71 research outputs found
Helicity amplitudes for QCD with massive quarks
The novel massive spinor-helicity formalism of Arkani-Hamed, Huang and Huang
provides an elegant way to calculate scattering amplitudes in quantum
chromodynamics for arbitrary quark spin projections. In this note we compute
two families of tree-level QCD amplitudes with one massive quark pair and n-2
gluons. The two cases include all gluons with identical helicity and one
opposite-helicity gluon being color-adjacent to one of the quarks. Our results
naturally incorporate the previously known amplitudes for both quark spins
quantized along one of the gluonic momenta. In the all-multiplicity formulae
presented here the spin quantization axes can be tuned at will, which includes
the case of the definite-helicity quark states.Comment: v3 conventions tweaked to match further work by author, supersedes
journal versio
On-shell recursion for massive fermion currents
We analyze the validity of BCFW recursion relations for currents of n - 2
gluons and two massive quarks, where one of the quarks is off shell and the
remaining particles are on shell. These currents are gauge-dependent and can be
used as ingredients in the unitarity-based approach to computing one-loop
amplitudes. The validity of BCFW recursion relations is well known to depend on
the so-called boundary behavior of the currents as the momentum shift parameter
goes to infinity. With off-shell currents, a new potential problem arises,
namely unphysical poles that depend on the choice of gauge. We identify
conditions under which boundary terms are absent and unphysical poles are
avoided, so that there is a natural recursion relation. In particular, we are
able to choose a gauge in which we construct a valid shift for currents with at
least n - 3 gluons of the same helicity. We derive an analytic formula in the
case where all gluons have the same helicity. As by-products, we prove the
vanishing boundary behavior of general off-shell objects in Feynman gauge, and
we find a compact generalization of Berends-Giele gluon currents with a generic
reference spinor.Comment: 30 pages, 8 figures; v2 minor corrections, journal versio
Pure Gravities via Color-Kinematics Duality for Fundamental Matter
We give a prescription for the computation of loop-level scattering
amplitudes in pure Einstein gravity, and four-dimensional pure supergravities,
using the color-kinematics duality. Amplitudes are constructed using double
copies of pure (super-)Yang-Mills parts and additional contributions from
double copies of fundamental matter, which are treated as ghosts. The
opposite-statistics states cancel the unwanted dilaton and axion in the bosonic
theory, as well as the extra matter supermultiplets in supergravities. As a
spinoff, we obtain a prescription for obtaining amplitudes in supergravities
with arbitrary non-self-interacting matter. As a prerequisite, we extend the
color-kinematics duality from the adjoint to the fundamental representation of
the gauge group. We explain the numerator relations that the fundamental
kinematic Lie algebra should satisfy. We give nontrivial evidence supporting
our construction using explicit tree and loop amplitudes, as well as more
general arguments.Comment: 48 pages + refs, 15 figures, 3 tables; v2 minor corrections, journal
versio
Color-Kinematics Duality for QCD Amplitudes
We show that color-kinematics duality is present in tree-level amplitudes of
quantum chromodynamics with massive flavored quarks. Starting with the color
structure of QCD, we work out a new color decomposition for n-point tree
amplitudes in a reduced basis of primitive amplitudes. These primitives, with k
quark-antiquark pairs and (n-2k) gluons, are taken in the (n-2)!/k! Melia
basis, and are independent under the color-algebra Kleiss-Kuijf relations. This
generalizes the color decomposition of Del Duca, Dixon, and Maltoni to an
arbitrary number of quarks. The color coefficients in the new decomposition are
given by compact expressions valid for arbitrary gauge group and
representation. Considering the kinematic structure, we show through explicit
calculations that color-kinematics duality holds for amplitudes with general
configurations of gluons and massive quarks. The new (massive) amplitude
relations that follow from the duality can be mapped to a well-defined subset
of the familiar BCJ relations for gluons. They restrict the amplitude basis
further down to (n-3)!(2k-2)/k! primitives, for two or more quark lines. We
give a decomposition of the full amplitude in that basis. The presented results
provide strong evidence that QCD obeys the color-kinematics duality, at least
at tree level. The results are also applicable to supersymmetric and
D-dimensional extensions of QCD.Comment: 33 pages + refs, 7 figures, 4 tables; v3 minor corrections, journal
versio
BCJ duality and double copy in the closed string sector
This paper is focused on the loop-level understanding of the
Bern-Carrasco-Johansson double copy procedure that relates the integrands of
gauge theory and gravity scattering amplitudes. At four points, the first
non-trivial example of that construction is one-loop amplitudes in N=2
super-Yang-Mills theory and the symmetric realization of N=4 matter-coupled
supergravity. Our approach is to use both field and string theory in parallel
to analyze these amplitudes. The closed string provides a natural framework to
analyze the BCJ construction, in which the left- and right-moving sectors
separately create the color and kinematics at the integrand level. At tree
level, in a five-point example, we show that the Mafra-Schlotterer-Stieberger
procedure gives a new direct proof of the color-kinematics double copy. We
outline the extension of that argument to n points. At loop level, the
field-theoretic BCJ construction of N=2 SYM amplitudes introduces new terms,
unexpected from the string theory perspective. We discuss to what extent we can
relate them to the terms coming from the interactions between left- and
right-movers in the string-theoretic gravity construction.Comment: 46 pages, 8 figures, 2 tables; v3 significantly revised published
versio
Scattering amplitudes in gauge theories with and without supersymmetry
