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VBFNLO: A parton level Monte Carlo for processes with electroweak bosons

K. Arnold, M. Bahr, G. Bozzi, F. Campanario, C. Englert, T. Figy, N. Greiner, C. Hackstein, V. Hankele, B. Jager, G. Klamke, M. Kubocz, C. Oleari, S. Platzer, S. Prestel, M. Worek, D. Zeppenfeld

arXiv:0811.4559v2hep-ph

TL;DR

Accurate predictions for vector-boson processes with realistic cuts require assessing QCD corrections. VBFNLO provides a flexible parton-level Monte Carlo at NLO QCD, with validation showing agreement against independent calculations.

  • Problem

    Realistic decay-product and jet cuts raise questions about scale dependence and the NLO-to-LO cross-section ratio.

  • Method

    VBFNLO implements one-loop QCD corrections for vector-boson fusion and double- and triple-vector-boson production at NLO accuracy.

  • Results

    Independent checks find complete or good agreement for total cross sections and CP-even and CP-odd Higgs production results.

  • Takeaways & Limitations

    VBFNLO supplies a flexible parton-level Monte Carlo for simulating these vector-boson production processes at NLO QCD accuracy.

Abstract

from arXiv · show

VBFNLO is a fully flexible parton level Monte Carlo program for the simulation of vector boson fusion, double and triple vector boson production in hadronic collisions at next-to-leading order in the strong coupling constant. VBFNLO includes Higgs and vector boson decays with full spin correlations and all off-shell effects. In addition, VBFNLO implements CP-even and CP-odd Higgs boson via gluon fusion, associated with two jets, at the leading-order one-loop level with the full top- and bottom-quark mass dependence in a generic two-Higgs-doublet model. A variety of effects arising from beyond the Standard Model physics are implemented for selected processes. This includes anomalous couplings of Higgs and vector bosons and a Warped Higgsless extra dimension model. The program offers the possibility to generate Les Houches Accord event files for all processes available at leading order.

G. Klämk e1

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VBFNLO is a flexible parton-level Monte Carlo for electroweak-boson processes in hadronic collisions, including next-to-leading-order strong-coupling effects and detailed Higgs/vector-boson decays. It also supports loop-level Higgs-plus-two-jet production, selected beyond-Standard-Model effects, and Les Houches Accord event generation.

  • Core simulation capabilities: VBFNLO simulates vector boson fusion and double and triple vector boson production in hadronic collisions at next-to-leading order in the strong coupling constant.It is described as a fully flexible parton-level Monte Carlo program.
  • Core simulation capabilities: Higgs and vector boson decays are included with full spin correlations and all off-shell effects.
  • Higgs production: CP-even and CP-odd Higgs production via gluon fusion with two jets is implemented at leading-order one-loop level with full top- and bottom-quark mass dependence.The implementation is formulated in a generic two-Higgs-doublet model.
  • Beyond the Standard Model: Selected beyond-the-Standard-Model effects include anomalous Higgs and vector-boson couplings and a Warped Higgsless extra dimension model.
  • Event generation: The program can generate Les Houches Accord event files for all processes available at leading order.

Program summary · Pr o gr am Title: Vbfnlo

VBFNLO addresses scale dependence and parton-distribution uncertainties by implementing one-loop QCD corrections in a flexible NLO parton-level Monte Carlo. It supports arbitrary cuts, scale choices, and parton distribution function sets through LHAPDF.

  • Pr o gr am Title: Vbfnlo: The program can be obtained from the specified VBFNLO website and optionally uses the Les Houches Accord PDF Interface library and GNU Scientific library.These are listed as distribution and external-library information for the program.
  • Pr o gr am Title: Vbfnlo: The program is written in Fortran with parts in C++ and is distributed as a tar gzip file.Its stated operating system is Linux, with expected portability to other systems.
  • Pr o gr am Title: Vbfnlo: VBFNLO is characterized as an NLO Monte Carlo program providing one-loop QCD corrections for electroweak bosons in hadronic processes.The keyword description identifies its focus on NLO calculations, QCD corrections, electroweak bosons, and hadronic physics.
  • Pr o gr am Title: Vbfnlo: VBFNLO targets the large scale dependence of leading-order calculations and cross-section uncertainties from parton distribution functions.These uncertainties motivate including NLO corrections, particularly when stringent cuts are imposed on decay products or identified jets.
  • Pr o gr am Title: Vbfnlo: One-loop QCD corrections are implemented in a fully flexible NLO parton-level Monte Carlo program.The approach is designed to address the limitations of leading-order predictions in relevant search regions.
  • Pr o gr am Title: Vbfnlo: Users can specify arbitrary cuts and choose among various scales within the Monte Carlo framework.This flexibility allows analyses to match the selection requirements and scale choices of the process under study.
  • Pr o gr am Title: Vbfnlo: Any currently available parton distribution function set can be used through the LHAPDF library.This supports evaluating predictions with different parton-distribution inputs.

