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Register a new userMany-gluon tree amplitudes on modern GPUs: A case study for novel event generators
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The compute efficiency of Monte-Carlo event generators for the Large Hadron Collider is expected to become a major bottleneck for simulations in the high-luminosity phase. Aiming at the development of a full-fledged generator for modern GPUs, we study the performance of various recursive strategies to compute multi-gluon tree-level amplitudes. We investigate the scaling of the algorithms on both CPU and GPU hardware. Finally, we provide practical recommendations as well as baseline implementations for the development of future simulation programs. The GPU implementations can be found at: https://www.gitlab.com/ebothmann/blockgen-archive.
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We have developed a numerical framework for a full solution of the relativistic Boltzmann equations for the quark-gluon matter using the multiple Graphics Processing Units (GPUs) on distributed clusters. Including all the $2 to 2$ scattering processes of 3-flavor quarks and gluons, we compute the time evolution of distribution functions in both coordinate and momentum spaces for the cases of pure gluons, quarks and the mixture of quarks and gluons. By introducing a symmetrical sampling method on GPUs which ensures the particle number conservation, our framework is able to perform the space-time evolution of quark-gluon system towards thermal equilibrium with high performance. We also observe that the gluons naturally accumulate in the soft region at the early time, which may indicate the gluon condensation.
Recently, Bjerrum-Bohr, Damgaard, Feng and Sondergaard derived a set of new interesting quadratic identities of the Yang-Mills tree scattering amplitudes. Here we comment that these quadratic identities of YM amplitudes actually follow directly from the KLT relation for graviton-dilaton-axion scattering amplitudes (in 4 dimensional spacetime). This clarifies their physical origin and also provides a simpler version of the new identities. We also comment that the recently discovered Bern-Carrasco-Johansson identities of YM helicity amplitudes can be verified by using (repeatedly) the Schouten identity. We also point out additional quadratic identities that can be written down from the KLT relations.
We present a compact analytic expression for the leading colour two-loop five-gluon amplitude in Yang-Mills theory with a single negative helicity and four positive helicities. The analytic result is reconstructed from numerical evaluations over finite fields. The numerical method combines integrand reduction, integration-by-parts identities and Laurent expansion into a basis of pentagon functions to compute the coefficients directly from six-dimensional generalised unitarity cuts.
The rational parts of 5-gluon one-loop amplitudes are computed by using the newly developed method for computing the rational parts directly from Feynman integrals. We found complete agreement with the previously well-known results of Bern, Dixon and Kosower obtained by using the string theory method. Intermediate results for some combinations of Feynman diagrams are presented in order to show the efficiency of the method and the local cancellation between different contributions.
The rational parts of 6-gluon one-loop amplitudes with scalars circulating in the loop are computed by using the newly developed method for computing the rational parts directly from Feynman integrals. We present the analytic results for the two MHV helicity configurations: $(1^-2^+3^+4^-5^+6^+)$ and $(1^-2^+3^-4^+5^+6^+)$, and the two NMHV helicity configurations: $(1^-2^-3^+4^-5^+6^+)$ and $(1^-2^+3^-4^+5^-6^+)$. Combined with the previously computed results for the cut-constructible part, our results are the last missing pieces for the complete partial helicity amplitudes of the 6-gluon one-loop QCD amplitude.
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