This thesis aims at providing better understanding of the perturbative
expansion of gauge theories with and without supersymmetry. At tree level, the
BCFW recursion relations are analyzed with respect to their validity for
general off-shell objects in Yang-Mills theory, which is a significant step
away from their established zone of applicability. Unphysical poles constitute
a new potential problem in addition to the boundary behavior issue, common to
the on-shell case as well. For an infinite family of massive fermion currents,
both obstacles are shown to be avoided under the certain conditions, which
provides a natural recursion relation. At one loop, scattering amplitudes can
be calculated from unitarity cuts through their expansion into known scalar
integrals with free coefficients. A powerful method to obtain these
coefficients, namely spinor integration, is discussed and rederived in a
somewhat novel form. It is then used to compute analytically the infinite
series of one-loop gluon amplitudes in N = 1 super-Yang-Mills theory with
exactly three negative helicities. The final part of this thesis concerns the
intriguing relationship between gluon and graviton scattering amplitudes, which
involves a beautiful duality between the color and kinematic content of gauge
theories. This BCJ duality is extended to include particles in the fundamental
representation of the gauge group, which is shown to relieve the restriction of
the BCJ construction to factorizable gravities and thus give access to
amplitudes in generic (super-)gravity theories.Comment: 111 pages, PhD thesis defended on 12/09/201
Scattering of Spinning Black Holes from Exponentiated Soft Factors
We provide evidence that the classical scattering of two spinning black holes
is controlled by the soft expansion of exchanged gravitons. We show how an
exponentiation of Cachazo-Strominger soft factors, acting on massive
higher-spin amplitudes, can be used to find spin contributions to the
aligned-spin scattering angle, conjecturally extending previously known results
to higher orders in spin at one-loop order. The extraction of the classical
limit is accomplished via the on-shell leading-singularity method and using
massive spinor-helicity variables. The three-point amplitude for arbitrary-spin
massive particles minimally coupled to gravity is expressed in an exponential
form, and in the infinite-spin limit it matches the effective stress-energy
tensor of the linearized Kerr solution. A four-point gravitational Compton
amplitude is obtained from an extrapolated soft theorem, equivalent to gluing
two exponential three-point amplitudes, and becomes itself an exponential
operator. The construction uses these amplitudes to: 1) recover the known
tree-level scattering angle at all orders in spin, 2) recover the known
one-loop linear-in-spin interaction, 3) match a previous conjectural expression
for the one-loop scattering angle at quadratic order in spin, 4) propose new
one-loop results through quartic order in spin. These connections link the
computation of higher-multipole interactions to the study of deeper orders in
the soft expansion.Comment: 29 pages + appendices + refs, 3 figures; v3 minor corrections,
journal versio
All one-loop NMHV gluon amplitudes in N=1 SYM
We compute the next-to-maximally-helicity-violating one-loop n-gluon
amplitudes in N=1 super-Yang-Mills theory. These amplitudes contain three
negative-helicity gluons and an arbitrary number of positive-helicity gluons,
and constitute the first infinite series of amplitudes beyond the simplest,
MHV, amplitudes. We assemble ingredients from the N=4 NMHV tree super-amplitude
into previously unwritten double cuts and use the spinor integration technique
to calculate all bubble coefficients. We also derive the missing box
coefficients from quadruple cuts. Together with the known formula for
three-mass triangles, this completes the set of NMHV one-loop master integral
coefficients in N=1 SYM. To facilitate further use of our results, we provide
their Mathematica implementation.Comment: 49 pages, 12 figures, 2 Mathematica files attached: N1chiralAll.nb,
Ammppmppp.nb; v2 minor corrections, journal versio
Gravitational partial-wave absorption from scattering amplitudes
We study gravitational absorption effects using effective on-shell scattering
amplitudes. We develop an in-in probability-based framework involving plane-
and partial-wave coherent states for the incoming wave to describe the
interaction of the wave with a black hole or another compact object. We connect
this framework to a simplified single-quantum analysis. The basic ingredients
are mass-changing three-point amplitudes that model the leading absorption
effects. As an application, we consider a non-spinning black hole that may
start spinning as a consequence of the dynamics. The corresponding amplitudes
are found to correspond to covariant spin-weighted spherical harmonics, the
properties of which we formulate and make use of. We perform a matching
calculation at the cross-section level to general-relativity results and derive
the effective absorptive three-point couplings. They are found to behave as
, where is the spin of the outgoing massive state.Comment: 33 pages + appendices + refs, 5 figure
One-loop monodromy relations on single cuts
The discovery of colour-kinematic duality has led to significant progress in
the computation of scattering amplitudes in quantum field theories. At tree
level, the origin of the duality can be traced back to the monodromies of
open-string amplitudes. This construction has recently been extended to all
loop orders. In the present paper, we dissect some consequences of these new
monodromy relations at one loop. We use single cuts in order to relate them to
the tree-level relations. We show that there are new classes of kinematically
independent single-cut amplitudes. Then we turn to the Feynman diagrammatics of
the string-theory monodromy relations. We revisit the string-theoretic
derivation and argue that some terms, that vanish upon integration in string
and field theory, provide a characterisation of momentum-shifting ambiguities
in these representations. We observe that colour-dual representations are
compatible with this analysis
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