52,957 research outputs found
Next-to-next-to-leading order -jettiness soft function for production
We calculate the -jettiness soft function for production up to
next-to-next-to-leading order in QCD, which is an important ingredient of the
-jettiness subtraction method for predicting the differential cross sections
of massive coloured particle productions. The divergent parts of the results
have been checked using the renormalization group equations controlled by the
soft anomalous dimension.Comment: 14 pages, 3 figures, published version in PL
Fully Differential Higgs Pair Production in Association With a Boson at Next-to-Next-to-Leading Order in QCD
To clarify the electroweak symmetry breaking mechanism, we need to probe the
Higgs self-couplings, which can be measured in Higgs pair productions. The
associated production with a vector boson is special due to a clear tag in the
final state. We perform a fully differential next-to-next-to-leading-order
calculation of the Higgs pair production in association with a boson at
hadron colliders, and present numerical results at the 14 TeV LHC and a future
100 TeV hadron collider.Comment: 7 pages, 7 figures, matched to the published version in PL
Rational spectral methods for PDEs involving fractional Laplacian in unbounded domains
Many PDEs involving fractional Laplacian are naturally set in unbounded
domains with underlying solutions decay very slowly, subject to certain power
laws. Their numerical solutions are under-explored. This paper aims at
developing accurate spectral methods using rational basis (or modified mapped
Gegenbauer functions) for such models in unbounded domains. The main building
block of the spectral algorithms is the explicit representations for the
Fourier transform and fractional Laplacian of the rational basis, derived from
some useful integral identites related to modified Bessel functions. With these
at our disposal, we can construct rational spectral-Galerkin and direct
collocation schemes by pre-computing the associated fractional differentiation
matrices. We obtain optimal error estimates of rational spectral approximation
in the fractional Sobolev spaces, and analyze the optimal convergence of the
proposed Galerkin scheme. We also provide ample numerical results to show that
the rational method outperforms the Hermite function approach
A quadratic bound on the number of boundary slopes of essential surfaces with bounded genus
Let be an orientable 3-manifold with a single torus. We show
that the number of boundary slopes of immersed essential surfaces with genus at
most is bounded by a quadratic function of . In the hyperbolic case,
this was proved earlier by Hass, Rubinstein and Wang.Comment: 11 pages, 1 figur
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