2,160 research outputs found
All tree-level amplitudes in massless QCD
We derive compact analytical formulae for all tree-level color-ordered gauge
theory amplitudes involving any number of external gluons and up to three
massless quark-anti-quark pairs. A general formula is presented based on the
combinatorics of paths along a rooted tree and associated determinants.
Explicit expressions are displayed for the next-to-maximally helicity violating
(NMHV) and next-to-next-to-maximally helicity violating (NNMHV) gauge theory
amplitudes. Our results are obtained by projecting the previously-found
expressions for the super-amplitudes of the maximally supersymmetric Yang-Mills
theory (N=4 SYM) onto the relevant components yielding all gluon-gluino tree
amplitudes in N=4 SYM. We show how these results carry over to the
corresponding QCD amplitudes, including massless quarks of different flavors as
well as a single electroweak vector boson. The public Mathematica package GGT
is described, which encodes the results of this work and yields analytical
formulae for all N=4 SYM gluon-gluino trees. These in turn yield all QCD trees
with up to four external arbitrary-flavored massless quark-anti-quark-pairs.Comment: 40 pages, Mathematica package GGT.m and example notebook is included
in submission, v2: QCD four fermion line translations provided; GGT version
1.1 update with a numerical evaluation function; comments on computer speed
optimizations, v3: Minor changes, version to be published in JHEP, v4:
published version in JHE
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Re-generated youth citizenship: youth civic and electoral mobilisation at the 2017 General Election
Now the dust has settled, how should we account for the surge in youth turnout at the 2017 UK General Election with estimates that 64% of those aged 18-24 cast a vote (Hart and Henn 2017) – representing a significant 21-point increase from the 2015 General Election and a departure from recent patterns of youth abstention? After all, our youth are often decried as apathetic and having no sense of civic responsibility or commitment to social and collective endeavour. So when Theresa May unexpectedly called a snap election on 18 April 2017, such an outcome seemed virtually unthinkable. The Conservative lead over Labour in the pre-election polls appeared unassailable (YouGov 2017), and the 50-day campaign period loomed long, flat and predictable. For many young people, another vote, soon after what they considered a deeply disappointing 2016 Referendum outcome to leave the EU, heralded little more than the prospect of another five years in which their concerns would remain ignored by the political elite. The likelihood that Britain's youth would flock to the polls seemed somewhat remote
Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits
We compute the three-loop contribution to the N=4 supersymmetric Yang-Mills
planar four-gluon amplitude using the recently-proposed Higgs IR regulator of
Alday, Henn, Plefka, and Schuster. In particular, we test the proposed
exponential ansatz for the four-gluon amplitude that is the analog of the BDS
ansatz in dimensional regularization. By evaluating our results at a number of
kinematic points, and also in several kinematic limits, we establish the
validity of this ansatz at the three-loop level.
We also examine the Regge limit of the planar four-gluon amplitude using
several different IR regulators: dimensional regularization, Higgs
regularization, and a cutoff regularization. In the latter two schemes, it is
shown that the leading logarithmic (LL) behavior of the amplitudes, and
therefore the lowest-order approximation to the gluon Regge trajectory, can be
correctly obtained from the ladder approximation of the sum of diagrams. In
dimensional regularization, on the other hand, there is no single dominant set
of diagrams in the LL approximation. We also compute the NLL and NNLL behavior
of the L-loop ladder diagram using Higgs regularization.Comment: 45 pages, 9 figures; v3: major revision (more stringent tests,
discussion of order of limits in the Regge regime
The two-loop five-particle amplitude in supergravity
We compute for the first time the two-loop five-particle amplitude in
supergravity. Starting from the known integrand, we perform an
integration-by-parts reduction and express the answer in terms of uniform
weight master integrals. The latter are known to evaluate to non-planar
pentagon functions, described by a 31-letter symbol alphabet. We express the
final result for the amplitude in terms of uniform weight four symbols,
multiplied by a small set of rational factors. The amplitude satisfies the
expected factorization properties when one external graviton becomes soft, and
when two external gravitons become collinear. We verify that the soft
divergences of the amplitude exponentiate, and extract the finite remainder
function. The latter depends on fewer rational factors, and is independent of
one of the symbol letters. By analyzing identities involving rational factors
and symbols we find a remarkably compact representation in terms of a single
seed function, summed over all permutations of external particles. Finally, we
work out the multi-Regge limit, and present explicitly the leading logarithmic
terms in the limit. The full symbol of the IR-subtracted hard function is
provided as an ancillary file.Comment: 22 pages, 1 figure, 8 ancillary file
Emergence of turbulence in an oscillating Bose-Einstein condensate
We report on the experimental observation of vortices tangle in an atomic BEC
of Rb-87 atoms when an external oscillatory perturbation is introduced in the
trap. The vortices tangle configuration is a signature of the presence of a
turbulent regime in the cloud. We also show that this turbulent cloud has
suppression of the aspect ratio inversion typically observed in quantum
degenerate bosonic gases during free expansion. Instead, the cloud expands
keeping the ratio between their axis constant. Turbulence in atomic superfluids
may constitute an alternative system to investigate decay mechanisms as well as
to test fundamental theoretical aspects in this field.Comment: accepted for Phys. Rev. Let
Cenários futuros da infraestrutura de transporte e seus impactos na competitividade das exportações de carne suÃna e nas suas emissões de gases de efeito estufa.
bitstream/item/78909/1/Comunicado-505.pdfProjeto/Plano de Ação: 04.08.08.017
The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
As a test of the gluon scattering amplitude/Wilson loop duality, we evaluate
the hexagonal light-like Wilson loop at two loops in N=4 super Yang-Mills
theory. We compare its finite part to the Bern-Dixon-Smirnov (BDS) conjecture
for the finite part of the six-gluon amplitude. We find that the two
expressions have the same behavior in the collinear limit, but they differ by a
non-trivial function of the three (dual) conformally invariant variables. This
implies that either the BDS conjecture or the gluon amplitude/Wilson loop
duality fails for the six-gluon amplitude, starting from two loops. Our results
are in qualitative agreement with the analysis of Alday and Maldacena of
scattering amplitudes with infinitely many external gluons.Comment: 8 pages, 3 figures; typos correcte
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