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

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 N=8\mathcal{N}=8 supergravity

We compute for the first time the two-loop five-particle amplitude in $\mathcal{N}=8$ 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 suína 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