1 In tro du tion

Accurate NLO QCD predictions and parton-level Monte Carlo simulation are needed for hadron-collider processes with vector bosons. VBFNLO provides flexible NLO calculations for vector-boson fusion and multi-boson production, plus selected extensions and event-file generation.

  • Motivation: Hadron-collider physics requires accurate signal and background cross sections, precise hard-QCD descriptions, and simulations of measurable hadronic final states.The introduction motivates NLO QCD calculations in parton-level Monte Carlo generators as an efficient solution for complex final states with jets or identified particles.
  • VBFNLO capabilities: VBFNLO is a fully flexible parton-level Monte Carlo program for vector-boson fusion, double-vector-boson, and triple-vector-boson production at NLO QCD accuracy.Real-emission contributions included in NLO cross sections also allow corresponding processes with one additional jet at leading order.
  • Beyond-standard-model processes: Higgs-boson production through gluon fusion with two additional jets is implemented at leading order with full top- and bottom-quark mass dependence in a generic two-Higgs-doublet model.The program also implements anomalous Higgs and vector-boson couplings and a Warped Higgsless extra-dimension model.
  • Event generation: For processes implemented at leading order, VBFNLO can generate event files in the Les Houches Accord format.The introduction identifies Les Houches event-file generation as an available program capability.

2 Pro esses · 3 Installing VBFNLO

VBFNLO models electroweak-boson-fusion, multiboson, and gluon-fusion Higgs processes with NLO QCD accuracy where specified, retaining relevant off-shell and spin-correlation effects. It is distributed with a configurable GNU build and standard installation layout supporting selectable processes, external libraries, and runtime input files.

  • 2 Pro esses: VBFNLO disregards s-channel electroweak exchange, kinematically suppressed fermion interference, and numerically small Pauli-interference effects for identical charged leptons.The implementation considers weak-boson decays and obtains leptonic results through appropriate combinatorial factors.
  • 2.1 VBF Higgs pro duction in asso ciation with t w o jets: VBF Higgs-plus-two- and three-jet production, vector-boson-plus-two-jet production, and two-vector-boson-plus-two-jet channels are implemented at NLO QCD accuracy.Higgs decays use the narrow-width approximation where stated, while relevant calculations retain full off-shell effects, finite widths, and lepton spin correlations.
  • 2.4 VBF pro duction of t w o v e tor b osons and t w o jets: Double- and triple-vector-boson production processes are implemented to NLO QCD accuracy with full off-shell effects and final-state lepton spin correlations.The listed four- and six-lepton final states include the relevant resonant and decay contributions.
  • 2.6 Higgs pro duction in gluon fusion with t w o jets: CP-even and CP-odd Higgs production through gluon fusion with two additional jets is simulated at leading order in the strong coupling with full top- and bottom-quark mass dependence.The calculation uses a generic two-Higgs-doublet model and begins at one-loop level.
  • 3 Installing VBFNLO / 3.1 Prerequisites: The source distribution provides a GNU-conforming build system; basic installation requires GNU make, a Fortran77 compiler, and a C++ compiler, with optional LHAPDF and GSL support.Kaluza–Klein resonance simulation requires the GNU Scientific Library, while LHAPDF can replace built-in PDF sets.
  • 3.2 Build and installation: The configure script selects the installation path, compiled processes, NLO QCD availability, Kaluza–Klein simulation, LHAPDF, and GSL before make and make install build and install VBFNLO.Available process groups include vbf, diboson, triboson, hjjj, and ggf; tested compilers include g77 and gfortran.
  • 3.3 Sp e ial notes for Ma OS X / 3.4 Sour e and installation dire tory la y out: The installation uses a standard Unix layout containing executables in bin/, headers in include/VBFNLO/, libraries in lib/VBFNLO/, and input files plus PDF tables in share/VBFNLO/.On Mac OS X, static libraries must be disabled for linking, and DYLD_LIBRARY_PATH must point to the installation library directory.
  • 3.5 Running the program / 3.6 Bug rep orts / 3.7 Li ense: Runtime executables read input files from the working directory or an explicit input=path, while users should copy default inputs before customizing settings; VBFNLO is distributed under GPL version 2.Bug reports should include configure options and compiler and external-library versions.

