Giampiero Passarino

NLO Electroweak Corrections to Higgs Boson Production at Hadron Colliders

Results for the complete NLO electroweak corrections to Standard Model Higgs production via gluon fusion are included in the total cross section for hadronic collisions. Artificially large threshold effects are avoided working in the complex-mass scheme. The numerical impact at LHC (Tevatron) energies is explored for Higgs mass values up to 500 GeV (200 GeV). Assuming a complete factorization of the electroweak corrections, one finds a +5% shift with respect to the NNLO QCD cross section for a Higgs mass of 120 GeV both at the LHC and the Tevatron. Adopting two different factorization schemes for the electroweak effects, an estimate of the corresponding total theoretical uncertainty is computed.

All-purpose numerical evaluation of one-loop multi-leg Feynman diagrams

Abstract A detailed investigation is presented of a set of algorithms which form the basis for a fast and reliable numerical integration of one-loop multi-leg (up to six) Feynman diagrams, with special attention to the behavior around (possibly) singular points in phase space. No particular restriction is imposed on kinematics, and complex masses (poles) are allowed.

NNLO Computational Techniques: the Cases H -> gamma gamma and H -> g g

A large set of techniques needed to compute decay rates at the two-loop level are derived and systematized. The main emphasis of the paper is on the two Standard Model decays H → γγ and H → gg. The techniques, however, have a much wider range of application: they give practical examples of general rules for two-loop renormalization; they introduce simple recipes for handling internal unstable particles in two-loop processes; they illustrate simple procedures for the extraction of collinear logarithms from the amplitude. The latter is particularly relevant to show cancellations, e.g. cancellation of collinear divergencies. Furthermore, the paper deals with the proper treatment of non-enhanced two-loop QCD and electroweak contributions to different physical (pseudo-)observables, showing how they can be transformed in a way that allows for a stable numerical integration. Numerical results for the two-loop percentage corrections to H → γγ, gg are presented and discussed. When applied to the process pp → gg +X → H +X , the results show that the electroweak scaling factor for the cross section is between −4% and +6% in the range 100 GeV < M H < 500 GeV, without incongruent large effects around the physical electroweak thresholds, thereby showing that only a complete implementation of the computational scheme keeps two-loop corrections under control.

Stable calculations for unstable particles: Restoring gauge invariance

We discuss theoretical and phenomenological aspects of the use of boson propagators with energy-dependent widths in predictions for high-energy scattering processes. In general, gauge invariance is violated in such calculations. We discuss several approaches to restore gauge invariance, necessary for a reliable result. The most promising method is the addition of the relevant parts of the fermionic corrections, which fulfills all Ward identities. The numerical difference between this and other approaches is studied. A number of recommendations are given for LEP2 computations.

A Proposal for a standard interface between Monte Carlo tools and one-loop programs

Many highly developed Monte Carlo tools for the evaluation of cross sections based on tree matrix elements exist and are used by experimental collaborations in high energy physics. As the evaluation of one-loop matrix elements has recently been undergoing enormous progress, the combination of one-loop matrix elements with existing Monte Carlo tools is on the horizon. This would lead to phenomenological predictions at the next-to-leading order level. This note summarises the discussion of the next-to-leading order multi-leg (NLM) working group on this issue which has been taking place during the workshop on Physics at TeV Colliders at Les Houches, France, in June 2009. The result is a proposal for a standard interface between Monte Carlo tools and one-loop matrix element programs. Dedicated to the memory of, and in tribute to, Thomas Binoth, who led the effort to develop this proposal for Les Houches 2009. Thomas led the discussions, set up the subgroups, collected the contributions, and wrote and edited this paper. He made a promise that the paper would be on the arXiv the first week of January, and we are faithfully fulfilling his promise. In his honour, we would like to call this the Binoth Les Houches Accord.

