88 research outputs found
On BCFW shifts of integrands and integrals
In this article a first step is made towards the extension of
Britto-Cachazo-Feng-Witten (BCFW) tree level on-shell recursion relations to
integrands and integrals of scattering amplitudes to arbitrary loop order.
Surprisingly, it is shown that the large BCFW shift limit of the integrands has
the same structure as the corresponding tree level amplitude in any minimally
coupled Yang-Mills theory in four or more dimensions. This implies that these
integrands can be reconstructed from a subset of their `single cuts'. The main
tool is powercounting Feynman graphs in a special lightcone gauge choice
employed earlier at tree level by Arkani-Hamed and Kaplan. The relation between
shifts of integrands and shifts of its integrals is investigated explicitly at
one loop. Two particular sources of discrepancy between the integral and
integrand are identified related to UV and IR divergences. This is
cross-checked with known results for helicity equal amplitudes at one loop. The
nature of the on-shell residue at each of the single-cut singularities of the
integrand is commented upon. Several natural conjectures and opportunities for
further research present themselves.Comment: 43 pages, 6 figures, v2: minor improvement in exposition, typos
fixed, bibliography update
Antenna subtraction with massive fermions at NNLO: Double real initial-final configurations
We derive the integrated forms of specific initial-final tree-level
four-parton antenna functions involving a massless initial-state parton and a
massive final-state fermion as hard radiators. These antennae are needed in the
subtraction terms required to evaluate the double real corrections to
hadronic production at the NNLO level stemming from the partonic
processes and .Comment: 24 pages, 1 figure, 1 Mathematica file attache
Antenna subtraction for gluon scattering at NNLO
We use the antenna subtraction method to isolate the double real radiation
infrared singularities present in gluonic scattering amplitudes at
next-to-next-to-leading order. The antenna subtraction framework has been
successfully applied to the calculation of NNLO corrections to the 3-jet cross
section and related event shape distributions in electron-positron
annihilation. Here we consider processes with two coloured particles in the
initial state, and in particular two-jet production at hadron colliders such as
the Large Hadron Collider (LHC). We construct a subtraction term that describes
the single and double unresolved contributions from the six-gluon tree-level
process using antenna functions with initial state partons and show numerically
that the subtraction term correctly approximates the matrix elements in the
various single and double unresolved configurations.Comment: 71 pages, JHEP3 class; corrected typos, equivalent but more compact
version of eq. (5.12), results unchange
The fully differential hadronic production of a Higgs boson via bottom quark fusion at NNLO
The fully differential computation of the hadronic production cross section
of a Higgs boson via bottom quarks is presented at NNLO in QCD. Several
differential distributions with their corresponding scale uncertainties are
presented for the 8 TeV LHC. This is the first application of the method of
non-linear mappings for NNLO differential calculations at hadron colliders.Comment: 27 pages, 13 figures, 1 lego plo
Developing family-based care: complexities in implementing the UN Guidelines for the Alternative Care of Children
Effects of antiplatelet therapy on stroke risk by brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases: subgroup analyses of the RESTART randomised, open-label trial
Background
Findings from the RESTART trial suggest that starting antiplatelet therapy might reduce the risk of recurrent symptomatic intracerebral haemorrhage compared with avoiding antiplatelet therapy. Brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases (such as cerebral microbleeds) are associated with greater risks of recurrent intracerebral haemorrhage. We did subgroup analyses of the RESTART trial to explore whether these brain imaging features modify the effects of antiplatelet therapy
Primary Feynman rules to calculate the epsilon-dimensional integrand of any 1-loop amplitude
When using dimensional regularization/reduction the epsilon-dimensional
numerator of the 1-loop Feynman diagrams gives rise to rational contributions.
I list the set of fundamental rules that allow the extraction of such terms at
the integrand level in any theory containing scalars, vectors and fermions,
such as the electroweak standard model, QCD and SUSY.Comment: 19 pages, 14 figures, uses axodraw.sty. Version accepted for
publication in JHE
Integrands for QCD rational terms and N=4 SYM from massive CSW rules
We use massive CSW rules to derive explicit compact expressions for
integrands of rational terms in QCD with any number of external legs.
Specifically, we present all-n integrands for the one-loop all-plus and
one-minus gluon amplitudes in QCD. We extract the finite part of spurious
external-bubble contributions systematically; this is crucial for the
application of integrand-level CSW rules in theories without supersymmetry. Our
approach yields integrands that are independent of the choice of CSW reference
spinor even before integration.
Furthermore, we present a recursive derivation of the recently proposed
massive CSW-style vertex expansion for massive tree amplitudes and loop
integrands on the Coulomb-branch of N=4 SYM. The derivation requires a careful
study of boundary terms in all-line shift recursion relations, and provides a
rigorous (albeit indirect) proof of the recently proposed construction of
massive amplitudes from soft-limits of massless on-shell amplitudes. We show
that the massive vertex expansion manifestly preserves all holomorphic and half
of the anti-holomorphic supercharges, diagram-by-diagram, even off-shell.Comment: 30 pages, many figure
The real radiation antenna function for at NNLO QCD
As a first step towards the application of the antenna subtraction formalism
to NNLO QCD reactions with massive quarks, we determine the real radiation
antenna function and its integrated counterpart for reactions of the type , where denotes an uncolored initial state and
, a massive and massless quark, respectively. We compute the
corresponding integrated antenna function in terms of harmonic polylogarithms.
As an application and check of our results we calculate the contribution
proportional to to the inclusive heavy-quark pair
production cross ection in annihilation.Comment: Latex, 32 page
Antenna subtraction at NNLO with hadronic initial states: real-virtual initial-initial configurations
The antenna subtraction method handles real radiation contributions in higher
order corrections to jet observables. The method is based on antenna functions,
which encapsulate all unresolved radiation between a pair of hard radiator
partons. To apply this method to compute hadron collider observables,
initial-initial antenna functions with both radiators in the initial state are
required. In view of extending the antenna subtraction method to
next-to-next-to-leading order (NNLO) calculations at hadron colliders, we
derive the one-loop initial-initial antenna functions in unintegrated and
integrated form.Comment: 24 page
- …