4 Input les and parameters · 3. The parameterization of the anomalous ouplings in terms of o e ien ts fi/Λ2

VBFNLO is configured through dedicated input files for general settings, process-specific parameters, kinematic cuts, anomalous couplings, event output, PDFs, and histograms. Its anomalous-coupling framework covers HVV and gauge-boson interactions, with parameterizations selectable through input controls.

  • 4 Input les and parameters: VBFNLO is steered through input files defining general run parameters, ggflo settings, kinematic cuts, anomalous Higgs couplings, anomalous triple gauge-boson couplings, and random seeds.The listed files are vbfnlo.dat, ggflo.dat, cuts.dat, anom_HVV.dat, anom_WW.dat, and random.dat.
  • 4.1 vbfnlo.dat − general parameters: The NLO_SWITCH option enables cross sections and histograms to be calculated to NLO QCD accuracy when set to .true..Its default setting is described as false.
  • 4.3 vbfnlo.dat − parameters for ev en t output: VBFNLO generates parton-level events in the Les Houches Accord format for processes available at leading order.LHA_SWITCH controls event-file output, while UNWEIGHTING_SWITCH selects unweighted or weighted events.
  • 4.5 vbfnlo.dat − parameters for histograms: Histogram output can be enabled in ROOT, Topdrawer, and Gnuplot formats, with GNU enabled by default and ROOT and TOP disabled by default.ROOTFILE and TOPFILE default to histograms.
  • 4.7 P arameters for anomalous ouplings: VBFNLO supports anomalous HVV couplings with V = W, Z, γ in production and Higgs decay for VBF process IDs 100–107.These parameters are specified in anom_HVV.dat.
  • 4.7 P arameters for anomalous ouplings: Triple and quartic anomalous gauge-boson couplings are included for pp → W+W−jj(j) and can be set in anom_WW.dat.The passage identifies these as VBF-process couplings.
  • 4.7 P arameters for anomalous ouplings: Users can choose among three anomalous-coupling parameterizations, including an effective-Lagrangian formulation with CP-even and CP-odd dimension-six operators.The supplied passage also identifies an L3 Collaboration parameterization and a coefficient-based parameterization section.

, OBB · , ODW

The section documents anomalous Higgs–vector-boson coupling parameters, including CP-even and CP-odd operator coefficients, selectable HVV structures, and optional momentum-dependent form factors. It also specifies parameters for rescaling Standard Model HVV couplings and setting the characteristic new-physics scale.

  • , OBB: CP-even operator coefficients FWW_EVEN, FBB_EVEN, FW_EVEN, and FB_EVEN default to 0.
  • , OBB: CP-odd operator coefficients FWW_ODD, FBB_ODD, and FB_ODD default to 0.
  • , OBB: HVV2 selects anomalous couplings: 0 gives HZγ, 1 Hγγ, 2 HZZ, 3 HWW, and 4 enables all possible anomalous couplings.The default value is 4.
  • , OBB: FORMFACTOR switches on the momentum-dependent HVV form-factor parameterization and defaults to .false..Two different form factors can be chosen; they model effective momentum-dependent HVV vertices motivated by new physics at loop level.
  • , OBB: MASS_SCALE specifies the characteristic new-physics mass scale Λ in GeV and defaults to 200 GeV.
  • , OBB: FFAC selects one particular form factor from Eqs. (3), and that choice is also the default value.
  • , OBB: TREEFAC rescales the Standard Model HVV tensor, while LOOPFAC rescales HZγ and Hγγ vertices induced by Standard Model loops; both default to 1.
  • , OBB: The anom_WW.dat file sets anomalous triple and quartic gauge-boson couplings.

, OBB

VBFNLO calculates weak-boson-fusion VV+2-jet processes in the Warped Higgsless scenario at LO and NLO QCD. Its implementation generates model parameters from input settings and documents masses, couplings, and widths for reuse with user-defined parameters.