NNLO computational techniques: The cases H→γγ and H→gg

A large set of techniques needed to compute decay rates at the two-loop level are derived and systematized. The main emphasis of the paper is on the two Standard Model decays H → γγ and H → gg. The techniques, however, have a much wider range of application: they give practical examples of general rules for two-loop renormalization; they introduce simple recipes for handling internal unstable particles in two-loop processes; they illustrate simple procedures for the extraction of collinear logarithms from the amplitude. The latter is particularly relevant to show cancellations, e.g. cancellation of collinear divergencies. Furthermore, the paper deals with the proper treatment of non-enhanced two-loop QCD and electroweak contributions to different physical (pseudo-)observables, showing how they can be transformed in a way that allows for a stable numerical integration. Numerical results for the two-loop percentage corrections to H → γγ, gg are presented and discussed. When applied to the process pp → gg +X → H +X , the results show that the electroweak scaling factor for the cross section is between −4% and +6% in the range 100 GeV < M H < 500 GeV, without incongruent large effects around the physical electroweak thresholds, thereby showing that only a complete implementation of the computational scheme keeps two-loop corrections under control.

Two-loop renormalization in the Standard Model. Part I: Prolegomena ☆

In this paper the building blocks for the two-loop renormalization of the Standard Model are introduced with a comprehensive discussion of the special vertices induced in the Lagrangian by a particular diagonalization of the neutral sector and by two alternative treatments of the Higgs tadpoles. Dyson resummed propagators for the gauge bosons are derived, and two-loop Ward–Slavnov–Taylor identities are discussed. In part II, the complete set of counterterms needed for the two-loop renormalization will be derived. In part III, a renormalization scheme will be introduced, connecting the renormalized quantities to an input parameter set of (pseudo-)experimental data, critically discussing renormalization of a gauge theory with unstable particles.

The Fermion loop scheme for finite width effects in

Abstract We describe the gauge-invariant treatment of the finite-width effects of W and Z bosons in the fermion-loop scheme and its application to the six-fermion (LEP2) processes et-e+ → four fermions, with massless external fermions. The fermion-loop scheme consists in including all fertnionic one-loop corrections in tree-level amplitudes and resumming the self-energies. We give explicit results for the unrenormalized fermionic one-loop contributions to the gauge-boson self-energies and the triple gauge-boson vertices, and perform the renormalization in a gauge invariant way by introducing complex pole positions and running couplings. A simple effective Born prescription is presented, which allows for a relatively straightforward implementation of the fermion-loop scheme in LEP1 and LEP2 processes. We apply this prescription to typical LEP2 processes, i.e. e t- e + → μ t- ν μ u d , e t- e + → s c u d , and e t- e + → e t- ν e r d , and give numerical comparisons with other gauge-invariance-preserving schemes in the energy range of LEP2, NLC and beyond.

e^{+} e^{-}

Abstract The heavy Higgs searches at LHC are carried out in g g → H → W W → l ν l ν , g g → H → Z Z → l l l l , l l ν ν , l l q q channels. The current searches for a heavy Higgs boson assume on-shell (stable) Higgs-boson production. The Higgs-boson production cross-section is then sampled with a Breit–Wigner distribution (with fixed-width or running-width) and implemented in Monte Carlo simulations. Therefore the question remains of what is the limitation of the narrow Higgs-width approximation. The main focus of this work is on the description of the Standard Model Higgs-boson lineshape in the heavy Higgs region, typically M H above 600 GeV . The framework discussed in this paper is general enough and can be used for all processes and for all kinematical regions. Numerical results are shown for the gluon-fusion process. Issues of gauge invariance and residual theoretical uncertainties are also discussed. Limitations due to a breakdown of the perturbative expansion are comprehensively discussed, including a discussion of the equivalence theorem for (off-shell) virtual vector-bosons. Analytic continuation in a theory with unstable particles is thoroughly discussed.

annihilation into four fermions

The relation between physical observables measured at LHC and Tevatron and standard model Higgs pseudo-observables (production cross section and partial decay widths) is revised by extensively using the notion of the Higgs complex pole on the second Riemann sheet of the S-matrix. The extension of their definition to higher orders is considered, confronting the problems that arise when QED (QCD) corrections are included in computing realistic observables. Numerical results are presented for pseudo-observables related to the standard model Higgs boson decay and production. The relevance of the result for exclusion plots of the standard model Higgs boson for high masses (up to 600 GeV) is discussed. Furthermore, a recipe for the analytical continuation of Feynman loop integrals from real to complex internal masses and complex Mandelstam invariants is thoroughly discussed.