Precision calculations for collider physics
  1. Objectives


    The overarching objective of our research is to improve our understanding of the SM by enhancing our ability to perform accurate and precise predictions for key observables at present and future colliders. Our research activities can be broadly organised in 5 main directions to which several units contribute. More specifically we will work on

    • High-Precision Fixed Order SM : NNLO/MIXED EW-QCD/N3LO

      • the theoretical study of advanced techniques to perform N3LO QCD calculations at the differential level and analytic resummation at N3LL accuracy;

      • the development of new techniques to compute multi-loop multi-leg scattering amplitudes

    • Monte Carlo programs and Resummation: fixed-orders, POWHEG BOX, GENEVA, soft and collinear resummation

      • the implementation of (NLO and) NNLO QCD and mixed QCDxEW corrections in parton shower Monte Carlo generators;

      • the development of NNLO and resummation methods and of the corresponding specific calculations for SM processes with high-multiplicity final states that involve heavy quarks, heavy bosons and jets;

    • Precision for BSM and EFT

      • the implementation in Monte Carlo generators of several improvements such as: adding new interfaces to cutting-edge matrix element generators and including new SMEFT operators;

      • the improvement of the SMEFT computational framework, useful to parameterize the possible New Physics, also making available improved automatic computational tools and envisaging strategies to constrain operators, e.g. via global fits on observables;

      • Investigations to constrain EFTs via RG studies at perturbative and non perturba- tive level will be also considered.

    • High-energy QCD/small-x
  • the study of new QCD processes in the Regge limit and new formal development of this physics framework.


  •    Future Colliders/HEP experiments
  • novel phenomenological investigations of processes at future hadron and lepton colliders, including muon colliders; strategies for precise luminosity monitoring in future lepton colliders;
  • Activities on the newly proposed MUonE experiment, which will allow to independently estimate the hadronic contribution to the muon g-2.


Scientific activities of the various Research Units


Precision computations in the SM

Theoretical predictions will have to at least match the foreseen experimental precision. It is then needed to continuously improve the technology required to perform challenging calcula- tions and also to study their impact on the LHC physics. In particular, recently, our group has gained experience on two-loop computations with internal and/or external masses making sig- nificant contributions to the methods as well as to phenomenology. We plan to continue working on the development of the new methods (numerical and analytical) to compute multi-loop ampli- tudes and apply them to cutting edge precision studies at the LHC. In particular, we will also explore the possibility of making two-loop computations relevant for NLO loop-induced process- es in the context of the EFT.


The extension of the Standard Model to include higher-dimensional operators which respect the gauge and global symmetries (SMEFT) is an efficient way to parametrize in a general way New Physics which resides at scales beyond the reach of the current accelerators, in particular, the LHC. The SMEFT has been implemented at LO in FeynRules and is now available since some time and used in various contexts. Automatic NLO computations in QCD in the Mad- Graph5_aMC@NLO have been performed for various important channels at the LHC, covering Higgs, top and EW physics and their impact on phenomenology studies. We have demonstrated the capability of covering all NLO QCD corrections to arbitrary processes/operators, in particular those which entail four-fermion operators very recently and now validating the new complete release of the SMEFT@NLO model. At the same time, we have started performing global fits of the Wilson coefficients in the top-quark sector.

Our goal for the next three years is:

  • Identify through global fits the operators that are the least constrained and explore new ways to constrain them at the LHC with a global approach by considering new observables and strategies, at NLO QCD accuracy.
  • Extend the global fitting approach from the top-sector to include EW, Higgs and, possibly, flavour.
  • Improve our ability to make automatic predictions which are accurate also at NLO EW level at least for key specific observables, in particular for those ones whose leading contribu- tions arise at one loop.

A more theoretical research will be carried on to understand the constraints on the EFTs coming from UV complete scenarios, taking into account the RG flows (with different formulations both at perturbative and non perturbative level) in a theory space.