  • Warped Higgsless scenario: VBFNLO calculates weak-boson-fusion VV+2-jet processes in the Warped Higgsless scenario at LO and NLO QCD.The model parameters can be generated through the input file le kk_input.dat.
  • Warped Higgsless scenario: The default UV-brane choice yields Kaluza-Klein excitations with masses mW2 = 700 GeV, mZ2 = 695 GeV, and mZ′1 = 718 GeV.Smaller values of R produce a heavier Kaluza-Klein spectrum.
  • Warped Higgsless scenario: VBFNLO writes le kk_oupl_inp.dat with calculated Kaluza-Klein gauge-boson masses, couplings, and widths for the specified input parameters.Advanced users can reuse this file with their own parameter set by selecting .false. in le kk_input.dat.
  • Warped Higgsless scenario: With user-supplied parameters, VBFNLO calculates gauge-boson widths from decays to lower-lying states and records widths and coupling sum rules in to kk_ he k.dat.This workflow is enabled by selecting .false. in le kk_input.dat.

5 Che ks

VBFNLO underwent extensive validation against automated generators, event-generator interfaces, and published calculations. The checks found complete or good agreement across implemented processes, including vector-boson fusion, triboson, and CP-even/odd Higgs production.

  • Automated-generator checks: Complete agreement was found between VBFNLO Born and real-emission amplitudes and MadGraph’s automatically generated results for each case.Total LO cross sections with minimal cuts also agreed with MadEvent results.
  • Event-file checks: All LO Les Houches Accord event files were tested with Herwig++, a general-purpose Monte Carlo event generator for hard lepton-lepton and hadron-hadron collisions.
  • Published-result checks: Good agreement was found for dominant t- and u-channel contributions in VBFNLO’s comparison with published Higgs vector-boson-fusion results and VV2H.The comparison cross-checked VBFNLO with Refs. [44, 45] and VV2H.
  • Published-result checks: Good agreement was also found for triboson production and for CP-odd and CP-even Higgs production via gluon fusion against published results.The triboson comparison used on-shell gauge bosons without leptonic decays.

6 Summary & Outlo ok · A kno wledgmen ts

VBFNLO provides flexible parton-level simulations of vector-boson and Higgs production, including NLO QCD processes and selected beyond-Standard-Model effects. Future development targets additional NLO processes, new model features, MSSM Higgs simulations, and parton-shower matching, while the work received support from multiple funding programs.

  • 6 Summary & Outlo ok: VBFNLO simulates vector-boson fusion, double-vector-boson, and triple-vector-boson production processes at NLO QCD accuracy.The program is described as a fully flexible parton-level Monte Carlo.
  • 6 Summary & Outlo ok: CP-even and CP-odd Higgs production through gluon fusion with two additional jets is implemented at leading order, whose first contribution is one-loop level.
  • 6 Summary & Outlo ok: Further NLO QCD processes are planned, including pp → WWγ and pp → Wγj.
  • 6 Summary & Outlo ok: Planned additions include anomalous triple and quartic gauge-boson couplings and Kaluza-Klein excitations.
  • 6 Summary & Outlo ok: Gluon-fusion Higgs production in the generic two-Higgs-doublet model is planned for extension to a complete MSSM simulation.The existing implementation depends on scalar top- and bottom-quark masses.
  • 6 Summary & Outlo ok: Matching the NLO QCD processes to a parton shower at next-to-leading-logarithmic accuracy is in progress.

Referen es

The references cover prior studies of Higgs-plus-jet production, vector-boson-fusion corrections, anomalous couplings, and warped Higgsless models. They also cite computational tools, parton distributions, event formats, and related higher-order calculations.

  • Higgs-plus-jet production: Prior work addresses Higgs-plus-two-jet production through gluon fusion and its use as a signal at the CERN LHC.The cited studies include H + 2 jets via gluon fusion and Higgs plus two jet production via gluon fusion as a signal.
  • Beyond the Standard Model: The bibliography includes studies of anomalous Higgs couplings, effective Lagrangians, strongly interacting vector-boson systems, and warped Higgsless models.These references cover anomalous couplings in Higgs-sector and vector-boson-fusion studies, effective interactions, and vector-boson fusion in warped Higgsless models.
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