the scalar boson $A$ for various combinations of $m_A$ and $\tan\beta$. The 5FS and the 5FMS are computed at MC@NLO accuracy while the DIRE prediction is obtained matching a LO matrix element with the NLL shower Hoche:2017iemHoche:2017hno.