Future Colliders

We have participated in the European Strategy Update activities and dedicated effort into studying the reach of future colliders in particular regarding the determination of the Higgs cou- plings. We have also started the exploration of the physics that could take place at very high- energy lepton colliders, such a muon-collider in the multi-TeV energy range. We are now in- volved in the Snowmass process (the update of the US strategy) with particular interest in phe- nomenology at future colliders, including precision measurements and their interpretation in the context of SMEFT Higgs/top physics. We also plan to continue exploring, much more in detail, the reach of multi-TeV lepton colliders. In this context, we are also working in improving our MC tools in order to include initial state radiation effects and the integration of very energetic final states.

QCD in the high-energy limit

We shall continue the activity devoted to push the BFKL formalisms in the non perturbative domain using functional renormalization group techniques to constraint the related effective action in the Regge limit and large transverse distances in order to describe non linear rapidity evolution dynamics.Later we shall also include in our studies the so called Odderon exchange which might be rele- vant for the analysis which covers also the recent and future data from the TOTEM collabora- tion.


QCD in the high-energy limit

It is planned to continue the study of possible applications of the BFKL approach to phenomenology of hard and semi-hard processes:

  • study, with partial inclusion of NLA effects, of the inclusive production at the LHC of (a) a forward Higgs and a high transverse-momentum backward jet (or hadron) and (b) of two heavy mesons, separated by a large rapidity gap;

  • study in full NLA of the inclusive production of a single high transverse-momentum forward jet or charded-light hadron or heavy meson, with the aim of a better understanding of the unintegrated gluon distribution in the proton;

  • study of the above processes in kinematic regions where both BFKL and threshold resummations are applicable.

    Formal developments of the BFKL approach
    We plan also to perform the calculation of the Reggeon-Reggeon-Gluon vertex with the

    accuracy up to terms of order ε=D-4 (D-space-time dimension), which is necessary for the estimation of discontinuities of multiple production amplitudes in the multi-Regge kinematics (MRK). They are, in turn, needed to get the discontinuities of multiple production amplitudes in the MRK, which are necessary for development of the BFKL approach in the NNLLA.

  1. NNLO qt subtraction method and phenomenology at hadron colliders

    We shall extend the NNLO QCD formulation of the qt subtraction method to a large class of hadron collision processes for the production of heavy quarks, heavy bosons and jets. The NNLO formulation will also be extended to treat mixed QCDxEW radiative corrections. We plan detailed calculations and related phenomenological studies for bottom quark and top quark production, including their associated production with vector and Higgs bosons.


    Soft/collinear factorization in QCD

    We shall study the structure of infrared factorization of QCD scattering amplitudes in various soft and collinear limits. The study includes the explicit computation up to order $\alpha_s^3$ of loop radiative corrections to multiparton soft currents and collinear splitting kernels. These are basic ingredients for high-order QCD computations, and we plan to exploit them to develop methods for fixed-order (up to the N3LO level) and resummed (up to N3LL accuracy) calculations. Moreover, amplitude factorization will be used to define and compute inclusive collinear functions and effective soft couplings that are suitable for process-independent resummations of large classes of observables. These studies can also shed light on possible factorization breaking effects for multi-jet hard-scattering processes in hadron collisions.


    QCD in the high-energy regime

    Dijet production with a large rapidity gap (Mueller-Tang-Navelet jets) is a process that can be used to investigate BFKL dynamics in hadronic collisions at high energies. We shall compute this process at NLL accuracy by combining the corresponding impact factor with process- independent BFKL resummation and perform ensuing phenomenological studies and comparisons with dijet cross section measurements at LHC energies.

Milano Bicocca

  • We plan to extend existing calculation to include QCD correction at NNLO and NNLL accuracy or higher, not only in fixed-order calculation, but also in the shower Monte Carlo programs that some members of the Unit have developed in the past years: the POWHEG BOX and GENEVA framework.

  • We plan to interface our Monte Carlo codes to more recent and efficient generators of matrix elements at higher order of accuracy both in QCD and EW.

