40 research outputs found
Next-to-leading-order QCD Corrections to Higgs Production in association with a Jet
We compute the next-to-leading-order (NLO) QCD corrections to the Higgs pT
distribution in Higgs production in association with a jet via gluon fusion at
the LHC, with exact dependence on the mass of the quark circulating in the
heavy-quark loops. The NLO corrections are presented including the top-quark
mass, and for the first time, the bottom-quark mass as well. Further, besides
the on-shell mass scheme, we consider for the first time a running mass
renormalisation scheme. The computation is based on amplitudes which are valid
for arbitrary heavy-quark masses.Comment: LaTeX, 7 pages, 5 figure
Hepta-Cuts of Two-Loop Scattering Amplitudes
We present a method for the computation of hepta-cuts of two loop scattering
amplitudes. Four dimensional unitarity cuts are used to factorise the integrand
onto the product of six tree-level amplitudes evaluated at complex momentum
values. Using Gram matrix constraints we derive a general parameterisation of
the integrand which can be computed using polynomial fitting techniques. The
resulting expression is further reduced to master integrals using conventional
integration by parts methods. We consider both planar and non-planar topologies
for 2 to 2 scattering processes and apply the method to compute hepta-cut
contributions to gluon-gluon scattering in Yang-Mills theory with adjoint
fermions and scalars.Comment: 37 pages, 6 figures. version 2 : minor updates, published versio
Cuts from residues: the one-loop case
Using the multivariate residue calculus of Leray, we give a precise
definition of the notion of a cut Feynman integral in dimensional
regularization, as a residue evaluated on the variety where some of the
propagators are put on shell. These are naturally associated to Landau
singularities of the first type. Focusing on the one-loop case, we give an
explicit parametrization to compute such cut integrals, with which we study
some of their properties and list explicit results for maximal and
next-to-maximal cuts. By analyzing homology groups, we show that cut integrals
associated to Landau singularities of the second type are specific combinations
of the usual cut integrals, and we obtain linear relations among different cuts
of the same integral. We also show that all one-loop Feynman integrals and
their cuts belong to the same class of functions, which can be written as
parametric integrals.Comment: v2: fixed minor typos in the normalisation of cut integral
The double-soft integral for an arbitrary angle between hard radiators
We consider the double-soft limit of a generic QCD process involving massless partons and integrate analytically the double-soft eikonal functions over the phase-space of soft partons (gluons or quarks) allowing for an arbitrary relative angle between the three-momenta of two hard massless radiators. This result provides one of the missing ingredients for a fully analytic formulation of the nested soft-collinear subtraction scheme described in Caola et al. (Eur Phys J C 77(4):248, 2017)
Non-planar two-loop Feynman integrals contributing to Higgs plus jet production
This is a contribution to the proceedings of the 2018 âLoops and Legsâ conference. It is based on a talk by HF on ongoing work on the non-planar Feynman integrals contributing to H + j production at Next-to Leading order in QCD, retaining the complete dependence on the mass of the top-quark. The various non-planar sectors are discussed along with the elliptic structures that appear
Vector Space of Feynman Integrals and Multivariate Intersection Numbers
Feynman integrals obey linear relations governed by intersection numbers,
which act as scalar products between vector spaces. We present a general
algorithm for constructing multivariate intersection numbers relevant to
Feynman integrals, and show for the first time how they can be used to solve
the problem of integral reduction to a basis of master integrals by
projections, and to directly derive functional equations fulfilled by the
latter. We apply it to the derivation of contiguity relations for special
functions admitting multi-fold integral representations, and to the
decomposition of a few Feynman integrals at one- and two-loops, as first steps
towards potential applications to generic multi-loop integrals.Comment: 11 pages, 4 figure
Decomposition of Feynman integrals by multivariate intersection numbers
We present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections, as well as a direct derivation of the differential equations satisfied by the master integrals, employing multivariate intersection numbers. We discuss a recursive algorithm for the computation of multivariate intersection numbers, and provide three different approaches for a direct decomposition of Feynman integrals, which we dub the straight decomposition, the bottom-up decomposition, and the top-down decomposition. These algorithms exploit the unitarity structure of Feynman integrals by computing intersection numbers supported on cuts, in various orders, thus showing the synthesis of the intersection-theory concepts with unitarity-based methods and integrand decomposition. We perform explicit computations to exemplify all of these approaches applied to Feynman integrals, paving a way towards potential applications to generic multi-loop integrals