  • We plan to include EW corrections for more processes in the aforementioned shower Monte Carlo codes. Only for a few processes the accuracy at NLO in QCD+EW is available. A proper treatment of initial-state and final-state photons has to be implemented, in order to deal also with couplings to charged leptons, and fragmentation-function/isolation issues have to be faced, when interfacing these tools to shower Monte Carlo programs such as Pythia and Herwig.

  • Due to the complexity of the EW virtual contributions, the evaluation of such terms is very time consuming. For these reasons, using approximations of the EW virtual contributions would improve the speed of the codes. Re-weighting the results computed in the approximated way with the exact EW virtual corrections would give the correct results with less CPU time. There are general rules to build these approximation that need to be implemented and automatized in the shower Monte Carlo codes.

  • We plan to extend the calculation of higher-order power corrections in a transverse- momentum cut for colour-singlet production from NLO to NNLO and to complete a study of renormalon effects in several observables at hadronic colliders.

  • We plan to extend the inclusion of dimension-6 SM effective-field-theory (SMEFT) operators in Monte Carlo programs, including also the corresponding NLO QCD corrections, and to study the phenomenological impact of dimension-8 operators on specific processes at hadron colliders, with particular attention to blind spots in current experimental searches.


  1. The future activity will continue and broaden the research carried out in the latest years and will contribute to the following topics:

    • study of charged and neutral Drell-Yan processes at LHC and development of relevant Monte Carlo tools including EW and QCD corrections at NLO+parton shower (PS)

      accuracy. For instance, a newly proposed EW input scheme using (α (MZ ), MZ , sin θleff  ) or

      (GμM, sin θleff) can be used to directly measure sin θleff at HL-LHC in neutral Drell-Yan

      events through a template fit method. Phenomenological studies are planned to explore

      the potential of HL-LHC for the measurement sin θleff with high precision;

    • calculation of W()+jet and Z(l+l)+jet production at EW and QCD NLO accuracy, matched to parton shower. The calculation will be made available in the POWHEG BOX framework using the POWHEG+MiNLO approach;

    • Higgs boson decay into four charged leptons, including both EW corrections at NLOPS accuracy and BSM effects within a EFT approach. The developed code Hto4l can be interfaced to any Monte Carlo simulating Higgs boson production at hadron colliders. Extensions are planned to improve the theoretical precision of the Monte Carlo code;

    • proposal of the MUonE experiment, which is currently under review by the CERN SPSC committee. A test run has already been approved for 2021. The experiment aims at a precise measurement of the hadronic contribution to the running of the QED coupling constant in the space-like region, by scattering 150 GeV muons off electrons in a fixed target. This can be in turn used to estimate the hadronic contribution to the muon g2, in a completely independent and complementary way with respect to the standard approach based on dispersion relations and the optical theorem. In order to be competitive with current estimates, the muon-electron scattering cross section must be known with a challenging accuracy of 10ppm. On the theory side, this requires the inclusion of EW NLO, QED NNLO corrections and higher-order QED contributions, consistently implemented into a Monte Carlo generator for data analysis. In its completeness such simulation tool is not available yet but it is under development;

  • study of the process e+e− → γ γ at large angles at future e+e− colliders. The process has been identified as a promising monitor for precise luminosity determination at FCC-ee/ CEPC, as a channel complementary to the usual small-angle Bhabha scattering. In particular, theoretical uncertainties stemming from hadronic effects, a limiting factor for Bhabha scattering, enter the process only at NNLO. By including the relevant radiative corrections, a theoretical accuracy at the level of 10can be achieved, and any further improvement will require a careful assessment of missing higher-order effects and possibly their inclusion;

  • phenomenology of processes at a future multi-TeV muon collider, exploring the complementarity of this machine with respect to different future high-energy colliders. For instance, it was recently shown that a muon collider will have promising sensitivity to quartic Higgs self-coupling in triple Higgs production. The study will be further developed by considering different channels and background processes.



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